Design of exchange-correlation functionals through the correlation factor approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pavlíková Přecechtělová, Jana, E-mail: j.precechtelova@gmail.com, E-mail: Matthias.Ernzerhof@UMontreal.ca; Institut für Chemie, Theoretische Chemie / Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17. Juni 135, 10623 Berlin; Bahmann, Hilke

The correlation factor model is developed in which the spherically averaged exchange-correlation hole of Kohn-Sham theory is factorized into an exchange hole model and a correlation factor. The exchange hole model reproduces the exact exchange energy per particle. The correlation factor is constructed in such a manner that the exchange-correlation energy correctly reduces to exact exchange in the high density and rapidly varying limits. Four different correlation factor models are presented which satisfy varying sets of physical constraints. Three models are free from empirical adjustments to experimental data, while one correlation factor model draws on one empirical parameter. The correlationmore » factor models are derived in detail and the resulting exchange-correlation holes are analyzed. Furthermore, the exchange-correlation energies obtained from the correlation factor models are employed to calculate total energies, atomization energies, and barrier heights. It is shown that accurate, non-empirical functionals can be constructed building on exact exchange. Avenues for further improvements are outlined as well.« less

Electron Correlation from the Adiabatic Connection for Multireference Wave Functions

NASA Astrophysics Data System (ADS)

Pernal, Katarzyna

2018-01-01

An adiabatic connection (AC) formula for the electron correlation energy is derived for a broad class of multireference wave functions. The AC expression recovers dynamic correlation energy and assures a balanced treatment of the correlation energy. Coupling the AC formalism with the extended random phase approximation allows one to find the correlation energy only from reference one- and two-electron reduced density matrices. If the generalized valence bond perfect pairing model is employed a simple closed-form expression for the approximate AC formula is obtained. This results in the overall M5 scaling of the computation cost making the method one of the most efficient multireference approaches accounting for dynamic electron correlation also for the strongly correlated systems.

Effect of in-medium nucleon-nucleon cross section on proton-proton momentum correlation in intermediate-energy heavy-ion collisions

NASA Astrophysics Data System (ADS)

Wang, Ting-Ting; Ma, Yu-Gang; Zhang, Chun-Jian; Zhang, Zheng-Qiao

2018-03-01

The proton-proton momentum correlation function from different rapidity regions is systematically investigated for the Au + Au collisions at different impact parameters and different energies from 400 A MeV to 1500 A MeV in the framework of the isospin-dependent quantum molecular dynamics model complemented by the Lednický-Lyuboshitz analytical method. In particular, the in-medium nucleon-nucleon cross-section dependence of the correlation function is brought into focus, while the impact parameter and energy dependence of the momentum correlation function are also explored. The sizes of the emission source are extracted by fitting the momentum correlation functions using the Gaussian source method. We find that the in-medium nucleon-nucleon cross section obviously influences the proton-proton momentum correlation function, which is from the whole-rapidity or projectile or target rapidity region at smaller impact parameters, but there is no effect on the mid-rapidity proton-proton momentum correlation function, which indicates that the emission mechanism differs between projectile or target rapidity and mid-rapidity protons.

Derivation of the density functional theory from the cluster expansion.

PubMed

Hsu, J Y

2003-09-26

The density functional theory is derived from a cluster expansion by truncating the higher-order correlations in one and only one term in the kinetic energy. The formulation allows self-consistent calculation of the exchange correlation effect without imposing additional assumptions to generalize the local density approximation. The pair correlation is described as a two-body collision of bound-state electrons, and modifies the electron- electron interaction energy as well as the kinetic energy. The theory admits excited states, and has no self-interaction energy.

Free-energy functional of the Debye-Hückel model of simple fluids

NASA Astrophysics Data System (ADS)

Piron, R.; Blenski, T.

2016-12-01

The Debye-Hückel approximation to the free energy of a simple fluid is written as a functional of the pair correlation function. This functional can be seen as the Debye-Hückel equivalent to the functional derived in the hypernetted chain framework by Morita and Hiroike, as well as by Lado. It allows one to obtain the Debye-Hückel integral equation through a minimization with respect to the pair correlation function, leads to the correct form of the internal energy, and fulfills the virial theorem.

Exchange-Correlation Effects for Noncovalent Interactions in Density Functional Theory.

PubMed

Otero-de-la-Roza, A; DiLabio, Gino A; Johnson, Erin R

2016-07-12

In this article, we develop an understanding of how errors from exchange-correlation functionals affect the modeling of noncovalent interactions in dispersion-corrected density-functional theory. Computed CCSD(T) reference binding energies for a collection of small-molecule clusters are decomposed via a molecular many-body expansion and are used to benchmark density-functional approximations, including the effect of semilocal approximation, exact-exchange admixture, and range separation. Three sources of error are identified. Repulsion error arises from the choice of semilocal functional approximation. This error affects intermolecular repulsions and is present in all n-body exchange-repulsion energies with a sign that alternates with the order n of the interaction. Delocalization error is independent of the choice of semilocal functional but does depend on the exact exchange fraction. Delocalization error misrepresents the induction energies, leading to overbinding in all induction n-body terms, and underestimates the electrostatic contribution to the 2-body energies. Deformation error affects only monomer relaxation (deformation) energies and behaves similarly to bond-dissociation energy errors. Delocalization and deformation errors affect systems with significant intermolecular orbital interactions (e.g., hydrogen- and halogen-bonded systems), whereas repulsion error is ubiquitous. Many-body errors from the underlying exchange-correlation functional greatly exceed in general the magnitude of the many-body dispersion energy term. A functional built to accurately model noncovalent interactions must contain a dispersion correction, semilocal exchange, and correlation components that minimize the repulsion error independently and must also incorporate exact exchange in such a way that delocalization error is absent.

Subsystem density functional theory with meta-generalized gradient approximation exchange-correlation functionals.

PubMed

Śmiga, Szymon; Fabiano, Eduardo; Laricchia, Savio; Constantin, Lucian A; Della Sala, Fabio

2015-04-21

We analyze the methodology and the performance of subsystem density functional theory (DFT) with meta-generalized gradient approximation (meta-GGA) exchange-correlation functionals for non-bonded molecular systems. Meta-GGA functionals depend on the Kohn-Sham kinetic energy density (KED), which is not known as an explicit functional of the density. Therefore, they cannot be directly applied in subsystem DFT calculations. We propose a Laplacian-level approximation to the KED which overcomes this limitation and provides a simple and accurate way to apply meta-GGA exchange-correlation functionals in subsystem DFT calculations. The so obtained density and energy errors, with respect to the corresponding supermolecular calculations, are comparable with conventional approaches, depending almost exclusively on the approximations in the non-additive kinetic embedding term. An embedding energy error decomposition explains the accuracy of our method.

Generalized Jastrow Variational Method for Liquid HELIUM-3-HELIUM-4 Mixtures at T = 0 K.

NASA Astrophysics Data System (ADS)

Mirabbaszadeh, Kavoos

Microscopic theory of dilute liquid { ^3 He}-{^4 He} mixtures is of great interest, because it provides a physical realization of a nearly degenerate weakly interacting Fermion system. An understanding of properties of the mixtures has received considerable attention both theoretically and experimentally over the past thirty years. We present here a variational procedure based on the Jastrow function for the ground state of {^3 He}- {^4 He} mixtures by minimizing the total energy of the mixture using the hypernetted-chain (HNC) approximation and the Percus-Yevick (PY) approximation for the two body correlation functions. Our goal is to compute from first principles the internal energy of the system and the various two body correlation functions at various densities and compare the results with experiment. The Jastrow variational method for the ground state energy of liquid {^4 He} consists of the following ansatz for the wave function Psi_alpha {rm(vec r_{1 alpha},} {vec r_{2alpha},} dots, {vec r_{N _alpha})} = prod _{rm i < j} {rm f_ {alphaalpha}(r_{ij}). } For a {^3 He } system the corresponding ansatz is Psi_beta {rm( vec r_{1beta},} {vec r_{2beta },} dots, {vec r_{N_beta})} = {[prod _{i < j} f_{betabeta }(r_{ij})]} Phi {rm( vec r_{1beta},} {vec r_{2beta },} dots, {vec r_{Nbeta}),} where Phi is a Slater determinant of plane waves for the ground state of the Fermion system. The total energy per particle can be written in the form: E = x_sp{alpha}{2} E_{alphaalpha} + x_sp{beta}{2 }E_{betabeta } + 2x_{alpha} x_{beta}E _{alphabeta}, where E_{alphaalpha} , E_{betabeta} , E_{alphabeta} are unknown parameters to be determined from a microscopic theory. Using the Jastrow wave function Psi for the mixture, a general expression is given for the ground state energy in terms of the two body potential and two and three body correlation functions. The Kirkwood Super-position Approximation (KSA) is used for the three-body correlation functions. The antisymmetry of the wave function for Fermions is incorporated following the procedure given earlier by Lado, Inguva and Smith. This procedure for treating the antisymmetry of the wave function simplifies the equations for the two-body correlation functions considerably. The equations for the correlation functions are solved in the hypernetted-chain approximation. Once the two-particle correlation functions for the mixture ( ^3He-^4He) have been obtained, the energy is minimized with respect to the variational parameters involved in the Jastrow wave function. The binding energy and the optimal correlation functions are then obtained as a function of the concentration of ^3He atoms in the mixture. (Abstract shortened with permission of author.).

Assessing the role of Hartree-Fock exchange, correlation energy and long range corrections in evaluating ionization potential, and electron affinity in density functional theory.

PubMed

Vikramaditya, Talapunur; Lin, Shiang-Tai

2017-06-05

Accurate determination of ionization potentials (IPs), electron affinities (EAs), fundamental gaps (FGs), and HOMO, LUMO energy levels of organic molecules play an important role in modeling and predicting the efficiencies of organic photovoltaics, OLEDs etc. In this work, we investigate the effects of Hartree Fock (HF) Exchange, correlation energy, and long range corrections in predicting IP and EA in Hybrid Functionals. We observe increase in percentage of HF exchange results in increase of IPs and decrease in EAs. Contrary to the general expectations inclusion of both HF exchange and correlation energy (from the second order perturbation theory MP2) leads to poor prediction. Range separated Hybrid Functionals are found to be more reliable among various DFT Functionals investigated. DFT Functionals predict accurate IPs whereas post HF methods predict accurate EAs. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Cumulants vs correlation functions and the QCD phase diagram at low energies

DOE PAGES

Bzdak, A.; Koch, V.; Skokov, V.; ...

2017-09-25

We discuss the relation between particle number cumulants and genuine correlation functions. Here, it is argued that measuring multi-particle correlation functions could provide cleaner information on possible non-trivial dynamics in heavy-ion collisions.

Cumulants vs correlation functions and the QCD phase diagram at low energies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bzdak, A.; Koch, V.; Skokov, V.

We discuss the relation between particle number cumulants and genuine correlation functions. Here, it is argued that measuring multi-particle correlation functions could provide cleaner information on possible non-trivial dynamics in heavy-ion collisions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gledhill, Jonathan D.; Tozer, David J., E-mail: d.j.tozer@durham.ac.uk

Density scaling considerations are used to derive an exchange–correlation explicit density functional that is appropriate for the electron deficient side of the integer and which recovers the exact r → ∞ asymptotic behaviour of the exchange–correlation potential. The functional has an unconventional mathematical form with parameters that are system-dependent; the parameters for an N-electron system are determined in advance from generalised gradient approximation (GGA) calculations on the N- and (N − 1)-electron systems. Compared to GGA results, the functional yields similar exchange–correlation energies, but HOMO energies that are an order of magnitude closer to the negative of the vertical ionisationmore » potential; for anions, the HOMO energies are negative, as required. Rydberg excitation energies are also notably improved and the exchange–correlation potential is visibly lowered towards the near-exact potential. Further development is required to improve valence excitations, static isotropic polarisabilities, and the shape of the potential in non-asymptotic regions. The functional is fundamentally different to conventional approximations.« less

N-Ω Interaction from High-Energy Heavy Ion Collisions

NASA Astrophysics Data System (ADS)

Morita, Kenji; Ohnishi, Akira; Hatsuda, Tetsuo

We discuss possible observation of the N-Ω interaction from intensity correlation function in high energy heavy ion collisions. Recently a lattice QCD simulation by the HAL QCD collaboration predicts the existence of a N-Ω bound state in the 5S2 channel. We adopt the N-Ω interaction potential obtained by the lattice simulation and use it to calculate the N-Ω correlation function. We also study the variation of the correlation function with respect to the change of the binding energy and scattering parameters. Our result indicates that heavy ion collisions at RHIC and LHC may provide information on the possible existence of the N-Ω dibaryon.

Quantum Monte Carlo analysis of a charge ordered insulating antiferromagnet: The Ti 4O 7 Magneli phase

DOE PAGES

Benali, Anouar; Shulenburger, Luke; Krogel, Jaron T.; ...

2016-06-07

The Magneli phase Ti 4O 7 is an important transition metal oxide with a wide range of applications because of its interplay between charge, spin, and lattice degrees of freedom. At low temperatures, it has non-trivial magnetic states very close in energy, driven by electronic exchange and correlation interactions. We have examined three low- lying states, one ferromagnetic and two antiferromagnetic, and calculated their energies as well as Ti spin moment distributions using highly accurate Quantum Monte Carlo methods. We compare our results to those obtained from density functional theory- based methods that include approximate corrections for exchange and correlation.more » Our results confirm the nature of the states and their ordering in energy, as compared with density-functional theory methods. However, the energy differences and spin distributions differ. Here, a detailed analysis suggests that non-local exchange-correlation functionals, in addition to other approximations such as LDA+U to account for correlations, are needed to simultaneously obtain better estimates for spin moments, distributions, energy differences and energy gaps.« less

Exact kinetic energy enables accurate evaluation of weak interactions by the FDE-vdW method.

PubMed

Sinha, Debalina; Pavanello, Michele

2015-08-28

The correlation energy of interaction is an elusive and sought-after interaction between molecular systems. By partitioning the response function of the system into subsystem contributions, the Frozen Density Embedding (FDE)-vdW method provides a computationally amenable nonlocal correlation functional based on the adiabatic connection fluctuation dissipation theorem applied to subsystem density functional theory. In reproducing potential energy surfaces of weakly interacting dimers, we show that FDE-vdW, either employing semilocal or exact nonadditive kinetic energy functionals, is in quantitative agreement with high-accuracy coupled cluster calculations (overall mean unsigned error of 0.5 kcal/mol). When employing the exact kinetic energy (which we term the Kohn-Sham (KS)-vdW method), the binding energies are generally closer to the benchmark, and the energy surfaces are also smoother.

Exact kinetic energy enables accurate evaluation of weak interactions by the FDE-vdW method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sinha, Debalina; Pavanello, Michele, E-mail: m.pavanello@rutgers.edu

2015-08-28

The correlation energy of interaction is an elusive and sought-after interaction between molecular systems. By partitioning the response function of the system into subsystem contributions, the Frozen Density Embedding (FDE)-vdW method provides a computationally amenable nonlocal correlation functional based on the adiabatic connection fluctuation dissipation theorem applied to subsystem density functional theory. In reproducing potential energy surfaces of weakly interacting dimers, we show that FDE-vdW, either employing semilocal or exact nonadditive kinetic energy functionals, is in quantitative agreement with high-accuracy coupled cluster calculations (overall mean unsigned error of 0.5 kcal/mol). When employing the exact kinetic energy (which we term themore » Kohn-Sham (KS)-vdW method), the binding energies are generally closer to the benchmark, and the energy surfaces are also smoother.« less

Kinetic energy as functional of the correlation hole

NASA Astrophysics Data System (ADS)

Nalewajski, Roman F.

2003-01-01

Using the marginal decomposition of the many-body probability distribution the electronic kinetic energy is expressed as the functional of the electron density and correlation hole. The analysis covers both the molecule as a whole and its constituent subsystems. The importance of the Fisher information for locality is emphasized.

Dispersion- and Exchange-Corrected Density Functional Theory for Sodium Ion Hydration.

PubMed

Soniat, Marielle; Rogers, David M; Rempe, Susan B

2015-07-14

A challenge in density functional theory is developing functionals that simultaneously describe intermolecular electron correlation and electron delocalization. Recent exchange-correlation functionals address those two issues by adding corrections important at long ranges: an atom-centered pairwise dispersion term to account for correlation and a modified long-range component of the electron exchange term to correct for delocalization. Here we investigate how those corrections influence the accuracy of binding free energy predictions for sodium-water clusters. We find that the dual-corrected ωB97X-D functional gives cluster binding energies closest to high-level ab initio methods (CCSD(T)). Binding energy decomposition shows that the ωB97X-D functional predicts the smallest ion-water (pairwise) interaction energy and larger multibody contributions for a four-water cluster than most other functionals - a trend consistent with CCSD(T) results. Also, ωB97X-D produces the smallest amounts of charge transfer and the least polarizable waters of the density functionals studied, which mimics the lower polarizability of CCSD. When compared with experimental binding free energies, however, the exchange-corrected CAM-B3LYP functional performs best (error <1 kcal/mol), possibly because of its parametrization to experimental formation enthalpies. For clusters containing more than four waters, "split-shell" coordination must be considered to obtain accurate free energies in comparison with experiment.

Constraint on the second functional derivative of the exchange-correlation energy

NASA Astrophysics Data System (ADS)

Joubert, D. P.

2012-09-01

Using the density functional adiabatic connection approach for an N-electron system it is shown that ? γ is the coupling constant that scales the electron-electron interaction strength. For the non-interacting Kohn-Sham Hamiltonian γ = 0 and for the fully interacting system γ = 1. ? is the Hartree plus exchange-correlation energy while f 0(r) and fγ(r) are the Fukui functions of the non-interacting and interacting systems, respectively. This identity can serve to test the internal self-consistency or quality of approximate functionals. The quality of some popular approximate exchange and correlation functionals are tested for a simple model system.

Hartree-Fock implementation using a Laguerre-based wave function for the ground state and correlation energies of two-electron atoms.

PubMed

King, Andrew W; Baskerville, Adam L; Cox, Hazel

2018-03-13

An implementation of the Hartree-Fock (HF) method using a Laguerre-based wave function is described and used to accurately study the ground state of two-electron atoms in the fixed nucleus approximation, and by comparison with fully correlated (FC) energies, used to determine accurate electron correlation energies. A variational parameter A is included in the wave function and is shown to rapidly increase the convergence of the energy. The one-electron integrals are solved by series solution and an analytical form is found for the two-electron integrals. This methodology is used to produce accurate wave functions, energies and expectation values for the helium isoelectronic sequence, including at low nuclear charge just prior to electron detachment. Additionally, the critical nuclear charge for binding two electrons within the HF approach is calculated and determined to be Z HF C =1.031 177 528.This article is part of the theme issue 'Modern theoretical chemistry'. © 2018 The Author(s).

Influence of molecular geometry, exchange-correlation functional, and solvent effects in the modeling of vertical excitation energies in phthalocyanines using time-dependent density functional theory (TDDFT) and polarized continuum model TDDFT methods: can modern computational chemistry methods explain experimental controversies?

PubMed

Nemykin, Victor N; Hadt, Ryan G; Belosludov, Rodion V; Mizuseki, Hiroshi; Kawazoe, Yoshiyuki

2007-12-20

A time-dependent density functional theory (TDDFT) approach coupled with 14 different exchange-correlation functionals was used for the prediction of vertical excitation energies in zinc phthalocyanine (PcZn). In general, the TDDFT approach provides a more accurate description of both visible and ultraviolet regions of the UV-vis and magnetic circular dichroism (MCD) spectra of PcZn in comparison to the more popular semiempirical ZINDO/S and PM3 methods. It was found that the calculated vertical excitation energies of PcZn correlate with the amount of Hartree-Fock exchange involved in the exchange-correlation functional. The correlation was explained on the basis of the calculated difference in energy between occupied and unoccupied molecular orbitals. The influence of PcZn geometry, optimized using different exchange-correlation functionals, on the calculated vertical excitation energies in PcZn was found to be relatively small. The influence of solvents on the calculated vertical excitation energies in PcZn was considered for the first time using a polarized continuum model TDDFT (PCM-TDDFT) method and was found to be relatively small in excellent agreement with the experimental data. For all tested TDDFT and PCM-TDDFT cases, an assignment of the Q-band as an almost pure a1u (HOMO)-->eg (LUMO) transition, initially suggested by Gouterman, was confirmed. Pure exchange-correlation functionals indicate the presence of six 1Eu states in the B-band region of the UV-vis spectrum of PcZn, while hybrid exchange-correlation functionals predict only five 1Eu states for the same energy envelope. The first two symmetry-forbidden n-->pi* transitions were predicted in the Q0-2 region and in the low-energy tail of the B-band, while the first two symmetry-allowed n-->pi* transitions were found within the B-band energy envelope when pure exchange-correlation functionals were used for TDDFT calculations. The presence of a symmetry-forbidden but vibronically allowed n-->pi* transition in the Q0-2 spectral envelope explains the long-time controversy between the experimentally observed low-intensity transition in the Q0-2 region and previous semiempirical and TDDFT calculations, which were unable to predict any electronic transitions in this area. To prove the conceptual possibility of the presence of several degenerate 1Eu states in the B-band region of PcZn, room-temperature UV-vis and MCD spectra of zinc tetra-tert-butylphthalocyanine (PctZn) in non-coordinating solvents were recorded and analyzed using band deconvolution analysis. It was found that the B-band region of the UV-vis and MCD spectra of PctZn can be easily deconvoluted using six MCD Faraday A-terms and two MCD Faraday B-terms with energies close to those predicted by TDDFT calculations for 1Eu and 1A2u excited states, respectively. Such a good agreement between theory and experiment clearly indicates the possibility of employing a TDDFT approach for the accurate prediction of vertical excitation energies in phthalocyanines within a large energy range.

Modeling of two-particle femtoscopic correlations at top RHIC energy

NASA Astrophysics Data System (ADS)

Ermakov, N.; Nigmatkulov, G.

2017-01-01

The spatial and temporal characteristics of particle emitting source produced in particle and/or nuclear collisions can be measured by using two-particle femtoscopic correlations. These correlations arise due to quantum statistics, Coulomb and strong final state interactions. In this paper we report on the calculations of like-sign pion femtoscopic correlations produced in p+p, p+Au, d+Au, Au+Au at top RHIC energy using Ultra Relativistic Quantum Molecular Dynamics Model (UrQMD). Three-dimensional correlation functions are constructed using the Bertsch-Pratt parametrization of the two-particle relative momentum. The correlation functions are studied in several transverse mass ranges. The emitting source radii of charged pions, Rout, Rside, Rlong , are obtained from Gaussian fit to the correlation functions and compared to data from the STAR and PHENIX experiments.

Beyond Kohn-Sham Approximation: Hybrid Multistate Wave Function and Density Functional Theory.

PubMed

Gao, Jiali; Grofe, Adam; Ren, Haisheng; Bao, Peng

2016-12-15

A multistate density functional theory (MSDFT) is presented in which the energies and densities for the ground and excited states are treated on the same footing using multiconfigurational approaches. The method can be applied to systems with strong correlation and to correctly describe the dimensionality of the conical intersections between strongly coupled dissociative potential energy surfaces. A dynamic-then-static framework for treating electron correlation is developed to first incorporate dynamic correlation into contracted state functions through block-localized Kohn-Sham density functional theory (KSDFT), followed by diagonalization of the effective Hamiltonian to include static correlation. MSDFT can be regarded as a hybrid of wave function and density functional theory. The method is built on and makes use of the current approximate density functional developed in KSDFT, yet it retains its computational efficiency to treat strongly correlated systems that are problematic for KSDFT but too large for accurate WFT. The results presented in this work show that MSDFT can be applied to photochemical processes involving conical intersections.

Pair correlation function and nonlinear kinetic equation for a spatially uniform polarizable nonideal plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Belyi, V.V.; Kukharenko, Y.A.; Wallenborn, J.

Taking into account the first non-Markovian correction to the Balescu-Lenard equation, we have derived an expression for the pair correlation function and a nonlinear kinetic equation valid for a nonideal polarized classical plasma. This last equation allows for the description of the correlational energy evolution and shows the global conservation of energy with dynamical polarization. {copyright} {ital 1996 The American Physical Society.}

Effective homogeneity of the exchange-correlation and non-interacting kinetic energy functionals under density scaling.

PubMed

Borgoo, Alex; Teale, Andrew M; Tozer, David J

2012-01-21

Correlated electron densities, experimental ionisation potentials, and experimental electron affinities are used to investigate the homogeneity of the exchange-correlation and non-interacting kinetic energy functionals of Kohn-Sham density functional theory under density scaling. Results are presented for atoms and small molecules, paying attention to the influence of the integer discontinuity and the choice of the electron affinity. For the exchange-correlation functional, effective homogeneities are highly system-dependent on either side of the integer discontinuity. By contrast, the average homogeneity-associated with the potential that averages over the discontinuity-is generally close to 4/3 when the discontinuity is computed using positive affinities for systems that do bind an excess electron and negative affinities for those that do not. The proximity to 4/3 becomes increasingly pronounced with increasing atomic number. Evaluating the discontinuity using a zero affinity in systems that do not bind an excess electron instead leads to effective homogeneities on the electron abundant side that are close to 4/3. For the non-interacting kinetic energy functional, the effective homogeneities are less system-dependent and the effect of the integer discontinuity is less pronounced. Average values are uniformly below 5/3. The study provides information that may aid the development of improved exchange-correlation and non-interacting kinetic energy functionals. © 2012 American Institute of Physics

A density difference based analysis of orbital-dependent exchange-correlation functionals

NASA Astrophysics Data System (ADS)

Grabowski, Ireneusz; Teale, Andrew M.; Fabiano, Eduardo; Śmiga, Szymon; Buksztel, Adam; Della Sala, Fabio

2014-03-01

We present a density difference based analysis for a range of orbital-dependent Kohn-Sham functionals. Results for atoms, some members of the neon isoelectronic series and small molecules are reported and compared with ab initio wave function calculations. Particular attention is paid to the quality of approximations to the exchange-only optimised effective potential (OEP) approach: we consider both the localised Hartree-Fock as well as the Krieger-Li-Iafrate methods. Analysis of density differences at the exchange-only level reveals the impact of the approximations on the resulting electronic densities. These differences are further quantified in terms of the ground state energies, frontier orbital energy differences and highest occupied orbital energies obtained. At the correlated level, an OEP approach based on a perturbative second-order correlation energy expression is shown to deliver results comparable with those from traditional wave function approaches, making it suitable for use as a benchmark against which to compare standard density functional approximations.

Generic expansion of the Jastrow correlation factor in polynomials satisfying symmetry and cusp conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lüchow, Arne, E-mail: luechow@rwth-aachen.de; Jülich Aachen Research Alliance; Sturm, Alexander

2015-02-28

Jastrow correlation factors play an important role in quantum Monte Carlo calculations. Together with an orbital based antisymmetric function, they allow the construction of highly accurate correlation wave functions. In this paper, a generic expansion of the Jastrow correlation function in terms of polynomials that satisfy both the electron exchange symmetry constraint and the cusp conditions is presented. In particular, an expansion of the three-body electron-electron-nucleus contribution in terms of cuspless homogeneous symmetric polynomials is proposed. The polynomials can be expressed in fairly arbitrary scaling function allowing a generic implementation of the Jastrow factor. It is demonstrated with a fewmore » examples that the new Jastrow factor achieves 85%–90% of the total correlation energy in a variational quantum Monte Carlo calculation and more than 90% of the diffusion Monte Carlo correlation energy.« less

Exchange and correlation in positronium-molecule scattering

NASA Astrophysics Data System (ADS)

Fabrikant, I. I.; Wilde, R. S.

2018-05-01

Exchange and correlations play a particularly important role in positronium (Ps) collisions with atoms and molecules, since the static potential for Ps interaction with a neutral system is zero. Theoretical description of both effects is a very challenging task. In the present work we use the free-electron-gas model to describe exchange and correlations in Ps collisions with molecules similar to the approach widely used in the theory of electron-molecule collisions. The results for exchange and correlation energies are presented as functions of the Fermi momentum of the electron gas and the Ps incident energy. Using the Thomas-Fermi model, these functions can be converted into exchange and correlation potentials for Ps interaction with molecules as functions of the distance between the projectile and the target.

Locality of correlation in density functional theory.

PubMed

Burke, Kieron; Cancio, Antonio; Gould, Tim; Pittalis, Stefano

2016-08-07

The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi (TF) approximation in the non-relativistic semiclassical (or large-Z) limit for all matter, i.e., the kinetic energy becomes local. Exchange also becomes local in this limit. Numerical data on the correlation energy of atoms support the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around a large particle number are equivalent to local density approximations and their strong relevance to density functional approximations. Analyzing highly accurate atomic correlation energies, we show that EC → -AC ZlnZ + BCZ as Z → ∞, where Z is the atomic number, AC is known, and we estimate BC to be about 37 mhartree. The local density approximation yields AC exactly, but a very incorrect value for BC, showing that the local approximation is less relevant for the correlation alone. This limit is a benchmark for the non-empirical construction of density functional approximations. We conjecture that, beyond atoms, the leading correction to the local density approximation in the large-Z limit generally takes this form, but with BC a functional of the TF density for the system. The implications for the construction of approximate density functionals are discussed.

Bond breaking and bond formation: how electron correlation is captured in many-body perturbation theory and density-functional theory.

PubMed

Caruso, Fabio; Rohr, Daniel R; Hellgren, Maria; Ren, Xinguo; Rinke, Patrick; Rubio, Angel; Scheffler, Matthias

2013-04-05

For the paradigmatic case of H(2) dissociation, we compare state-of-the-art many-body perturbation theory in the GW approximation and density-functional theory in the exact-exchange plus random-phase approximation (RPA) for the correlation energy. For an unbiased comparison and to prevent spurious starting point effects, both approaches are iterated to full self-consistency (i.e., sc-RPA and sc-GW). The exchange-correlation diagrams in both approaches are topologically identical, but in sc-RPA they are evaluated with noninteracting and in sc-GW with interacting Green functions. This has a profound consequence for the dissociation region, where sc-RPA is superior to sc-GW. We argue that for a given diagrammatic expansion, sc-RPA outperforms sc-GW when it comes to bond breaking. We attribute this to the difference in the correlation energy rather than the treatment of the kinetic energy.

Density Functionals of Chemical Bonding

PubMed Central

Putz, Mihai V.

2008-01-01

The behavior of electrons in general many-electronic systems throughout the density functionals of energy is reviewed. The basic physico-chemical concepts of density functional theory are employed to highlight the energy role in chemical structure while its extended influence in electronic localization function helps in chemical bonding understanding. In this context the energy functionals accompanied by electronic localization functions may provide a comprehensive description of the global-local levels electronic structures in general and of chemical bonds in special. Becke-Edgecombe and author’s Markovian electronic localization functions are discussed at atomic, molecular and solid state levels. Then, the analytical survey of the main workable kinetic, exchange, and correlation density functionals within local and gradient density approximations is undertaken. The hierarchy of various energy functionals is formulated by employing both the parabolic and statistical correlation degree of them with the electronegativity and chemical hardness indices by means of quantitative structure-property relationship (QSPR) analysis for basic atomic and molecular systems. PMID:19325846

Accurate calculation and modeling of the adiabatic connection in density functional theory

NASA Astrophysics Data System (ADS)

Teale, A. M.; Coriani, S.; Helgaker, T.

2010-04-01

Using a recently implemented technique for the calculation of the adiabatic connection (AC) of density functional theory (DFT) based on Lieb maximization with respect to the external potential, the AC is studied for atoms and molecules containing up to ten electrons: the helium isoelectronic series, the hydrogen molecule, the beryllium isoelectronic series, the neon atom, and the water molecule. The calculation of AC curves by Lieb maximization at various levels of electronic-structure theory is discussed. For each system, the AC curve is calculated using Hartree-Fock (HF) theory, second-order Møller-Plesset (MP2) theory, coupled-cluster singles-and-doubles (CCSD) theory, and coupled-cluster singles-doubles-perturbative-triples [CCSD(T)] theory, expanding the molecular orbitals and the effective external potential in large Gaussian basis sets. The HF AC curve includes a small correlation-energy contribution in the context of DFT, arising from orbital relaxation as the electron-electron interaction is switched on under the constraint that the wave function is always a single determinant. The MP2 and CCSD AC curves recover the bulk of the dynamical correlation energy and their shapes can be understood in terms of a simple energy model constructed from a consideration of the doubles-energy expression at different interaction strengths. Differentiation of this energy expression with respect to the interaction strength leads to a simple two-parameter doubles model (AC-D) for the AC integrand (and hence the correlation energy of DFT) as a function of the interaction strength. The structure of the triples-energy contribution is considered in a similar fashion, leading to a quadratic model for the triples correction to the AC curve (AC-T). From a consideration of the structure of a two-level configuration-interaction (CI) energy expression of the hydrogen molecule, a simple two-parameter CI model (AC-CI) is proposed to account for the effects of static correlation on the AC. When parametrized in terms of the same input data, the AC-CI model offers improved performance over the corresponding AC-D model, which is shown to be the lowest-order contribution to the AC-CI model. The utility of the accurately calculated AC curves for the analysis of standard density functionals is demonstrated for the BLYP exchange-correlation functional and the interaction-strength-interpolation (ISI) model AC integrand. From the results of this analysis, we investigate the performance of our proposed two-parameter AC-D and AC-CI models when a simple density functional for the AC at infinite interaction strength is employed in place of information at the fully interacting point. The resulting two-parameter correlation functionals offer a qualitatively correct behavior of the AC integrand with much improved accuracy over previous attempts. The AC integrands in the present work are recommended as a basis for further work, generating functionals that avoid spurious error cancellations between exchange and correlation energies and give good accuracy for the range of densities and types of correlation contained in the systems studied here.

Multiconfiguration pair-density functional theory: barrier heights and main group and transition metal energetics.

PubMed

Carlson, Rebecca K; Li Manni, Giovanni; Sonnenberger, Andrew L; Truhlar, Donald G; Gagliardi, Laura

2015-01-13

Kohn-Sham density functional theory, resting on the representation of the electronic density and kinetic energy by a single Slater determinant, has revolutionized chemistry, but for open-shell systems, the Kohn-Sham Slater determinant has the wrong symmetry properties as compared to an accurate wave function. We have recently proposed a theory, called multiconfiguration pair-density functional theory (MC-PDFT), in which the electronic kinetic energy and classical Coulomb energy are calculated from a multiconfiguration wave function with the correct symmetry properties, and the rest of the energy is calculated from a density functional, called the on-top density functional, that depends on the density and the on-top pair density calculated from this wave function. We also proposed a simple way to approximate the on-top density functional by translation of Kohn-Sham exchange-correlation functionals. The method is much less expensive than other post-SCF methods for calculating the dynamical correlation energy starting with a multiconfiguration self-consistent-field wave function as the reference wave function, and initial tests of the theory were quite encouraging. Here, we provide a broader test of the theory by applying it to bond energies of main-group molecules and transition metal complexes, barrier heights and reaction energies for diverse chemical reactions, proton affinities, and the water dimerization energy. Averaged over 56 data points, the mean unsigned error is 3.2 kcal/mol for MC-PDFT, as compared to 6.9 kcal/mol for Kohn-Sham theory with a comparable density functional. MC-PDFT is more accurate on average than complete active space second-order perturbation theory (CASPT2) for main-group small-molecule bond energies, alkyl bond dissociation energies, transition-metal-ligand bond energies, proton affinities, and the water dimerization energy.

Hartree-Fock theory of the inhomogeneous electron gas at a jellium metal surface: Rigorous upper bounds to the surface energy and accurate work functions

NASA Astrophysics Data System (ADS)

Sahni, V.; Ma, C. Q.

1980-12-01

The inhomogeneous electron gas at a jellium metal surface is studied in the Hartree-Fock approximation by Kohn-Sham density functional theory. Rigorous upper bounds to the surface energy are derived by application of the Rayleigh-Ritz variational principle for the energy, the surface kinetic, electrostatic, and nonlocal exchange energy functionals being determined exactly for the accurate linear-potential model electronic wave functions. The densities obtained by the energy minimization constraint are then employed to determine work-function results via the variationally accurate "displaced-profile change-in-self-consistent-field" expression. The theoretical basis of this non-self-consistent procedure and its demonstrated accuracy for the fully correlated system (as treated within the local-density approximation for exchange and correlation) leads us to conclude these results for the surface energies and work functions to be essentially exact. Work-function values are also determined by the Koopmans'-theorem expression, both for these densities as well as for those obtained by satisfaction of the constraint set on the electrostatic potential by the Budd-Vannimenus theorem. The use of the Hartree-Fock results in the accurate estimation of correlation-effect contributions to these surface properties of the nonuniform electron gas is also indicated. In addition, the original work and approximations made by Bardeen in this attempt at a solution of the Hartree-Fock problem are briefly reviewed in order to contrast with the present work.

Short-range density functional correlation within the restricted active space CI method

NASA Astrophysics Data System (ADS)

Casanova, David

2018-03-01

In the present work, I introduce a hybrid wave function-density functional theory electronic structure method based on the range separation of the electron-electron Coulomb operator in order to recover dynamic electron correlations missed in the restricted active space configuration interaction (RASCI) methodology. The working equations and the computational algorithm for the implementation of the new approach, i.e., RAS-srDFT, are presented, and the method is tested in the calculation of excitation energies of organic molecules. The good performance of the RASCI wave function in combination with different short-range exchange-correlation functionals in the computation of relative energies represents a quantitative improvement with respect to the RASCI results and paves the path for the development of RAS-srDFT as a promising scheme in the computation of the ground and excited states where nondynamic and dynamic electron correlations are important.

Performance of correlation receivers in the presence of impulse noise.

NASA Technical Reports Server (NTRS)

Moore, J. D.; Houts, R. C.

1972-01-01

An impulse noise model, which assumes that each noise burst contains a randomly weighted version of a basic waveform, is used to derive the performance equations for a correlation receiver. The expected number of bit errors per noise burst is expressed as a function of the average signal energy, signal-set correlation coefficient, bit time, noise-weighting-factor variance and probability density function, and a time range function which depends on the crosscorrelation of the signal-set basis functions and the noise waveform. Unlike the performance results for additive white Gaussian noise, it is shown that the error performance for impulse noise is affected by the choice of signal-set basis function, and that Orthogonal signaling is not equivalent to On-Off signaling with the same average energy. Furthermore, it is demonstrated that the correlation-receiver error performance can be improved by inserting a properly specified nonlinear device prior to the receiver input.

Discontinuity of the exchange-correlation potential and the functional derivative of the noninteracting kinetic energy as the number of electrons crosses integer boundaries in Li, Be, and B.

PubMed

Morrison, Robert C

2015-01-07

Accurate densities were determined from configuration interaction wave functions for atoms and ions of Li, Be, and B with up to four electrons. Exchange-correlation potentials, Vxc(r), and functional derivatives of the noninteracting kinetic energy, δK[ρ]/δρ(r), obtained from these densities were used to examine their discontinuities as the number of electrons N increases across integer boundaries for N = 1, N = 2, and N = 3. These numerical results are consistent with conclusions that the discontinuities are characterized by a jump in the chemical potential while the shape of Vxc(r) varies continuously as an integer boundary is crossed. The discontinuity of the Vxc(r) is positive, depends on the ionization potential, electron affinity, and orbital energy differences, and the discontinuity in δK[ρ]/δρ(r) depends on the difference between the energies of the highest occupied and lowest unoccupied orbitals. The noninteracting kinetic energy and the exchange correlation energy have been computed for integer and noninteger values of N between 1 and 4.

Combining Density Functional Theory and Green's Function Theory: Range-Separated, Nonlocal, Dynamic, and Orbital-Dependent Hybrid Functional.

PubMed

Kananenka, Alexei A; Zgid, Dominika

2017-11-14

We present a rigorous framework which combines single-particle Green's function theory with density functional theory based on a separation of electron-electron interactions into short- and long-range components. Short-range contribution to the total energy and exchange-correlation potential is provided by a density functional approximation, while the long-range contribution is calculated using an explicit many-body Green's function method. Such a hybrid results in a nonlocal, dynamic, and orbital-dependent exchange-correlation functional of a single-particle Green's function. In particular, we present a range-separated hybrid functional called srSVWN5-lrGF2 which combines the local-density approximation and the second-order Green's function theory. We illustrate that similarly to density functional approximations, the new functional is weakly basis-set dependent. Furthermore, it offers an improved description of the short-range dynamic correlation. The many-body contribution to the functional mitigates the many-electron self-interaction error present in many density functional approximations and provides a better description of molecular properties. Additionally, we illustrate that the new functional can be used to scale down the self-energy and, therefore, introduce an additional sparsity to the self-energy matrix that in the future can be exploited in calculations for large molecules or periodic systems.

Understanding the atomic-level Green-Kubo stress correlation function for a liquid through phonons in a model crystal

NASA Astrophysics Data System (ADS)

Levashov, V. A.

2014-11-01

In order to gain insight into the connection between the vibrational dynamics and the atomic-level Green-Kubo stress correlation function in liquids, we consider this connection in a model crystal instead. Of course, vibrational dynamics in liquids and crystals are quite different and it is not expected that the results obtained on a model crystal should be valid for liquids. However, these considerations provide a benchmark to which the results of the previous molecular dynamics simulations can be compared. Thus, assuming that vibrations are plane waves, we derive analytical expressions for the atomic-level stress correlation functions in the classical limit and analyze them. These results provide, in particular, a recipe for analysis of the atomic-level stress correlation functions in Fourier space and extraction of the wave-vector and frequency-dependent information. We also evaluate the energies of the atomic-level stresses. The energies obtained are significantly smaller than the energies previously determined in molecular dynamics simulations of several model liquids. This result suggests that the average energies of the atomic-level stresses in liquids and glasses are largely determined by the structural disorder. We discuss this result in the context of equipartition of the atomic-level stress energies. Analysis of the previously published data suggests that it is possible to speak about configurational and vibrational contributions to the average energies of the atomic-level stresses in a glass state. However, this separation in a liquid state is problematic. We also introduce and briefly consider the atomic-level transverse current correlation function. Finally, we address the broadening of the peaks in the pair distribution function with increase of distance. We find that the peaks' broadening (by ≈40 % ) occurs due to the transverse vibrational modes, while contribution from the longitudinal modes does not change with distance.

Signatures of van der Waals binding: A coupling-constant scaling analysis

NASA Astrophysics Data System (ADS)

Jiao, Yang; Schröder, Elsebeth; Hyldgaard, Per

2018-02-01

The van der Waals (vdW) density functional (vdW-DF) method [Rep. Prog. Phys. 78, 066501 (2015), 10.1088/0034-4885/78/6/066501] describes dispersion or vdW binding by tracking the effects of an electrodynamic coupling among pairs of electrons and their associated exchange-correlation holes. This is done in a nonlocal-correlation energy term Ecnl, which permits density functional theory calculation in the Kohn-Sham scheme. However, to map the nature of vdW forces in a fully interacting materials system, it is necessary to also account for associated kinetic-correlation energy effects. Here, we present a coupling-constant scaling analysis, which permits us to compute the kinetic-correlation energy Tcnl that is specific to the vdW-DF account of nonlocal correlations. We thus provide a more complete spatially resolved analysis of the electrodynamical-coupling nature of nonlocal-correlation binding, including vdW attraction, in both covalently and noncovalently bonded systems. We find that kinetic-correlation energy effects play a significant role in the account of vdW or dispersion interactions among molecules. Furthermore, our mapping shows that the total nonlocal-correlation binding is concentrated to pockets in the sparse electron distribution located between the material fragments.

Efficient construction of exchange and correlation potentials by inverting the Kohn-Sham equations.

PubMed

Kananenka, Alexei A; Kohut, Sviataslau V; Gaiduk, Alex P; Ryabinkin, Ilya G; Staroverov, Viktor N

2013-08-21

Given a set of canonical Kohn-Sham orbitals, orbital energies, and an external potential for a many-electron system, one can invert the Kohn-Sham equations in a single step to obtain the corresponding exchange-correlation potential, vXC(r). For orbitals and orbital energies that are solutions of the Kohn-Sham equations with a multiplicative vXC(r) this procedure recovers vXC(r) (in the basis set limit), but for eigenfunctions of a non-multiplicative one-electron operator it produces an orbital-averaged potential. In particular, substitution of Hartree-Fock orbitals and eigenvalues into the Kohn-Sham inversion formula is a fast way to compute the Slater potential. In the same way, we efficiently construct orbital-averaged exchange and correlation potentials for hybrid and kinetic-energy-density-dependent functionals. We also show how the Kohn-Sham inversion approach can be used to compute functional derivatives of explicit density functionals and to approximate functional derivatives of orbital-dependent functionals.

Locality of correlation in density functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burke, Kieron; Cancio, Antonio; Gould, Tim

The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi (TF) approximation in the non-relativistic semiclassical (or large-Z) limit for all matter, i.e., the kinetic energy becomes local. Exchange also becomes local in this limit. Numerical data on the correlation energy of atoms support the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around a large particle number are equivalent to local density approximations and their strong relevance to density functional approximations. Analyzing highly accurate atomic correlation energies, we show that E{sub C} → −A{sub C} ZlnZ +more » B{sub C}Z as Z → ∞, where Z is the atomic number, A{sub C} is known, and we estimate B{sub C} to be about 37 mhartree. The local density approximation yields A{sub C} exactly, but a very incorrect value for B{sub C}, showing that the local approximation is less relevant for the correlation alone. This limit is a benchmark for the non-empirical construction of density functional approximations. We conjecture that, beyond atoms, the leading correction to the local density approximation in the large-Z limit generally takes this form, but with B{sub C} a functional of the TF density for the system. The implications for the construction of approximate density functionals are discussed.« less

Statistical model of a flexible inextensible polymer chain: The effect of kinetic energy.

PubMed

Pergamenshchik, V M; Vozniak, A B

2017-01-01

Because of the holonomic constraints, the kinetic energy contribution in the partition function of an inextensible polymer chain is difficult to find, and it has been systematically ignored. We present the first thermodynamic calculation incorporating the kinetic energy of an inextensible polymer chain with the bending energy. To explore the effect of the translation-rotation degrees of freedom, we propose and solve a statistical model of a fully flexible chain of N+1 linked beads which, in the limit of smooth bending, is equivalent to the well-known wormlike chain model. The partition function with the kinetic and bending energies and correlations between orientations of any pair of links and velocities of any pair of beads are found. This solution is precise in the limits of small and large rigidity-to-temperature ratio b/T. The last exact solution is essential as even very "harmless" approximation results in loss of the important effects when the chain is very rigid. For very high b/T, the orientations of different links become fully correlated. Nevertheless, the chain does not go over into a hard rod even in the limit b/T→∞: While the velocity correlation length diverges, the correlations themselves remain weak and tend to the value ∝T/(N+1). The N dependence of the partition function is essentially determined by the kinetic energy contribution. We demonstrate that to obtain the correct energy and entropy in a constrained system, the T derivative of the partition function has to be applied before integration over the constraint-setting variable.

Statistical model of a flexible inextensible polymer chain: The effect of kinetic energy

NASA Astrophysics Data System (ADS)

Pergamenshchik, V. M.; Vozniak, A. B.

2017-01-01

Because of the holonomic constraints, the kinetic energy contribution in the partition function of an inextensible polymer chain is difficult to find, and it has been systematically ignored. We present the first thermodynamic calculation incorporating the kinetic energy of an inextensible polymer chain with the bending energy. To explore the effect of the translation-rotation degrees of freedom, we propose and solve a statistical model of a fully flexible chain of N +1 linked beads which, in the limit of smooth bending, is equivalent to the well-known wormlike chain model. The partition function with the kinetic and bending energies and correlations between orientations of any pair of links and velocities of any pair of beads are found. This solution is precise in the limits of small and large rigidity-to-temperature ratio b /T . The last exact solution is essential as even very "harmless" approximation results in loss of the important effects when the chain is very rigid. For very high b /T , the orientations of different links become fully correlated. Nevertheless, the chain does not go over into a hard rod even in the limit b /T →∞ : While the velocity correlation length diverges, the correlations themselves remain weak and tend to the value ∝T /(N +1 ). The N dependence of the partition function is essentially determined by the kinetic energy contribution. We demonstrate that to obtain the correct energy and entropy in a constrained system, the T derivative of the partition function has to be applied before integration over the constraint-setting variable.

Synthesis of correlation filters: a generalized space-domain approach for improved filter characteristics

NASA Astrophysics Data System (ADS)

Sudharsanan, Subramania I.; Mahalanobis, Abhijit; Sundareshan, Malur K.

1990-12-01

Discrete frequency domain design of Minimum Average Correlation Energy filters for optical pattern recognition introduces an implementational limitation of circular correlation. An alternative methodology which uses space domain computations to overcome this problem is presented. The technique is generalized to construct an improved synthetic discriminant function which satisfies the conflicting requirements of reduced noise variance and sharp correlation peaks to facilitate ease of detection. A quantitative evaluation of the performance characteristics of the new filter is conducted and is shown to compare favorably with the well known Minimum Variance Synthetic Discriminant Function and the space domain Minimum Average Correlation Energy filter, which are special cases of the present design.

Correlated wave functions for three-particle systems with Coulomb interaction - The muonic helium atom

NASA Technical Reports Server (NTRS)

Huang, K.-N.

1977-01-01

A computational procedure for calculating correlated wave functions is proposed for three-particle systems interacting through Coulomb forces. Calculations are carried out for the muonic helium atom. Variational wave functions which explicitly contain interparticle coordinates are presented for the ground and excited states. General Hylleraas-type trial functions are used as the basis for the correlated wave functions. Excited-state energies of the muonic helium atom computed from 1- and 35-term wave functions are listed for four states.

Global hybrids from the semiclassical atom theory satisfying the local density linear response.

PubMed

Fabiano, Eduardo; Constantin, Lucian A; Cortona, Pietro; Della Sala, Fabio

2015-01-13

We propose global hybrid approximations of the exchange-correlation (XC) energy functional which reproduce well the modified fourth-order gradient expansion of the exchange energy in the semiclassical limit of many-electron neutral atoms and recover the full local density approximation (LDA) linear response. These XC functionals represent the hybrid versions of the APBE functional [Phys. Rev. Lett. 2011, 106, 186406] yet employing an additional correlation functional which uses the localization concept of the correlation energy density to improve the compatibility with the Hartree-Fock exchange as well as the coupling-constant-resolved XC potential energy. Broad energetic and structural testing, including thermochemistry and geometry, transition metal complexes, noncovalent interactions, gold clusters and small gold-molecule interfaces, as well as an analysis of the hybrid parameters, show that our construction is quite robust. In particular, our testing shows that the resulting hybrid, including 20% of Hartree-Fock exchange and named hAPBE, performs remarkably well for a broad palette of systems and properties, being generally better than popular hybrids (PBE0 and B3LYP). Semiempirical dispersion corrections are also provided.

Water 16-mers and hexamers: assessment of the three-body and electrostatically embedded many-body approximations of the correlation energy or the nonlocal energy as ways to include cooperative effects.

PubMed

Qi, Helena W; Leverentz, Hannah R; Truhlar, Donald G

2013-05-30

This work presents a new fragment method, the electrostatically embedded many-body expansion of the nonlocal energy (EE-MB-NE), and shows that it, along with the previously proposed electrostatically embedded many-body expansion of the correlation energy (EE-MB-CE), produces accurate results for large systems at the level of CCSD(T) coupled cluster theory. We primarily study water 16-mers, but we also test the EE-MB-CE method on water hexamers. We analyze the distributions of two-body and three-body terms to show why the many-body expansion of the electrostatically embedded correlation energy converges faster than the many-body expansion of the entire electrostatically embedded interaction potential. The average magnitude of the dimer contributions to the pairwise additive (PA) term of the correlation energy (which neglects cooperative effects) is only one-half of that of the average dimer contribution to the PA term of the expansion of the total energy; this explains why the mean unsigned error (MUE) of the EE-PA-CE approximation is only one-half of that of the EE-PA approximation. Similarly, the average magnitude of the trimer contributions to the three-body (3B) term of the EE-3B-CE approximation is only one-fourth of that of the EE-3B approximation, and the MUE of the EE-3B-CE approximation is one-fourth that of the EE-3B approximation. Finally, we test the efficacy of two- and three-body density functional corrections. One such density functional correction method, the new EE-PA-NE method, with the OLYP or the OHLYP density functional (where the OHLYP functional is the OptX exchange functional combined with the LYP correlation functional multiplied by 0.5), has the best performance-to-price ratio of any method whose computational cost scales as the third power of the number of monomers and is competitive in accuracy in the tests presented here with even the electrostatically embedded three-body approximation.

Gradient corrections to the exchange-correlation free energy

DOE PAGES

Sjostrom, Travis; Daligault, Jerome

2014-10-07

We develop the first-order gradient correction to the exchange-correlation free energy of the homogeneous electron gas for use in finite-temperature density functional calculations. Based on this, we propose and implement a simple temperature-dependent extension for functionals beyond the local density approximation. These finite-temperature functionals show improvement over zero-temperature functionals, as compared to path-integral Monte Carlo calculations for deuterium equations of state, and perform without computational cost increase compared to zero-temperature functionals and so should be used for finite-temperature calculations. Furthermore, while the present functionals are valid at all temperatures including zero, non-negligible difference with zero-temperature functionals begins at temperatures abovemore » 10 000 K.« less

Field theoretic approach to roughness corrections

NASA Astrophysics Data System (ADS)

Wu, Hua Yao; Schaden, Martin

2012-02-01

We develop a systematic field theoretic description of roughness corrections to the Casimir free energy of a massless scalar field in the presence of parallel plates with mean separation a. Roughness is modeled by specifying a generating functional for correlation functions of the height profile. The two-point correlation function being characterized by its variance, σ2, and correlation length, ℓ. We obtain the partition function of a massless scalar quantum field interacting with the height profile of the surface via a δ-function potential. The partition function is given by a holographic reduction of this model to three coupled scalar fields on a two-dimensional plane. The original three-dimensional space with a flat parallel plate at a distance a from the rough plate is encoded in the nonlocal propagators of the surface fields on its boundary. Feynman rules for this equivalent 2+1-dimensional model are derived and its counterterms constructed. The two-loop contribution to the free energy of this model gives the leading roughness correction. The effective separation, aeff, to a rough plate is measured to a plane that is displaced a distance ρ∝σ2/ℓ from the mean of its profile. This definition of the separation eliminates corrections to the free energy of order 1/a4 and results in unitary scattering matrices. We obtain an effective low-energy model in the limit ℓ≪a. It determines the scattering matrix and equivalent planar scattering surface of a very rough plate in terms of the single length scale ρ. The Casimir force on a rough plate is found to always weaken with decreasing correlation length ℓ. The two-loop approximation to the free energy interpolates between the free energy of the effective low-energy model and that of the proximity force approximation - the force on a very rough plate with σ≳0.5ℓ being weaker than on a planar Dirichlet surface at any separation.

From The Cover: The X3LYP extended density functional for accurate descriptions of nonbond interactions, spin states, and thermochemical properties.

PubMed

Xu, Xin; Goddard, William A

2004-03-02

We derive the form for an exact exchange energy density for a density decaying with Gaussian-like behavior at long range. Based on this, we develop the X3LYP (extended hybrid functional combined with Lee-Yang-Parr correlation functional) extended functional for density functional theory to significantly improve the accuracy for hydrogen-bonded and van der Waals complexes while also improving the accuracy in heats of formation, ionization potentials, electron affinities, and total atomic energies [over the most popular and accurate method, B3LYP (Becke three-parameter hybrid functional combined with Lee-Yang-Parr correlation functional)]. X3LYP also leads to a good description of dipole moments, polarizabilities, and accurate excitation energies from s to d orbitals for transition metal atoms and ions. We suggest that X3LYP will be useful for predicting ligand binding in proteins and DNA.

From The Cover: The X3LYP extended density functional for accurate descriptions of nonbond interactions, spin states, and thermochemical properties

NASA Astrophysics Data System (ADS)

Xu, Xin; Goddard, William A., III

2004-03-01

We derive the form for an exact exchange energy density for a density decaying with Gaussian-like behavior at long range. Based on this, we develop the X3LYP (extended hybrid functional combined with Lee-Yang-Parr correlation functional) extended functional for density functional theory to significantly improve the accuracy for hydrogen-bonded and van der Waals complexes while also improving the accuracy in heats of formation, ionization potentials, electron affinities, and total atomic energies [over the most popular and accurate method, B3LYP (Becke three-parameter hybrid functional combined with Lee-Yang-Parr correlation functional)]. X3LYP also leads to a good description of dipole moments, polarizabilities, and accurate excitation energies from s to d orbitals for transition metal atoms and ions. We suggest that X3LYP will be useful for predicting ligand binding in proteins and DNA.

The X3LYP extended density functional for accurate descriptions of nonbond interactions, spin states, and thermochemical properties

PubMed Central

Xu, Xin; Goddard, William A.

2004-01-01

We derive the form for an exact exchange energy density for a density decaying with Gaussian-like behavior at long range. Based on this, we develop the X3LYP (extended hybrid functional combined with Lee–Yang–Parr correlation functional) extended functional for density functional theory to significantly improve the accuracy for hydrogen-bonded and van der Waals complexes while also improving the accuracy in heats of formation, ionization potentials, electron affinities, and total atomic energies [over the most popular and accurate method, B3LYP (Becke three-parameter hybrid functional combined with Lee–Yang–Parr correlation functional)]. X3LYP also leads to a good description of dipole moments, polarizabilities, and accurate excitation energies from s to d orbitals for transition metal atoms and ions. We suggest that X3LYP will be useful for predicting ligand binding in proteins and DNA. PMID:14981235

Finite-T correlations and free exchange-correlation energy of quasi-one-dimensional electron gas

NASA Astrophysics Data System (ADS)

Garg, Vinayak; Sharma, Akariti; Moudgil, R. K.

2018-02-01

We have studied the effect of temperature on static density-density correlations and plasmon excitation spectrum of quasi-one-dimensional electron gas (Q1DEG) using the random phase approximation (RPA). Numerical results for static structure factor, pair-correlation function, static density susceptibility, free exchange-correlation energy and plasmon dispersion are presented over a wide range of temperature and electron density. As an interesting result, we find that the short-range correlations exhibit a non-monotonic dependence on temperature T, initially growing stronger (i.e. the pair-correlation function at small inter-electron spacing assuming relatively smaller values) with increasing T and then weakening above a critical T. The cross-over temperature is found to increase with increasing coupling among electrons. Also, the q = 2kF peak in the static density susceptibility χ(q,ω = 0,T) at T = 0 K smears out with rising T. The free exchange-correlation energy and plasmon dispersion show a significant variation with T, and the trend is qualitatively the same as in higher dimensions.

Complex Correlation Kohn-T Method of Calculating Total and Elastic Cross Sections. Part 1; Electron-Hydrogen Elastic Scattering

NASA Technical Reports Server (NTRS)

Bhatia, A. K.; Temkin, A.; Fisher, Richard R. (Technical Monitor)

2001-01-01

We report on the first part of a study of electron-hydrogen scattering, using a method which allows for the ab initio calculation of total and elastic cross sections at higher energies. In its general form the method uses complex 'radial' correlation functions, in a (Kohn) T-matrix formalism. The titled method, abbreviated Complex Correlation Kohn T (CCKT) method, is reviewed, in the context of electron-hydrogen scattering, including the derivation of the equation for the (complex) scattering function, and the extraction of the scattering information from the latter. The calculation reported here is restricted to S-waves in the elastic region, where the correlation functions can be taken, without loss of generality, to be real. Phase shifts are calculated using Hylleraas-type correlation functions with up to 95 terms. Results are rigorous lower bounds; they are in general agreement with those of Schwartz, but they are more accurate and outside his error bounds at a couple of energies,

Cumulants and correlation functions versus the QCD phase diagram

DOE PAGES

Bzdak, Adam; Koch, Volker; Strodthoff, Nils

2017-05-12

Here, we discuss the relation of particle number cumulants and correlation functions. It is argued that measuring couplings of the genuine multiparticle correlation functions could provide cleaner information on possible nontrivial dynamics in heavy-ion collisions. We also extract integrated multiproton correlation functions from the presently available experimental data on proton cumulants. We find that the STAR data contain significant four-proton correlations, at least at the lower energies, with indication of changing dynamics in central collisions. We also find that these correlations are rather long ranged in rapidity. Finally, using the Ising model, we demonstrate how the signs of the multiprotonmore » correlation functions may be used to exclude certain regions of the phase diagram close to the critical point.« less

Cumulants and correlation functions versus the QCD phase diagram

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bzdak, Adam; Koch, Volker; Strodthoff, Nils

Here, we discuss the relation of particle number cumulants and correlation functions. It is argued that measuring couplings of the genuine multiparticle correlation functions could provide cleaner information on possible nontrivial dynamics in heavy-ion collisions. We also extract integrated multiproton correlation functions from the presently available experimental data on proton cumulants. We find that the STAR data contain significant four-proton correlations, at least at the lower energies, with indication of changing dynamics in central collisions. We also find that these correlations are rather long ranged in rapidity. Finally, using the Ising model, we demonstrate how the signs of the multiprotonmore » correlation functions may be used to exclude certain regions of the phase diagram close to the critical point.« less

Double-hybrid density-functional theory with meta-generalized-gradient approximations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Souvi, Sidi M. O., E-mail: sidi.souvi@irsn.fr; Sharkas, Kamal; Toulouse, Julien, E-mail: julien.toulouse@upmc.fr

2014-02-28

We extend the previously proposed one-parameter double-hybrid density-functional theory [K. Sharkas, J. Toulouse, and A. Savin, J. Chem. Phys. 134, 064113 (2011)] to meta-generalized-gradient-approximation (meta-GGA) exchange-correlation density functionals. We construct several variants of one-parameter double-hybrid approximations using the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA functional and test them on test sets of atomization energies and reaction barrier heights. The most accurate variant uses the uniform coordinate scaling of the density and of the kinetic energy density in the correlation functional, and improves over both standard Kohn-Sham TPSS and second-order Møller-Plesset calculations.

Four-electron model for singlet and triplet excitation energy transfers with inclusion of coherence memory, inelastic tunneling and nuclear quantum effects

NASA Astrophysics Data System (ADS)

Suzuki, Yosuke; Ebina, Kuniyoshi; Tanaka, Shigenori

2016-08-01

A computational scheme to describe the coherent dynamics of excitation energy transfer (EET) in molecular systems is proposed on the basis of generalized master equations with memory kernels. This formalism takes into account those physical effects in electron-bath coupling system such as the spin symmetry of excitons, the inelastic electron tunneling and the quantum features of nuclear motions, thus providing a theoretical framework to perform an ab initio description of EET through molecular simulations for evaluating the spectral density and the temporal correlation function of electronic coupling. Some test calculations have then been carried out to investigate the dependence of exciton population dynamics on coherence memory, inelastic tunneling correlation time, magnitude of electronic coupling, quantum correction to temporal correlation function, reorganization energy and energy gap.

Augmented potential, energy densities, and virial relations in the weak- and strong-interaction limits of DFT

NASA Astrophysics Data System (ADS)

Vuckovic, Stefan; Levy, Mel; Gori-Giorgi, Paola

2017-12-01

The augmented potential introduced by Levy and Zahariev [Phys. Rev. Lett. 113, 113002 (2014)] is shifted with respect to the standard exchange-correlation potential of the Kohn-Sham density functional theory by a density-dependent constant that makes the total energy become equal to the sum of the occupied orbital energies. In this work, we analyze several features of this approach, focusing on the limit of infinite coupling strength and studying the shift and the corresponding energy density at different correlation regimes. We present and discuss coordinate scaling properties of the augmented potential, study its connection to the response potential, and use the shift to analyze the classical jellium and uniform gas models. We also study other definitions of the energy densities in relation to the functional construction by local interpolations along the adiabatic connection. Our findings indicate that the energy density that is defined in terms of the electrostatic potential of the exchange-correlation hole is particularly well suited for this purpose.

Importance of the correlation contribution for local hybrid functionals: range separation and self-interaction corrections.

PubMed

Arbuznikov, Alexei V; Kaupp, Martin

2012-01-07

Local hybrid functionals with their position-dependent exact-exchange admixture are a conceptually simple and promising extension of the concept of a hybrid functional. Local hybrids based on a simple mixing of the local spin density approximation (LSDA) with exact exchange have been shown to be successful for thermochemistry, reaction barriers, and a range of other properties. So far, the combination of this generation of local hybrids with an LSDA correlation functional has been found to give the most favorable results for atomization energies, for a range of local mixing functions (LMFs) governing the exact-exchange admixture. Here, we show that the choice of correlation functional to be used with local hybrid exchange crucially influences the parameterization also of the exchange part as well as the overall performance. A novel ansatz for the correlation part of local hybrids is suggested based on (i) range-separation of LSDA correlation into short-range (SR) and long-range (LR) parts, and (ii) partial or full elimination of the one-electron self-correlation from the SR part. It is shown that such modified correlation functionals allow overall larger exact exchange admixture in thermochemically competitive local hybrids than before. This results in improvements for reaction barriers and for other properties crucially influenced by self-interaction errors, as demonstrated by a number of examples. Based on the range-separation approach, a fresh view on the breakdown of the correlation energy into dynamical and non-dynamical parts is suggested.

A new parallel algorithm of MP2 energy calculations.

PubMed

Ishimura, Kazuya; Pulay, Peter; Nagase, Shigeru

2006-03-01

A new parallel algorithm has been developed for second-order Møller-Plesset perturbation theory (MP2) energy calculations. Its main projected applications are for large molecules, for instance, for the calculation of dispersion interaction. Tests on a moderate number of processors (2-16) show that the program has high CPU and parallel efficiency. Timings are presented for two relatively large molecules, taxol (C(47)H(51)NO(14)) and luciferin (C(11)H(8)N(2)O(3)S(2)), the former with the 6-31G* and 6-311G** basis sets (1,032 and 1,484 basis functions, 164 correlated orbitals), and the latter with the aug-cc-pVDZ and aug-cc-pVTZ basis sets (530 and 1,198 basis functions, 46 correlated orbitals). An MP2 energy calculation on C(130)H(10) (1,970 basis functions, 265 correlated orbitals) completed in less than 2 h on 128 processors.

Feasibility of antihydrogen atom containment in helium: a problem of electron-positron correlation investigated by the Monte Carol method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jackman, T.M.

1987-01-01

A theoretical investigation of the interaction potential between the helium atom and the antihydrogen atom was performed for the purpose of determining the feasibility of antihydrogen atom containment. The interaction potential showed an energy barrier to collapse of this system. A variational estimate of the height of this energy barrier and estimates of lifetime with respect to electron-positron annihilation were determined by the Variational Monte Carlo method. This calculation allowed for an improvement over an SCF result through the inclusion of explicit correlation factors in the trial wave function. An estimate of the correlation energy of this system was determinedmore » by the Green's Function Monte Carlo (GFMC) method.« less

Imaging the square of the correlated two-electron wave function of a hydrogen molecule

DOE PAGES

Waitz, M.; Bello, R. Y.; Metz, D.; ...

2017-12-22

The toolbox for imaging molecules is well-equipped today. Some techniques visualize the geometrical structure, others the electron density or electron orbitals. Molecules are many-body systems for which the correlation between the constituents is decisive and the spatial and the momentum distribution of one electron depends on those of the other electrons and the nuclei. Such correlations have escaped direct observation by imaging techniques so far. Here, we implement an imaging scheme which visualizes correlations between electrons by coincident detection of the reaction fragments after high energy photofragmentation. With this technique, we examine the H 2 two-electron wave function in whichmore » electron-electron correlation beyond the mean-field level is prominent. We visualize the dependence of the wave function on the internuclear distance. High energy photoelectrons are shown to be a powerful tool for molecular imaging. Finally, our study paves the way for future time resolved correlation imaging at FELs and laser based X-ray sources.« less

Imaging the square of the correlated two-electron wave function of a hydrogen molecule.

PubMed

Waitz, M; Bello, R Y; Metz, D; Lower, J; Trinter, F; Schober, C; Keiling, M; Lenz, U; Pitzer, M; Mertens, K; Martins, M; Viefhaus, J; Klumpp, S; Weber, T; Schmidt, L Ph H; Williams, J B; Schöffler, M S; Serov, V V; Kheifets, A S; Argenti, L; Palacios, A; Martín, F; Jahnke, T; Dörner, R

2017-12-22

The toolbox for imaging molecules is well-equipped today. Some techniques visualize the geometrical structure, others the electron density or electron orbitals. Molecules are many-body systems for which the correlation between the constituents is decisive and the spatial and the momentum distribution of one electron depends on those of the other electrons and the nuclei. Such correlations have escaped direct observation by imaging techniques so far. Here, we implement an imaging scheme which visualizes correlations between electrons by coincident detection of the reaction fragments after high energy photofragmentation. With this technique, we examine the H 2 two-electron wave function in which electron-electron correlation beyond the mean-field level is prominent. We visualize the dependence of the wave function on the internuclear distance. High energy photoelectrons are shown to be a powerful tool for molecular imaging. Our study paves the way for future time resolved correlation imaging at FELs and laser based X-ray sources.

Imaging the square of the correlated two-electron wave function of a hydrogen molecule

DOE Office of Scientific and Technical Information (OSTI.GOV)

Waitz, M.; Bello, R. Y.; Metz, D.

The toolbox for imaging molecules is well-equipped today. Some techniques visualize the geometrical structure, others the electron density or electron orbitals. Molecules are many-body systems for which the correlation between the constituents is decisive and the spatial and the momentum distribution of one electron depends on those of the other electrons and the nuclei. Such correlations have escaped direct observation by imaging techniques so far. Here, we implement an imaging scheme which visualizes correlations between electrons by coincident detection of the reaction fragments after high energy photofragmentation. With this technique, we examine the H 2 two-electron wave function in whichmore » electron-electron correlation beyond the mean-field level is prominent. We visualize the dependence of the wave function on the internuclear distance. High energy photoelectrons are shown to be a powerful tool for molecular imaging. Finally, our study paves the way for future time resolved correlation imaging at FELs and laser based X-ray sources.« less

Bonding in the first-row diatomic molecules within the local spin-density approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Painter, G.S.; Averill, F.W.

1982-08-15

The Hohenberg-Kohn-Sham density-functional equations in the local spin-density approximation (LSDA) have been solved with essentially no loss of accuracy for dimers of the first row of the Periodic Table with the use of a fully-self-consistent spin-polarized Gaussian-orbital approach. Spectroscopic constants (binding energies, equilibrium separations, and ground-state vibrational frequencies) have been derived from the calculated potential-energy curves. Intercomparison of results obtained using the exchange-correlation functionals of Slater (scaled exchange or X..cap alpha..), Gunnarsson and Lundqvist (GL), and Vosko, Wilk, and Nusair (VWN) permits assessment of the relative merits of each and serves to identify general shortcomings in the LSDA. Basic trendsmore » are similar for each functional, but the treatment of the spin dependence of the exchange-correlation energy in the GL and VWN functionals yields a variation of the binding energy across the series which is more systematic than that in the X..cap alpha.. approximation. Agreement between the present results and those of Dunlap, Connolly, and Sabin in the X..cap alpha.., approximation confirms the accuracy of the variational charge-density-fit procedure used in the latter work. The refinements in correlation treatment within the VWN functional are reflected in improvements in binding energies which are only slight for most dimers in the series. This behavior is attributed to the error remaining in the exchange channel within the LSDA and demonstrates the necessity for self-interaction corrections for more accurate binding-energy determinations. Within the current LSDA, absolute accuracies of the VWN functional for the first-row dimers are within 2.3 eV for binding energies, 0.07 a.u. for bond lengths, and approx.200 cm/sup -1/ for vibrational frequencies.« less

Quantum Critical Point revisited by the Dynamical Mean Field Theory

NASA Astrophysics Data System (ADS)

Xu, Wenhu; Kotliar, Gabriel; Tsvelik, Alexei

Dynamical mean field theory is used to study the quantum critical point (QCP) in the doped Hubbard model on a square lattice. The QCP is characterized by a universal scaling form of the self energy and a spin density wave instability at an incommensurate wave vector. The scaling form unifies the low energy kink and the high energy waterfall feature in the spectral function, while the spin dynamics includes both the critical incommensurate and high energy antiferromagnetic paramagnons. We use the frequency dependent four-point correlation function of spin operators to calculate the momentum dependent correction to the electron self energy. Our results reveal a substantial difference with the calculations based on the Spin-Fermion model which indicates that the frequency dependence of the the quasiparitcle-paramagnon vertices is an important factor. The authors are supported by Center for Computational Design of Functional Strongly Correlated Materials and Theoretical Spectroscopy under DOE Grant DE-FOA-0001276.

Energy and energy gradient matrix elements with N-particle explicitly correlated complex Gaussian basis functions with L =1

NASA Astrophysics Data System (ADS)

Bubin, Sergiy; Adamowicz, Ludwik

2008-03-01

In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N-particle system with the L =1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.

Energy and energy gradient matrix elements with N-particle explicitly correlated complex Gaussian basis functions with L=1.

PubMed

Bubin, Sergiy; Adamowicz, Ludwik

2008-03-21

In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N-particle system with the L=1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.

Electronic Zero-Point Oscillations in the Strong-Interaction Limit of Density Functional Theory.

PubMed

Gori-Giorgi, Paola; Vignale, Giovanni; Seidl, Michael

2009-04-14

The exchange-correlation energy in Kohn-Sham density functional theory can be expressed exactly in terms of the change in the expectation of the electron-electron repulsion operator when, in the many-electron Hamiltonian, this same operator is multiplied by a real parameter λ varying between 0 (Kohn-Sham system) and 1 (physical system). In this process, usually called adiabatic connection, the one-electron density is kept fixed by a suitable local one-body potential. The strong-interaction limit of density functional theory, defined as the limit λ→∞, turns out to be like the opposite noninteracting Kohn-Sham limit (λ→0) mathematically simpler than the physical (λ = 1) case and can be used to build an approximate interpolation formula between λ→0 and λ→∞ for the exchange-correlation energy. Here we extend the systematic treatment of the λ→∞ limit [Phys. Rev. A 2007, 75, 042511] to the next leading term, describing zero-point oscillations of strictly correlated electrons, with numerical examples for small spherical atoms. We also propose an improved approximate functional for the zero-point term and a revised interpolation formula for the exchange-correlation energy satisfying more exact constraints.

On-top density functionals for the short-range dynamic correlation between electrons of opposite and parallel spin

NASA Astrophysics Data System (ADS)

Hollett, Joshua W.; Pegoretti, Nicholas

2018-04-01

Separate, one-parameter, on-top density functionals are derived for the short-range dynamic correlation between opposite and parallel-spin electrons, in which the electron-electron cusp is represented by an exponential function. The combination of both functionals is referred to as the Opposite-spin exponential-cusp and Fermi-hole correction (OF) functional. The two parameters of the OF functional are set by fitting the ionization energies and electron affinities, of the atoms He to Ar, predicted by ROHF in combination with the OF functional to the experimental values. For ionization energies, the overall performance of ROHF-OF is better than completely renormalized coupled-cluster [CR-CC(2,3)] and better than, or as good as, conventional density functional methods. For electron affinities, the overall performance of ROHF-OF is less impressive. However, for both ionization energies and electron affinities of third row atoms, the mean absolute error of ROHF-OF is only 3 kJ mol-1.

Bose--Einstein Correlations and Thermal Cluster Formation in High-energy Collisions

NASA Astrophysics Data System (ADS)

Bialas, A.; Florkowski, W.; Zalewski, K.

The blast wave model is generalized to include the production of thermal clusters, as suggested by the apparent success of the statistical model of particle production at high energies. The formulae for the HBT correlation functions and the corresponding HBT radii are derived.

Excited-State Effective Masses in Lattice QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

George Fleming, Saul Cohen, Huey-Wen Lin

2009-10-01

We apply black-box methods, i.e. where the performance of the method does not depend upon initial guesses, to extract excited-state energies from Euclidean-time hadron correlation functions. In particular, we extend the widely used effective-mass method to incorporate multiple correlation functions and produce effective mass estimates for multiple excited states. In general, these excited-state effective masses will be determined by finding the roots of some polynomial. We demonstrate the method using sample lattice data to determine excited-state energies of the nucleon and compare the results to other energy-level finding techniques.

On the effects of surrogacy of energy dissipation in determining the intermittency exponent in fully developed turbulence

NASA Astrophysics Data System (ADS)

Cleve, J.; Greiner, M.; Sreenivasan, K. R.

2003-03-01

The two-point correlation function of the energy dissipation, obtained from a one-point time record of an atmospheric boundary layer, reveals a rigorous power law scaling with intermittency exponent μ approx 0.20 over almost the entire inertial range of scales. However, for the related integral moment, the power law scaling is restricted to the upper part of the inertial range only. This observation is explained in terms of the operational surrogacy of the construction of energy dissipation, which influences the behaviour of the correlation function for small separation distances.

Multiconfiguration Pair-Density Functional Theory Spectral Calculations Are Stable to Adding Diffuse Basis Functions.

PubMed

Hoyer, Chad E; Gagliardi, Laura; Truhlar, Donald G

2015-11-05

Time-dependent Kohn-Sham density functional theory (TD-KS-DFT) is useful for calculating electronic excitation spectra of large systems, but the low-energy spectra are often complicated by artificially lowered higher-energy states. This affects even the lowest energy excited states. Here, by calculating the lowest energy spin-conserving excited state for atoms from H to K and for formaldehyde, we show that this problem does not occur in multiconfiguration pair-density functional theory (MC-PDFT). We use the tPBE on-top density functional, which is a translation of the PBE exchange-correlation functional. We compare to a robust multireference method, namely, complete active space second-order perturbation theory (CASPT2), and to TD-KS-DFT with two popular exchange-correlation functionals, PBE and PBE0. We find for atoms that the mean unsigned error (MUE) of MC-PDFT with the tPBE functional improves from 0.42 to 0.40 eV with a double set of diffuse functions, whereas the MUEs for PBE and PBE0 drastically increase from 0.74 to 2.49 eV and from 0.45 to 1.47 eV, respectively.

Ground-state properties of trapped Bose-Fermi mixtures: Role of exchange correlation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Albus, Alexander P.; Wilkens, Martin; Illuminati, Fabrizio

2003-06-01

We introduce density-functional theory for inhomogeneous Bose-Fermi mixtures, derive the associated Kohn-Sham equations, and determine the exchange-correlation energy in local-density approximation. We solve numerically the Kohn-Sham system, and determine the boson and fermion density distributions and the ground-state energy of a trapped, dilute mixture beyond mean-field approximation. The importance of the corrections due to exchange correlation is discussed by a comparison with current experiments; in particular, we investigate the effect of the repulsive potential-energy contribution due to exchange correlation on the stability of the mixture against collapse.

Multiconfiguration Pair-Density Functional Theory: A New Way To Treat Strongly Correlated Systems.

PubMed

Gagliardi, Laura; Truhlar, Donald G; Li Manni, Giovanni; Carlson, Rebecca K; Hoyer, Chad E; Bao, Junwei Lucas

2017-01-17

The electronic energy of a system provides the Born-Oppenheimer potential energy for internuclear motion and thus determines molecular structure and spectra, bond energies, conformational energies, reaction barrier heights, and vibrational frequencies. The development of more efficient and more accurate ways to calculate the electronic energy of systems with inherently multiconfigurational electronic structure is essential for many applications, including transition metal and actinide chemistry, systems with partially broken bonds, many transition states, and most electronically excited states. Inherently multiconfigurational systems are called strongly correlated systems or multireference systems, where the latter name refers to the need for using more than one ("multiple") configuration state function to provide a good zero-order reference wave function. This Account describes multiconfiguration pair-density functional theory (MC-PDFT), which was developed as a way to combine the advantages of wave function theory (WFT) and density functional theory (DFT) to provide a better treatment of strongly correlated systems. First we review background material: the widely used Kohn-Sham DFT (which uses only a single Slater determinant as reference wave function), multiconfiguration WFT methods that treat inherently multiconfigurational systems based on an active space, and previous attempts to combine multiconfiguration WFT with DFT. Then we review the formulation of MC-PDFT. It is a generalization of Kohn-Sham DFT in that the electron kinetic energy and classical electrostatic energy are calculated from a reference wave function, while the rest of the energy is obtained from a density functional. However, there are two main differences with respent to Kohn-Sham DFT: (i) The reference wave function is multiconfigurational rather than being a single Slater determinant. (ii) The density functional is a function of the total density and the on-top pair density rather than being a function of the spin-up and spin-down densities. In work carried out so far, the multiconfigurational wave function is a multiconfiguration self-consistent-field wave function. The new formulation has the advantage that the reference wave function has the correct spatial and spin symmetry and can describe bond dissociation (of both single and multiple bonds) and electronic excitations in a formally and physically correct way. We then review the formulation of density functionals in terms of the on-top pair density. Finally we review successful applications of the theory to bond energies and bond dissociation potential energy curves of main-group and transition metal bonds, to barrier heights (including pericyclic reactions), to proton affinities, to the hydrogen bond energy of water dimer, to ground- and excited-state charge transfer, to valence and Rydberg excitations of molecules, and to singlet-triplet splittings of radicals. We find that that MC-PDFT can give accurate results not only with complete-active-space multiconfiguration wave functions but also with generalized-active-space multiconfiguration wave functions, which are practical for larger numbers of active electrons and active orbitals than are complete-active-space wave functions. The separated-pair approximation, which is a special case of generalized active space self-consistent-field theory, is especially promising. MC-PDFT, because it requires much less computer time and storage than pure WFT methods, has the potential to open larger and more complex strongly correlated systems to accurate simulation.

Exact relations for energy transfer in self-gravitating isothermal turbulence

NASA Astrophysics Data System (ADS)

Banerjee, Supratik; Kritsuk, Alexei G.

2017-11-01

Self-gravitating isothermal supersonic turbulence is analyzed in the asymptotic limit of large Reynolds numbers. Based on the inviscid invariance of total energy, an exact relation is derived for homogeneous (not necessarily isotropic) turbulence. A modified definition for the two-point energy correlation functions is used to comply with the requirement of detailed energy equipartition in the acoustic limit. In contrast to the previous relations (S. Galtier and S. Banerjee, Phys. Rev. Lett. 107, 134501 (2011), 10.1103/PhysRevLett.107.134501; S. Banerjee and S. Galtier, Phys. Rev. E 87, 013019 (2013), 10.1103/PhysRevE.87.013019), the current exact relation shows that the pressure dilatation terms play practically no role in the energy cascade. Both the flux and source terms are written in terms of two-point differences. Sources enter the relation in a form of mixed second-order structure functions. Unlike the kinetic and thermodynamic potential energies, the gravitational contribution is absent from the flux term. An estimate shows that, for the isotropic case, the correlation between density and gravitational acceleration may play an important role in modifying the energy transfer in self-gravitating turbulence. The exact relation is also written in an alternative form in terms of two-point correlation functions, which is then used to describe scale-by-scale energy budget in spectral space.

Coupled-cluster based basis sets for valence correlation calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Claudino, Daniel; Bartlett, Rodney J., E-mail: bartlett@qtp.ufl.edu; Gargano, Ricardo

Novel basis sets are generated that target the description of valence correlation in atoms H through Ar. The new contraction coefficients are obtained according to the Atomic Natural Orbital (ANO) procedure from CCSD(T) (coupled-cluster singles and doubles with perturbative triples correction) density matrices starting from the primitive functions of Dunning et al. [J. Chem. Phys. 90, 1007 (1989); ibid. 98, 1358 (1993); ibid. 100, 2975 (1993)] (correlation consistent polarized valence X-tuple zeta, cc-pVXZ). The exponents of the primitive Gaussian functions are subject to uniform scaling in order to ensure satisfaction of the virial theorem for the corresponding atoms. These newmore » sets, named ANO-VT-XZ (Atomic Natural Orbital Virial Theorem X-tuple Zeta), have the same number of contracted functions as their cc-pVXZ counterparts in each subshell. The performance of these basis sets is assessed by the evaluation of the contraction errors in four distinct computations: correlation energies in atoms, probing the density in different regions of space via 〈r{sup n}〉 (−3 ≤ n ≤ 3) in atoms, correlation energies in diatomic molecules, and the quality of fitting potential energy curves as measured by spectroscopic constants. All energy calculations with ANO-VT-QZ have contraction errors within “chemical accuracy” of 1 kcal/mol, which is not true for cc-pVQZ, suggesting some improvement compared to the correlation consistent series of Dunning and co-workers.« less

Fission barriers from multidimensionally-constrained covariant density functional theories

NASA Astrophysics Data System (ADS)

Lu, Bing-Nan; Zhao, Jie; Zhao, En-Guang; Zhou, Shan-Gui

2017-11-01

In recent years, we have developed the multidimensionally-constrained covariant density functional theories (MDC-CDFTs) in which both axial and spatial reflection symmetries are broken and all shape degrees of freedom described by βλμ with even μ, such as β20, β22, β30, β32, β40, etc., are included self-consistently. The MDC-CDFTs have been applied to the investigation of potential energy surfaces and fission barriers of actinide nuclei, third minima in potential energy surfaces of light actinides, shapes and potential energy surfaces of superheavy nuclei, octupole correlations between multiple chiral doublet bands in 78Br, octupole correlations in Ba isotopes, the Y32 correlations in N = 150 isotones and Zr isotopes, the spontaneous fission of Fm isotopes, and shapes of hypernuclei. In this contribution we present the formalism of MDC-CDFTs and the application of these theories to the study of fission barriers and potential energy surfaces of actinide nuclei.

Functional renormalization group and Kohn-Sham scheme in density functional theory

NASA Astrophysics Data System (ADS)

Liang, Haozhao; Niu, Yifei; Hatsuda, Tetsuo

2018-04-01

Deriving accurate energy density functional is one of the central problems in condensed matter physics, nuclear physics, and quantum chemistry. We propose a novel method to deduce the energy density functional by combining the idea of the functional renormalization group and the Kohn-Sham scheme in density functional theory. The key idea is to solve the renormalization group flow for the effective action decomposed into the mean-field part and the correlation part. Also, we propose a simple practical method to quantify the uncertainty associated with the truncation of the correlation part. By taking the φ4 theory in zero dimension as a benchmark, we demonstrate that our method shows extremely fast convergence to the exact result even for the highly strong coupling regime.

Molecular Excitation Energies from Time-Dependent Density Functional Theory Employing Random-Phase Approximation Hessians with Exact Exchange.

PubMed

Heßelmann, Andreas

2015-04-14

Molecular excitation energies have been calculated with time-dependent density-functional theory (TDDFT) using random-phase approximation Hessians augmented with exact exchange contributions in various orders. It has been observed that this approach yields fairly accurate local valence excitations if combined with accurate asymptotically corrected exchange-correlation potentials used in the ground-state Kohn-Sham calculations. The inclusion of long-range particle-particle with hole-hole interactions in the kernel leads to errors of 0.14 eV only for the lowest excitations of a selection of three alkene, three carbonyl, and five azabenzene molecules, thus surpassing the accuracy of a number of common TDDFT and even some wave function correlation methods. In the case of long-range charge-transfer excitations, the method typically underestimates accurate reference excitation energies by 8% on average, which is better than with standard hybrid-GGA functionals but worse compared to range-separated functional approximations.

Wigner molecules: the strong-correlation limit of the three-electron harmonium.

PubMed

Cioslowski, Jerzy; Pernal, Katarzyna

2006-08-14

At the strong-correlation limit, electronic states of the three-electron harmonium atom are described by asymptotically exact wave functions given by products of distinct Slater determinants and a common Gaussian factor that involves interelectron distances and the center-of-mass position. The Slater determinants specify the angular dependence and the permutational symmetry of the wave functions. As the confinement strength becomes infinitesimally small, the states of different spin multiplicities become degenerate, their limiting energy reflecting harmonic vibrations of the electrons about their equilibrium positions. The corresponding electron densities are given by products of angular factors and a Gaussian function centered at the radius proportional to the interelectron distance at equilibrium. Thanks to the availability of both the energy and the electron density, the strong-correlation limit of the three-electron harmonium is well suited for testing of density functionals.

Ionization energies and electron affinities from a random-phase-approximation many-body Green's-function method including exchange interactions

NASA Astrophysics Data System (ADS)

Heßelmann, Andreas

2017-06-01

A many-body Green's-function method employing an infinite order summation of ring and exchange-ring contributions to the self-energy is presented. The individual correlation and relaxation contributions to the quasiparticle energies are calculated using an iterative scheme which utilizes density fitting of the particle-hole, particle-particle and hole-hole densities. It is shown that the ionization energies and electron affinities of this approach agree better with highly accurate coupled-cluster singles and doubles with perturbative triples energy difference results than those obtained with second-order Green's-function approaches. An analysis of the correlation and relaxation terms of the self-energy for the direct- and exchange-random-phase-approximation (RPA) Green's-function methods shows that the inclusion of exchange interactions leads to a reduction of the two contributions in magnitude. These differences, however, strongly cancel each other when summing the individual terms to the quasiparticle energies. Due to this, the direct- and exchange-RPA methods perform similarly for the description of ionization energies (IPs) and electron affinities (EAs). The coupled-cluster reference IPs and EAs, if corrected to the adiabatic energy differences between the neutral and charged molecules, were shown to be in very good agreement with experimental measurements.

The RPA Atomization Energy Puzzle.

PubMed

Ruzsinszky, Adrienn; Perdew, John P; Csonka, Gábor I

2010-01-12

There is current interest in the random phase approximation (RPA), a "fifth-rung" density functional for the exchange-correlation energy. RPA has full exact exchange and constructs the correlation with the help of the unoccupied Kohn-Sham orbitals. In many cases (uniform electron gas, jellium surface, and free atom), the correction to RPA is a short-ranged effect that is captured by a local spin density approximation (LSDA) or a generalized gradient approximation (GGA). Nonempirical density functionals for the correction to RPA were constructed earlier at the LSDA and GGA levels (RPA+), but they are constructed here at the fully nonlocal level (RPA++), using the van der Waals density functional (vdW-DF) of Langreth, Lundqvist, and collaborators. While they make important and helpful corrections to RPA total and ionization energies of free atoms, they correct the RPA atomization energies of molecules by only about 1 kcal/mol. Thus, it is puzzling that RPA atomization energies are, on average, about 10 kcal/mol lower than those of accurate values from experiment. We find here that a hybrid of 50% Perdew-Burke-Ernzerhof GGA with 50% RPA+ yields atomization energies much more accurate than either one does alone. This suggests a solution to the puzzle: While the proper correction to RPA is short-ranged in some systems, its contribution to the correlation hole can spread out in a molecule with multiple atomic centers, canceling part of the spread of the exact exchange hole (more so than in RPA or RPA+), making the true exchange-correlation hole more localized than in RPA or RPA+. This effect is not captured even by the vdW-DF nonlocality, but it requires the different kind of full nonlocality present in a hybrid functional.

Incident Energy Dependence of p t Correlations at RHIC

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adams, J.; Aggarwal, M. M.; Ahammed, Z.

2005-10-01

We present results for two-particle transverse momentum correlations, Δp t,iΔ t,j, as a function of event centrality for Au+Au collisions at √( sNN) = 20, 62, 130, and 200 GeV at the Relativistic Heavy Ion Collider. We observe correlations decreasing with centrality that are similar at all four incident energies. The correlations multiplied by the multiplicity density increase with incident energy and the centrality dependence may show evidence of processes such as thermalization, jet production, or the saturation of transverse flow. The square root of the correlations divided by the event-wise average transverse momentum per event shows little or nomore » beam energy dependence and generally agrees with previous measurements at the Super Proton Synchrotron.« less

Short-range second order screened exchange correction to RPA correlation energies

NASA Astrophysics Data System (ADS)

Beuerle, Matthias; Ochsenfeld, Christian

2017-11-01

Direct random phase approximation (RPA) correlation energies have become increasingly popular as a post-Kohn-Sham correction, due to significant improvements over DFT calculations for properties such as long-range dispersion effects, which are problematic in conventional density functional theory. On the other hand, RPA still has various weaknesses, such as unsatisfactory results for non-isogyric processes. This can in parts be attributed to the self-correlation present in RPA correlation energies, leading to significant self-interaction errors. Therefore a variety of schemes have been devised to include exchange in the calculation of RPA correlation energies in order to correct this shortcoming. One of the most popular RPA plus exchange schemes is the second order screened exchange (SOSEX) correction. RPA + SOSEX delivers more accurate absolute correlation energies and also improves upon RPA for non-isogyric processes. On the other hand, RPA + SOSEX barrier heights are worse than those obtained from plain RPA calculations. To combine the benefits of RPA correlation energies and the SOSEX correction, we introduce a short-range RPA + SOSEX correction. Proof of concept calculations and benchmarks showing the advantages of our method are presented.

Short-range second order screened exchange correction to RPA correlation energies.

PubMed

Beuerle, Matthias; Ochsenfeld, Christian

2017-11-28

Direct random phase approximation (RPA) correlation energies have become increasingly popular as a post-Kohn-Sham correction, due to significant improvements over DFT calculations for properties such as long-range dispersion effects, which are problematic in conventional density functional theory. On the other hand, RPA still has various weaknesses, such as unsatisfactory results for non-isogyric processes. This can in parts be attributed to the self-correlation present in RPA correlation energies, leading to significant self-interaction errors. Therefore a variety of schemes have been devised to include exchange in the calculation of RPA correlation energies in order to correct this shortcoming. One of the most popular RPA plus exchange schemes is the second order screened exchange (SOSEX) correction. RPA + SOSEX delivers more accurate absolute correlation energies and also improves upon RPA for non-isogyric processes. On the other hand, RPA + SOSEX barrier heights are worse than those obtained from plain RPA calculations. To combine the benefits of RPA correlation energies and the SOSEX correction, we introduce a short-range RPA + SOSEX correction. Proof of concept calculations and benchmarks showing the advantages of our method are presented.

Correlational signatures of time-reversal symmetry breaking in two-dimensional flow

NASA Astrophysics Data System (ADS)

Hogg, Charlie; Ouellette, Nicholas

2015-11-01

Classical turbulence theories posit that broken spatial symmetries should be (statistically) restored at small scales. But since turbulent flows are inherently dissipative, time reversal symmetry is expected to remain broken throughout the cascade. However, the precise dynamical signature of this broken symmetry is not well understood. Recent work has shed new light on this fundamental question by considering the Lagrangian structure functions of power. Here, we take a somewhat different approach by studying the Lagrangian correlation functions of velocity and acceleration. We measured these correlations using particle tracking velocimetry in a quasi-two-dimensional electromagnetically driven flow that displayed net inverse energy transfer. We show that the correlation functions of the velocity and acceleration magnitudes are not symmetric in time, and that the degree of asymmetry can be related to the flux of energy between scales, suggesting that the asymmetry has a dynamical origin.

Random-Phase Approximation Methods

NASA Astrophysics Data System (ADS)

Chen, Guo P.; Voora, Vamsee K.; Agee, Matthew M.; Balasubramani, Sree Ganesh; Furche, Filipp

2017-05-01

Random-phase approximation (RPA) methods are rapidly emerging as cost-effective validation tools for semilocal density functional computations. We present the theoretical background of RPA in an intuitive rather than formal fashion, focusing on the physical picture of screening and simple diagrammatic analysis. A new decomposition of the RPA correlation energy into plasmonic modes leads to an appealing visualization of electron correlation in terms of charge density fluctuations. Recent developments in the areas of beyond-RPA methods, RPA correlation potentials, and efficient algorithms for RPA energy and property calculations are reviewed. The ability of RPA to approximately capture static correlation in molecules is quantified by an analysis of RPA natural occupation numbers. We illustrate the use of RPA methods in applications to small-gap systems such as open-shell d- and f-element compounds, radicals, and weakly bound complexes, where semilocal density functional results exhibit strong functional dependence.

Universal noise and Efimov physics

NASA Astrophysics Data System (ADS)

Nicholson, Amy N.

2016-03-01

Probability distributions for correlation functions of particles interacting via random-valued fields are discussed as a novel tool for determining the spectrum of a theory. In particular, this method is used to determine the energies of universal N-body clusters tied to Efimov trimers, for even N, by investigating the distribution of a correlation function of two particles at unitarity. Using numerical evidence that this distribution is log-normal, an analytical prediction for the N-dependence of the N-body binding energies is made.

Spectral functions at small energies and the electrical conductivity in hot quenched lattice QCD.

PubMed

Aarts, Gert; Allton, Chris; Foley, Justin; Hands, Simon; Kim, Seyong

2007-07-13

In lattice QCD, the maximum entropy method can be used to reconstruct spectral functions from Euclidean correlators obtained in numerical simulations. We show that at finite temperature the most commonly used algorithm, employing Bryan's method, is inherently unstable at small energies and gives a modification that avoids this. We demonstrate this approach using the vector current-current correlator obtained in quenched QCD at finite temperature. Our first results indicate a small electrical conductivity above the deconfinement transition.

Quantification of uncertainty in first-principles predicted mechanical properties of solids: Application to solid ion conductors

NASA Astrophysics Data System (ADS)

Ahmad, Zeeshan; Viswanathan, Venkatasubramanian

2016-08-01

Computationally-guided material discovery is being increasingly employed using a descriptor-based screening through the calculation of a few properties of interest. A precise understanding of the uncertainty associated with first-principles density functional theory calculated property values is important for the success of descriptor-based screening. The Bayesian error estimation approach has been built in to several recently developed exchange-correlation functionals, which allows an estimate of the uncertainty associated with properties related to the ground state energy, for example, adsorption energies. Here, we propose a robust and computationally efficient method for quantifying uncertainty in mechanical properties, which depend on the derivatives of the energy. The procedure involves calculating energies around the equilibrium cell volume with different strains and fitting the obtained energies to the corresponding energy-strain relationship. At each strain, we use instead of a single energy, an ensemble of energies, giving us an ensemble of fits and thereby, an ensemble of mechanical properties associated with each fit, whose spread can be used to quantify its uncertainty. The generation of ensemble of energies is only a post-processing step involving a perturbation of parameters of the exchange-correlation functional and solving for the energy non-self-consistently. The proposed method is computationally efficient and provides a more robust uncertainty estimate compared to the approach of self-consistent calculations employing several different exchange-correlation functionals. We demonstrate the method by calculating the uncertainty bounds for several materials belonging to different classes and having different structures using the developed method. We show that the calculated uncertainty bounds the property values obtained using three different GGA functionals: PBE, PBEsol, and RPBE. Finally, we apply the approach to calculate the uncertainty associated with the DFT-calculated elastic properties of solid state Li-ion and Na-ion conductors.

Nontrivial thermodynamics in 't Hooft's large-N limit

NASA Astrophysics Data System (ADS)

Cubero, Axel Cortés

2015-05-01

We study the finite volume/temperature correlation functions of the (1 +1 )-dimensional SU (N ) principal chiral sigma model in the planar limit. The exact S-matrix of the sigma model is known to simplify drastically at large N , and this leads to trivial thermodynamic Bethe ansatz (TBA) equations. The partition function, if derived using the TBA, can be shown to be that of free particles. We show that the correlation functions and expectation values of operators at finite volume/temperature are not those of the free theory, and that the TBA does not give enough information to calculate them. Our analysis is done using the Leclair-Mussardo formula for finite-volume correlators, and knowledge of the exact infinite-volume form factors. We present analytical results for the one-point function of the energy-momentum tensor, and the two-point function of the renormalized field operator. The results for the energy-momentum tensor can be used to define a nontrivial partition function.

Some Fundamental Issues in Ground-State Density Functional Theory: A Guide for the Perplexed.

PubMed

Perdew, John P; Ruzsinszky, Adrienn; Constantin, Lucian A; Sun, Jianwei; Csonka, Gábor I

2009-04-14

Some fundamental issues in ground-state density functional theory are discussed without equations: (1) The standard Hohenberg-Kohn and Kohn-Sham theorems were proven for a Hamiltonian that is not quite exact for real atoms, molecules, and solids. (2) The density functional for the exchange-correlation energy, which must be approximated, arises from the tendency of electrons to avoid one another as they move through the electron density. (3) In the absence of a magnetic field, either spin densities or total electron density can be used, although the former choice is better for approximations. (4) "Spin contamination" of the determinant of Kohn-Sham orbitals for an open-shell system is not wrong but right. (5) Only to the extent that symmetries of the interacting wave function are reflected in the spin densities should those symmetries be respected by the Kohn-Sham noninteracting or determinantal wave function. Functionals below the highest level of approximations should however sometimes break even those symmetries, for good physical reasons. (6) Simple and commonly used semilocal (lower-level) approximations for the exchange-correlation energy as a functional of the density can be accurate for closed systems near equilibrium and yet fail for open systems of fluctuating electron number. (7) The exact Kohn-Sham noninteracting state need not be a single determinant, but common approximations can fail when it is not. (8) Over an open system of fluctuating electron number, connected to another such system by stretched bonds, semilocal approximations make the exchange-correlation energy and hole-density sum rule too negative. (9) The gap in the exact Kohn-Sham band structure of a crystal underestimates the real fundamental gap but may approximate the first exciton energy in the large-gap limit. (10) Density functional theory is not really a mean-field theory, although it looks like one. The exact functional includes strong correlation, and semilocal approximations often overestimate the strength of static correlation through their semilocal exchange contributions. (11) Only under rare conditions can excited states arise directly from a ground-state theory.

Optimised effective potential for ground states, excited states, and time-dependent phenomena

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gross, E.K.U.

1996-12-31

(1) The optimized effective potential method is a variant of the traditional Kohn-Sham scheme. In this variant, the exchange-correlation energy E{sub xc} is an explicit functional of single-particle orbitals. The exchange-correlation potential, given as usual by the functional derivative v{sub xc} = {delta}E{sub xc}/{delta}{rho}, then satisfies as integral equation involving the single-particle orbitals. This integral equation in solved semi-analytically using a scheme recently proposed by Krieger, Li and Iafrate. If the exact (Fock) exchange-energy functional is employed together with the Colle-Salvetti orbital functional for the correlation energy, the mean absolute deviation of the resulting ground-state energies from the exact nonrelativisticmore » values is CT mH for the first-row atoms, as compared to 4.5 mH in a state-of-the-art CI calculation. The proposed scheme is thus significantly more accurate than the conventional Kohn-Sham method while the numerical effort involved is about the same as for an ordinary Hanree-Fock calculation. (2) A time-dependent generalization of the optimized-potential method is presented and applied to the linear-response regime. Since time-dependent density functional theory leads to a formally exact representation of the frequency-dependent linear density response and since the latter, as a function of frequency, has poles at the excitation energies of the fully interacting system, the formalism is suitable for the calculation of excitation energies. A simple additive correction to the Kohn-Sham single-particle excitation energies will be deduced and first results for atomic and molecular singlet and triplet excitation energies will be presented. (3) Beyond the regime of linear response, the time-dependent optimized-potential method is employed to describe atoms in strong emtosecond laser pulses. Ionization yields and harmonic spectra will be presented and compared with experimental data.« less

Motivational Impact of Palatable Food Correlates With Functional Brain Responses to Food Images in Adolescents.

PubMed

Jensen, Chad D; Duraccio, Kara M; Carbine, Kaylie A; Barnett, Kimberly A; Kirwan, C Brock

2017-06-01

To examine associations between motivational impact of palatable foods and neural activity in brain regions involved in inhibitory control among adolescents. Thirty-four adolescents aged 14-20 years underwent functional magnetic resonance imaging while viewing images of high- and low-energy foods. Participants completed the Power of Food Scale (PFS). Whole-brain analyses of variance tested for neural activation differences and correlations between brain activation and PFS scores were tested. We found an interaction between food type (high energy vs. low energy) and PFS scores in the right dorsolateral prefrontal cortex and right inferior parietal lobule. We also found that PFS scores correlated negatively with activation to high-energy foods in prefrontal cortical and parietal regions. These findings suggest that individuals with high motivation for high-energy foods also demonstrate lower neural activation in inhibition-related brain regions when viewing images of high-energy foods, indicating that they may have difficulty inhibiting consumption impulses. © The Author 2016. Published by Oxford University Press on behalf of the Society of Pediatric Psychology. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com

Density functional study of double ionization energies

NASA Astrophysics Data System (ADS)

Chong, D. P.

2008-02-01

In this paper, double ionization energies (DIEs) of gas-phase atoms and molecules are calculated by energy difference method with density functional theory. To determine the best functional for double ionization energies, we first study 24 main group atoms in the second, third, and fourth periods. An approximation is used in which the electron density is first obtained from a density functional computation with the exchange-correlation potential Vxc known as statistical average of orbital potentials, after which the energy is computed from that density with 59 different exchange-correlation energy functionals Exc. For the 24 atoms, the two best Exc functional providing DIEs with average absolute deviation (AAD) of only 0.25eV are the Perdew-Burke-Ernzerhof functional modified by Hammer et al. [Phys. Rev. B 59, 6413 (1999)] and one known as the Krieger-Chen-Iafrate-Savin functional modified by Krieger et al. (unpublished). Surprisingly, none of the 20 available hybrid functionals is among the top 15 functionals for the DIEs of the 24 atoms. A similar procedure is then applied to molecules, with opposite results: Only hybrid functionals are among the top 15 functionals for a selection of 29molecules. The best Exc functional for the 29molecules is found to be the Becke 1997 functional modified by Wilson et al. [J. Chem. Phys. 115, 9233 (2001)]. With that functional, the AAD from experiment for DIEs of 29molecules is just under 0.5eV. If the two suspected values for C2H2 and Fe(CO)5 are excluded, the AAD improves to 0.32eV. Many other hybrid functionals perform almost as well.

Relativistic calculation of correlational energy for a helium-like atom

DOE Office of Scientific and Technical Information (OSTI.GOV)

Palchikov, V.G.

This paper presents an analytical method for calculating the firstorder correlational energy from the electron interaction, taking account of lag effects. Explicit analytical expressions are obtained for radial matrix elements. The nonrelativistic limit is investigated. The given method may be used to calculate correlation effects in higher orders of perturbation theory (second and higher orders with respect to 1/z) using the Strum expansion for the Coulomb Green's functions.

Increasing the applicability of density functional theory. V. X-ray absorption spectra with ionization potential corrected exchange and correlation potentials.

PubMed

Verma, Prakash; Bartlett, Rodney J

2016-07-21

Core excitation energies are computed with time-dependent density functional theory (TD-DFT) using the ionization energy corrected exchange and correlation potential QTP(0,0). QTP(0,0) provides C, N, and O K-edge spectra to about an electron volt. A mean absolute error (MAE) of 0.77 and a maximum error of 2.6 eV is observed for QTP(0,0) for many small molecules. TD-DFT based on QTP (0,0) is then used to describe the core-excitation spectra of the 22 amino acids. TD-DFT with conventional functionals greatly underestimates core excitation energies, largely due to the significant error in the Kohn-Sham occupied eigenvalues. To the contrary, the ionization energy corrected potential, QTP(0,0), provides excellent approximations (MAE of 0.53 eV) for core ionization energies as eigenvalues of the Kohn-Sham equations. As a consequence, core excitation energies are accurately described with QTP(0,0), as are the core ionization energies important in X-ray photoionization spectra or electron spectroscopy for chemical analysis.

Rapid estimation of the electron correlation energy for van der Waals complexes RgX (Rg = Kr, Xe, X = Br, I)

NASA Astrophysics Data System (ADS)

Xinying, Li; Yongfang, Zhao; Xiaogong, Jing; Fengli, Liu; Fengyou, Hao

2006-01-01

We present the rules of electron correlation energies for RgX (Rg = Kr, Xe, X = Br, I) van der Waals (vdW) complex systems at CCSD(T) theoretical level with SDB-cc-pVQZ basis set by the Gaussian 98 program. A new method to derive the dispersion coefficient C6 by fitting the intermonomer electron correlation energies to C6R-6 function is introduced. The present C6 values are compared with the corresponding theoretical ones.

Semilocal density functional obeying a strongly tightened bound for exchange

PubMed Central

Sun, Jianwei; Perdew, John P.; Ruzsinszky, Adrienn

2015-01-01

Because of its useful accuracy and efficiency, density functional theory (DFT) is one of the most widely used electronic structure theories in physics, materials science, and chemistry. Only the exchange-correlation energy is unknown, and needs to be approximated in practice. Exact constraints provide useful information about this functional. The local spin-density approximation (LSDA) was the first constraint-based density functional. The Lieb–Oxford lower bound on the exchange-correlation energy for any density is another constraint that plays an important role in the development of generalized gradient approximations (GGAs) and meta-GGAs. Recently, a strongly and optimally tightened lower bound on the exchange energy was proved for one- and two-electron densities, and conjectured for all densities. In this article, we present a realistic “meta-GGA made very simple” (MGGA-MVS) for exchange that respects this optimal bound, which no previous beyond-LSDA approximation satisfies. This constraint might have been expected to worsen predicted thermochemical properties, but in fact they are improved over those of the Perdew–Burke–Ernzerhof GGA, which has nearly the same correlation part. MVS exchange is however radically different from that of other GGAs and meta-GGAs. Its exchange enhancement factor has a very strong dependence upon the orbital kinetic energy density, which permits accurate energies even with the drastically tightened bound. When this nonempirical MVS meta-GGA is hybridized with 25% of exact exchange, the resulting global hybrid gives excellent predictions for atomization energies, reaction barriers, and weak interactions of molecules. PMID:25561554

Semilocal density functional obeying a strongly tightened bound for exchange.

PubMed

Sun, Jianwei; Perdew, John P; Ruzsinszky, Adrienn

2015-01-20

Because of its useful accuracy and efficiency, density functional theory (DFT) is one of the most widely used electronic structure theories in physics, materials science, and chemistry. Only the exchange-correlation energy is unknown, and needs to be approximated in practice. Exact constraints provide useful information about this functional. The local spin-density approximation (LSDA) was the first constraint-based density functional. The Lieb-Oxford lower bound on the exchange-correlation energy for any density is another constraint that plays an important role in the development of generalized gradient approximations (GGAs) and meta-GGAs. Recently, a strongly and optimally tightened lower bound on the exchange energy was proved for one- and two-electron densities, and conjectured for all densities. In this article, we present a realistic "meta-GGA made very simple" (MGGA-MVS) for exchange that respects this optimal bound, which no previous beyond-LSDA approximation satisfies. This constraint might have been expected to worsen predicted thermochemical properties, but in fact they are improved over those of the Perdew-Burke-Ernzerhof GGA, which has nearly the same correlation part. MVS exchange is however radically different from that of other GGAs and meta-GGAs. Its exchange enhancement factor has a very strong dependence upon the orbital kinetic energy density, which permits accurate energies even with the drastically tightened bound. When this nonempirical MVS meta-GGA is hybridized with 25% of exact exchange, the resulting global hybrid gives excellent predictions for atomization energies, reaction barriers, and weak interactions of molecules.

Testing time-dependent density functional theory with depopulated molecular orbitals for predicting electronic excitation energies of valence, Rydberg, and charge-transfer states and potential energies near a conical intersection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Shaohong L.; Truhlar, Donald G., E-mail: truhlar@umn.edu

2014-09-14

Kohn-Sham (KS) time-dependent density functional theory (TDDFT) with most exchange-correlation functionals is well known to systematically underestimate the excitation energies of Rydberg and charge-transfer excited states of atomic and molecular systems. To improve the description of Rydberg states within the KS TDDFT framework, Gaiduk et al. [Phys. Rev. Lett. 108, 253005 (2012)] proposed a scheme that may be called HOMO depopulation. In this study, we tested this scheme on an extensive dataset of valence and Rydberg excitation energies of various atoms, ions, and molecules. It is also tested on a charge-transfer excitation of NH{sub 3}-F{sub 2} and on the potentialmore » energy curves of NH{sub 3} near a conical intersection. We found that the method can indeed significantly improve the accuracy of predicted Rydberg excitation energies while preserving reasonable accuracy for valence excitation energies. However, it does not appear to improve the description of charge-transfer excitations that are severely underestimated by standard KS TDDFT with conventional exchange-correlation functionals, nor does it perform appreciably better than standard TDDFT for the calculation of potential energy surfaces.« less

Density-functional theory based on the electron distribution on the energy coordinate

NASA Astrophysics Data System (ADS)

Takahashi, Hideaki

2018-03-01

We developed an electronic density functional theory utilizing a novel electron distribution n(ɛ) as a basic variable to compute ground state energy of a system. n(ɛ) is obtained by projecting the electron density n({\\boldsymbol{r}}) defined on the space coordinate {\\boldsymbol{r}} onto the energy coordinate ɛ specified with the external potential {\\upsilon }ext}({\\boldsymbol{r}}) of interest. It was demonstrated that the Kohn-Sham equation can also be formulated with the exchange-correlation functional E xc[n(ɛ)] that employs the density n(ɛ) as an argument. It turned out an exchange functional proposed in our preliminary development suffices to describe properly the potential energies of several types of chemical bonds with comparable accuracies to the corresponding functional based on local density approximation. As a remarkable feature of the distribution n(ɛ) it inherently involves the spatially non-local information of the exchange hole at the bond dissociation limit in contrast to conventional approximate functionals. By taking advantage of this property we also developed a prototype of the static correlation functional E sc including no empirical parameters, which showed marked improvements in describing the dissociations of covalent bonds in {{{H}}}2,{{{C}}}2{{{H}}}4 and {CH}}4 molecules.

Benchmarking singlet and triplet excitation energies of molecular semiconductors for singlet fission: Tuning the amount of HF exchange and adjusting local correlation to obtain accurate functionals for singlet-triplet gaps

NASA Astrophysics Data System (ADS)

Brückner, Charlotte; Engels, Bernd

2017-01-01

Vertical and adiabatic singlet and triplet excitation energies of molecular p-type semiconductors calculated with various DFT functionals and wave-function based approaches are benchmarked against MS-CASPT2/cc-pVTZ reference values. A special focus lies on the singlet-triplet gaps that are very important in the process of singlet fission. Singlet fission has the potential to boost device efficiencies of organic solar cells, but the scope of existing singlet-fission compounds is still limited. A computational prescreening of candidate molecules could enlarge it; yet it requires efficient methods accurately predicting singlet and triplet excitation energies. Different DFT formulations (Tamm-Dancoff approximation, linear response time-dependent DFT, Δ-SCF) and spin scaling schemes along with several ab initio methods (CC2, ADC(2)/MP2, CIS(D), CIS) are evaluated. While wave-function based methods yield rather reliable singlet-triplet gaps, many DFT functionals are shown to systematically underestimate triplet excitation energies. To gain insight, the impact of exact exchange and correlation is in detail addressed.

Alternative separation of exchange and correlation energies in multi-configuration range-separated density-functional theory.

PubMed

Stoyanova, Alexandrina; Teale, Andrew M; Toulouse, Julien; Helgaker, Trygve; Fromager, Emmanuel

2013-10-07

The alternative separation of exchange and correlation energies proposed by Toulouse et al. [Theor. Chem. Acc. 114, 305 (2005)] is explored in the context of multi-configuration range-separated density-functional theory. The new decomposition of the short-range exchange-correlation energy relies on the auxiliary long-range interacting wavefunction rather than the Kohn-Sham (KS) determinant. The advantage, relative to the traditional KS decomposition, is that the wavefunction part of the energy is now computed with the regular (fully interacting) Hamiltonian. One potential drawback is that, because of double counting, the wavefunction used to compute the energy cannot be obtained by minimizing the energy expression with respect to the wavefunction parameters. The problem is overcome by using short-range optimized effective potentials (OEPs). The resulting combination of OEP techniques with wavefunction theory has been investigated in this work, at the Hartree-Fock (HF) and multi-configuration self-consistent-field (MCSCF) levels. In the HF case, an analytical expression for the energy gradient has been derived and implemented. Calculations have been performed within the short-range local density approximation on H2, N2, Li2, and H2O. Significant improvements in binding energies are obtained with the new decomposition of the short-range energy. The importance of optimizing the short-range OEP at the MCSCF level when static correlation becomes significant has also been demonstrated for H2, using a finite-difference gradient. The implementation of the analytical gradient for MCSCF wavefunctions is currently in progress.

Quantum Monte Carlo for atoms and molecules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barnett, R.N.

1989-11-01

The diffusion quantum Monte Carlo with fixed nodes (QMC) approach has been employed in studying energy-eigenstates for 1--4 electron systems. Previous work employing the diffusion QMC technique yielded energies of high quality for H{sub 2}, LiH, Li{sub 2}, and H{sub 2}O. Here, the range of calculations with this new approach has been extended to include additional first-row atoms and molecules. In addition, improvements in the previously computed fixed-node energies of LiH, Li{sub 2}, and H{sub 2}O have been obtained using more accurate trial functions. All computations were performed within, but are not limited to, the Born-Oppenheimer approximation. In our computations,more » the effects of variation of Monte Carlo parameters on the QMC solution of the Schroedinger equation were studied extensively. These parameters include the time step, renormalization time and nodal structure. These studies have been very useful in determining which choices of such parameters will yield accurate QMC energies most efficiently. Generally, very accurate energies (90--100% of the correlation energy is obtained) have been computed with single-determinant trail functions multiplied by simple correlation functions. Improvements in accuracy should be readily obtained using more complex trial functions.« less

Magnetic properties and core electron binding energies of liquid water

NASA Astrophysics Data System (ADS)

Galamba, N.; Cabral, Benedito J. C.

2018-01-01

The magnetic properties and the core and inner valence electron binding energies of liquid water are investigated. The adopted methodology relies on the combination of molecular dynamics and electronic structure calculations. Born-Oppenheimer molecular dynamics with the Becke and Lee-Yang-Parr functionals for exchange and correlation, respectively, and includes an empirical correction (BLYP-D3) functional and classical molecular dynamics with the TIP4P/2005-F model were carried out. The Keal-Tozer functional was applied for predicting magnetic shielding and spin-spin coupling constants. Core and inner valence electron binding energies in liquid water were calculated with symmetry adapted cluster-configuration interaction. The relationship between the magnetic shielding constant σ(17O), the role played by the oxygen atom as a proton acceptor and donor, and the tetrahedral organisation of liquid water are investigated. The results indicate that the deshielding of the oxygen atom in water is very dependent on the order parameter (q) describing the tetrahedral organisation of the hydrogen bond network. The strong sensitivity of magnetic properties on changes of the electronic density in the nuclei environment is illustrated by a correlation between σ(17O) and the energy gap between the 1a1[O1s] (core) and the 2a1 (inner valence) orbitals of water. Although several studies discussed the eventual connection between magnetic properties and core electron binding energies, such a correlation could not be clearly established. Here, we demonstrate that for liquid water this correlation exists although involving the gap between electron binding energies of core and inner valence orbitals.

Characterization of impulse noise and analysis of its effect upon correlation receivers

NASA Technical Reports Server (NTRS)

Houts, R. C.; Moore, J. D.

1971-01-01

A noise model is formulated to describe the impulse noise in many digital systems. A simplified model, which assumes that each noise burst contains a randomly weighted version of the same basic waveform, is used to derive the performance equations for a correlation receiver. The expected number of bit errors per noise burst is expressed as a function of the average signal energy, signal-set correlation coefficient, bit time, noise-weighting-factor variance and probability density function, and a time range function which depends on the crosscorrelation of the signal-set basis functions and the noise waveform. A procedure is established for extending the results for the simplified noise model to the general model. Unlike the performance results for Gaussian noise, it is shown that for impulse noise the error performance is affected by the choice of signal-set basis functions and that Orthogonal signaling is not equivalent to On-Off signaling with the same average energy.

Nonlinearity of the forward-backward correlation function in the model with string fusion

NASA Astrophysics Data System (ADS)

Vechernin, Vladimir

2017-12-01

The behavior of the forward-backward correlation functions and the corresponding correlation coefficients between multiplicities and transverse momenta of particles produced in high energy hadronic interactions is analyzed by analytical and MC calculations in the models with and without string fusion. The string fusion is taking into account in simplified form by introducing the lattice in the transverse plane. The results obtained with two alternative definitions of the forward-backward correlation coefficient are compared. It is shown that the nonlinearity of correlation functions increases with the width of observation windows, leading at small string density to a strong dependence of correlation coefficient value on the definition. The results of the modeling enable qualitatively to explain the experimentally observed features in the behavior of the correlation functions between multiplicities and mean transverse momenta at small and large multiplicities.

One-electron reduced density matrices of strongly correlated harmonium atoms.

PubMed

Cioslowski, Jerzy

2015-03-21

Explicit asymptotic expressions are derived for the reduced one-electron density matrices (the 1-matrices) of strongly correlated two- and three-electron harmonium atoms in the ground and first excited states. These expressions, which are valid at the limit of small confinement strength ω, yield electron densities and kinetic energies in agreement with the published values. In addition, they reveal the ω(5/6) asymptotic scaling of the exchange components of the electron-electron repulsion energies that differs from the ω(2/3) scaling of their Coulomb and correlation counterparts. The natural orbitals of the totally symmetric ground state of the two-electron harmonium atom are found to possess collective occupancies that follow a mixed power/Gaussian dependence on the angular momentum in variance with the simple power-law prediction of Hill's asymptotics. Providing rigorous constraints on energies as functionals of 1-matrices, these results are expected to facilitate development of approximate implementations of the density matrix functional theory and ensure their proper description of strongly correlated systems.

Probing Ligand Effects on the Redox Energies of [4Fe-4S] Clusters Using Broken-Symmetry Density Functional Theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Niu, Shuqiang; Ichiye, Toshiko

A central issue in understanding redox properties of iron-sulfur proteins is determining the factors that tune the reduction potentials of the Fe-S clusters. Recently, Solomon and coworkers have shown that the Fe-S bond covalency of protein analogs measured by %L, the percent ligand character of the Fe 3d orbitals, from ligand K-edge X-ray absorption spectroscopy (XAS) correlates with the electrochemical redox potentials. Also, Wang and coworkers have measured electron detachment energies for iron-sulfur clusters without environmental perturbations by gas-phase photoelectron spectroscopy (PES). Here the correlations of the ligand character with redox energy and %L character are examined in [Fe₄S₄L₄]2⁻ clustersmore » with different ligands by broken symmetry density functional theory (BS-DFT) calculations using the B3LYP functional together with PES and XAS experimental results. These gas-phase studies assess ligand effects independently of environmental perturbations and thus provide essential information for computational studies of iron-sulfur proteins. The B3LYP oxidation energies agree well with PES data, and the %L character obtained from natural bond orbital analysis correlates with XAS values, although it systematically underestimates them because of basis set effects. The results show that stronger electron-donating terminal ligands increase %Lt, the percent ligand character from terminal ligands, but decrease %Sb, the percent ligand character from the bridging sulfurs. Because the oxidized orbital has significant Fe-Lt antibonding character, the oxidation energy correlates well with %Lt. However, because the reduced orbital has varying contributions of both Fe-Lt and Fe-Sb antibonding character, the reduction energy does not correlate with either %Lt or %Sb. Overall, BSDFT calculations together with XAS and PES experiments can unravel the complex underlying factors in the redox energy and chemical bonding of the [4Fe-4S] clusters in iron-sulfur proteins.« less

Approximating the Shifted Hartree-Exchange-Correlation Potential in Direct Energy Kohn-Sham Theory.

PubMed

Sharpe, Daniel J; Levy, Mel; Tozer, David J

2018-02-13

Levy and Zahariev [Phys. Rev. Lett. 113 113002 (2014)] have proposed a new approach for performing density functional theory calculations, termed direct energy Kohn-Sham (DEKS) theory. In this approach, the electronic energy equals the sum of orbital energies, obtained from Kohn-Sham-like orbital equations involving a shifted Hartree-exchange-correlation potential, which must be approximated. In the present study, density scaling homogeneity considerations are used to facilitate DEKS calculations on a series of atoms and molecules, leading to three nonlocal approximations to the shifted potential. The first two rely on preliminary Kohn-Sham calculations using a standard generalized gradient approximation (GGA) exchange-correlation functional and the results illustrate the benefit of describing the dominant Hartree component of the shift exactly. A uniform electron gas analysis is used to eliminate the need for these preliminary Kohn-Sham calculations, leading to a potential with an unconventional form that yields encouraging results, providing strong motivation for further research in DEKS theory.

Exact Asymptotics of the Freezing Transition of a Logarithmically Correlated Random Energy Model

NASA Astrophysics Data System (ADS)

Webb, Christian

2011-12-01

We consider a logarithmically correlated random energy model, namely a model for directed polymers on a Cayley tree, which was introduced by Derrida and Spohn. We prove asymptotic properties of a generating function of the partition function of the model by studying a discrete time analogy of the KPP-equation—thus translating Bramson's work on the KPP-equation into a discrete time case. We also discuss connections to extreme value statistics of a branching random walk and a rescaled multiplicative cascade measure beyond the critical point.

Accurate potential energy surface for the 1(2)A' state of NH(2): scaling of external correlation versus extrapolation to the complete basis set limit.

PubMed

Li, Y Q; Varandas, A J C

2010-09-16

An accurate single-sheeted double many-body expansion potential energy surface is reported for the title system which is suitable for dynamics and kinetics studies of the reactions of N(2D) + H2(X1Sigmag+) NH(a1Delta) + H(2S) and their isotopomeric variants. It is obtained by fitting ab initio energies calculated at the multireference configuration interaction level with the aug-cc-pVQZ basis set, after slightly correcting semiempirically the dynamical correlation using the double many-body expansion-scaled external correlation method. The function so obtained is compared in detail with a potential energy surface of the same family obtained by extrapolating the calculated raw energies to the complete basis set limit. The topographical features of the novel global potential energy surface are examined in detail and found to be in general good agreement with those calculated directly from the raw ab initio energies, as well as previous calculations available in the literature. The novel function has been built so as to become degenerate at linear geometries with the ground-state potential energy surface of A'' symmetry reported by our group, where both form a Renner-Teller pair.

Multiconfiguration Pair-Density Functional Theory.

PubMed

Li Manni, Giovanni; Carlson, Rebecca K; Luo, Sijie; Ma, Dongxia; Olsen, Jeppe; Truhlar, Donald G; Gagliardi, Laura

2014-09-09

We present a new theoretical framework, called Multiconfiguration Pair-Density Functional Theory (MC-PDFT), which combines multiconfigurational wave functions with a generalization of density functional theory (DFT). A multiconfigurational self-consistent-field (MCSCF) wave function with correct spin and space symmetry is used to compute the total electronic density, its gradient, the on-top pair density, and the kinetic and Coulomb contributions to the total electronic energy. We then use a functional of the total density, its gradient, and the on-top pair density to calculate the remaining part of the energy, which we call the on-top-density-functional energy in contrast to the exchange-correlation energy of Kohn-Sham DFT. Because the on-top pair density is an element of the two-particle density matrix, this goes beyond the Hohenberg-Kohn theorem that refers only to the one-particle density. To illustrate the theory, we obtain first approximations to the required new type of density functionals by translating conventional density functionals of the spin densities using a simple prescription, and we perform post-SCF density functional calculations using the total density, density gradient, and on-top pair density from the MCSCF calculations. Double counting of dynamic correlation or exchange does not occur because the MCSCF energy is not used. The theory is illustrated by applications to the bond energies and potential energy curves of H2, N2, F2, CaO, Cr2, and NiCl and the electronic excitation energies of Be, C, N, N(+), O, O(+), Sc(+), Mn, Co, Mo, Ru, N2, HCHO, C4H6, c-C5H6, and pyrazine. The method presented has a computational cost and scaling similar to MCSCF, but a quantitative accuracy, even with the present first approximations to the new types of density functionals, that is comparable to much more expensive multireference perturbation theory methods.

Molecular basis of crystal morphology-dependent adhesion behavior of mefenamic acid during tableting.

PubMed

Waknis, Vrushali; Chu, Elza; Schlam, Roxana; Sidorenko, Alexander; Badawy, Sherif; Yin, Shawn; Narang, Ajit S

2014-01-01

The molecular basis of crystal surface adhesion leading to sticking was investigated by exploring the correlation of crystal adhesion to oxidized iron coated atomic force microscope (AFM) tips and bulk powder sticking behavior during tableting of two morphologically different crystals of a model drug, mefenamic acid (MA), to differences in their surface functional group orientation and energy. MA was recrystallized into two morphologies (plates and needles) of the same crystalline form. Crystal adhesion to oxidized iron coated AFM tips and bulk powder sticking to tablet punches was assessed using a direct compression formulation. Surface functional group orientation and energies on crystal faces were modeled using Accelrys Material Studio software. Needle-shaped morphology showed higher sticking tendency than plates despite similar particle size. This correlated with higher crystal surface adhesion of needle-shaped morphology to oxidized iron coated AFM probe tips, and greater surface energy and exposure of polar functional groups. Higher surface exposure of polar functional groups correlates with higher tendency to stick to metal surfaces and AFM tips, indicating involvement of specific polar interactions in the adhesion behavior. In addition, an AFM method is identified to prospectively assess the risk of sticking during the early stages of drug development.

Recent developments in LIBXC - A comprehensive library of functionals for density functional theory

NASA Astrophysics Data System (ADS)

Lehtola, Susi; Steigemann, Conrad; Oliveira, Micael J. T.; Marques, Miguel A. L.

2018-01-01

LIBXC is a library of exchange-correlation functionals for density-functional theory. We are concerned with semi-local functionals (or the semi-local part of hybrid functionals), namely local-density approximations, generalized-gradient approximations, and meta-generalized-gradient approximations. Currently we include around 400 functionals for the exchange, correlation, and the kinetic energy, spanning more than 50 years of research. Moreover, LIBXC is by now used by more than 20 codes, not only from the atomic, molecular, and solid-state physics, but also from the quantum chemistry communities.

Shape and energy consistent pseudopotentials for correlated electron systems

PubMed Central

Needs, R. J.

2017-01-01

A method is developed for generating pseudopotentials for use in correlated-electron calculations. The paradigms of shape and energy consistency are combined and defined in terms of correlated-electron wave-functions. The resulting energy consistent correlated electron pseudopotentials (eCEPPs) are constructed for H, Li–F, Sc–Fe, and Cu. Their accuracy is quantified by comparing the relaxed molecular geometries and dissociation energies which they provide with all electron results, with all quantities evaluated using coupled cluster singles, doubles, and triples calculations. Errors inherent in the pseudopotentials are also compared with those arising from a number of approximations commonly used with pseudopotentials. The eCEPPs provide a significant improvement in optimised geometries and dissociation energies for small molecules, with errors for the latter being an order-of-magnitude smaller than for Hartree-Fock-based pseudopotentials available in the literature. Gaussian basis sets are optimised for use with these pseudopotentials. PMID:28571391

Searches for correlation between UHECR events and high-energy gamma-ray Fermi-LAT data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Álvarez, Ezequiel; Cuoco, Alessandro; Mirabal, Nestor

The astrophysical sources responsible for ultra high-energy cosmic rays (UHECRs) continue to be one of the most intriguing mysteries in astrophysics. We present a comprehensive search for correlations between high-energy (∼> 1 GeV) gamma-ray events from the Fermi Large Area Telescope (LAT) and UHECRs (∼> 60 EeV) detected by the Telescope Array and the Pierre Auger Observatory. We perform two separate searches. First, we conduct a standard cross-correlation analysis between the arrival directions of 148 UHECRs and 360 gamma-ray sources in the Second Catalog of Hard Fermi-LAT sources (2FHL). Second, we search for a possible correlation between UHECR directions andmore » unresolved Fermi -LAT gamma-ray emission. For the latter, we use three different methods: a stacking technique with both a model-dependent and model-independent background estimate, and a cross-correlation function analysis. We also test for statistically significant excesses in gamma rays from signal regions centered on Cen A and the Telescope Array hotspot. No significant correlation is found in any of the analyses performed, except a weak (∼< 2σ) hint of signal with the correlation function method on scales ∼ 1°. Upper limits on the flux of possible power-law gamma-ray sources of UHECRs are derived.« less

Searches for correlation between UHECR events and high-energy gamma-ray Fermi-LAT data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Álvarez, Ezequiel; Cuoco, Alessandro; Mirabal, Nestor

The astrophysical sources responsible for ultra high-energy cosmic rays (UHECRs) continue to be one of the most intriguing mysteries in astrophysics. Here, we present a comprehensive search for correlations between high-energy (≳ 1 GeV) gamma-ray events from the Fermi Large Area Telescope (LAT) and UHECRs (≳ 60 EeV) detected by the Telescope Array and the Pierre Auger Observatory. We perform two separate searches. First, we conduct a standard cross-correlation analysis between the arrival directions of 148 UHECRs and 360 gamma-ray sources in the Second Catalog of Hard Fermi-LAT sources (2FHL). Second, we search for a possible correlation between UHECR directionsmore » and unresolved Fermi-LAT gamma-ray emission. For the latter, we use three different methods: a stacking technique with both a model-dependent and model-independent background estimate, and a cross-correlation function analysis. We also test for statistically significant excesses in gamma rays from signal regions centered on Cen A and the Telescope Array hotspot. There was no significant correlation is found in any of the analyses performed, except a weak (≲ 2σ) hint of signal with the correlation function method on scales ~ 1°. Upper limits on the flux of possible power-law gamma-ray sources of UHECRs are derived.« less

Searches for correlation between UHECR events and high-energy gamma-ray Fermi-LAT data

DOE PAGES

Álvarez, Ezequiel; Cuoco, Alessandro; Mirabal, Nestor; ...

2016-12-13

The astrophysical sources responsible for ultra high-energy cosmic rays (UHECRs) continue to be one of the most intriguing mysteries in astrophysics. Here, we present a comprehensive search for correlations between high-energy (≳ 1 GeV) gamma-ray events from the Fermi Large Area Telescope (LAT) and UHECRs (≳ 60 EeV) detected by the Telescope Array and the Pierre Auger Observatory. We perform two separate searches. First, we conduct a standard cross-correlation analysis between the arrival directions of 148 UHECRs and 360 gamma-ray sources in the Second Catalog of Hard Fermi-LAT sources (2FHL). Second, we search for a possible correlation between UHECR directionsmore » and unresolved Fermi-LAT gamma-ray emission. For the latter, we use three different methods: a stacking technique with both a model-dependent and model-independent background estimate, and a cross-correlation function analysis. We also test for statistically significant excesses in gamma rays from signal regions centered on Cen A and the Telescope Array hotspot. There was no significant correlation is found in any of the analyses performed, except a weak (≲ 2σ) hint of signal with the correlation function method on scales ~ 1°. Upper limits on the flux of possible power-law gamma-ray sources of UHECRs are derived.« less

Log-correlated random-energy models with extensive free-energy fluctuations: Pathologies caused by rare events as signatures of phase transitions

NASA Astrophysics Data System (ADS)

Cao, Xiangyu; Fyodorov, Yan V.; Le Doussal, Pierre

2018-02-01

We address systematically an apparent nonphysical behavior of the free-energy moment generating function for several instances of the logarithmically correlated models: the fractional Brownian motion with Hurst index H =0 (fBm0) (and its bridge version), a one-dimensional model appearing in decaying Burgers turbulence with log-correlated initial conditions and, finally, the two-dimensional log-correlated random-energy model (logREM) introduced in Cao et al. [Phys. Rev. Lett. 118, 090601 (2017), 10.1103/PhysRevLett.118.090601] based on the two-dimensional Gaussian free field with background charges and directly related to the Liouville field theory. All these models share anomalously large fluctuations of the associated free energy, with a variance proportional to the log of the system size. We argue that a seemingly nonphysical vanishing of the moment generating function for some values of parameters is related to the termination point transition (i.e., prefreezing). We study the associated universal log corrections in the frozen phase, both for logREMs and for the standard REM, filling a gap in the literature. For the above mentioned integrable instances of logREMs, we predict the nontrivial free-energy cumulants describing non-Gaussian fluctuations on the top of the Gaussian with extensive variance. Some of the predictions are tested numerically.

Four-body correlation embedded in antisymmetrized geminal power wave function.

PubMed

Kawasaki, Airi; Sugino, Osamu

2016-12-28

We extend the Coleman's antisymmetrized geminal power (AGP) to develop a wave function theory that can incorporate up to four-body correlation in a region of strong correlation. To facilitate the variational determination of the wave function, the total energy is rewritten in terms of the traces of geminals. This novel trace formula is applied to a simple model system consisting of one dimensional Hubbard ring with a site of strong correlation. Our scheme significantly improves the result obtained by the AGP-configuration interaction scheme of Uemura et al. and also achieves more efficient compression of the degrees of freedom of the wave function. We regard the result as a step toward a first-principles wave function theory for a strongly correlated point defect or adsorbate embedded in an AGP-based mean-field medium.

Multireference Density Functional Theory with Generalized Auxiliary Systems for Ground and Excited States.

PubMed

Chen, Zehua; Zhang, Du; Jin, Ye; Yang, Yang; Su, Neil Qiang; Yang, Weitao

2017-09-21

To describe static correlation, we develop a new approach to density functional theory (DFT), which uses a generalized auxiliary system that is of a different symmetry, such as particle number or spin, from that of the physical system. The total energy of the physical system consists of two parts: the energy of the auxiliary system, which is determined with a chosen density functional approximation (DFA), and the excitation energy from an approximate linear response theory that restores the symmetry to that of the physical system, thus rigorously leading to a multideterminant description of the physical system. The electron density of the physical system is different from that of the auxiliary system and is uniquely determined from the functional derivative of the total energy with respect to the external potential. Our energy functional is thus an implicit functional of the physical system density, but an explicit functional of the auxiliary system density. We show that the total energy minimum and stationary states, describing the ground and excited states of the physical system, can be obtained by a self-consistent optimization with respect to the explicit variable, the generalized Kohn-Sham noninteracting density matrix. We have developed the generalized optimized effective potential method for the self-consistent optimization. Among options of the auxiliary system and the associated linear response theory, reformulated versions of the particle-particle random phase approximation (pp-RPA) and the spin-flip time-dependent density functional theory (SF-TDDFT) are selected for illustration of principle. Numerical results show that our multireference DFT successfully describes static correlation in bond dissociation and double bond rotation.

Correlational and thermodynamic properties of finite-temperature electron liquids in the hypernetted-chain approximation.

PubMed

Tanaka, Shigenori

2016-12-07

Correlational and thermodynamic properties of homogeneous electron liquids at finite temperatures are theoretically analyzed in terms of dielectric response formalism with the hypernetted-chain (HNC) approximation and its modified version. The static structure factor and the local-field correction to describe the strong Coulomb-coupling effects beyond the random-phase approximation are self-consistently calculated through solution to integral equations in the paramagnetic (spin unpolarized) and ferromagnetic (spin polarized) states. In the ground state with the normalized temperature θ=0, the present HNC scheme well reproduces the exchange-correlation energies obtained by quantum Monte Carlo (QMC) simulations over the whole fluid phase (the coupling constant r s ≤100), i.e., within 1% and 2% deviations from putative best QMC values in the paramagnetic and ferromagnetic states, respectively. As compared with earlier studies based on the Singwi-Tosi-Land-Sjölander and modified convolution approximations, some improvements on the correlation energies and the correlation functions including the compressibility sum rule are found in the intermediate to strong coupling regimes. When applied to the electron fluids at intermediate Fermi degeneracies (θ≈1), the static structure factors calculated in the HNC scheme show good agreements with the results obtained by the path integral Monte Carlo (PIMC) simulation, while a small negative region in the radial distribution function is observed near the origin, which may be associated with a slight overestimation for the exchange-correlation hole in the HNC approximation. The interaction energies are calculated for various combinations of density and temperature parameters ranging from strong to weak degeneracy and from weak to strong coupling, and the HNC values are then parametrized as functions of r s and θ. The HNC exchange-correlation free energies obtained through the coupling-constant integration show reasonable agreements with earlier results including the PIMC-based fitting over the whole fluid region at finite degeneracies in the paramagnetic state. In contrast, a systematic difference between the HNC and PIMC results is observed in the ferromagnetic state, which suggests a necessity of further studies on the exchange-correlation free energies from both aspects of analytical theory and simulation.

Correlation functions of net-proton multiplicity distributions in Au + Au collisions at energies available at the BNL Relativistic Heavy Ion Collider from a multiphase transport model

NASA Astrophysics Data System (ADS)

Lin, Yufu; Chen, Lizhu; Li, Zhiming

2017-10-01

Fluctuations of conserved quantities are believed to be sensitive observables to probe the signature of the QCD phase transition and critical point. It was argued recently that measuring the genuine correlation functions (CFs) could provide cleaner information on possible nontrivial dynamics in heavy-ion collisions. With the AMPT (a multiphase transport) model, the centrality and energy dependence of various orders of CFs of net protons in Au + Au collisions at √{sN N}=7.7 , 11.5, 19.6, 27, 39, 62.4, and 200 GeV are investigated. The model results show that the number of antiprotons is important and should be taken into account in the calculation of CFs at high energy and/or in peripheral collisions. It is also found that the contribution of antiprotons is more important for higher order correlations than for lower ones. The CFs of antiprotons and mixed correlations play roles comparable to those of protons at high energies. Finally, we make comparisons between the model calculation and experimental data measured in the STAR experiment at the BNL Relativistic Heavy Ion Collider.

Self-consistent implementation of meta-GGA functionals for the ONETEP linear-scaling electronic structure package.

PubMed

Womack, James C; Mardirossian, Narbe; Head-Gordon, Martin; Skylaris, Chris-Kriton

2016-11-28

Accurate and computationally efficient exchange-correlation functionals are critical to the successful application of linear-scaling density functional theory (DFT). Local and semi-local functionals of the density are naturally compatible with linear-scaling approaches, having a general form which assumes the locality of electronic interactions and which can be efficiently evaluated by numerical quadrature. Presently, the most sophisticated and flexible semi-local functionals are members of the meta-generalized-gradient approximation (meta-GGA) family, and depend upon the kinetic energy density, τ, in addition to the charge density and its gradient. In order to extend the theoretical and computational advantages of τ-dependent meta-GGA functionals to large-scale DFT calculations on thousands of atoms, we have implemented support for τ-dependent meta-GGA functionals in the ONETEP program. In this paper we lay out the theoretical innovations necessary to implement τ-dependent meta-GGA functionals within ONETEP's linear-scaling formalism. We present expressions for the gradient of the τ-dependent exchange-correlation energy, necessary for direct energy minimization. We also derive the forms of the τ-dependent exchange-correlation potential and kinetic energy density in terms of the strictly localized, self-consistently optimized orbitals used by ONETEP. To validate the numerical accuracy of our self-consistent meta-GGA implementation, we performed calculations using the B97M-V and PKZB meta-GGAs on a variety of small molecules. Using only a minimal basis set of self-consistently optimized local orbitals, we obtain energies in excellent agreement with large basis set calculations performed using other codes. Finally, to establish the linear-scaling computational cost and applicability of our approach to large-scale calculations, we present the outcome of self-consistent meta-GGA calculations on amyloid fibrils of increasing size, up to tens of thousands of atoms.

Self-consistent implementation of meta-GGA functionals for the ONETEP linear-scaling electronic structure package

NASA Astrophysics Data System (ADS)

Womack, James C.; Mardirossian, Narbe; Head-Gordon, Martin; Skylaris, Chris-Kriton

2016-11-01

Accurate and computationally efficient exchange-correlation functionals are critical to the successful application of linear-scaling density functional theory (DFT). Local and semi-local functionals of the density are naturally compatible with linear-scaling approaches, having a general form which assumes the locality of electronic interactions and which can be efficiently evaluated by numerical quadrature. Presently, the most sophisticated and flexible semi-local functionals are members of the meta-generalized-gradient approximation (meta-GGA) family, and depend upon the kinetic energy density, τ, in addition to the charge density and its gradient. In order to extend the theoretical and computational advantages of τ-dependent meta-GGA functionals to large-scale DFT calculations on thousands of atoms, we have implemented support for τ-dependent meta-GGA functionals in the ONETEP program. In this paper we lay out the theoretical innovations necessary to implement τ-dependent meta-GGA functionals within ONETEP's linear-scaling formalism. We present expressions for the gradient of the τ-dependent exchange-correlation energy, necessary for direct energy minimization. We also derive the forms of the τ-dependent exchange-correlation potential and kinetic energy density in terms of the strictly localized, self-consistently optimized orbitals used by ONETEP. To validate the numerical accuracy of our self-consistent meta-GGA implementation, we performed calculations using the B97M-V and PKZB meta-GGAs on a variety of small molecules. Using only a minimal basis set of self-consistently optimized local orbitals, we obtain energies in excellent agreement with large basis set calculations performed using other codes. Finally, to establish the linear-scaling computational cost and applicability of our approach to large-scale calculations, we present the outcome of self-consistent meta-GGA calculations on amyloid fibrils of increasing size, up to tens of thousands of atoms.

A diagnostic for determining the quality of single-reference electron correlation methods

NASA Technical Reports Server (NTRS)

Lee, Timothy J.; Taylor, Peter R.

1989-01-01

It was recently proposed that the Euclidian norm of the t(sub 1) vector of the coupled cluster wave function (normalized by the number of electrons included in the correlation procedure) could be used to determine whether a single-reference-based electron correlation procedure is appopriate. This diagnostic, T(sub 1) is defined for use with self-consistent-field molecular orbitals and is invariant to the same orbital rotations as the coupled cluster energy. T(sub 1) is investigated for several different chemical systems which exhibit a range of multireference behavior, and is shown to be an excellent measure of the importance of non-dynamical electron correlation and is far superior to C(sub 0) from a singles and doubles configuration interaction wave function. It is further suggested that when the aim is to recover a large fraction of the dynamical electron correlation energy, a large T(sub 1) (i.e., greater than 0.02) probably indicates the need for a multireference electron correlation procedure.

A diagnostic for determining the quality of single-reference electron correlation methods

NASA Technical Reports Server (NTRS)

Lee, Timothy J.; Taylor, Peter R.

1989-01-01

It was recently proposed that the Euclidian norm of the t sub 1 vector of the coupled cluster wave function (normalized by the number of electrons included in the correlation procedure) could be used to determine whether a single-reference-based electron correlation procedure is appropriate. This diagnostic, T sub 1, is defined for use with self consistent field molecular orbitals and is invariant to the same orbital rotations as the coupled cluster energy. T sub 1 is investigated for several different chemical systems which exhibit a range of multireference behavior, and is shown to be an excellent measure of the importance of nondynamical electron correlation and is far superior to C sub 0 from a singles and doubles configuration interaction wave function. It is further suggested that when the aim is to recover a large fraction of the dynamical electron correlation energy, a large T sub 1 (i.e., greater than 0.02) probably indicates the need for a multireference electron correlation procedure.

Nonlocal correlations in the orbital selective Mott phase of a one-dimensional multiorbital Hubbard model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, S.; Kaushal, N.; Wang, Y.

Here, we study nonlocal correlations in a three-orbital Hubbard model defined on an extended one-dimensional chain using determinant quantum Monte Carlo and density matrix renormalization group methods. We focus on a parameter regime with robust Hund's coupling, which produces an orbital selective Mott phase (OSMP) at intermediate values of the Hubbard U, as well as an orbitally ordered ferromagnetic insulating state at stronger coupling. An examination of the orbital- and spin-correlation functions indicates that the orbital ordering occurs before the onset of magnetic correlations in this parameter regime as a function of temperature. In the OSMP, we find that themore » self-energy for the itinerant electrons is momentum dependent, indicating a degree of nonlocal correlations while the localized electrons have largely momentum independent self-energies. These nonlocal correlations also produce relative shifts of the holelike and electronlike bands within our model. The overall momentum dependence of these quantities is strongly suppressed in the orbitally ordered insulating phase.« less

Nonlocal correlations in the orbital selective Mott phase of a one-dimensional multiorbital Hubbard model

DOE PAGES

Li, S.; Kaushal, N.; Wang, Y.; ...

2016-12-12

Here, we study nonlocal correlations in a three-orbital Hubbard model defined on an extended one-dimensional chain using determinant quantum Monte Carlo and density matrix renormalization group methods. We focus on a parameter regime with robust Hund's coupling, which produces an orbital selective Mott phase (OSMP) at intermediate values of the Hubbard U, as well as an orbitally ordered ferromagnetic insulating state at stronger coupling. An examination of the orbital- and spin-correlation functions indicates that the orbital ordering occurs before the onset of magnetic correlations in this parameter regime as a function of temperature. In the OSMP, we find that themore » self-energy for the itinerant electrons is momentum dependent, indicating a degree of nonlocal correlations while the localized electrons have largely momentum independent self-energies. These nonlocal correlations also produce relative shifts of the holelike and electronlike bands within our model. The overall momentum dependence of these quantities is strongly suppressed in the orbitally ordered insulating phase.« less

How to calculate H3 better.

PubMed

Pavanello, Michele; Tung, Wei-Cheng; Adamowicz, Ludwik

2009-11-14

Efficient optimization of the basis set is key to achieving a very high accuracy in variational calculations of molecular systems employing basis functions that are explicitly dependent on the interelectron distances. In this work we present a method for a systematic enlargement of basis sets of explicitly correlated functions based on the iterative-complement-interaction approach developed by Nakatsuji [Phys. Rev. Lett. 93, 030403 (2004)]. We illustrate the performance of the method in the variational calculations of H(3) where we use explicitly correlated Gaussian functions with shifted centers. The total variational energy (-1.674 547 421 Hartree) and the binding energy (-15.74 cm(-1)) obtained in the calculation with 1000 Gaussians are the most accurate results to date.

Vector and Axial-Vector Correlators in AN Instanton-Like Quark Model

NASA Astrophysics Data System (ADS)

Dorokhov, Alexander E.

The behavior of the vector Adler function at spacelike momenta is studied in the framework of a covariant chiral quark model with instanton-like quark-quark interaction. This function describes the transition between the high energy asymptotically free region of almost massless current quarks to the low energy hadronized regime with massive constituent quarks. The model reproduces the Adler function and V-A correlator extracted from the ALEPH and OPAL data on hadronic τ lepton decays, transformed into the Euclidean domain via dispersion relations. The leading order contribution from hadronic part of the photon vacuum polarization to the anomalous magnetic moment of the muon, aμ hvp(1), is estimated.

Comparing ab initio density-functional and wave function theories: the impact of correlation on the electronic density and the role of the correlation potential.

PubMed

Grabowski, Ireneusz; Teale, Andrew M; Śmiga, Szymon; Bartlett, Rodney J

2011-09-21

The framework of ab initio density-functional theory (DFT) has been introduced as a way to provide a seamless connection between the Kohn-Sham (KS) formulation of DFT and wave-function based ab initio approaches [R. J. Bartlett, I. Grabowski, S. Hirata, and S. Ivanov, J. Chem. Phys. 122, 034104 (2005)]. Recently, an analysis of the impact of dynamical correlation effects on the density of the neon atom was presented [K. Jankowski, K. Nowakowski, I. Grabowski, and J. Wasilewski, J. Chem. Phys. 130, 164102 (2009)], contrasting the behaviour for a variety of standard density functionals with that of ab initio approaches based on second-order Møller-Plesset (MP2) and coupled cluster theories at the singles-doubles (CCSD) and singles-doubles perturbative triples [CCSD(T)] levels. In the present work, we consider ab initio density functionals based on second-order many-body perturbation theory and coupled cluster perturbation theory in a similar manner, for a range of small atomic and molecular systems. For comparison, we also consider results obtained from MP2, CCSD, and CCSD(T) calculations. In addition to this density based analysis, we determine the KS correlation potentials corresponding to these densities and compare them with those obtained for a range of ab initio density functionals via the optimized effective potential method. The correlation energies, densities, and potentials calculated using ab initio DFT display a similar systematic behaviour to those derived from electronic densities calculated using ab initio wave function theories. In contrast, typical explicit density functionals for the correlation energy, such as VWN5 and LYP, do not show behaviour consistent with this picture of dynamical correlation, although they may provide some degree of correction for already erroneous explicitly density-dependent exchange-only functionals. The results presented here using orbital dependent ab initio density functionals show that they provide a treatment of exchange and correlation contributions within the KS framework that is more consistent with traditional ab initio wave function based methods.

Search for correlations between the arrival directions of IceCube neutrino events and ultrahigh-energy cosmic rays detected by the Pierre Auger Observatory and the Telescope Array

DOE Office of Scientific and Technical Information (OSTI.GOV)

IceCube Collaboration; Pierre Auger Collaboration; Telescope Array Collaboration

2016-01-01

This paper presents the results of different searches for correlations between very high-energy neutrino candidates detected by IceCube and the highest-energy cosmic rays measured by the Pierre Auger Observatory and the Telescope Array. We first consider samples of cascade neutrino events and of high-energy neutrino-induced muon tracks, which provided evidence for a neutrino flux of astrophysical origin, and study their cross-correlation with the ultrahigh-energy cosmic ray (UHECR) samples as a function of angular separation. We also study their possible directional correlations using a likelihood method stacking the neutrino arrival directions and adopting different assumptions on the size of the UHECRmore » magnetic deflections. Finally, we perform another likelihood analysis stacking the UHECR directions and using a sample of through-going muon tracks optimized for neutrino point-source searches with sub-degree angular resolution. No indications of correlations at discovery level are obtained for any of the searches performed. The smallest of the p-values comes from the search for correlation between UHECRs with IceCube high-energy cascades, a result that should continue to be monitored.« less

Search for correlations between the arrival directions of IceCube neutrino events and ultrahigh-energy cosmic rays detected by the Pierre Auger Observatory and the Telescope Array

DOE PAGES

Aartsen, M. G.

2016-01-20

This study presents the results of different searches for correlations between very high-energy neutrino candidates detected by IceCube and the highest-energy cosmic rays measured by the Pierre Auger Observatory and the Telescope Array. We first consider samples of cascade neutrino events and of high-energy neutrino-induced muon tracks, which provided evidence for a neutrino flux of astrophysical origin, and study their cross-correlation with the ultrahigh-energy cosmic ray (UHECR) samples as a function of angular separation. We also study their possible directional correlations using a likelihood method stacking the neutrino arrival directions and adopting different assumptions on the size of the UHECRmore » magnetic deflections. Finally, we perform another likelihood analysis stacking the UHECR directions and using a sample of through-going muon tracks optimized for neutrino point-source searches with sub-degree angular resolution. No indications of correlations at discovery level are obtained for any of the searches performed. The smallest of the p-values comes from the search for correlation between UHECRs with IceCube high-energy cascades, a result that should continue to be monitored.« less

FDE-vdW: A van der Waals inclusive subsystem density-functional theory.

PubMed

Kevorkyants, Ruslan; Eshuis, Henk; Pavanello, Michele

2014-07-28

We present a formally exact van der Waals inclusive electronic structure theory, called FDE-vdW, based on the Frozen Density Embedding formulation of subsystem Density-Functional Theory. In subsystem DFT, the energy functional is composed of subsystem additive and non-additive terms. We show that an appropriate definition of the long-range correlation energy is given by the value of the non-additive correlation functional. This functional is evaluated using the fluctuation-dissipation theorem aided by a formally exact decomposition of the response functions into subsystem contributions. FDE-vdW is derived in detail and several approximate schemes are proposed, which lead to practical implementations of the method. We show that FDE-vdW is Casimir-Polder consistent, i.e., it reduces to the generalized Casimir-Polder formula for asymptotic inter-subsystems separations. Pilot calculations of binding energies of 13 weakly bound complexes singled out from the S22 set show a dramatic improvement upon semilocal subsystem DFT, provided that an appropriate exchange functional is employed. The convergence of FDE-vdW with basis set size is discussed, as well as its dependence on the choice of associated density functional approximant.

FDE-vdW: A van der Waals inclusive subsystem density-functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kevorkyants, Ruslan; Pavanello, Michele, E-mail: m.pavanello@rutgers.edu; Eshuis, Henk

2014-07-28

We present a formally exact van der Waals inclusive electronic structure theory, called FDE-vdW, based on the Frozen Density Embedding formulation of subsystem Density-Functional Theory. In subsystem DFT, the energy functional is composed of subsystem additive and non-additive terms. We show that an appropriate definition of the long-range correlation energy is given by the value of the non-additive correlation functional. This functional is evaluated using the fluctuation–dissipation theorem aided by a formally exact decomposition of the response functions into subsystem contributions. FDE-vdW is derived in detail and several approximate schemes are proposed, which lead to practical implementations of the method.more » We show that FDE-vdW is Casimir-Polder consistent, i.e., it reduces to the generalized Casimir-Polder formula for asymptotic inter-subsystems separations. Pilot calculations of binding energies of 13 weakly bound complexes singled out from the S22 set show a dramatic improvement upon semilocal subsystem DFT, provided that an appropriate exchange functional is employed. The convergence of FDE-vdW with basis set size is discussed, as well as its dependence on the choice of associated density functional approximant.« less

Isentropic calculation for thermodynamic properties of polarized liquid 3He by considering the effect of spin-dependent correlation function

NASA Astrophysics Data System (ADS)

Bordbar, G. H.; Hosseini, S.; Poostforush, A.

2017-05-01

Correlations in quantum fluids such as liquid 3He continue to be of high interest to scientists. Based on this prospect, the present work is devoted to study the effects of spin-spin correlation function on the thermodynamic properties of polarized liquid 3He such as pressure, velocity of sound, adiabatic index and adiabatic compressibility along different isentropic paths, using the Lennard-Jones potential and employing the variational approach based on cluster expansion of the energy functional. The inclusion of this correlation improves our previous calculations and leads to good agreements with experimental results.

Importance of the Kinetic Energy Density for Band Gap Calculations in Solids with Density Functional Theory.

PubMed

Tran, Fabien; Blaha, Peter

2017-05-04

Recently, exchange-correlation potentials in density functional theory were developed with the goal of providing improved band gaps in solids. Among them, the semilocal potentials are particularly interesting for large systems since they lead to calculations that are much faster than with hybrid functionals or methods like GW. We present an exhaustive comparison of semilocal exchange-correlation potentials for band gap calculations on a large test set of solids, and particular attention is paid to the potential HLE16 proposed by Verma and Truhlar. It is shown that the most accurate potential is the modified Becke-Johnson potential, which, most noticeably, is much more accurate than all other semilocal potentials for strongly correlated systems. This can be attributed to its additional dependence on the kinetic energy density. It is also shown that the modified Becke-Johnson potential is at least as accurate as the hybrid functionals and more reliable for solids with large band gaps.

The relationship between noise correlation and the Green's function in the presence of degeneracy and the absence of equipartition

USGS Publications Warehouse

Tsai, V.C.

2010-01-01

Recent derivations have shown that when noise in a physical system has its energy equipartitioned into the modes of the system, there is a convenient relationship between the cross correlation of time-series recorded at two points and the Green's function of the system. Here, we show that even when energy is not fully equipartitioned and modes are allowed to be degenerate, a similar (though less general) property holds for equations with wave equation structure. This property can be used to understand why certain seismic noise correlation measurements are successful despite known degeneracy and lack of equipartition on the Earth. No claim to original US government works Journal compilation ?? 2010 RAS.

The Hubbard Dimer: A Complete DFT Solution to a Many-Body Problem

NASA Astrophysics Data System (ADS)

Smith, Justin; Carrascal, Diego; Ferrer, Jaime; Burke, Kieron

2015-03-01

In this work we explain the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site asymmetric Hubbard model. We discuss the connection between the lattice and real-space and how this is a simple model for stretched H2. We can solve this elementary example analytically, and with that we can illuminate the underlying logic and aims of DFT. While the many-body solution is analytic, the density functional is given only implicitly. We overcome this difficulty by creating a highly accurate parameterization of the exact function. We use this parameterization to perform benchmark calculations of correlation kinetic energy, the adiabatic connection, etc. We also test Hartree-Fock and the Bethe Ansatz Local Density Approximation. We also discuss and illustrate the derivative discontinuity in the exchange-correlation energy and the infamous gap problem in DFT. DGE-1321846, DE-FG02-08ER46496.

Kinetic Energy of Hydrocarbons as a Function of Electron Density and Convolutional Neural Networks.

PubMed

Yao, Kun; Parkhill, John

2016-03-08

We demonstrate a convolutional neural network trained to reproduce the Kohn-Sham kinetic energy of hydrocarbons from an input electron density. The output of the network is used as a nonlocal correction to conventional local and semilocal kinetic functionals. We show that this approximation qualitatively reproduces Kohn-Sham potential energy surfaces when used with conventional exchange correlation functionals. The density which minimizes the total energy given by the functional is examined in detail. We identify several avenues to improve on this exploratory work, by reducing numerical noise and changing the structure of our functional. Finally we examine the features in the density learned by the neural network to anticipate the prospects of generalizing these models.

Molecular excited states from the SCAN functional

NASA Astrophysics Data System (ADS)

Tozer, David J.; Peach, Michael J. G.

2018-06-01

The performance of the strongly constrained and appropriately normed (SCAN) meta-generalised gradient approximation exchange-correlation functional is investigated for the calculation of time-dependent density-functional theory molecular excitation energies of local, charge-transfer and Rydberg character, together with the excited ? potential energy curve in H2. The SCAN results frequently resemble those obtained using a global hybrid functional, with either a standard or increased fraction of exact orbital exchange. For local excitations, SCAN can exhibit significant triplet instability problems, resulting in imaginary triplet excitation energies for a number of cases. The Tamm-Dancoff approximation offers a simple approach to improve the situation, but the excitation energies are still significantly underestimated. Understanding the origin of these (near)-triplet instabilities may provide useful insight into future functional development.

Improving Density Functionals with Quantum Harmonic Oscillators

NASA Astrophysics Data System (ADS)

Tkatchenko, Alexandre

2013-03-01

Density functional theory (DFT) is the most widely used and successful approach for electronic structure calculations. However, one of the pressing challenges for DFT is developing efficient functionals that can accurately capture the omnipresent long-range electron correlations, which determine the structure and stability of many molecules and materials. Here we show that, under certain conditions, the problem of computing the long-range correlation energy of interacting electrons can be mapped to a system of coupled quantum harmonic oscillators (QHOs). The proposed model allows us to synergistically combine concepts from DFT, quantum chemistry, and the widely discussed random-phase approximation for the correlation energy. In the dipole limit, the interaction energy for a system of coupled QHOs can be calculated exactly, thereby leading to an efficient and accurate model for the many-body dispersion energy of complex molecules and materials. The studied examples include intermolecular binding energies, the conformational hierarchy of DNA structures, the geometry and stability of molecular crystals, and supramolecular host-guest complexes (A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, Phys. Rev. Lett. 108, 236402 (2012); R. A. DiStasio Jr., A. von Lilienfeld, A. Tkatchenko, PNAS 109, 14791 (2012); A. Tkatchenko, D. Alfe, K. S. Kim, J. Chem. Theory and Comp. (2012), doi: 10.1021/ct300711r; A. Tkatchenko, A. Ambrosetti, R. A. DiStasio Jr., arXiv:1210.8343v1).

Charge and Spin Dynamics of the Hubbard Chains

NASA Technical Reports Server (NTRS)

Park, Youngho; Liang, Shoudan

1999-01-01

We calculate the local correlation functions of charge and spin for the one-chain and two-chain Hubbard model using density matrix renormalization group method and the recursion technique. Keeping only finite number of states we get good accuracy for the low energy excitations. We study the charge and spin gaps, bandwidths and weights of the spectra for various values of the on-site Coulomb interaction U and the electron filling. In the low energy part, the local correlation functions are different for the charge and spin. The bandwidths are proportional to t for the charge and J for the spin respectively.

Ab initio DFT+U study of He atom incorporation into UO(2) crystals.

PubMed

Gryaznov, Denis; Heifets, Eugene; Kotomin, Eugene

2009-09-07

We present and discuss results of the density functional theory (DFT) for perfect UO(2) crystals with He atoms in octahedral interstitial positions therein. We have calculated basic bulk crystal properties and He incorporation energies into the low temperature anti-ferromagnetic UO(2) phase using several exchange-correlation functionals within the spin-polarized local density (LDA) and generalized gradient (GGA) approximations. In all DFT calculations we included the on-site correlation corrections using the Hubbard model (DFT+U approach). We analysed a potential crystalline symmetry reduction from tetragonal down to orthorhombic structure and confirmed the presence of the Jahn-Teller effect in a perfect UO(2). We discuss also the problem of a conducting electronic state arising when He is placed into a tetragonal antiferromagnetic phase of UO(2) commonly used in defect modelling. Consequently, we found a specific monoclinic lattice distortion which allowed us to restore the semiconducting state and properly estimate He incorporation energies. Unlike the bulk properties, the He incorporation energy strongly depends on several factors, including the supercell size, the use of spin polarization, the exchange-correlation functionals and on-site correlation corrections. We compare our results for the He incorporation with the previous shell model and ab initio DFT calculations.

ERP Energy and Cognitive Activity Correlates

NASA Astrophysics Data System (ADS)

Schillaci, Michael Jay; Vendemia, Jennifer M. C.

2014-03-01

We propose a novel analysis approach for high-density event related scalp potential (ERP) data where the integrated channel-power is used to attain an energy density functional state for channel-clusters of neurophysiological significance. The method is applied to data recorded during a two-stimulus, directed lie paradigm and shows that deceptive responses emit between 8% and 10% less power. A time course analysis of these cognitive activity measures over posterior and anterior regions of the cortex suggests that neocortical interactions, reflecting the differing workload demands during executive and semantic processes, take about 50% longer for the case of deception. These results suggest that the proposed method may provide a useful tool for the analysis of ERP correlates of high-order cognitive functioning. We also report on a possible equivalence between the energy functional distribution and near-infrared signatures that have been measured with other modalities.

Upside/Downside statistical mechanics of nonequilibrium Brownian motion. I. Distributions, moments, and correlation functions of a free particle.

PubMed

Craven, Galen T; Nitzan, Abraham

2018-01-28

Statistical properties of Brownian motion that arise by analyzing, separately, trajectories over which the system energy increases (upside) or decreases (downside) with respect to a threshold energy level are derived. This selective analysis is applied to examine transport properties of a nonequilibrium Brownian process that is coupled to multiple thermal sources characterized by different temperatures. Distributions, moments, and correlation functions of a free particle that occur during upside and downside events are investigated for energy activation and energy relaxation processes and also for positive and negative energy fluctuations from the average energy. The presented results are sufficiently general and can be applied without modification to the standard Brownian motion. This article focuses on the mathematical basis of this selective analysis. In subsequent articles in this series, we apply this general formalism to processes in which heat transfer between thermal reservoirs is mediated by activated rate processes that take place in a system bridging them.

Upside/Downside statistical mechanics of nonequilibrium Brownian motion. I. Distributions, moments, and correlation functions of a free particle

NASA Astrophysics Data System (ADS)

Craven, Galen T.; Nitzan, Abraham

2018-01-01

Statistical properties of Brownian motion that arise by analyzing, separately, trajectories over which the system energy increases (upside) or decreases (downside) with respect to a threshold energy level are derived. This selective analysis is applied to examine transport properties of a nonequilibrium Brownian process that is coupled to multiple thermal sources characterized by different temperatures. Distributions, moments, and correlation functions of a free particle that occur during upside and downside events are investigated for energy activation and energy relaxation processes and also for positive and negative energy fluctuations from the average energy. The presented results are sufficiently general and can be applied without modification to the standard Brownian motion. This article focuses on the mathematical basis of this selective analysis. In subsequent articles in this series, we apply this general formalism to processes in which heat transfer between thermal reservoirs is mediated by activated rate processes that take place in a system bridging them.

A recipe for free-energy functionals of polarizable molecular fluids

NASA Astrophysics Data System (ADS)

Sundararaman, Ravishankar; Letchworth-Weaver, Kendra; Arias, T. A.

2014-04-01

Classical density-functional theory is the most direct approach to equilibrium structures and free energies of inhomogeneous liquids, but requires the construction of an approximate free-energy functional for each liquid of interest. We present a general recipe for constructing functionals for small-molecular liquids based only on bulk experimental properties and ab initio calculations of a single solvent molecule. This recipe combines the exact free energy of the non-interacting system with fundamental measure theory for the repulsive contribution and a weighted density functional for the short-ranged attractive interactions. We add to these ingredients a weighted polarization functional for the long-range correlations in both the rotational and molecular-polarizability contributions to the dielectric response. We also perform molecular dynamics calculations for the free energy of cavity formation and the high-field dielectric response, and show that our free-energy functional adequately describes these properties (which are key for accurate solvation calculations) for all three solvents in our study: water, chloroform, and carbon tetrachloride.

A simple but fully nonlocal correction to the random phase approximation

NASA Astrophysics Data System (ADS)

Ruzsinszky, Adrienn; Perdew, John P.; Csonka, Gábor I.

2011-03-01

The random phase approximation (RPA) stands on the top rung of the ladder of ground-state density functional approximations. The simple or direct RPA has been found to predict accurately many isoelectronic energy differences. A nonempirical local or semilocal correction to this direct RPA leaves isoelectronic energy differences almost unchanged, while improving total energies, ionization energies, etc., but fails to correct the RPA underestimation of molecular atomization energies. Direct RPA and its semilocal correction may miss part of the middle-range multicenter nonlocality of the correlation energy in a molecule. Here we propose a fully nonlocal, hybrid-functional-like addition to the semilocal correction. The added full nonlocality is important in molecules, but not in atoms. Under uniform-density scaling, this fully nonlocal correction scales like the second-order-exchange contribution to the correlation energy, an important part of the correction to direct RPA, and like the semilocal correction itself. For the atomization energies of ten molecules, and with the help of one fit parameter, it performs much better than the elaborate second-order screened exchange correction.

Density functional with full exact exchange, balanced nonlocality of correlations, and constraint satisfaction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tao, Jianmin; Perdew, John P; Staroverov, Viktor N

2008-01-01

We construct a nonlocal density functional approximation with full exact exchange, while preserving the constraint-satisfaction approach and justified error cancellations of simpler semilocal functionals. This is achieved by interpolating between different approximations suitable for two extreme regions of the electron density. In a 'normal' region, the exact exchange-correlation hole density around an electron is semilocal because its spatial range is reduced by correlation and because it integrates over a narrow range to -1. These regions are well described by popular semilocal approximations (many of which have been constructed nonempirically), because of proper accuracy for a slowly-varying density or because ofmore » error cancellation between exchange and correlation. 'Abnormal' regions, where non locality is unveiled, include those in which exchange can dominate correlation (one-electron, nonuniform high-density, and rapidly-varying limits), and those open subsystems of fluctuating electron number over which the exact exchange-correlation hole integrates to a value greater than -1. Regions between these extremes are described by a hybrid functional mixing exact and semi local exchange energy densities locally (i.e., with a mixing fraction that is a function of position r and a functional of the density). Because our mixing fraction tends to 1 in the high-density limit, we employ full exact exchange according to the rigorous definition of the exchange component of any exchange-correlation energy functional. Use of full exact exchange permits the satisfaction of many exact constraints, but the nonlocality of exchange also requires balanced nonlocality of correlation. We find that this nonlocality can demand at least five empirical parameters (corresponding roughly to the four kinds of abnormal regions). Our local hybrid functional is perhaps the first accurate size-consistent density functional with full exact exchange. It satisfies other known exact constraints, including exactness for all one-electron densities, and provides an excellent, fit 1.0 the 223 molecular enthalpies of formation of the G3/99 set and the 42 reaction barrier heights of the BH42/03 set, improving both (but especially the latter) over most semilocal functionals and global hybrids. Exact constraints, physical insights, and paradigm examples hopefully suppress 'overfitting'.« less

Correlated natural transition orbital framework for low-scaling excitation energy calculations (CorNFLEx).

PubMed

Baudin, Pablo; Kristensen, Kasper

2017-06-07

We present a new framework for calculating coupled cluster (CC) excitation energies at a reduced computational cost. It relies on correlated natural transition orbitals (NTOs), denoted CIS(D')-NTOs, which are obtained by diagonalizing generalized hole and particle density matrices determined from configuration interaction singles (CIS) information and additional terms that represent correlation effects. A transition-specific reduced orbital space is determined based on the eigenvalues of the CIS(D')-NTOs, and a standard CC excitation energy calculation is then performed in that reduced orbital space. The new method is denoted CorNFLEx (Correlated Natural transition orbital Framework for Low-scaling Excitation energy calculations). We calculate second-order approximate CC singles and doubles (CC2) excitation energies for a test set of organic molecules and demonstrate that CorNFLEx yields excitation energies of CC2 quality at a significantly reduced computational cost, even for relatively small systems and delocalized electronic transitions. In order to illustrate the potential of the method for large molecules, we also apply CorNFLEx to calculate CC2 excitation energies for a series of solvated formamide clusters (up to 4836 basis functions).

Nuclear quantum effects in electronically adiabatic quantum time correlation functions: Application to the absorption spectrum of a hydrated electron

NASA Astrophysics Data System (ADS)

Turi, László; Hantal, György; Rossky, Peter J.; Borgis, Daniel

2009-07-01

A general formalism for introducing nuclear quantum effects in the expression of the quantum time correlation function of an operator in a multilevel electronic system is presented in the adiabatic limit. The final formula includes the nuclear quantum time correlation functions of the operator matrix elements, of the energy gap, and their cross terms. These quantities can be inferred and evaluated from their classical analogs obtained by mixed quantum-classical molecular dynamics simulations. The formalism is applied to the absorption spectrum of a hydrated electron, expressed in terms of the time correlation function of the dipole operator in the ground electronic state. We find that both static and dynamic nuclear quantum effects distinctly influence the shape of the absorption spectrum, especially its high energy tail related to transitions to delocalized electron states. Their inclusion does improve significantly the agreement between theory and experiment for both the low and high frequency edges of the spectrum. It does not appear sufficient, however, to resolve persistent deviations in the slow Lorentzian-like decay part of the spectrum in the intermediate 2-3 eV region.

Low-energy effective Hamiltonians for correlated electron systems beyond density functional theory

NASA Astrophysics Data System (ADS)

Hirayama, Motoaki; Miyake, Takashi; Imada, Masatoshi; Biermann, Silke

2017-08-01

We propose a refined scheme of deriving an effective low-energy Hamiltonian for materials with strong electronic Coulomb correlations beyond density functional theory (DFT). By tracing out the electronic states away from the target degrees of freedom in a controlled way by a perturbative scheme, we construct an effective Hamiltonian for a restricted low-energy target space incorporating the effects of high-energy degrees of freedom in an effective manner. The resulting effective Hamiltonian can afterwards be solved by accurate many-body solvers. We improve this "multiscale ab initio scheme for correlated electrons" (MACE) primarily in two directions by elaborating and combining two frameworks developed by Hirayama et al. [M. Hirayama, T. Miyake, and M. Imada, Phys. Rev. B 87, 195144 (2013), 10.1103/PhysRevB.87.195144] and Casula et al. [M. Casula, P. Werner, L. Vaugier, F. Aryasetiawan, T. Miyake, A. J. Millis, and S. Biermann, Phys. Rev. Lett. 109, 126408 (2012), 10.1103/PhysRevLett.109.126408]: (1) Double counting of electronic correlations between the DFT and the low-energy solver is avoided by using the constrained G W scheme; and (2) the frequency dependent interactions emerging from the partial trace summation are successfully separated into a nonlocal part that is treated following ideas by Hirayama et al. and a local part treated nonperturbatively in the spirit of Casula et al. and are incorporated into the renormalization of the low-energy dispersion. The scheme is favorably tested on the example of SrVO3.

Benchmark CCSD(T) and DFT study of binding energies in Be7 - 12: in search of reliable DFT functional for beryllium clusters

NASA Astrophysics Data System (ADS)

Labanc, Daniel; Šulka, Martin; Pitoňák, Michal; Černušák, Ivan; Urban, Miroslav; Neogrády, Pavel

2018-05-01

We present a computational study of the stability of small homonuclear beryllium clusters Be7 - 12 in singlet electronic states. Our predictions are based on highly correlated CCSD(T) coupled cluster calculations. Basis set convergence towards the complete basis set limit as well as the role of the 1s core electron correlation are carefully examined. Our CCSD(T) data for binding energies of Be7 - 12 clusters serve as a benchmark for performance assessment of several density functional theory (DFT) methods frequently used in beryllium cluster chemistry. We observe that, from Be10 clusters on, the deviation from CCSD(T) benchmarks is stable with respect to size, and fluctuating within 0.02 eV error bar for most examined functionals. This opens up the possibility of scaling the DFT binding energies for large Be clusters using CCSD(T) benchmark values for smaller clusters. We also tried to find analogies between the performance of DFT functionals for Be clusters and for the valence-isoelectronic Mg clusters investigated recently in Truhlar's group. We conclude that it is difficult to find DFT functionals that perform reasonably well for both beryllium and magnesium clusters. Out of 12 functionals examined, only the M06-2X functional gives reasonably accurate and balanced binding energies for both Be and Mg clusters.

Correlation of Particle-Induced Displacement Damage in Silicon

NASA Astrophysics Data System (ADS)

Summers, G. P.; Burke, E. A.; Dale, C. J.; Wolicki, E. A.; Marshall, P. W.; Gehlhausen, M. A.

1987-12-01

Correlation is made between the effects of displacement damage caused in several types of silicon bipolar transistors by protons, deuterons, helium ions, and by 1 MeV equivalent neutrons. These measurements are compared to calculations of the nonionizing energy deposition in silicon as a function of particle type and energy. Measurements were made of displacement damage factors for 2N2222A and 2N2907A switching transistors, and for 2N3055, 2N6678, and 2N6547 power transistors, as a function of collector current using 3.7 - 175 MeV protons, 4.3 - 37 MeV deuterons, and 16.8 - 65 MeV helium ions. Long term ionization effects on the value of the displacement damage factors were taken into account. In calculating the energy dependence of the nonionizing energy deposition, Rutherford, nuclear elastic, and nuclear inelastic interactions, and Lindhard energy partition were considered. The main conclusions of the work are as follows: 1) The ratio of the displacement damage factors for a given charged particle to the 1 MeV equivalent neutron damage factor, as a function of energy, falls on a common curve which is independent of collector current. 2) Deuterons of a given energy are about twice as damaging as protons and helium ions are about eighteen times as damaging as protons.

Water on BN doped benzene: A hard test for exchange-correlation functionals and the impact of exact exchange on weak binding

DOE PAGES

Al-Hamdani, Yasmine S.; Alfè, Dario; von Lilienfeld, O. Anatole; ...

2014-10-22

Density functional theory (DFT) studies of weakly interacting complexes have recently focused on the importance of van der Waals dispersion forces, whereas the role of exchange has received far less attention. Here, by exploiting the subtle binding between water and a boron and nitrogen doped benzene derivative (1,2-azaborine) we show how exact exchange can alter the binding conformation within a complex. Benchmark values have been calculated for three orientations of the water monomer on 1,2-azaborine from explicitly correlated quantum chemical methods, and we have also used diffusion quantum Monte Carlo. For a host of popular DFT exchange-correlation functionals we showmore » that the lack of exact exchange leads to the wrong lowest energy orientation of water on 1,2-azaborine. As such, we suggest that a high proportion of exact exchange and the associated improvement in the electronic structure could be needed for the accurate prediction of physisorption sites on doped surfaces and in complex organic molecules. Meanwhile to predict correct absolute interaction energies an accurate description of exchange needs to be augmented by dispersion inclusive functionals, and certain non-local van der Waals functionals (optB88- and optB86b-vdW) perform very well for absolute interaction energies. Through a comparison with water on benzene and borazine (B₃N₃H₆) we show that these results could have implications for the interaction of water with doped graphene surfaces, and suggest a possible way of tuning the interaction energy.« less

Robust validation of approximate 1-matrix functionals with few-electron harmonium atoms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cioslowski, Jerzy, E-mail: jerzy@wmf.univ.szczecin.pl; Piris, Mario; Matito, Eduard

2015-12-07

A simple comparison between the exact and approximate correlation components U of the electron-electron repulsion energy of several states of few-electron harmonium atoms with varying confinement strengths provides a stringent validation tool for 1-matrix functionals. The robustness of this tool is clearly demonstrated in a survey of 14 known functionals, which reveals their substandard performance within different electron correlation regimes. Unlike spot-testing that employs dissociation curves of diatomic molecules or more extensive benchmarking against experimental atomization energies of molecules comprising some standard set, the present approach not only uncovers the flaws and patent failures of the functionals but, even moremore » importantly, also allows for pinpointing their root causes. Since the approximate values of U are computed at exact 1-densities, the testing requires minimal programming and thus is particularly suitable for rapid screening of new functionals.« less

Density-dependent covariant energy density functionals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lalazissis, G. A.

2012-10-20

Relativistic nuclear energy density functionals are applied to the description of a variety of nuclear structure phenomena at and away fromstability line. Isoscalar monopole, isovector dipole and isoscalar quadrupole giant resonances are calculated using fully self-consistent relativistic quasiparticle randomphase approximation, based on the relativistic Hartree-Bogoliubovmodel. The impact of pairing correlations on the fission barriers in heavy and superheavy nuclei is examined. The role of pion in constructing desnity functionals is also investigated.

Engineering molecular machines

NASA Astrophysics Data System (ADS)

Erman, Burak

2016-04-01

Biological molecular motors use chemical energy, mostly in the form of ATP hydrolysis, and convert it to mechanical energy. Correlated thermal fluctuations are essential for the function of a molecular machine and it is the hydrolysis of ATP that modifies the correlated fluctuations of the system. Correlations are consequences of the molecular architecture of the protein. The idea that synthetic molecular machines may be constructed by designing the proper molecular architecture is challenging. In their paper, Sarkar et al (2016 New J. Phys. 18 043006) propose a synthetic molecular motor based on the coarse grained elastic network model of proteins and show by numerical simulations that motor function is realized, ranging from deterministic to thermal, depending on temperature. This work opens up a new range of possibilities of molecular architecture based engine design.

Magnetic-Field Density-Functional Theory (BDFT): Lessons from the Adiabatic Connection.

PubMed

Reimann, Sarah; Borgoo, Alex; Tellgren, Erik I; Teale, Andrew M; Helgaker, Trygve

2017-09-12

We study the effects of magnetic fields in the context of magnetic field density-functional theory (BDFT), where the energy is a functional of the electron density ρ and the magnetic field B. We show that this approach is a worthwhile alternative to current-density functional theory (CDFT) and may provide a viable route to the study of many magnetic phenomena using density-functional theory (DFT). The relationship between BDFT and CDFT is developed and clarified within the framework of the four-way correspondence of saddle functions and their convex and concave parents in convex analysis. By decomposing the energy into its Kohn-Sham components, we demonstrate that the magnetizability is mainly determined by those energy components that are related to the density. For existing density functional approximations, this implies that, for the magnetizability, improvements of the density will be more beneficial than introducing a magnetic-field dependence in the correlation functional. However, once a good charge density is achieved, we show that high accuracy is likely only obtainable by including magnetic-field dependence. We demonstrate that adiabatic-connection (AC) curves at different field strengths resemble one another closely provided each curve is calculated at the equilibrium geometry of that field strength. In contrast, if all AC curves are calculated at the equilibrium geometry of the field-free system, then the curves change strongly with increasing field strength due to the increasing importance of static correlation. This holds also for density functional approximations, for which we demonstrate that the main error encountered in the presence of a field is already present at zero field strength, indicating that density-functional approximations may be applied to systems in strong fields, without the need to treat additional static correlation.

Modeling Electronic-Nuclear Interactions for Excitation Energy Transfer Processes in Light-Harvesting Complexes.

PubMed

Lee, Mi Kyung; Coker, David F

2016-08-18

An accurate approach for computing intermolecular and intrachromophore contributions to spectral densities to describe the electronic-nuclear interactions relevant for modeling excitation energy transfer processes in light harvesting systems is presented. The approach is based on molecular dynamics (MD) calculations of classical correlation functions of long-range contributions to excitation energy fluctuations and a separate harmonic analysis and single-point gradient quantum calculations for electron-intrachromophore vibrational couplings. A simple model is also presented that enables detailed analysis of the shortcomings of standard MD-based excitation energy fluctuation correlation function approaches. The method introduced here avoids these problems, and its reliability is demonstrated in accurate predictions for bacteriochlorophyll molecules in the Fenna-Matthews-Olson pigment-protein complex, where excellent agreement with experimental spectral densities is found. This efficient approach can provide instantaneous spectral densities for treating the influence of fluctuations in environmental dissipation on fast electronic relaxation.

Electron binding energy of uranium-ligand and uranyl-ligand anions

NASA Astrophysics Data System (ADS)

Wang, Lei; Horowitz, Steven; Marston, Brad

2012-02-01

Electron binding energies of the early actinide element uranium in gas-phase anion complexes are calculated by relativistic density functional theory (DFT) with two different exchange-correlation functions (RPBE and B3LYP) and also in the Hartree-Fock (HF) approximationootnotetextADF2010.02, SCM.com. Scalar and spin-orbit calculations are performed, and the calculated energies are compared to available experimental measurements and shown to disagree by energies of order 1 eV. Strong correlations that are poorly treated in DFT and HF can be included by a hybrid approach in which a generalized Anderson impurity model is numerically diagonalized. Reduction-oxidation (redox) potentials of aqueous actinide ions show improved agreement with measured values in the hybrid approachootnotetextS. E. Horowitz and J. B. Marston, J. Chem. Phys 134 064510 (2011).. We test whether or not similar improvements are found in the gas-phase.

Energy-switching potential energy surface for the water molecule revisited: A highly accurate singled-sheeted form.

PubMed

Galvão, B R L; Rodrigues, S P J; Varandas, A J C

2008-07-28

A global ab initio potential energy surface is proposed for the water molecule by energy-switching/merging a highly accurate isotope-dependent local potential function reported by Polyansky et al. [Science 299, 539 (2003)] with a global form of the many-body expansion type suitably adapted to account explicitly for the dynamical correlation and parametrized from extensive accurate multireference configuration interaction energies extrapolated to the complete basis set limit. The new function mimics also the complicated Sigma/Pi crossing that arises at linear geometries of the water molecule.

Rapidity correlations in the RHIC Beam Energy Scan Data

NASA Astrophysics Data System (ADS)

Jowzaee, Sedigheh; STAR Collaboration

2017-11-01

A pair-normalized two-particle covariance versus the rapidity of the two particles, called R2, was originally studied in ISR and FNAL data in the 1970's. This variable has recently seen renewed interest for the study of the dynamics of heavy-ion collisions in the longitudinal direction. These rapidity correlations can be decomposed into a basis set of Legendre polynomials with prefactors 〈amn 〉, which can be considered the rapidity analog of the decomposition of azimuthal anisotropies into a set of cosine functions with prefactors vn. The 〈amn 〉 values have been suggested to be sensitive to the number of particle emitting sources, baryon stopping, viscosities, and critical behavior. The rapidity correlations have been measured by the STAR collaboration as a function of the beam energy for 0-5% central Au+Au collisions with beam energies ranging from 7.7 to 200 GeV. The experimental results and comparisons to the UrQMD model are presented.

Quantification of correlational selection on thermal physiology, thermoregulatory behavior, and energy metabolism in lizards

PubMed Central

Artacho, Paulina; Saravia, Julia; Ferrandière, Beatriz Decencière; Perret, Samuel; Le Galliard, Jean-François

2015-01-01

Phenotypic selection is widely accepted as the primary cause of adaptive evolution in natural populations, but selection on complex functional properties linking physiology, behavior, and morphology has been rarely quantified. In ectotherms, correlational selection on thermal physiology, thermoregulatory behavior, and energy metabolism is of special interest because of their potential coadaptation. We quantified phenotypic selection on thermal sensitivity of locomotor performance (sprint speed), thermal preferences, and resting metabolic rate in captive populations of an ectothermic vertebrate, the common lizard, Zootoca vivipara. No correlational selection between thermal sensitivity of performance, thermoregulatory behavior, and energy metabolism was found. A combination of high body mass and resting metabolic rate was positively correlated with survival and negatively correlated with fecundity. Thus, different mechanisms underlie selection on metabolism in lizards with small body mass than in lizards with high body mass. In addition, lizards that selected the near average preferred body temperature grew faster that their congeners. This is one of the few studies that quantifies significant correlational selection on a proxy of energy expenditure and stabilizing selection on thermoregulatory behavior. PMID:26380689

Quantification of correlational selection on thermal physiology, thermoregulatory behavior, and energy metabolism in lizards.

PubMed

Artacho, Paulina; Saravia, Julia; Ferrandière, Beatriz Decencière; Perret, Samuel; Le Galliard, Jean-François

2015-09-01

Phenotypic selection is widely accepted as the primary cause of adaptive evolution in natural populations, but selection on complex functional properties linking physiology, behavior, and morphology has been rarely quantified. In ectotherms, correlational selection on thermal physiology, thermoregulatory behavior, and energy metabolism is of special interest because of their potential coadaptation. We quantified phenotypic selection on thermal sensitivity of locomotor performance (sprint speed), thermal preferences, and resting metabolic rate in captive populations of an ectothermic vertebrate, the common lizard, Zootoca vivipara. No correlational selection between thermal sensitivity of performance, thermoregulatory behavior, and energy metabolism was found. A combination of high body mass and resting metabolic rate was positively correlated with survival and negatively correlated with fecundity. Thus, different mechanisms underlie selection on metabolism in lizards with small body mass than in lizards with high body mass. In addition, lizards that selected the near average preferred body temperature grew faster that their congeners. This is one of the few studies that quantifies significant correlational selection on a proxy of energy expenditure and stabilizing selection on thermoregulatory behavior.

Rigorous proof for the nonlocal correlation function in the transverse Ising model with ring frustration.

PubMed

Dong, Jian-Jun; Zheng, Zhen-Yu; Li, Peng

2018-01-01

An unusual correlation function was conjectured by Campostrini et al. [Phys. Rev. E 91, 042123 (2015)PLEEE81539-375510.1103/PhysRevE.91.042123] for the ground state of a transverse Ising chain with geometrical frustration. Later, we provided a rigorous proof for it and demonstrated its nonlocal nature based on an evaluation of a Toeplitz determinant in the thermodynamic limit [J. Stat. Mech. (2016) 11310210.1088/1742-5468/2016/11/113102]. In this paper, we further prove that all the low excited energy states forming the gapless kink phase share the same asymptotic correlation function with the ground state. As a consequence, the thermal correlation function almost remains constant at low temperatures if one assumes a canonical ensemble.

Exchange-Correlation Hole in Polarized Insulators: Implications for the Microscopic Functional Theory of Dielectrics

NASA Astrophysics Data System (ADS)

Ortiz, Gerardo; Souza, Ivo; Martin, Richard M.

1998-01-01

We present a simple and direct proof that the exchange-correlation hole, and therefore the exchange-correlation energy, in a polarized insulator is not determined by the bulk density alone. It is uniquely characterized by the density and the macroscopic electric polarization of the dielectric medium.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khachatryan, Vardan

Our results on two-particle angular correlations for charged particles produced in pp collisions at a center-of-mass energy of 13 TeV are presented. The data were taken with the CMS detector at the LHC and correspond to an integrated luminosity of about 270 nb -1. The correlations are studied over a broad range of pseudorapidity (|η| < 2.4) and over the full azimuth (Φ) as a function of charged particle multiplicity and transverse momentum (p T). In high-multiplicity events, a long-range (|Δη| > 2.0), near-side (ΔΦ≈ 0) structure emerges in the two-particle Dh–Df correlation functions. The magnitude of the correlation exhibitsmore » a pronounced maximum in the range 1.0 < p T < 2.0 GeV/c and an approximately linear increase with the charged particle multiplicity. The overall correlation strength at √s = 13 TeV is similar to that found in earlier pp data at √s = 7 TeV, but is measured up to much higher multiplicity values. We observed long-range correlations are compared to those seen in pp, pPb, and PbPb collisions at lower collision energies.« less

Single-particle energies and density of states in density functional theory

NASA Astrophysics Data System (ADS)

van Aggelen, H.; Chan, G. K.-L.

2015-07-01

Time-dependent density functional theory (TD-DFT) is commonly used as the foundation to obtain neutral excited states and transition weights in DFT, but does not allow direct access to density of states and single-particle energies, i.e. ionisation energies and electron affinities. Here we show that by extending TD-DFT to a superfluid formulation, which involves operators that break particle-number symmetry, we can obtain the density of states and single-particle energies from the poles of an appropriate superfluid response function. The standard Kohn- Sham eigenvalues emerge as the adiabatic limit of the superfluid response under the assumption that the exchange- correlation functional has no dependence on the superfluid density. The Kohn- Sham eigenvalues can thus be interpreted as approximations to the ionisation energies and electron affinities. Beyond this approximation, the formalism provides an incentive for creating a new class of density functionals specifically targeted at accurate single-particle eigenvalues and bandgaps.

Interatomic potentials in condensed matter via the maximum-entropy principle

NASA Astrophysics Data System (ADS)

Carlsson, A. E.

1987-09-01

A general method is described for the calculation of interatomic potentials in condensed-matter systems by use of a maximum-entropy Ansatz for the interatomic correlation functions. The interatomic potentials are given explicitly in terms of statistical correlation functions involving the potential energy and the structure factor of a ``reference medium.'' Illustrations are given for Al-Cu alloys and a model transition metal.

Linear-response time-dependent density-functional theory with pairing fields.

PubMed

Peng, Degao; van Aggelen, Helen; Yang, Yang; Yang, Weitao

2014-05-14

Recent development in particle-particle random phase approximation (pp-RPA) broadens the perspective on ground state correlation energies [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013), Y. Yang, H. van Aggelen, S. N. Steinmann, D. Peng, and W. Yang, J. Chem. Phys. 139, 174110 (2013); D. Peng, S. N. Steinmann, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 104112 (2013)] and N ± 2 excitation energies [Y. Yang, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 224105 (2013)]. So far Hartree-Fock and approximated density-functional orbitals have been utilized to evaluate the pp-RPA equation. In this paper, to further explore the fundamentals and the potential use of pairing matrix dependent functionals, we present the linear-response time-dependent density-functional theory with pairing fields with both adiabatic and frequency-dependent kernels. This theory is related to the density-functional theory and time-dependent density-functional theory for superconductors, but is applied to normal non-superconducting systems for our purpose. Due to the lack of the proof of the one-to-one mapping between the pairing matrix and the pairing field for time-dependent systems, the linear-response theory is established based on the representability assumption of the pairing matrix. The linear response theory justifies the use of approximated density-functionals in the pp-RPA equation. This work sets the fundamentals for future density-functional development to enhance the description of ground state correlation energies and N ± 2 excitation energies.

Source-Free Exchange-Correlation Magnetic Fields in Density Functional Theory.

PubMed

Sharma, S; Gross, E K U; Sanna, A; Dewhurst, J K

2018-03-13

Spin-dependent exchange-correlation energy functionals in use today depend on the charge density and the magnetization density: E xc [ρ, m]. However, it is also correct to define the functional in terms of the curl of m for physical external fields: E xc [ρ,∇ × m]. The exchange-correlation magnetic field, B xc , then becomes source-free. We study this variation of the theory by uniquely removing the source term from local and generalized gradient approximations to the functional. By doing so, the total Kohn-Sham moments are improved for a wide range of materials for both functionals. Significantly, the moments for the pnictides are now in good agreement with experiment. This source-free method is simple to implement in all existing density functional theory codes.

Statistics of baryon correlation functions in lattice QCD

NASA Astrophysics Data System (ADS)

Wagman, Michael L.; Savage, Martin J.; Nplqcd Collaboration

2017-12-01

A systematic analysis of the structure of single-baryon correlation functions calculated with lattice QCD is performed, with a particular focus on characterizing the structure of the noise associated with quantum fluctuations. The signal-to-noise problem in these correlation functions is shown, as long suspected, to result from a sign problem. The log-magnitude and complex phase are found to be approximately described by normal and wrapped normal distributions respectively. Properties of circular statistics are used to understand the emergence of a large time noise region where standard energy measurements are unreliable. Power-law tails in the distribution of baryon correlation functions, associated with stable distributions and "Lévy flights," are found to play a central role in their time evolution. A new method of analyzing correlation functions is considered for which the signal-to-noise ratio of energy measurements is constant, rather than exponentially degrading, with increasing source-sink separation time. This new method includes an additional systematic uncertainty that can be removed by performing an extrapolation, and the signal-to-noise problem reemerges in the statistics of this extrapolation. It is demonstrated that this new method allows accurate results for the nucleon mass to be extracted from the large-time noise region inaccessible to standard methods. The observations presented here are expected to apply to quantum Monte Carlo calculations more generally. Similar methods to those introduced here may lead to practical improvements in analysis of noisier systems.

Reference Determinant Dependence of the Random Phase Approximation in 3d Transition Metal Chemistry.

PubMed

Bates, J E; Mezei, P D; Csonka, G I; Sun, J; Ruzsinszky, A

2017-01-10

Without extensive fitting, accurate prediction of transition metal chemistry is a challenge for semilocal and hybrid density funcitonals. The Random Phase Approximation (RPA) has been shown to yield superior results to semilocal functionals for main group thermochemistry, but much less is known about its performance for transition metals. We have therefore analyzed the behavior of reaction energies, barrier heights, and ligand dissociation energies obtained with RPA and compare our results to several semilocal and hybrid functionals. Particular attention is paid to the reference determinant dependence of RPA. We find that typically the results do not vary much between semilocal or hybrid functionals as a reference, as long as the fraction of exact exchange (EXX) mixing in the hybrid functional is small. For large fractions of EXX mixing, however, the Hartree-Fock-like nature of the determinant can severely degrade the performance. Overall, RPA systematically reduces the errors of semilocal functionals and delivers excellent performance from a single reference determinant for inherently multireference reactions. The behavior of dual hybrids that combine RPA correlation with a hybrid exchange energy was also explored, but ultimately did not lead to a systematic improvement compared to traditional RPA for these systems. We rationalize this conclusion by decomposing the contributions to the reaction energies, and briefly discuss the possible implications for double-hybrid functionals based on RPA. The correlation between EXX mixing and spin-symmetry breaking is also discussed.

Solute-solvent cavity and bridge functions. I. Varying size of the solute

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vyalov, I., E-mail: ivan.vyalov@iit.it; Chuev, G., E-mail: genchuev@rambler.ru; Georgi, N., E-mail: georgi@mis.mpg.de

2014-08-21

In this work we present the results of the extensive molecular simulations of solute-solvent cavity and bridge functions. The mixtures of Lennard-Jones solvent with Lennard-Jones solute at infinite dilution are considered for different solute-solvent size ratios—up to 4:1. The Percus-Yevick and hypernetted chain closures deviate substantially from simulation results in the investigated temperature and density ranges. We also find that the behavior of the indirect and cavity correlation functions is non-monotonous within the hard-core region, but the latter can be successfully approximated by mean-field theory if the solute-solvent interaction energy is divided into repulsive and attractive contribution, according to Weeks-Chandler-Andersenmore » theory. Furthermore, in spite of the non-monotonous behavior of logarithm of the cavity function and the indirect correlation function, their difference, i.e., the bridge function remains constant within the hard-core region. Such behavior of the bridge and indirect correlation functions at small distances and for small values of indirect correlation function is well known from the Duh-Haymet plots, where the non-unique relationship results in loops of the bridge function vs. indirect correlation function graphs. We show that the same pathological behavior appears also when distance is small and indirect correlation function is large. We further show that the unique functional behavior of the bridge function can be established when bridge is represented as a function of the renormalized, repulsive indirect correlation function.« less

Genomic and Proteomic Profiling Reveals Reduced Mitochondrial Function and Disruption of the Neuromuscular Junction Driving Rat Sarcopenia

PubMed Central

Ibebunjo, Chikwendu; Chick, Joel M.; Kendall, Tracee; Eash, John K.; Li, Christine; Zhang, Yunyu; Vickers, Chad; Wu, Zhidan; Clarke, Brian A.; Shi, Jun; Cruz, Joseph; Fournier, Brigitte; Brachat, Sophie; Gutzwiller, Sabine; Ma, QiCheng; Markovits, Judit; Broome, Michelle; Steinkrauss, Michelle; Skuba, Elizabeth; Galarneau, Jean-Rene; Gygi, Steven P.

2013-01-01

Molecular mechanisms underlying sarcopenia, the age-related loss of skeletal muscle mass and function, remain unclear. To identify molecular changes that correlated best with sarcopenia and might contribute to its pathogenesis, we determined global gene expression profiles in muscles of rats aged 6, 12, 18, 21, 24, and 27 months. These rats exhibit sarcopenia beginning at 21 months. Correlation of the gene expression versus muscle mass or age changes, and functional annotation analysis identified gene signatures of sarcopenia distinct from gene signatures of aging. Specifically, mitochondrial energy metabolism (e.g., tricarboxylic acid cycle and oxidative phosphorylation) pathway genes were the most downregulated and most significantly correlated with sarcopenia. Also, perturbed were genes/pathways associated with neuromuscular junction patency (providing molecular evidence of sarcopenia-related functional denervation and neuromuscular junction remodeling), protein degradation, and inflammation. Proteomic analysis of samples at 6, 18, and 27 months confirmed the depletion of mitochondrial energy metabolism proteins and neuromuscular junction proteins. Together, these findings suggest that therapeutic approaches that simultaneously stimulate mitochondrogenesis and reduce muscle proteolysis and inflammation have potential for treating sarcopenia. PMID:23109432

Local-spin-density calculations for iron: Effect of spin interpolation on ground-state properties

DOE Office of Scientific and Technical Information (OSTI.GOV)

MacLaren, J.M.; Clougherty, D.P.; Albers, R.C.

1990-08-15

Scalar-relativistic self-consistent linear muffin-tin orbital (LMTO) calculations for bcc and fcc Fe have been performed with several different local approximations to the exchange and correlation energy density and potential. Overall, in contrast to the conclusions of previous studies, we find that the local-spin-density approximation to exchange and correlation can provide an adequate description of bulk Fe {ital provided} that a proper parametrization of the correlation energy density and potential of the homogeneous electron gas over both spin and density is used. Lattice constants, found from the position of the minimum of the total energy as a function of Wigner-Seitz radius,more » agree to within 1% (for {ital s},{ital p},{ital d} LMTO's only) and within 1--2% (for {ital s},{ital p},{ital d},{ital f} LMTO's) of the experimental lattice constants for all forms used for the local correlation. The best agreement, however, was obtained using a local correlation potential derived from the Vosko-Wilk-Nusair form for the spin dependence of the correlation energy density. The calculation performed with this correlation potential was also the only calculation to correctly predict a bcc ferromagnetic ground state.« less

Accuracy of electron densities obtained via Koopmans-compliant hybrid functionals

NASA Astrophysics Data System (ADS)

Elmaslmane, A. R.; Wetherell, J.; Hodgson, M. J. P.; McKenna, K. P.; Godby, R. W.

2018-04-01

We evaluate the accuracy of electron densities and quasiparticle energy gaps given by hybrid functionals by directly comparing these to the exact quantities obtained from solving the many-electron Schrödinger equation. We determine the admixture of Hartree-Fock exchange to approximate exchange-correlation in our hybrid functional via one of several physically justified constraints, including the generalized Koopmans' theorem. We find that hybrid functionals yield strikingly accurate electron densities and gaps in both exchange-dominated and correlated systems. We also discuss the role of the screened Fock operator in the success of hybrid functionals.

Seniority number description of potential energy surfaces: Symmetric dissociation of water, N{sub 2}, C{sub 2}, and Be{sub 2}

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bytautas, Laimutis; Scuseria, Gustavo E.; Chemistry Department, Faculty of Science, King Abdulaziz University, Jeddah 21589

2015-09-07

The present study further explores the concept of the seniority number (Ω) by examining different configuration interaction (CI) truncation strategies in generating compact wave functions in a systematic way. While the role of Ω in addressing static (strong) correlation problem has been addressed in numerous previous studies, the usefulness of seniority number in describing weak (dynamic) correlation has not been investigated in a systematic way. Thus, the overall objective in the present work is to investigate the role of Ω in addressing also dynamic electron correlation in addition to the static correlation. Two systematic CI truncation strategies are compared beyondmore » minimal basis sets and full valence active spaces. One approach is based on the seniority number (defined as the total number of singly occupied orbitals in a determinant) and another is based on an excitation-level limitation. In addition, molecular orbitals are energy-optimized using multiconfigurational-self-consistent-field procedure for all these wave functions. The test cases include the symmetric dissociation of water (6-31G), N{sub 2} (6-31G), C{sub 2} (6-31G), and Be{sub 2} (cc-pVTZ). We find that the potential energy profile for H{sub 2}O dissociation can be reasonably well described using only the Ω = 0 sector of the CI wave function. For the Be{sub 2} case, we show that the full CI potential energy curve (cc-pVTZ) is almost exactly reproduced using either Ω-based (including configurations having up to Ω = 2 in the virtual-orbital-space) or excitation-based (up to single-plus-double-substitutions) selection methods, both out of a full-valence-reference function. Finally, in dissociation cases of N{sub 2} and C{sub 2}, we shall also consider novel hybrid wave functions obtained by a union of a set of CI configurations representing the full valence space and a set of CI configurations where seniority-number restriction is imposed for a complete set (full-valence-space and virtual) of correlated molecular orbitals, simultaneously. We discuss the usefulness of the seniority number concept in addressing both static and dynamic electron correlation problems along dissociation paths.« less

EuropeaN Energy balance Research to prevent excessive weight Gain among Youth (ENERGY) project: Design and methodology of the ENERGY cross-sectional survey.

PubMed

van Stralen, Maartje M; te Velde, Saskia J; Singh, Amika S; De Bourdeaudhuij, Ilse; Martens, Marloes K; van der Sluis, Maria; Manios, Yannis; Grammatikaki, Evangelia; Chinapaw, Mai J M; Maes, Lea; Bere, Elling; Jensen, Jorgen; Moreno, Luis; Jan, Nataša; Molnár, Dénes; Moore, Helen; Brug, Johannes

2011-01-31

Obesity treatment is by large ineffective long term, and more emphasis on the prevention of excessive weight gain in childhood and adolescence is warranted. To inform energy balance related behaviour (EBRB) change interventions, insight in the potential personal, family and school environmental correlates of these behaviours is needed. Studies on such multilevel correlates of EBRB among schoolchildren in Europe are lacking. The ENERGY survey aims to (1) provide up-to-date prevalence rates of measured overweight, obesity, self-reported engagement in EBRBs, and objective accelerometer-based assessment of physical activity and sedentary behaviour and blood-sample biomarkers of metabolic function in countries in different regions of Europe, (2) to identify personal, family and school environmental correlates of these EBRBs. This paper describes the design, methodology and protocol of the survey. A school-based cross-sectional survey was carried out in 2010 in seven different European countries; Belgium, Greece, Hungary, the Netherlands, Norway, Slovenia, and Spain. The survey included measurements of anthropometrics, child, parent and school-staff questionnaires, and school observations to measure and assess outcomes (i.e. height, weight, and waist circumference), EBRBs and potential personal, family and school environmental correlates of these behaviours including the social-cultural, physical, political, and economic environmental factors. In addition, a selection of countries conducted accelerometer measurements to objectively assess physical activity and sedentary behaviour, and collected blood samples to assess several biomarkers of metabolic function. The ENERGY survey is a comprehensive cross-sectional study measuring anthropometrics and biomarkers as well as assessing a range of EBRBs and their potential correlates at the personal, family and school level, among 10-12 year old children in seven European countries. This study will result in a unique dataset, enabling cross country comparisons in overweight, obesity, risk behaviours for these conditions as well as the correlates of engagement in these risk behaviours.

Interplay between strong correlation and adsorption distances: Co on Cu(001)

NASA Astrophysics Data System (ADS)

Bahlke, Marc Philipp; Karolak, Michael; Herrmann, Carmen

2018-01-01

Adsorbed transition metal atoms can have partially filled d or f shells due to strong on-site Coulomb interaction. Capturing all effects originating from electron correlation in such strongly correlated systems is a challenge for electronic structure methods. It requires a sufficiently accurate description of the atomistic structure (in particular bond distances and angles), which is usually obtained from first-principles Kohn-Sham density functional theory (DFT), which due to the approximate nature of the exchange-correlation functional may provide an unreliable description of strongly correlated systems. To elucidate the consequences of this popular procedure, we apply a combination of DFT with the Anderson impurity model (AIM), as well as DFT + U for a calculation of the potential energy surface along the Co/Cu(001) adsorption coordinate, and compare the results with those obtained from DFT. The adsorption minimum is shifted towards larger distances by applying DFT+AIM, or the much cheaper DFT +U method, compared to the corresponding spin-polarized DFT results, by a magnitude comparable to variations between different approximate exchange-correlation functionals (0.08 to 0.12 Å). This shift originates from an increasing correlation energy at larger adsorption distances, which can be traced back to the Co 3 dx y and 3 dz2 orbitals being more correlated as the adsorption distance is increased. We can show that such considerations are important, as they may strongly affect electronic properties such as the Kondo temperature.

The effect of basis set and exchange-correlation functional on time-dependent density functional theory calculations within the Tamm-Dancoff approximation of the x-ray emission spectroscopy of transition metal complexes.

PubMed

Roper, Ian P E; Besley, Nicholas A

2016-03-21

The simulation of X-ray emission spectra of transition metal complexes with time-dependent density functional theory (TDDFT) is investigated. X-ray emission spectra can be computed within TDDFT in conjunction with the Tamm-Dancoff approximation by using a reference determinant with a vacancy in the relevant core orbital, and these calculations can be performed using the frozen orbital approximation or with the relaxation of the orbitals of the intermediate core-ionised state included. Both standard exchange-correlation functionals and functionals specifically designed for X-ray emission spectroscopy are studied, and it is shown that the computed spectral band profiles are sensitive to the exchange-correlation functional used. The computed intensities of the spectral bands can be rationalised by considering the metal p orbital character of the valence molecular orbitals. To compute X-ray emission spectra with the correct energy scale allowing a direct comparison with experiment requires the relaxation of the core-ionised state to be included and the use of specifically designed functionals with increased amounts of Hartree-Fock exchange in conjunction with high quality basis sets. A range-corrected functional with increased Hartree-Fock exchange in the short range provides transition energies close to experiment and spectral band profiles that have a similar accuracy to those from standard functionals.

Dependence of Excited State Potential Energy Surfaces on the Spatial Overlap of the Kohn-Sham Orbitals and the Amount of Nonlocal Hartree-Fock Exchange in Time-Dependent Density Functional Theory.

PubMed

Plötner, Jürgen; Tozer, David J; Dreuw, Andreas

2010-08-10

Time-dependent density functional theory (TDDFT) with standard GGA or hybrid exchange-correlation functionals is not capable of describing the potential energy surface of the S1 state of Pigment Yellow 101 correctly; an additional local minimum is observed at a twisted geometry with substantial charge transfer (CT) character. To investigate the influence of nonlocal exact orbital (Hartree-Fock) exchange on the shape of the potential energy surface of the S1 state in detail, it has been computed along the twisting coordinate employing the standard BP86, B3LYP, and BHLYP xc-functionals as well as the long-range separated (LRS) exchange-correlation (xc)-functionals LC-BOP, ωB97X, ωPBE, and CAM-B3LYP and compared to RI-CC2 benchmark results. Additionally, a recently suggested Λ-parameter has been employed that measures the amount of CT in an excited state by calculating the spatial overlap of the occupied and virtual molecular orbitals involved in the transition. Here, the error in the calculated S1 potential energy curves at BP86, B3LYP, and BHLYP can be clearly related to the Λ-parameter, i.e., to the extent of charge transfer. Additionally, it is demonstrated that the CT problem is largely alleviated when the BHLYP xc-functional is employed, although it still exhibits a weak tendency to underestimate the energy of CT states. The situation improves drastically when LRS-functionals are employed within TDDFT excited state calculations. All tested LRS-functionals give qualitatively the correct potential energy curves of the energetically lowest excited states of P. Y. 101 along the twisting coordinate. While LC-BOP and ωB97X overcorrect the CT problem and now tend to give too large excitation energies compared to other non-CT states, ωPBE and CAM-B3LYP are in excellent agreement with the RI-CC2 results, with respect to both the correct shape of the potential energy curve as well as the absolute values of the calculated excitation energies.

Performance of an Optimally Tuned Range-Separated Hybrid Functional for 0-0 Electronic Excitation Energies.

PubMed

Jacquemin, Denis; Moore, Barry; Planchat, Aurélien; Adamo, Carlo; Autschbach, Jochen

2014-04-08

Using a set of 40 conjugated molecules, we assess the performance of an "optimally tuned" range-separated hybrid functional in reproducing the experimental 0-0 energies. The selected protocol accounts for the impact of solvation using a corrected linear-response continuum approach and vibrational corrections through calculations of the zero-point energies of both ground and excited-states and provides basis set converged data thanks to the systematic use of diffuse-containing atomic basis sets at all computational steps. It turns out that an optimally tuned long-range corrected hybrid form of the Perdew-Burke-Ernzerhof functional, LC-PBE*, delivers both the smallest mean absolute error (0.20 eV) and standard deviation (0.15 eV) of all tested approaches, while the obtained correlation (0.93) is large but remains slightly smaller than its M06-2X counterpart (0.95). In addition, the efficiency of two other recently developed exchange-correlation functionals, namely SOGGA11-X and ωB97X-D, has been determined in order to allow more complete comparisons with previously published data.

Frequency and Wavevector Dependence of the Atomic Level Stress-Stress Correlation Function in a Model Supercooled Liquid

NASA Astrophysics Data System (ADS)

Levashov, Valentin A.; Morris, James R.; Egami, Takeshi

2012-02-01

Temporal and spatial correlations among the local atomic level shear stresses were studied for a model liquid iron by molecular dynamics simulation [PRL 106,115703]. Integration over time and space of the shear stress correlation function F(r,t) yields viscosity via Green-Kubo relation. The stress correlation function in time and space F(r,t) was Fourier transformed to study the dependence on frequency, E, and wave vector, Q. The results, F(Q,E), showed damped shear stress waves propagating in the liquid for small Q at high and low temperatures. We also observed additional diffuse feature that appears as temperature is reduced below crossover temperature of potential energy landscape at relatively low frequencies at small Q. We suggest that this additional feature might be related to dynamic heterogeneity and boson peaks. We also discuss a relation between the time-scale of the stress-stress correlation function and the alpha-relaxation time of the intermediate self-scattering function S(Q,E).

High-order Path Integral Monte Carlo methods for solving strongly correlated fermion problems

NASA Astrophysics Data System (ADS)

Chin, Siu A.

2015-03-01

In solving for the ground state of a strongly correlated many-fermion system, the conventional second-order Path Integral Monte Carlo method is plagued with the sign problem. This is due to the large number of anti-symmetric free fermion propagators that are needed to extract the square of the ground state wave function at large imaginary time. In this work, I show that optimized fourth-order Path Integral Monte Carlo methods, which uses no more than 5 free-fermion propagators, in conjunction with the use of the Hamiltonian energy estimator, can yield accurate ground state energies for quantum dots with up to 20 polarized electrons. The correlations are directly built-in and no explicit wave functions are needed. This work is supported by the Qatar National Research Fund NPRP GRANT #5-674-1-114.

Exploring excited eigenstates of many-body systems using the functional renormalization group

NASA Astrophysics Data System (ADS)

Klöckner, Christian; Kennes, Dante Marvin; Karrasch, Christoph

2018-05-01

We introduce approximate, functional renormalization group based schemes to obtain correlation functions in pure excited eigenstates of large fermionic many-body systems at arbitrary energies. The algorithms are thoroughly benchmarked and their strengths and shortcomings are documented using a one-dimensional interacting tight-binding chain as a prototypical testbed. We study two "toy applications" from the world of Luttinger liquid physics: the survival of power laws in lowly excited states as well as the spectral function of high-energy "block" excitations, which feature several single-particle Fermi edges.

Nuclear medium effects in structure functions of nucleon at moderate Q2

NASA Astrophysics Data System (ADS)

Haider, H.; Zaidi, F.; Sajjad Athar, M.; Singh, S. K.; Ruiz Simo, I.

2015-11-01

Recent experiments performed on inclusive electron scattering from nuclear targets have measured the nucleon electromagnetic structure functions F1 (x ,Q2), F2 (x ,Q2) and FL (x ,Q2) in 12C, 27Al, 56Fe and 64Cu nuclei. The measurements have been done in the energy region of 1 GeV2

Nonperturbative Series Expansion of Green's Functions: The Anatomy of Resonant Inelastic X-Ray Scattering in the Doped Hubbard Model

NASA Astrophysics Data System (ADS)

Lu, Yi; Haverkort, Maurits W.

2017-12-01

We present a nonperturbative, divergence-free series expansion of Green's functions using effective operators. The method is especially suited for computing correlators of complex operators as a series of correlation functions of simpler forms. We apply the method to study low-energy excitations in resonant inelastic x-ray scattering (RIXS) in doped one- and two-dimensional single-band Hubbard models. The RIXS operator is expanded into polynomials of spin, density, and current operators weighted by fundamental x-ray spectral functions. These operators couple to different polarization channels resulting in simple selection rules. The incident photon energy dependent coefficients help to pinpoint main RIXS contributions from different degrees of freedom. We show in particular that, with parameters pertaining to cuprate superconductors, local spin excitation dominates the RIXS spectral weight over a wide doping range in the cross-polarization channel.

Variational method for calculating the binding energy of the base state of an impurity D- centered on a quantum dot of GaAs-Ga1-xAlxAs

NASA Astrophysics Data System (ADS)

Durán-Flórez, F.; Caicedo, L. C.; Gonzalez, J. E.

2018-04-01

In quantum mechanics it is very difficult to obtain exact solutions, therefore, it is necessary to resort to tools and methods that facilitate the calculations of the solutions of these systems, one of these methods is the variational method that consists in proposing a wave function that depend on several parameters that are adjusted to get close to the exact solution. Authors in the past have performed calculations applying this method using exponential and Gaussian orbital functions with linear and quadratic correlation factors. In this paper, a Gaussian function with a linear correlation factor is proposed, for the calculation of the binding energy of an impurity D ‑ centered on a quantum dot of radius r, the Gaussian function is dependent on the radius of the quantum dot.

Microscopic theoretical study of frequency dependent dielectric constant of heavy fermion systems

NASA Astrophysics Data System (ADS)

Shadangi, Keshab Chandra; Rout, G. C.

2017-05-01

The dielectric polarization and the dielectric constant plays a vital role in the deciding the properties of the Heavy Fermion Systems. In the present communication we consider the periodic Anderson's Model which consists of conduction electron kinetic energy, localized f-electron kinetic energy and the hybridization between the conduction and localized electrons, besides the Coulomb correlation energy. We calculate dielectric polarization which involves two particle Green's functions which are calculated by using Zubarev's Green's function technique. Using the equations of motion of the fermion electron operators. Finally, the temperature and frequency dependent dielectric constant is calculated from the dielectric polarization function. The charge susceptibility and dielectric constant are computed numerically for different physical parameters like the position (Ef) of the f-electron level with respect to fermi level, the strength of the hybridization (V) between the conduction and localized f-electrons, Coulomb correlation potential temperature and optical phonon wave vector (q). The results will be discussed in a reference to the experimental observations of the dielectric constants.

A density functional for core-valence correlation energy

NASA Astrophysics Data System (ADS)

Ranasinghe, Duminda S.; Frisch, Michael J.; Petersson, George A.

2015-12-01

A density functional, ɛCV-DFT(ρc, ρv), describing the core-valence correlation energy has been constructed as a linear combination of ɛLY Pcorr(ρc), ɛV WN5corr(ρc, ρv), ɛPBEcorr(ρc, ρv), ɛSlaterex(ρc, ρv), ɛHCTHex(ρc, ρv), ɛHFex(ρc, ρv), and F CV -DFT (" separators=" N i , Z i ) , a function of the nuclear charges. This functional, with 6 adjustable parameters, reproduces (±0.27 kcal/mol rms error) a benchmark set of 194 chemical energy changes including 9 electron affinities, 18 ionization potentials, and 167 total atomization energies covering the first- and second-rows of the periodic table. This is almost twice the rms error (±0.16 kcal/mol) obtained with CCSD(T)/MTsmall calculations, but less than half the rms error (±0.65 kcal/mol) obtained with MP2/GTlargeXP calculations, and somewhat smaller than the rms error (±0.39 kcal/mol) obtained with CCSD/MTsmall calculations. The largest positive and negative errors from ɛCV-DFT(ρc, ρv) were 0.88 and -0.75 kcal/mol with the set of 194 core-valence energy changes ranging from +3.76 kcal/mol for the total atomization energy of propyne to -9.05 kcal/mol for the double ionization of Mg. Evaluation of the ɛCV-DFT(ρc, ρv) functional requires less time than a single SCF iteration, and the accuracy is adequate for any model chemistry based on the CCSD(T) level of theory.

Work-function calculations for a symmetrical total-charge-density profile at the metallic surface

NASA Astrophysics Data System (ADS)

Wojciechowski, K. F.; Sobańska-Nowotnik, M.

1983-07-01

It is shown that, if the total-charge-density profile nT(x) at the surface of jellium satisfies the Budd-Vannimenus constraint and also is a symmetrical function of x, relative to the ordinate axis, then the work-function variation versus the Wigner-Seitz radius rs does not depend on the form of nT(x). Also the simple linear-density profile is used to calculate the work function by application of the variational principle for the energy, including the first and second density-gradient corrections to the kinetic energy and the first gradient correction to the exchange and correlation energy. The results for the work function are in good agreement with the polycrystalline values for low-density metals.

Semiclassical neutral atom as a reference system in density functional theory.

PubMed

Constantin, Lucian A; Fabiano, E; Laricchia, S; Della Sala, F

2011-05-06

We use the asymptotic expansions of the semiclassical neutral atom as a reference system in density functional theory to construct accurate generalized gradient approximations (GGAs) for the exchange-correlation and kinetic energies without any empiricism. These asymptotic functionals are among the most accurate GGAs for molecular systems, perform well for solid state, and overcome current GGA state of the art in frozen density embedding calculations. Our results also provide evidence for the conjointness conjecture between exchange and kinetic energies of atomic systems.

The QTP family of consistent functionals and potentials in Kohn-Sham density functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jin, Yifan; Bartlett, Rodney J., E-mail: bartlett@qtp.ufl.edu

This manuscript presents the second, consistent density functional in the QTP (Quantum Theory Project) family, that is, the CAM-QTP(01). It is a new range-separated exchange-correlation functional in which the non-local exchange contribution is 100% at large separation. It follows the same basic principles of this family that the Kohn-Sham eigenvalues of the occupied orbitals approximately equal the vertical ionization energies, which is not fulfilled by most of the traditional density functional methods. This new CAM-QTP(01) functional significantly improves the accuracy of the vertical excitation energies especially for the Rydberg states in the test set. It also reproduces many other propertiesmore » such as geometries, reaction barrier heights, and atomization energies.« less

Methods for converging correlation energies within the dielectric matrix formalism

NASA Astrophysics Data System (ADS)

Dixit, Anant; Claudot, Julien; Gould, Tim; Lebègue, Sébastien; Rocca, Dario

2018-03-01

Within the dielectric matrix formalism, the random-phase approximation (RPA) and analogous methods that include exchange effects are promising approaches to overcome some of the limitations of traditional density functional theory approximations. The RPA-type methods however have a significantly higher computational cost, and, similarly to correlated quantum-chemical methods, are characterized by a slow basis set convergence. In this work we analyzed two different schemes to converge the correlation energy, one based on a more traditional complete basis set extrapolation and one that converges energy differences by accounting for the size-consistency property. These two approaches have been systematically tested on the A24 test set, for six points on the potential-energy surface of the methane-formaldehyde complex, and for reaction energies involving the breaking and formation of covalent bonds. While both methods converge to similar results at similar rates, the computation of size-consistent energy differences has the advantage of not relying on the choice of a specific extrapolation model.

Exact exchange and Wilson-Levy correlation: a pragmatic device for studying complex weakly-bonded systems.

PubMed

Walsh, T R

2005-02-07

The Wilson-Levy (WL) correlation functional is used together with Hartree-Fock (HF) theory to evaluate interaction energies at intermediate separations (i.e. around equilibrium separation) for several weakly-bonded systems. The HF+WL approach reproduces binding trends for all complexes studied: selected rare-gas dimers, isomers of the methane dimer, benzene dimer and naphthalene dimer, and base-pair stacking structures for pyrimidine, cytosine, uracil and guanine dimers. These HF+WL data are contrasted against results obtained from some popular functionals (including B3LYP and PBE), as well as two newly-developed functionals, X3LYP and xPBE. The utility of HF+WL, with reference to exact-exchange (EXX) density-functional theory, is discussed in terms of a suggested EXXWL exchange-correlation functional.

Theoretical dissociation energies for the alkali and alkaline-earth monofluorides and monochlorides

NASA Technical Reports Server (NTRS)

Langhoff, S. R.; Bauschlicher, C. W., Jr.; Partridge, H.

1986-01-01

Spectroscopic parameters are accurately determined for the alkali and alkaline-earth monofluorides and monochlorides by means of ab initio self-consistent field and correlated wave function calculations. Numerical Hartree-Fock calculations are performed on selected systems to ensure that the extended Slater basis sets employed are near the Hartree-Fock limit. Since the bonding is predominantly electrostatic in origin, a strong correlation exists between the dissociation energy (to ions) and the spectroscopic parameter r(e). By dissociating to the ionic limits, most of the differential correlation effects can be embedded in the accurate experimental electron affinities and ionization potentials.

The derivative discontinuity of the exchange-correlation functional.

PubMed

Mori-Sánchez, Paula; Cohen, Aron J

2014-07-28

The derivative discontinuity is a key concept in electronic structure theory in general and density functional theory in particular. The electronic energy of a quantum system exhibits derivative discontinuities with respect to different degrees of freedom that are a consequence of the integer nature of electrons. The classical understanding refers to the derivative discontinuity of the total energy as a function of the total number of electrons (N), but it can also manifest at constant N. Examples are shown in models including several hydrogen systems with varying numbers of electrons or nuclear charge (Z), as well as the 1-dimensional Hubbard model (1DHM). Two sides of the problem are investigated: first, the failure of currently used approximate exchange-correlation functionals in DFT and, second, the importance of the derivative discontinuity in the exact electronic structure of molecules, as revealed by full configuration interaction (FCI). Currently, all approximate functionals, including hybrids, miss the derivative discontinuity, leading to basic errors that can be seen in many ways: from the complete failure to give the total energy of H2 and H2(+), to the missing gap in Mott insulators such as stretched H2 and the thermodynamic limit of the 1DHM, or a qualitatively incorrect density in the HZ molecule with two electrons and incorrect electron transfer processes. Description of the exact particle behaviour of electrons is emphasised, which is key to many important physical processes in real systems, especially those involving electron transfer, and offers a challenge for the development of new exchange-correlation functionals.

Energy Weighted Angular Correlations Between Hadrons Produced in Electron-Positron Annihilation.

NASA Astrophysics Data System (ADS)

Strharsky, Roger Joseph

Electron-positron annihilation at large center of mass energy produces many hadronic particles. Experimentalists then measure the energies of these particles in calorimeters. This study investigated correlations between the angular locations of one or two such calorimeters and the angular orientation of the electron beam in the laboratory frame of reference. The calculation of these correlations includes weighting by the fraction of the total center of mass energy which the calorimeter measures. Starting with the assumption that the reaction proceeeds through the intermediate production of a single quark/anti-quark pair, a simple statistical model was developed to provide a phenomenological description of the distribution of final state hadrons. The model distributions were then used to calculate the one- and two-calorimeter correlation functions. Results of these calculations were compared with available data and several predictions were made for those quantities which had not yet been measured. Failure of the model to reproduce all of the data was discussed in terms of quantum chromodynamics, a fundamental theory which includes quark interactions.

Adsorption energies of benzene on close packed transition metal surfaces using the random phase approximation

NASA Astrophysics Data System (ADS)

Garrido Torres, José A.; Ramberger, Benjamin; Früchtl, Herbert A.; Schaub, Renald; Kresse, Georg

2017-11-01

The adsorption energy of benzene on various metal substrates is predicted using the random phase approximation (RPA) for the correlation energy. Agreement with available experimental data is systematically better than 10% for both coinage and reactive metals. The results are also compared with more approximate methods, including van der Waals density functional theory (DFT), as well as dispersion-corrected DFT functionals. Although dispersion-corrected DFT can yield accurate results, for instance, on coinage metals, the adsorption energies are clearly overestimated on more reactive transition metals. Furthermore, coverage dependent adsorption energies are well described by the RPA. This shows that for the description of aromatic molecules on metal surfaces further improvements in density functionals are necessary, or more involved many-body methods such as the RPA are required.

Cross-section fluctuations in chaotic scattering systems.

PubMed

Ericson, Torleif E O; Dietz, Barbara; Richter, Achim

2016-10-01

Exact analytical expressions for the cross-section correlation functions of chaotic scattering systems have hitherto been derived only under special conditions. The objective of the present article is to provide expressions that are applicable beyond these restrictions. The derivation is based on a statistical model of Breit-Wigner type for chaotic scattering amplitudes which has been shown to describe the exact analytical results for the scattering (S)-matrix correlation functions accurately. Our results are given in the energy and in the time representations and apply in the whole range from isolated to overlapping resonances. The S-matrix contributions to the cross-section correlations are obtained in terms of explicit irreducible and reducible correlation functions. Consequently, the model can be used for a detailed exploration of the key features of the cross-section correlations and the underlying physical mechanisms. In the region of isolated resonances, the cross-section correlations contain a dominant contribution from the self-correlation term. For narrow states the self-correlations originate predominantly from widely spaced states with exceptionally large partial width. In the asymptotic region of well-overlapping resonances, the cross-section autocorrelation functions are given in terms of the S-matrix autocorrelation functions. For inelastic correlations, in particular, the Ericson fluctuations rapidly dominate in that region. Agreement with known analytical and experimental results is excellent.

The use of least squares methods in functional optimization of energy use prediction models

NASA Astrophysics Data System (ADS)

Bourisli, Raed I.; Al-Shammeri, Basma S.; AlAnzi, Adnan A.

2012-06-01

The least squares method (LSM) is used to optimize the coefficients of a closed-form correlation that predicts the annual energy use of buildings based on key envelope design and thermal parameters. Specifically, annual energy use is related to a number parameters like the overall heat transfer coefficients of the wall, roof and glazing, glazing percentage, and building surface area. The building used as a case study is a previously energy-audited mosque in a suburb of Kuwait City, Kuwait. Energy audit results are used to fine-tune the base case mosque model in the VisualDOE{trade mark, serif} software. Subsequently, 1625 different cases of mosques with varying parameters were developed and simulated in order to provide the training data sets for the LSM optimizer. Coefficients of the proposed correlation are then optimized using multivariate least squares analysis. The objective is to minimize the difference between the correlation-predicted results and the VisualDOE-simulation results. It was found that the resulting correlation is able to come up with coefficients for the proposed correlation that reduce the difference between the simulated and predicted results to about 0.81%. In terms of the effects of the various parameters, the newly-defined weighted surface area parameter was found to have the greatest effect on the normalized annual energy use. Insulating the roofs and walls also had a major effect on the building energy use. The proposed correlation and methodology can be used during preliminary design stages to inexpensively assess the impacts of various design variables on the expected energy use. On the other hand, the method can also be used by municipality officials and planners as a tool for recommending energy conservation measures and fine-tuning energy codes.

Early Postnatal Cardiomyocyte Proliferation Requires High Oxidative Energy Metabolism.

PubMed

de Carvalho, Ana Elisa Teófilo Saturi; Bassaneze, Vinícius; Forni, Maria Fernanda; Keusseyan, Aline Alfonso; Kowaltowski, Alicia Juliana; Krieger, José Eduardo

2017-11-13

Cardiac energy metabolism must cope with early postnatal changes in tissue oxygen tensions, hemodynamics, and cell proliferation to sustain development. Here, we tested the hypothesis that proliferating neonatal cardiomyocytes are dependent on high oxidative energy metabolism. We show that energy-related gene expression does not correlate with functional oxidative measurements in the developing heart. Gene expression analysis suggests a gradual overall upregulation of oxidative-related genes and pathways, whereas functional assessment in both cardiac tissue and cultured cardiomyocytes indicated that oxidative metabolism decreases between the first and seventh days after birth. Cardiomyocyte extracellular flux analysis indicated that the decrease in oxidative metabolism between the first and seventh days after birth was mostly related to lower rates of ATP-linked mitochondrial respiration, suggesting that overall energetic demands decrease during this period. In parallel, the proliferation rate was higher for early cardiomyocytes. Furthermore, in vitro nonlethal chemical inhibition of mitochondrial respiration reduced the proliferative capacity of early cardiomyocytes, indicating a high energy demand to sustain cardiomyocyte proliferation. Altogether, we provide evidence that early postnatal cardiomyocyte proliferative capacity correlates with high oxidative energy metabolism. The energy requirement decreases as the proliferation ceases in the following days, and both oxidative-dependent metabolism and anaerobic glycolysis subside.

Cyber-Physical Correlations for Infrastructure Resilience: A Game-Theoretic Approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rao, Nageswara S; He, Fei; Ma, Chris Y. T.

In several critical infrastructures, the cyber and physical parts are correlated so that disruptions to one affect the other and hence the whole system. These correlations may be exploited to strategically launch components attacks, and hence must be accounted for ensuring the infrastructure resilience, specified by its survival probability. We characterize the cyber-physical interactions at two levels: (i) the failure correlation function specifies the conditional survival probability of cyber sub-infrastructure given the physical sub-infrastructure as a function of their marginal probabilities, and (ii) the individual survival probabilities of both sub-infrastructures are characterized by first-order differential conditions. We formulate a resiliencemore » problem for infrastructures composed of discrete components as a game between the provider and attacker, wherein their utility functions consist of an infrastructure survival probability term and a cost term expressed in terms of the number of components attacked and reinforced. We derive Nash Equilibrium conditions and sensitivity functions that highlight the dependence of infrastructure resilience on the cost term, correlation function and sub-infrastructure survival probabilities. These results generalize earlier ones based on linear failure correlation functions and independent component failures. We apply the results to models of cloud computing infrastructures and energy grids.« less

Calculating the n-point correlation function with general and efficient python code

NASA Astrophysics Data System (ADS)

Genier, Fred; Bellis, Matthew

2018-01-01

There are multiple approaches to understanding the evolution of large-scale structure in our universe and with it the role of baryonic matter, dark matter, and dark energy at different points in history. One approach is to calculate the n-point correlation function estimator for galaxy distributions, sometimes choosing a particular type of galaxy, such as luminous red galaxies. The standard way to calculate these estimators is with pair counts (for the 2-point correlation function) and with triplet counts (for the 3-point correlation function). These are O(n2) and O(n3) problems, respectively and with the number of galaxies that will be characterized in future surveys, having efficient and general code will be of increasing importance. Here we show a proof-of-principle approach to the 2-point correlation function that relies on pre-calculating galaxy locations in coarse “voxels”, thereby reducing the total number of necessary calculations. The code is written in python, making it easily accessible and extensible and is open-sourced to the community. Basic results and performance tests using SDSS/BOSS data will be shown and we discuss the application of this approach to the 3-point correlation function.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Azadi, Sam, E-mail: s.azadi@ucl.ac.uk; Cohen, R. E.

We report an accurate study of interactions between benzene molecules using variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods. We compare these results with density functional theory using different van der Waals functionals. In our quantum Monte Carlo (QMC) calculations, we use accurate correlated trial wave functions including three-body Jastrow factors and backflow transformations. We consider two benzene molecules in the parallel displaced geometry, and find that by highly optimizing the wave function and introducing more dynamical correlation into the wave function, we compute the weak chemical binding energy between aromatic rings accurately. We find optimalmore » VMC and DMC binding energies of −2.3(4) and −2.7(3) kcal/mol, respectively. The best estimate of the coupled-cluster theory through perturbative triplets/complete basis set limit is −2.65(2) kcal/mol [Miliordos et al., J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate that QMC methods give chemical accuracy for weakly bound van der Waals molecular interactions, comparable to results from the best quantum chemistry methods.« less

Accurate Semilocal Density Functional for Condensed-Matter Physics and Quantum Chemistry.

PubMed

Tao, Jianmin; Mo, Yuxiang

2016-08-12

Most density functionals have been developed by imposing the known exact constraints on the exchange-correlation energy, or by a fit to a set of properties of selected systems, or by both. However, accurate modeling of the conventional exchange hole presents a great challenge, due to the delocalization of the hole. Making use of the property that the hole can be made localized under a general coordinate transformation, here we derive an exchange hole from the density matrix expansion, while the correlation part is obtained by imposing the low-density limit constraint. From the hole, a semilocal exchange-correlation functional is calculated. Our comprehensive test shows that this functional can achieve remarkable accuracy for diverse properties of molecules, solids, and solid surfaces, substantially improving upon the nonempirical functionals proposed in recent years. Accurate semilocal functionals based on their associated holes are physically appealing and practically useful for developing nonlocal functionals.

Hypoxanthine is a checkpoint stress metabolite in colonic epithelial energy modulation and barrier function.

PubMed

Lee, J Scott; Wang, Ruth X; Alexeev, Erica E; Lanis, Jordi M; Battista, Kayla D; Glover, Louise E; Colgan, Sean P

2018-04-20

Intestinal epithelial cells form a selectively permeable barrier to protect colon tissues from luminal microbiota and antigens and to mediate nutrient, fluid, and waste flux in the intestinal tract. Dysregulation of the epithelial cell barrier coincides with profound shifts in metabolic energy, especially in the colon, which exists in an energetically depleting state of physiological hypoxia. However, studies that systematically examine energy flux and adenylate metabolism during intestinal epithelial barrier development and restoration after disruption are lacking. Here, to delineate barrier-related energy flux, we developed an HPLC-based profiling method to track changes in energy flux and adenylate metabolites during barrier development and restoration. Cultured epithelia exhibited pooling of phosphocreatine and maintained ATP during barrier development. EDTA-induced epithelial barrier disruption revealed that hypoxanthine levels correlated with barrier resistance. Further studies uncovered that hypoxanthine supplementation improves barrier function and wound healing and that hypoxanthine appears to do so by increasing intracellular ATP, which improved cytoskeletal G- to F-actin polymerization. Hypoxanthine supplementation increased the adenylate energy charge in the murine colon, indicating potential to regulate adenylate energy charge-mediated metabolism in intestinal epithelial cells. Moreover, experiments in a murine colitis model disclosed that hypoxanthine loss during active inflammation correlates with markers of disease severity. In summary, our results indicate that hypoxanthine modulates energy metabolism in intestinal epithelial cells and is critical for intestinal barrier function. © 2018 by The American Society for Biochemistry and Molecular Biology, Inc.

A density functional theory study of the correlation between analyte basicity, ZnPc adsorption strength, and sensor response.

PubMed

Tran, N L; Bohrer, F I; Trogler, W C; Kummel, A C

2009-05-28

Density functional theory (DFT) simulations were used to determine the binding strength of 12 electron-donating analytes to the zinc metal center of a zinc phthalocyanine molecule (ZnPc monomer). The analyte binding strengths were compared to the analytes' enthalpies of complex formation with boron trifluoride (BF(3)), which is a direct measure of their electron donating ability or Lewis basicity. With the exception of the most basic analyte investigated, the ZnPc binding energies were found to correlate linearly with analyte basicities. Based on natural population analysis calculations, analyte complexation to the Zn metal of the ZnPc monomer resulted in limited charge transfer from the analyte to the ZnPc molecule, which increased with analyte-ZnPc binding energy. The experimental analyte sensitivities from chemiresistor ZnPc sensor data were proportional to an exponential of the binding energies from DFT calculations consistent with sensitivity being proportional to analyte coverage and binding strength. The good correlation observed suggests DFT is a reliable method for the prediction of chemiresistor metallophthalocyanine binding strengths and response sensitivities.

Nonempirical Semilocal Free-Energy Density Functional for Matter under Extreme Conditions

DOE PAGES

Karasiev, Valentin V.; Dufty, James W.; Trickey, S. B.

2018-02-14

The potential for density functional calculations to predict the properties of matter under extreme conditions depends crucially upon having a non-empirical approximate free energy functional valid over a wide range of state conditions. Unlike the ground-state case, no such free-energy exchange- correlation (XC) functional exists. We remedy that with systematic construction of a generalized gradient approximation XC free-energy functional based on rigorous constraints, including the free energy gradient expansion. The new functional provides the correct temperature dependence in the slowly varying regime and the correct zero-T, high-T, and homogeneous electron gas limits. Application in Kohn-Sham calculations for hot electrons inmore » a static fcc Aluminum lattice demon- strates the combined magnitude of thermal and gradient effects handled by this functional. Its accuracy in the increasingly important warm dense matter regime is attested by excellent agreement of the calculated deuterium equation of state with reference path integral Monte Carlo results at intermediate and elevated temperatures and by low density Al calculations over a wide T range.« less

Nonempirical Semilocal Free-Energy Density Functional for Matter under Extreme Conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Karasiev, Valentin V.; Dufty, James W.; Trickey, S. B.

The potential for density functional calculations to predict the properties of matter under extreme conditions depends crucially upon having a non-empirical approximate free energy functional valid over a wide range of state conditions. Unlike the ground-state case, no such free-energy exchange- correlation (XC) functional exists. We remedy that with systematic construction of a generalized gradient approximation XC free-energy functional based on rigorous constraints, including the free energy gradient expansion. The new functional provides the correct temperature dependence in the slowly varying regime and the correct zero-T, high-T, and homogeneous electron gas limits. Application in Kohn-Sham calculations for hot electrons inmore » a static fcc Aluminum lattice demon- strates the combined magnitude of thermal and gradient effects handled by this functional. Its accuracy in the increasingly important warm dense matter regime is attested by excellent agreement of the calculated deuterium equation of state with reference path integral Monte Carlo results at intermediate and elevated temperatures and by low density Al calculations over a wide T range.« less

Nonseparable exchange–correlation functional for molecules, including homogeneous catalysis involving transition metals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu, Haoyu S.; Zhang, Wenjing; Verma, Pragya

2015-01-01

The goal of this work is to develop a gradient approximation to the exchange–correlation functional of Kohn–Sham density functional theory for treating molecular problems with a special emphasis on the prediction of quantities important for homogeneous catalysis and other molecular energetics. Our training and validation of exchange–correlation functionals is organized in terms of databases and subdatabases. The key properties required for homogeneous catalysis are main group bond energies (database MGBE137), transition metal bond energies (database TMBE32), reaction barrier heights (database BH76), and molecular structures (database MS10). We also consider 26 other databases, most of which are subdatabases of a newlymore » extended broad database called Database 2015, which is presented in the present article and in its ESI. Based on the mathematical form of a nonseparable gradient approximation (NGA), as first employed in the N12 functional, we design a new functional by using Database 2015 and by adding smoothness constraints to the optimization of the functional. The resulting functional is called the gradient approximation for molecules, or GAM. The GAM functional gives better results for MGBE137, TMBE32, and BH76 than any available generalized gradient approximation (GGA) or than N12. The GAM functional also gives reasonable results for MS10 with an MUE of 0.018 Å. The GAM functional provides good results both within the training sets and outside the training sets. The convergence tests and the smooth curves of exchange–correlation enhancement factor as a function of the reduced density gradient show that the GAM functional is a smooth functional that should not lead to extra expense or instability in optimizations. NGAs, like GGAs, have the advantage over meta-GGAs and hybrid GGAs of respectively smaller grid-size requirements for integrations and lower costs for extended systems. These computational advantages combined with the relatively high accuracy for all the key properties needed for molecular catalysis make the GAM functional very promising for future applications.« less

Locv Calculations for Polarized Liquid 3He with the Spin-Dependent Correlation

NASA Astrophysics Data System (ADS)

Bordbar, G. H.; Karimi, M. J.

We have used the lowest order constrained variational (LOCV) method to calculate some ground-state properties of polarized liquid 3 He at zero temperature with the spin-dependent correlation function employing the Lennard-Jones and Aziz pair potentials. We have seen that the total energy of polarized liquid 3He increases with increasing polarization. For all polarizations, it is shown that the total energy in the spin-dependent case is lower than the spin-independent case. We have seen that the difference between the energies of spin-dependent and spin-independent cases decreases by increasing the polarization. We have shown that the main contribution of the potential energy comes from the spin-triplet state.

Nonempirical Semilocal Free-Energy Density Functional for Matter under Extreme Conditions.

PubMed

Karasiev, Valentin V; Dufty, James W; Trickey, S B

2018-02-16

Realizing the potential for predictive density functional calculations of matter under extreme conditions depends crucially upon having an exchange-correlation (XC) free-energy functional accurate over a wide range of state conditions. Unlike the ground-state case, no such functional exists. We remedy that with systematic construction of a generalized gradient approximation XC free-energy functional based on rigorous constraints, including the free-energy gradient expansion. The new functional provides the correct temperature dependence in the slowly varying regime and the correct zero-T, high-T, and homogeneous electron gas limits. Its accuracy in the warm dense matter regime is attested by excellent agreement of the calculated deuterium equation of state with reference path integral Monte Carlo results at intermediate and elevated T. Pressure shifts for hot electrons in compressed static fcc Al and for low-density Al demonstrate the combined magnitude of thermal and gradient effects handled well by this functional over a wide T range.

Nonempirical Semilocal Free-Energy Density Functional for Matter under Extreme Conditions

NASA Astrophysics Data System (ADS)

Karasiev, Valentin V.; Dufty, James W.; Trickey, S. B.

2018-02-01

Realizing the potential for predictive density functional calculations of matter under extreme conditions depends crucially upon having an exchange-correlation (X C ) free-energy functional accurate over a wide range of state conditions. Unlike the ground-state case, no such functional exists. We remedy that with systematic construction of a generalized gradient approximation X C free-energy functional based on rigorous constraints, including the free-energy gradient expansion. The new functional provides the correct temperature dependence in the slowly varying regime and the correct zero-T , high-T , and homogeneous electron gas limits. Its accuracy in the warm dense matter regime is attested by excellent agreement of the calculated deuterium equation of state with reference path integral Monte Carlo results at intermediate and elevated T . Pressure shifts for hot electrons in compressed static fcc Al and for low-density Al demonstrate the combined magnitude of thermal and gradient effects handled well by this functional over a wide T range.

Activation thermodynamics of virus adsorption to solids.

PubMed Central

Preston, D R; Farrah, S R

1988-01-01

The kinetics of bacteriophage MS2, T2, and f2 adsorption to powdered nitrocellulose and disrupted Seitz S1 filters at pH 7 were determined as a function of temperature. Data from these studies were combined with data produced in a previous study on MS2 adsorption to clay by Stagg et al. (Appl. Environ. Microbiol. 33:385-391, 1977). These workers studied the adsorption of MS2 to bentonite clay as a function of temperature. Data from both this previous study and the current one were used to calculate the thermodynamic parameters of virus adsorption. The results show that adsorption of bacteriophages to the solids tested is a physical process (energy of activation, less than 40 kcal [168 J]/mol) rather than a chemical process (energy of activation, greater than 40 kcal/mol). The free energy of activation showed a high negative correlation (r = -0.904, r2 = 0.817) with the percentage of virus adsorption to the solids tested. The energy of activation was highly negatively correlated with the percentage of virus adsorption to nitrocellulose and clay (r = -0.913, r2 = 0.834) but poorly correlated with the percentage of virus adsorption to disrupted Seitz S1 filters (r = -0.348, r2 = 0.121). In general, under conditions in which the percentage of virus adsorption was low, the energy of activation, the free energy of activation, and the entropy of activation were high. Increasing the percentage of virus adsorbed by changing the adsorbing conditions or changing the adsorbing solid decreased the energy of activation, the free energy of activation, and the entropy of activation. PMID:3214152

Uniform quantized electron gas

NASA Astrophysics Data System (ADS)

Høye, Johan S.; Lomba, Enrique

2016-10-01

In this work we study the correlation energy of the quantized electron gas of uniform density at temperature T  =  0. To do so we utilize methods from classical statistical mechanics. The basis for this is the Feynman path integral for the partition function of quantized systems. With this representation the quantum mechanical problem can be interpreted as, and is equivalent to, a classical polymer problem in four dimensions where the fourth dimension is imaginary time. Thus methods, results, and properties obtained in the statistical mechanics of classical fluids can be utilized. From this viewpoint we recover the well known RPA (random phase approximation). Then to improve it we modify the RPA by requiring the corresponding correlation function to be such that electrons with equal spins can not be on the same position. Numerical evaluations are compared with well known results of a standard parameterization of Monte Carlo correlation energies.

Convergence behavior of the random phase approximation renormalized correlation energy

NASA Astrophysics Data System (ADS)

Bates, Jefferson E.; Sensenig, Jonathon; Ruzsinszky, Adrienn

2017-05-01

Based on the random phase approximation (RPA), RPA renormalization [J. E. Bates and F. Furche, J. Chem. Phys. 139, 171103 (2013), 10.1063/1.4827254] is a robust many-body perturbation theory that works for molecules and materials because it does not diverge as the Kohn-Sham gap approaches zero. Additionally, RPA renormalization enables the simultaneous calculation of RPA and beyond-RPA correlation energies since the total correlation energy is the sum of a series of independent contributions. The first-order approximation (RPAr1) yields the dominant beyond-RPA contribution to the correlation energy for a given exchange-correlation kernel, but systematically underestimates the total beyond-RPA correction. For both the homogeneous electron gas model and real systems, we demonstrate numerically that RPA renormalization beyond first order converges monotonically to the infinite-order beyond-RPA correlation energy for several model exchange-correlation kernels and that the rate of convergence is principally determined by the choice of the kernel and spin polarization of the ground state. The monotonic convergence is rationalized from an analysis of the RPA renormalized correlation energy corrections, assuming the exchange-correlation kernel and response functions satisfy some reasonable conditions. For spin-unpolarized atoms, molecules, and bulk solids, we find that RPA renormalization is typically converged to 1 meV error or less by fourth order regardless of the band gap or dimensionality. Most spin-polarized systems converge at a slightly slower rate, with errors on the order of 10 meV at fourth order and typically requiring up to sixth order to reach 1 meV error or less. Slowest to converge, however, open-shell atoms present the most challenging case and require many higher orders to converge.

Development of Fast and Reliable Free-Energy Density Functional Methods for Simulations of Dense Plasmas from Cold- to Hot-Temperature Regimes

NASA Astrophysics Data System (ADS)

Karasiev, V. V.

2017-10-01

Free-energy density functional theory (DFT) is one of the standard tools in high-energy-density physics used to determine the fundamental properties of dense plasmas, especially in cold and warm regimes when quantum effects are essential. DFT is usually implemented via the orbital-dependent Kohn-Sham (KS) procedure. There are two challenges of conventional implementation: (1) KS computational cost becomes prohibitively expensive at high temperatures; and (2) ground-state exchange-correlation (XC) functionals do not take into account the XC thermal effects. This talk will address both challenges and report details of the formal development of new generalized gradient approximation (GGA) XC free-energy functional which bridges low-temperature (ground state) and high-temperature (plasma) limits. Recent progress on development of functionals for orbital-free DFT as a way to address the second challenge will also be discussed. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944.

Connection formulas for thermal density functional theory

DOE PAGES

Pribram-Jones, A.; Burke, K.

2016-05-23

We show that the adiabatic connection formula of ground-state density functional theory relates the correlation energy to a coupling-constant integral over a purely potential contribution, and is widely used to understand and improve approximations. The corresponding formula for thermal density functional theory is cast as an integral over temperatures instead, ranging upward from the system's physical temperature. We also show how to relate different correlation components to each other, either in terms of temperature or coupling-constant integrations. Lastly, we illustrate our results on the uniform electron gas.

Statistical correlations in an ideal gas of particles obeying fractional exclusion statistics.

PubMed

Pellegrino, F M D; Angilella, G G N; March, N H; Pucci, R

2007-12-01

After a brief discussion of the concepts of fractional exchange and fractional exclusion statistics, we report partly analytical and partly numerical results on thermodynamic properties of assemblies of particles obeying fractional exclusion statistics. The effect of dimensionality is one focal point, the ratio mu/k_(B)T of chemical potential to thermal energy being obtained numerically as a function of a scaled particle density. Pair correlation functions are also presented as a function of the statistical parameter, with Friedel oscillations developing close to the fermion limit, for sufficiently large density.

Unitary Fermi gas in a harmonic trap

NASA Astrophysics Data System (ADS)

Chang, S. Y.; Bertsch, G. F.

2007-08-01

We present an ab initio calculation of small numbers of trapped, strongly interacting fermions using the Green’s function Monte Carlo method. The ground-state energy, density profile, and pairing gap are calculated for particle numbers N=2 22 using the parameter-free “unitary” interaction. Trial wave functions are taken in the form of correlated pairs in a harmonic oscillator basis. We find that the lowest energies are obtained with a minimum explicit pair correlation beyond that needed to exploit the degeneracy of oscillator states. We find that the energies can be well fitted by the expression aTFETF+Δmod(N,2) where ETF is the Thomas-Fermi energy of a noninteracting gas in the trap and Δ is the pairing gap. There is no evidence of a shell correction energy in the systematics, but the density distributions show pronounced shell effects. We find the value Δ=0.7±0.2ω for the pairing gap. This is smaller than the value found for the uniform gas at a density corresponding to the central density of the trapped gas.

Probing dark energy with lensing magnification in photometric surveys.

PubMed

Schneider, Michael D

2014-02-14

I present an estimator for the angular cross correlation of two tracers of the cosmological large-scale structure that utilizes redshift information to isolate separate physical contributions. The estimator is derived by solving the Limber equation for a reweighting of the foreground tracer that nulls either clustering or lensing contributions to the cross correlation function. Applied to future photometric surveys, the estimator can enhance the measurement of gravitational lensing magnification effects to provide a competitive independent constraint on the dark energy equation of state.

Benchmarking the Performance of Exchange-Correlation Functionals for Predicting Two-Photon Absorption Strengths.

PubMed

Beerepoot, Maarten T P; Alam, Md Mehboob; Bednarska, Joanna; Bartkowiak, Wojciech; Ruud, Kenneth; Zaleśny, Robert

2018-06-15

The present work investigates the performance of exchange-correlation functionals in the prediction of two-photon absorption (2PA) strengths. For this purpose, we considered six common functionals used for studying 2PA processes and tested these on six organoboron chelates. The set consisted of two semilocal (PBE and BLYP), two hybrid (B3LYP and PBE0), and two range-separated (LC-BLYP and CAM-B3LYP) functionals. The RI-CC2 method was chosen as a reference level and was found to give results consistent with the experimental data that are available for three of the molecules considered. Of the six exchange-correlation functionals studied, only the range-separated functionals predict an ordering of the 2PA strengths that is consistent with experimental and RI-CC2 results. Even though the range-separated functionals predict correct relative trends, the absolute values for the 2PA strengths are underestimated by a factor of 2-6 for the molecules considered. An in-depth analysis, on the basis of the derived generalized few-state model expression for the 2PA strength for a coupled-cluster wave function, reveals that the problem with these functionals can be linked to underestimated excited-state dipole moments and, to a lesser extent, overestimated excitation energies. The semilocal and hybrid functionals exhibit less predictable errors and a variation in the 2PA strengths in disagreement with the reference results. The semilocal and hybrid functionals show smaller average errors than the range-separated functionals, but our analysis reveals that this is due to fortuitous error cancellation between excitation energies and the transition dipole moments. Our results constitute a warning against using currently available exchange-correlation functionals in the prediction of 2PA strengths and highlight the need for functionals that correctly describe the electron density of excited electronic states.

Density functional theory calculations of the water interactions with ZrO2 nanoparticles Y2O3 doped

NASA Astrophysics Data System (ADS)

Subhoni, Mekhrdod; Kholmurodov, Kholmirzo; Doroshkevich, Aleksandr; Asgerov, Elmar; Yamamoto, Tomoyuki; Lyubchyk, Andrei; Almasan, Valer; Madadzada, Afag

2018-03-01

Development of a new electricity generation techniques is one of the most relevant tasks, especially nowadays under conditions of extreme growth in energy consumption. The exothermic heterogeneous electrochemical energy conversion to the electric energy through interaction of the ZrO2 based nanopowder system with atmospheric moisture is one of the ways of electric energy obtaining. The questions of conversion into the electric form of the energy of water molecules adsorption in 3 mol% Y2O3 doped ZrO2 nanopowder systems were investigated using the density functional theory calculations. The density functional theory calculations has been realized as in the Kohn-Sham formulation, where the exchange-correlation potential is approximated by a functional of the electronic density. The electronic density, total energy and band structure calculations are carried out using the all-electron, full potential, linear augmented plane wave method of the electronic density and related approximations, i.e. the local density, the generalized gradient and their hybrid approximations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ko, L.F.

Calculations for the two-point correlation functions in the scaling limit for two statistical models are presented. In Part I, the Ising model with a linear defect is studied for T < T/sub c/ and T > T/sub c/. The transfer matrix method of Onsager and Kaufman is used. The energy-density correlation is given by functions related to the modified Bessel functions. The dispersion expansion for the spin-spin correlation functions are derived. The dominant behavior for large separations at T not equal to T/sub c/ is extracted. It is shown that these expansions lead to systems of Fredholm integral equations. Inmore » Part II, the electric correlation function of the eight-vertex model for T < T/sub c/ is studied. The eight vertex model decouples to two independent Ising models when the four spin coupling vanishes. To first order in the four-spin coupling, the electric correlation function is related to a three-point function of the Ising model. This relation is systematically investigated and the full dispersion expansion (to first order in four-spin coupling) is obtained. The results is a new kind of structure which, unlike those of many solvable models, is apparently not expressible in terms of linear integral equations.« less

Performance of Frozen Density Embedding for Modeling Hole Transfer Reactions.

PubMed

Ramos, Pablo; Papadakis, Markos; Pavanello, Michele

2015-06-18

We have carried out a thorough benchmark of the frozen density-embedding (FDE) method for calculating hole transfer couplings. We have considered 10 exchange-correlation functionals, 3 nonadditive kinetic energy functionals, and 3 basis sets. Overall, we conclude that with a 7% mean relative unsigned error, the PBE and PW91 functionals coupled with the PW91k nonadditive kinetic energy functional and a TZP basis set constitute the most stable and accurate levels of theory for hole transfer coupling calculations. The FDE-ET method is found to be an excellent tool for computing diabatic couplings for hole transfer reactions.

Reexamine structures and relative stability of medium-sized silicon clusters: Low-lying endohedral fullerene-like clusters Si 30-Si 38

NASA Astrophysics Data System (ADS)

Yoo, Soohaeng; Shao, Nan; Zeng, X. C.

2009-10-01

We report improved results of lowest-lying silicon clusters Si 30-Si 38. A large population of low-energy clusters are collected from previous searches by several research groups and the binding energies of these clusters are computed using density-functional theory (DFT) methods. Best candidates (isomers with high binding energies) are identified from the screening calculations. Additional constrained search is then performed for the best candidates using the basin-hopping method combined with DFT geometry optimization. The obtained low-lying clusters are classified according to binding energies computed using either the Perdew-Burke-Ernzerhof (PBE) functional or the Becke exchange and Lee-Yang-Parr correlation (BLYP) functional. We propose to rank low-lying clusters according to the mean PBE/BLYP binding energies in view that the PBE functional tends to give greater binding energies for more compact clusters whereas the BLYP functional tends to give greater binding energies for less compact clusters or clusters composed of small-sized magic-number clusters. Except for Si 30, the new search confirms again that medium-size silicon clusters Si 31-Si 38 constructed with proper fullerene cage motifs are most promising to be the lowest-energy structures.

Measurement of long-range near-side two-particle angular correlations in pp collisions at $$\\sqrt{s}$$ = 13 TeV

DOE PAGES

Khachatryan, Vardan

2016-04-27

Our results on two-particle angular correlations for charged particles produced in pp collisions at a center-of-mass energy of 13 TeV are presented. The data were taken with the CMS detector at the LHC and correspond to an integrated luminosity of about 270 nb -1. The correlations are studied over a broad range of pseudorapidity (|η| < 2.4) and over the full azimuth (Φ) as a function of charged particle multiplicity and transverse momentum (p T). In high-multiplicity events, a long-range (|Δη| > 2.0), near-side (ΔΦ≈ 0) structure emerges in the two-particle Dh–Df correlation functions. The magnitude of the correlation exhibitsmore » a pronounced maximum in the range 1.0 < p T < 2.0 GeV/c and an approximately linear increase with the charged particle multiplicity. The overall correlation strength at √s = 13 TeV is similar to that found in earlier pp data at √s = 7 TeV, but is measured up to much higher multiplicity values. We observed long-range correlations are compared to those seen in pp, pPb, and PbPb collisions at lower collision energies.« less

FAST TRACK COMMUNICATION: Freezing and extreme-value statistics in a random energy model with logarithmically correlated potential

NASA Astrophysics Data System (ADS)

Fyodorov, Yan V.; Bouchaud, Jean-Philippe

2008-09-01

We investigate some implications of the freezing scenario proposed by Carpentier and Le Doussal (CLD) for a random energy model (REM) with logarithmically correlated random potential. We introduce a particular (circular) variant of the model, and show that the integer moments of the partition function in the high-temperature phase are given by the well-known Dyson Coulomb gas integrals. The CLD freezing scenario allows one to use those moments for extracting the distribution of the free energy in both high- and low-temperature phases. In particular, it yields the full distribution of the minimal value in the potential sequence. This provides an explicit new class of extreme-value statistics for strongly correlated variables, manifestly different from the standard Gumbel class.

Quantum Monte Carlo calculations of van der Waals interactions between aromatic benzene rings

NASA Astrophysics Data System (ADS)

Azadi, Sam; Kühne, T. D.

2018-05-01

The magnitude of finite-size effects and Coulomb interactions in quantum Monte Carlo simulations of van der Waals interactions between weakly bonded benzene molecules are investigated. To that extent, two trial wave functions of the Slater-Jastrow and Backflow-Slater-Jastrow types are employed to calculate the energy-volume equation of state. We assess the impact of the backflow coordinate transformation on the nonlocal correlation energy. We found that the effect of finite-size errors in quantum Monte Carlo calculations on energy differences is particularly large and may even be more important than the employed trial wave function. In addition to the cohesive energy, the singlet excitonic energy gap and the energy gap renormalization of crystalline benzene at different densities are computed.

Diagrammatic analysis of correlations in polymer fluids: Cluster diagrams via Edwards' field theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Morse, David C.

2006-10-15

Edwards' functional integral approach to the statistical mechanics of polymer liquids is amenable to a diagrammatic analysis in which free energies and correlation functions are expanded as infinite sums of Feynman diagrams. This analysis is shown to lead naturally to a perturbative cluster expansion that is closely related to the Mayer cluster expansion developed for molecular liquids by Chandler and co-workers. Expansion of the functional integral representation of the grand-canonical partition function yields a perturbation theory in which all quantities of interest are expressed as functionals of a monomer-monomer pair potential, as functionals of intramolecular correlation functions of non-interacting molecules,more » and as functions of molecular activities. In different variants of the theory, the pair potential may be either a bare or a screened potential. A series of topological reductions yields a renormalized diagrammatic expansion in which collective correlation functions are instead expressed diagrammatically as functionals of the true single-molecule correlation functions in the interacting fluid, and as functions of molecular number density. Similar renormalized expansions are also obtained for a collective Ornstein-Zernicke direct correlation function, and for intramolecular correlation functions. A concise discussion is given of the corresponding Mayer cluster expansion, and of the relationship between the Mayer and perturbative cluster expansions for liquids of flexible molecules. The application of the perturbative cluster expansion to coarse-grained models of dense multi-component polymer liquids is discussed, and a justification is given for the use of a loop expansion. As an example, the formalism is used to derive a new expression for the wave-number dependent direct correlation function and recover known expressions for the intramolecular two-point correlation function to first-order in a renormalized loop expansion for coarse-grained models of binary homopolymer blends and diblock copolymer melts.« less

Game-Theoretic strategies for systems of components using product-form utilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rao, Nageswara S; Ma, Cheng-Yu; Hausken, K.

Many critical infrastructures are composed of multiple systems of components which are correlated so that disruptions to one may propagate to others. We consider such infrastructures with correlations characterized in two ways: (i) an aggregate failure correlation function specifies the conditional failure probability of the infrastructure given the failure of an individual system, and (ii) a pairwise correlation function between two systems specifies the failure probability of one system given the failure of the other. We formulate a game for ensuring the resilience of the infrastructure, wherein the utility functions of the provider and attacker are products of an infrastructuremore » survival probability term and a cost term, both expressed in terms of the numbers of system components attacked and reinforced. The survival probabilities of individual systems satisfy first-order differential conditions that lead to simple Nash Equilibrium conditions. We then derive sensitivity functions that highlight the dependence of infrastructure resilience on the cost terms, correlation functions, and individual system survival probabilities. We apply these results to simplified models of distributed cloud computing and energy grid infrastructures.« less

Two-body Schrödinger wave functions in a plane-wave basis via separation of dimensions

NASA Astrophysics Data System (ADS)

Jerke, Jonathan; Poirier, Bill

2018-03-01

Using a combination of ideas, the ground and several excited electronic states of the helium atom and the hydrogen molecule are computed to chemical accuracy—i.e., to within 1-2 mhartree or better. The basic strategy is very different from the standard electronic structure approach in that the full two-electron six-dimensional (6D) problem is tackled directly, rather than starting from a single-electron Hartree-Fock approximation. Electron correlation is thus treated exactly, even though computational requirements remain modest. The method also allows for exact wave functions to be computed, as well as energy levels. From the full-dimensional 6D wave functions computed here, radial distribution functions and radial correlation functions are extracted—as well as a 2D probability density function exhibiting antisymmetry for a single Cartesian component. These calculations support a more recent interpretation of Hund's rule, which states that the lower energy of the higher spin-multiplicity states is actually due to reduced screening, rather than reduced electron-electron repulsion. Prospects for larger systems and/or electron dynamics applications appear promising.

Site-occupation embedding theory using Bethe ansatz local density approximations

NASA Astrophysics Data System (ADS)

Senjean, Bruno; Nakatani, Naoki; Tsuchiizu, Masahisa; Fromager, Emmanuel

2018-06-01

Site-occupation embedding theory (SOET) is an alternative formulation of density functional theory (DFT) for model Hamiltonians where the fully interacting Hubbard problem is mapped, in principle exactly, onto an impurity-interacting (rather than a noninteracting) one. It provides a rigorous framework for combining wave-function (or Green function)-based methods with DFT. In this work, exact expressions for the per-site energy and double occupation of the uniform Hubbard model are derived in the context of SOET. As readily seen from these derivations, the so-called bath contribution to the per-site correlation energy is, in addition to the latter, the key density functional quantity to model in SOET. Various approximations based on Bethe ansatz and perturbative solutions to the Hubbard and single-impurity Anderson models are constructed and tested on a one-dimensional ring. The self-consistent calculation of the embedded impurity wave function has been performed with the density-matrix renormalization group method. It has been shown that promising results are obtained in specific regimes of correlation and density. Possible further developments have been proposed in order to provide reliable embedding functionals and potentials.

Two-body Schrödinger wave functions in a plane-wave basis via separation of dimensions.

PubMed

Jerke, Jonathan; Poirier, Bill

2018-03-14

Using a combination of ideas, the ground and several excited electronic states of the helium atom and the hydrogen molecule are computed to chemical accuracy-i.e., to within 1-2 mhartree or better. The basic strategy is very different from the standard electronic structure approach in that the full two-electron six-dimensional (6D) problem is tackled directly, rather than starting from a single-electron Hartree-Fock approximation. Electron correlation is thus treated exactly, even though computational requirements remain modest. The method also allows for exact wave functions to be computed, as well as energy levels. From the full-dimensional 6D wave functions computed here, radial distribution functions and radial correlation functions are extracted-as well as a 2D probability density function exhibiting antisymmetry for a single Cartesian component. These calculations support a more recent interpretation of Hund's rule, which states that the lower energy of the higher spin-multiplicity states is actually due to reduced screening, rather than reduced electron-electron repulsion. Prospects for larger systems and/or electron dynamics applications appear promising.

Landscape of an exact energy functional

NASA Astrophysics Data System (ADS)

Cohen, Aron J.; Mori-Sánchez, Paula

2016-04-01

One of the great challenges of electronic structure theory is the quest for the exact functional of density functional theory. Its existence is proven, but it is a complicated multivariable functional that is almost impossible to conceptualize. In this paper the asymmetric two-site Hubbard model is studied, which has a two-dimensional universe of density matrices. The exact functional becomes a simple function of two variables whose three-dimensional energy landscape can be visualized and explored. A walk on this unique landscape, tilted to an angle defined by the one-electron Hamiltonian, gives a valley whose minimum is the exact total energy. This is contrasted with the landscape of some approximate functionals, explaining their failure for electron transfer in the strongly correlated limit. We show concrete examples of pure-state density matrices that are not v representable due to the underlying nonconvex nature of the energy landscape. The exact functional is calculated for all numbers of electrons, including fractional, allowing the derivative discontinuity to be visualized and understood. The fundamental gap for all possible systems is obtained solely from the derivatives of the exact functional.

Neutron-fragment and Neutron-neutron Correlations in Low-energy Fission

NASA Astrophysics Data System (ADS)

Lestone, J. P.

2016-01-01

A computational method has been developed to simulate neutron emission from thermal-neutron induced fission of 235U and from spontaneous fission of 252Cf. Measured pre-emission mass-yield curves, average total kinetic energies and their variances, both as functions of mass split, are used to obtain a representation of the distribution of fragment velocities. Measured average neutron multiplicities as a function of mass split and their dependence on total kinetic energy are used. Simulations can be made to reproduce measured factorial moments of neutron-multiplicity distributions with only minor empirical adjustments to some experimental inputs. The neutron-emission spectra in the rest-frame of the fragments are highly constrained by ENDF/B-VII.1 prompt-fission neutron-spectra evaluations. The n-f correlation measurements of Vorobyev et al. (2010) are consistent with predictions where all neutrons are assumed to be evaporated isotropically from the rest frame of fully accelerated fragments. Measured n-f and n-n correlations of others are a little weaker than the predictions presented here. These weaker correlations could be used to infer a weak scission-neutron source. However, the effect of neutron scattering on the experimental results must be studied in detail before moving away from a null hypothesis that all neutrons are evaporated from the fragments.

Exploring the boundary between aromatic and olefinic character: Bad news for second-order perturbation theory and density functional schemes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sulzbach, H.M.; Schaefer, H.F. III; Klopper, W.

1996-04-10

The question whether [10]annulene prefers olefinic structures with alternate single and double bonds or aromatic structures like all other small to medium sized uncharged (4n + 2){pi} electron homologs (e.g. benzene, [14]annulene) has been controversial for more than 20 years. Our new results suggest that only the high-order correlated methods will be able to correctly predict the [10]annulene potential energy surface. The UNO-CAS results and the strong oscillation of the MP series show that nondynamical electron correlation is important. Consequently, reliable results can only be expected at the highest correlated levels like CCSD(T) method, which predicts the olefinic twist structuremore » to be lower in energy by 3-7 kcal/mol. This prediction that the twist structure is lower in energy is supported by (a) the MP2-R12 method, which shows that large basis sets favor the olefinic structure relative to the aromatic, and (b) the fact that both structures are about equally affected by nondynamical electron correlation. We conclude that [10]annulene is a system which cannot be described adequately by either second-order Moller-Plesset perturbation theory or density functional methods. 13 refs., 3 tabs.« less

The X3LYP extended density functional accurately describes H-bonding but fails completely for stacking.

PubMed

Cerný, Jirí; Hobza, Pavel

2005-04-21

The performance of the recently introduced X3LYP density functional which was claimed to significantly improve the accuracy for H-bonded and van der Waals complexes was tested for extended H-bonded and stacked complexes (nucleic acid base pairs and amino acid pairs). In the case of planar H-bonded complexes (guanine...cytosine, adenine...thymine) the DFT results nicely agree with accurate correlated ab initio results. For the stacked pairs (uracil dimer, cytosine dimer, adenine...thymine and guanine...cytosine) the DFT fails completely and it was even not able to localize any minimum at the stacked subspace of the potential energy surface. The geometry optimization of all these stacked clusters leads systematically to the planar H-bonded pairs. The amino acid pairs were investigated in the crystal geometry. DFT again strongly underestimates the accurate correlated ab initio stabilization energies and usually it was not able to describe the stabilization of a pair. The X3LYP functional thus behaves similarly to other current functionals. Stacking of nucleic acid bases as well as interaction of amino acids was described satisfactorily by using the tight-binding DFT method, which explicitly covers the London dispersion energy.

Determining the static electronic and vibrational energy correlations via two-dimensional electronic-vibrational spectroscopy

DOE PAGES

Dong, Hui; Lewis, Nicholas H. C.; Oliver, Thomas A. A.; ...

2015-05-07

Changes in the electronic structure of pigments in protein environments and of polar molecules in solution inevitably induce a re-adaption of molecular nuclear structure. Both changes of electronic and vibrational energies can be probed with visible or infrared lasers, such as two-dimensional electronic spectroscopy or vibrational spectroscopy. The extent to which the two changes are correlated remains elusive. The recent demonstration of two-dimensional electronic-vibrational (2DEV) spectroscopy potentially enables a direct measurement of this correlation experimentally. However, it has hitherto been unclear how to characterize the correlation from the spectra. In this report, we present a theoretical formalism to demonstrate themore » slope of the nodal line between the excited state absorption and ground state bleach peaks in the spectra as a characterization of the correlation between electronic and vibrational transition energies. In conclusion, we also show the dynamics of the nodal line slope is correlated to the vibrational spectral dynamics. Additionally, we demonstrate the fundamental 2DEV spectral line-shape of a monomer with newly developed response functions« less

Determining the static electronic and vibrational energy correlations via two-dimensional electronic-vibrational spectroscopy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dong, Hui; Lewis, Nicholas H. C.; Oliver, Thomas A. A.

2015-05-07

Changes in the electronic structure of pigments in protein environments and of polar molecules in solution inevitably induce a re-adaption of molecular nuclear structure. Both changes of electronic and vibrational energies can be probed with visible or infrared lasers, such as two-dimensional electronic spectroscopy or vibrational spectroscopy. The extent to which the two changes are correlated remains elusive. The recent demonstration of two-dimensional electronic-vibrational (2DEV) spectroscopy potentially enables a direct measurement of this correlation experimentally. However, it has hitherto been unclear how to characterize the correlation from the spectra. In this paper, we present a theoretical formalism to demonstrate themore » slope of the nodal line between the excited state absorption and ground state bleach peaks in the spectra as a characterization of the correlation between electronic and vibrational transition energies. We also show the dynamics of the nodal line slope is correlated to the vibrational spectral dynamics. Additionally, we demonstrate the fundamental 2DEV spectral line-shape of a monomer with newly developed response functions.« less

Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters

NASA Astrophysics Data System (ADS)

Bubin, Sergiy; Adamowicz, Ludwik

2006-06-01

In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters.

PubMed

Bubin, Sergiy; Adamowicz, Ludwik

2006-06-14

In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programmed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

Self-consistent field model for strong electrostatic correlations and inhomogeneous dielectric media.

PubMed

Ma, Manman; Xu, Zhenli

2014-12-28

Electrostatic correlations and variable permittivity of electrolytes are essential for exploring many chemical and physical properties of interfaces in aqueous solutions. We propose a continuum electrostatic model for the treatment of these effects in the framework of the self-consistent field theory. The model incorporates a space- or field-dependent dielectric permittivity and an excluded ion-size effect for the correlation energy. This results in a self-energy modified Poisson-Nernst-Planck or Poisson-Boltzmann equation together with state equations for the self energy and the dielectric function. We show that the ionic size is of significant importance in predicting a finite self energy for an ion in an inhomogeneous medium. Asymptotic approximation is proposed for the solution of a generalized Debye-Hückel equation, which has been shown to capture the ionic correlation and dielectric self energy. Through simulating ionic distribution surrounding a macroion, the modified self-consistent field model is shown to agree with particle-based Monte Carlo simulations. Numerical results for symmetric and asymmetric electrolytes demonstrate that the model is able to predict the charge inversion at high correlation regime in the presence of multivalent interfacial ions which is beyond the mean-field theory and also show strong effect to double layer structure due to the space- or field-dependent dielectric permittivity.

Pair correlations in low-lying T =0 states of odd-odd nuclei with six nucleons

NASA Astrophysics Data System (ADS)

Fu, G. J.; Zhao, Y. M.; Arima, A.

2018-02-01

In this paper, we study pair correlations in low-lying T =0 states for two typical cases of odd-odd N =Z nuclei. The first case is six nucleons in a single j =9 /2 shell, for which we study the S -broken-pair approximation, the isoscalar spin-1 pair condensation, and the isoscalar spin-aligned pair condensation, with schematic interactions. In the second case, we study pair approximations and correlation energies for 22Na, 34Cl, 46V, 62Ga, and 94Ag in multi-j shells with effective interactions. A few T =0 states are found to be well represented by isoscalar nucleon pairs. The isoscalar spin-aligned pairs play an important role for the yrast T =0 states with I ˜2 j and I ˜Imax in 22Na, 46V, and 94Ag. The overlap between the isoscalar J =1 pair wave function and the shell-model wave function is around 0.5 for the I =1 ,3 states of 34Cl and the I =1 state of 94Ag. The I =9 state of 62Ga is very well described by the isoscalar J =3 pair condensation. The broken-pair approximation (which is similar to the 2-quasiparticle excitation of the isovector pair condensation) is appropriate for quite few states, such as the I =1 -3 states of 34Cl and the I =5 state of 62Ga. The correlation energies are presented in this paper. It is noted that the picture based on nucleon-pair wave functions is not always in agreement with the picture based on correlation energies.

Method and basis set dependence of anharmonic ground state nuclear wave functions and zero-point energies: application to SSSH.

PubMed

Kolmann, Stephen J; Jordan, Meredith J T

2010-02-07

One of the largest remaining errors in thermochemical calculations is the determination of the zero-point energy (ZPE). The fully coupled, anharmonic ZPE and ground state nuclear wave function of the SSSH radical are calculated using quantum diffusion Monte Carlo on interpolated potential energy surfaces (PESs) constructed using a variety of method and basis set combinations. The ZPE of SSSH, which is approximately 29 kJ mol(-1) at the CCSD(T)/6-31G* level of theory, has a 4 kJ mol(-1) dependence on the treatment of electron correlation. The anharmonic ZPEs are consistently 0.3 kJ mol(-1) lower in energy than the harmonic ZPEs calculated at the Hartree-Fock and MP2 levels of theory, and 0.7 kJ mol(-1) lower in energy at the CCSD(T)/6-31G* level of theory. Ideally, for sub-kJ mol(-1) thermochemical accuracy, ZPEs should be calculated using correlated methods with as big a basis set as practicable. The ground state nuclear wave function of SSSH also has significant method and basis set dependence. The analysis of the nuclear wave function indicates that SSSH is localized to a single symmetry equivalent global minimum, despite having sufficient ZPE to be delocalized over both minima. As part of this work, modifications to the interpolated PES construction scheme of Collins and co-workers are presented.

Method and basis set dependence of anharmonic ground state nuclear wave functions and zero-point energies: Application to SSSH

NASA Astrophysics Data System (ADS)

Kolmann, Stephen J.; Jordan, Meredith J. T.

2010-02-01

One of the largest remaining errors in thermochemical calculations is the determination of the zero-point energy (ZPE). The fully coupled, anharmonic ZPE and ground state nuclear wave function of the SSSH radical are calculated using quantum diffusion Monte Carlo on interpolated potential energy surfaces (PESs) constructed using a variety of method and basis set combinations. The ZPE of SSSH, which is approximately 29 kJ mol-1 at the CCSD(T)/6-31G∗ level of theory, has a 4 kJ mol-1 dependence on the treatment of electron correlation. The anharmonic ZPEs are consistently 0.3 kJ mol-1 lower in energy than the harmonic ZPEs calculated at the Hartree-Fock and MP2 levels of theory, and 0.7 kJ mol-1 lower in energy at the CCSD(T)/6-31G∗ level of theory. Ideally, for sub-kJ mol-1 thermochemical accuracy, ZPEs should be calculated using correlated methods with as big a basis set as practicable. The ground state nuclear wave function of SSSH also has significant method and basis set dependence. The analysis of the nuclear wave function indicates that SSSH is localized to a single symmetry equivalent global minimum, despite having sufficient ZPE to be delocalized over both minima. As part of this work, modifications to the interpolated PES construction scheme of Collins and co-workers are presented.

Fundamental gaps with approximate density functionals: The derivative discontinuity revealed from ensemble considerations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kraisler, Eli; Kronik, Leeor

2014-05-14

The fundamental gap is a central quantity in the electronic structure of matter. Unfortunately, the fundamental gap is not generally equal to the Kohn-Sham gap of density functional theory (DFT), even in principle. The two gaps differ precisely by the derivative discontinuity, namely, an abrupt change in slope of the exchange-correlation energy as a function of electron number, expected across an integer-electron point. Popular approximate functionals are thought to be devoid of a derivative discontinuity, strongly compromising their performance for prediction of spectroscopic properties. Here we show that, in fact, all exchange-correlation functionals possess a derivative discontinuity, which arises naturallymore » from the application of ensemble considerations within DFT, without any empiricism. This derivative discontinuity can be expressed in closed form using only quantities obtained in the course of a standard DFT calculation of the neutral system. For small, finite systems, addition of this derivative discontinuity indeed results in a greatly improved prediction for the fundamental gap, even when based on the most simple approximate exchange-correlation density functional – the local density approximation (LDA). For solids, the same scheme is exact in principle, but when applied to LDA it results in a vanishing derivative discontinuity correction. This failure is shown to be directly related to the failure of LDA in predicting fundamental gaps from total energy differences in extended systems.« less

Band structures in coupled-cluster singles-and-doubles Green's function (GFCCSD)

NASA Astrophysics Data System (ADS)

Furukawa, Yoritaka; Kosugi, Taichi; Nishi, Hirofumi; Matsushita, Yu-ichiro

2018-05-01

We demonstrate that the coupled-cluster singles-and-doubles Green's function (GFCCSD) method is a powerful and prominent tool drawing the electronic band structures and the total energies, which many theoretical techniques struggle to reproduce. We have calculated single-electron energy spectra via the GFCCSD method for various kinds of systems, ranging from ionic to covalent and van der Waals, for the first time: the one-dimensional LiH chain, one-dimensional C chain, and one-dimensional Be chain. We have found that the bandgap becomes narrower than in HF due to the correlation effect. We also show that the band structures obtained from the GFCCSD method include both quasiparticle and satellite peaks successfully. Besides, taking one-dimensional LiH as an example, we discuss the validity of restricting the active space to suppress the computational cost of the GFCCSD method. We show that the calculated results without bands that do not contribute to the chemical bonds are in good agreement with full-band calculations. With the GFCCSD method, we can calculate the total energies and spectral functions for periodic systems in an explicitly correlated manner.

Density matrix embedding in an antisymmetrized geminal power bath

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsuchimochi, Takashi; Welborn, Matthew; Van Voorhis, Troy, E-mail: tvan@mit.edu

2015-07-14

Density matrix embedding theory (DMET) has emerged as a powerful tool for performing wave function-in-wave function embedding for strongly correlated systems. In traditional DMET, an accurate calculation is performed on a small impurity embedded in a mean field bath. Here, we extend the original DMET equations to account for correlation in the bath via an antisymmetrized geminal power (AGP) wave function. The resulting formalism has a number of advantages. First, it allows one to properly treat the weak correlation limit of independent pairs, which DMET is unable to do with a mean-field bath. Second, it associates a size extensive correlationmore » energy with a given density matrix (for the models tested), which AGP by itself is incapable of providing. Third, it provides a reasonable description of charge redistribution in strongly correlated but non-periodic systems. Thus, AGP-DMET appears to be a good starting point for describing electron correlation in molecules, which are aperiodic and possess both strong and weak electron correlation.« less

Magnetized liquid 3He at finite temperature: A variational calculation approach

NASA Astrophysics Data System (ADS)

Bordbar, Gholam Hossein; Mohammadi Sabet, Mohammad Taghi

2016-08-01

Using the spin-dependent (SD) and spin-independent (SI) correlation functions, we have investigated the properties of liquid 3He in the presence of magnetic field at finite temperature. Our calculations have been done using the variational method based on cluster expansion of the energy functional. Our results show that the low field magnetic susceptibility obeys Curie law at high temperatures. This behavior is in a good agreement with the experimental data as well as the molecular field theory results in which the spin dependency has been introduced in correlation function. Reduced susceptibility as a function of temperature as well as reduced temperature has been also investigated, and again we have seen that the spin-dependent correlation function leads to a good agreement with the experimental data. The Landau parameter, F0a, has been calculated, and for this parameter, a value about - 0.75 has been found in the case of spin-spin correlation. In the case of spin-independent correlation function, this value is about - 0.7. Therefore, inclusion of spin dependency in the correlation function leads to a more compatible value of F0a with experimental data. The magnetization and susceptibility of liquid 3He have also been investigated as a function of magnetic field. Our results show a downward curvature in magnetization of system with spin-dependent correlation for all densities and relevant temperatures. A metamagnetic behavior has been observed as a maximum in susceptibility versus magnetic field, when the spin-spin correlation has been considered. This maximum occurs at 45T ≤ B ≤ 100T for all densities and temperatures. This behavior has not been observed in the case of spin-independent correlation function.

Energy level alignment and quantum conductance of functionalized metal-molecule junctions: Density functional theory versus GW calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jin, Chengjun; Markussen, Troels; Thygesen, Kristian S., E-mail: thygesen@fysik.dtu.dk

We study the effect of functional groups (CH{sub 3}*4, OCH{sub 3}, CH{sub 3}, Cl, CN, F*4) on the electronic transport properties of 1,4-benzenediamine molecular junctions using the non-equilibrium Green function method. Exchange and correlation effects are included at various levels of theory, namely density functional theory (DFT), energy level-corrected DFT (DFT+Σ), Hartree-Fock and the many-body GW approximation. All methods reproduce the expected trends for the energy of the frontier orbitals according to the electron donating or withdrawing character of the substituent group. However, only the GW method predicts the correct ordering of the conductance amongst the molecules. The absolute GWmore » (DFT) conductance is within a factor of two (three) of the experimental values. Correcting the DFT orbital energies by a simple physically motivated scissors operator, Σ, can bring the DFT conductances close to experiments, but does not improve on the relative ordering. We ascribe this to a too strong pinning of the molecular energy levels to the metal Fermi level by DFT which suppresses the variation in orbital energy with functional group.« less

Fermi orbital derivatives in self-interaction corrected density functional theory: Applications to closed shell atoms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pederson, Mark R., E-mail: mark.pederson@science.doe.gov

2015-02-14

A recent modification of the Perdew-Zunger self-interaction-correction to the density-functional formalism has provided a framework for explicitly restoring unitary invariance to the expression for the total energy. The formalism depends upon construction of Löwdin orthonormalized Fermi-orbitals which parametrically depend on variational quasi-classical electronic positions. Derivatives of these quasi-classical electronic positions, required for efficient minimization of the self-interaction corrected energy, are derived and tested, here, on atoms. Total energies and ionization energies in closed-shell singlet atoms, where correlation is less important, using the Perdew-Wang 1992 Local Density Approximation (PW92) functional, are in good agreement with experiment and non-relativistic quantum-Monte-Carlo results albeitmore » slightly too low.« less

Topologically massive gravity and galilean conformal algebra: a study of correlation functions

NASA Astrophysics Data System (ADS)

Bagchi, Arjun

2011-02-01

The Galilean Conformal Algebra (GCA) arises from the conformal algebra in the non-relativistic limit. In two dimensions, one can view it as a limit of linear combinations of the two copies Virasoro algebra. Recently, it has been argued that Topologically Massive Gravity (TMG) realizes the quantum 2d GCA in a particular scaling limit of the gravitational Chern-Simons term. To add strength to this claim, we demonstrate a matching of correlation functions on both sides of this correspondence. A priori looking for spatially dependent correlators seems to force us to deal with high spin operators in the bulk. We get around this difficulty by constructing the non-relativistic Energy-Momentum tensor and considering its correlation functions. On the gravity side, our analysis makes heavy use of recent results of Holographic Renormalization in Topologically Massive Gravity.

Power Series Approximation for the Correlation Kernel Leading to Kohn-Sham Methods Combining Accuracy, Computational Efficiency, and General Applicability

NASA Astrophysics Data System (ADS)

Erhard, Jannis; Bleiziffer, Patrick; Görling, Andreas

2016-09-01

A power series approximation for the correlation kernel of time-dependent density-functional theory is presented. Using this approximation in the adiabatic-connection fluctuation-dissipation (ACFD) theorem leads to a new family of Kohn-Sham methods. The new methods yield reaction energies and barriers of unprecedented accuracy and enable a treatment of static (strong) correlation with an accuracy of high-level multireference configuration interaction methods but are single-reference methods allowing for a black-box-like handling of static correlation. The new methods exhibit a better scaling of the computational effort with the system size than rivaling wave-function-based electronic structure methods. Moreover, the new methods do not suffer from the problem of singularities in response functions plaguing previous ACFD methods and therefore are applicable to any type of electronic system.

Measurement of Long-Range Near-Side Two-Particle Angular Correlations in pp Collisions at sqrt[s]=13  TeV.

PubMed

Khachatryan, V; Sirunyan, A M; Tumasyan, A; Adam, W; Asilar, E; Bergauer, T; Brandstetter, J; Brondolin, E; Dragicevic, M; Erö, J; Flechl, M; Friedl, M; Frühwirth, R; Ghete, V M; Hartl, C; Hörmann, N; Hrubec, J; Jeitler, M; Knünz, V; König, A; Krammer, M; Krätschmer, I; Liko, D; Matsushita, T; Mikulec, I; Rabady, D; Rahbaran, B; Rohringer, H; Schieck, J; Schöfbeck, R; Strauss, J; Treberer-Treberspurg, W; Waltenberger, W; Wulz, C-E; Mossolov, V; Shumeiko, N; Suarez Gonzalez, J; Alderweireldt, S; Cornelis, T; De Wolf, E A; Janssen, X; Knutsson, A; Lauwers, J; Luyckx, S; Van De Klundert, M; Van Haevermaet, H; Van Mechelen, P; Van Remortel, N; Van Spilbeeck, A; Abu Zeid, S; Blekman, F; D'Hondt, J; Daci, N; De Bruyn, I; Deroover, K; Heracleous, N; Keaveney, J; Lowette, S; Moreels, L; Olbrechts, A; Python, Q; Strom, D; Tavernier, S; Van Doninck, W; Van Mulders, P; Van Onsem, G P; Van Parijs, I; Barria, P; Brun, H; Caillol, C; Clerbaux, B; De Lentdecker, G; Fasanella, G; Favart, L; Grebenyuk, A; Karapostoli, G; Lenzi, T; Léonard, A; Maerschalk, T; Marinov, A; Perniè, L; Randle-Conde, A; Seva, T; Vander Velde, C; Vanlaer, P; Yonamine, R; Zenoni, F; Zhang, F; Beernaert, K; Benucci, L; Cimmino, A; Crucy, S; Dobur, D; Fagot, A; Garcia, G; Gul, M; Mccartin, J; Ocampo Rios, A A; Poyraz, D; Ryckbosch, D; Salva, S; Sigamani, M; Tytgat, M; Van Driessche, W; Yazgan, E; Zaganidis, N; Basegmez, S; Beluffi, C; Bondu, O; Brochet, S; Bruno, G; Caudron, A; Ceard, L; Da Silveira, G G; Delaere, C; Favart, D; Forthomme, L; Giammanco, A; Hollar, J; Jafari, A; Jez, P; Komm, M; Lemaitre, V; Mertens, A; Musich, M; Nuttens, C; Perrini, L; Pin, A; Piotrzkowski, K; Popov, A; Quertenmont, L; Selvaggi, M; Vidal Marono, M; Beliy, N; Hammad, G H; Aldá Júnior, W L; Alves, F L; Alves, G A; Brito, L; Correa Martins Junior, M; Hamer, M; Hensel, C; Moraes, A; Pol, M E; Rebello Teles, P; Belchior Batista Das Chagas, E; Carvalho, W; Chinellato, J; Custódio, A; Da Costa, E M; De Jesus Damiao, D; De Oliveira Martins, C; Fonseca De Souza, S; Huertas Guativa, L M; Malbouisson, H; Matos Figueiredo, D; Mora Herrera, C; Mundim, L; Nogima, H; Prado Da Silva, W L; Santoro, A; Sznajder, A; Tonelli Manganote, E J; Vilela Pereira, A; Ahuja, S; Bernardes, C A; De Souza Santos, A; Dogra, S; Tomei, T R Fernandez Perez; Gregores, E M; Mercadante, P G; Moon, C S; Novaes, S F; Padula, Sandra S; Romero Abad, D; Ruiz Vargas, J C; Aleksandrov, A; Hadjiiska, R; Iaydjiev, P; Rodozov, M; Stoykova, S; Sultanov, G; Vutova, M; Dimitrov, A; Glushkov, I; Litov, L; Pavlov, B; Petkov, P; Ahmad, M; Bian, J G; Chen, G M; Chen, H S; Chen, M; Cheng, T; Du, R; Jiang, C H; Plestina, R; Romeo, F; Shaheen, S M; Spiezia, A; Tao, J; Wang, C; Wang, Z; Zhang, H; Asawatangtrakuldee, C; Ban, Y; Li, Q; Liu, S; Mao, Y; Qian, S J; Wang, D; Xu, Z; Avila, C; Cabrera, A; Chaparro Sierra, L F; Florez, C; Gomez, J P; Gomez Moreno, B; Sanabria, J C; Godinovic, N; Lelas, D; Puljak, I; Ribeiro Cipriano, P M; Antunovic, Z; Kovac, M; Brigljevic, V; Kadija, K; Luetic, J; Micanovic, S; Sudic, L; Attikis, A; Mavromanolakis, G; Mousa, J; Nicolaou, C; Ptochos, F; Razis, P A; Rykaczewski, H; Bodlak, M; Finger, M; Finger, M; El-Khateeb, E; Elkafrawy, T; Mohamed, A; Salama, E; Calpas, B; Kadastik, M; Murumaa, M; Raidal, M; Tiko, A; Veelken, C; Eerola, P; Pekkanen, J; Voutilainen, M; Härkönen, J; Karimäki, V; Kinnunen, R; Lampén, T; Lassila-Perini, K; Lehti, S; Lindén, T; Luukka, P; Peltola, T; Tuominen, E; Tuominiemi, J; Tuovinen, E; Wendland, L; Talvitie, J; Tuuva, T; Besancon, M; Couderc, F; Dejardin, M; Denegri, D; Fabbro, B; Faure, J L; Favaro, C; Ferri, F; Ganjour, S; Givernaud, A; Gras, P; Hamel de Monchenault, G; Jarry, P; Locci, E; Machet, M; Malcles, J; Rander, J; Rosowsky, A; Titov, M; Zghiche, A; Antropov, I; Baffioni, S; Beaudette, F; Busson, P; Cadamuro, L; Chapon, E; Charlot, C; Davignon, O; Filipovic, N; Granier de Cassagnac, R; Jo, M; Lisniak, S; Mastrolorenzo, L; Miné, P; Naranjo, I N; Nguyen, M; Ochando, C; Ortona, G; Paganini, P; Pigard, P; Regnard, S; Salerno, R; Sauvan, J B; Sirois, Y; Strebler, T; Yilmaz, Y; Zabi, A; Agram, J-L; Andrea, J; Aubin, A; Bloch, D; Brom, J-M; Buttignol, M; Chabert, E C; Chanon, N; Collard, C; Conte, E; Coubez, X; Fontaine, J-C; Gelé, D; Goerlach, U; Goetzmann, C; Le Bihan, A-C; Merlin, J A; Skovpen, K; Van Hove, P; Gadrat, S; Beauceron, S; Bernet, C; Boudoul, G; Bouvier, E; Carrillo Montoya, C A; Chierici, R; Contardo, D; Courbon, B; Depasse, P; El Mamouni, H; Fan, J; Fay, J; Gascon, S; Gouzevitch, M; Ille, B; Lagarde, F; Laktineh, I B; Lethuillier, M; Mirabito, L; Pequegnot, A L; Perries, S; Ruiz Alvarez, J D; Sabes, D; Sgandurra, L; Sordini, V; Vander Donckt, M; Verdier, P; Viret, S; Toriashvili, T; Tsamalaidze, Z; Autermann, C; Beranek, S; Feld, L; Heister, A; Kiesel, M K; Klein, K; Lipinski, M; Ostapchuk, A; Preuten, M; Raupach, F; Schael, S; Schulte, J F; Verlage, T; Weber, H; Zhukov, V; Ata, M; Brodski, M; Dietz-Laursonn, E; Duchardt, D; Endres, M; Erdmann, M; Erdweg, S; Esch, T; 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Lammel, S; Linacre, J; Lincoln, D; Lipton, R; Liu, T; Lopes De Sá, R; Lykken, J; Maeshima, K; Marraffino, J M; Maruyama, S; Mason, D; McBride, P; Merkel, P; Mrenna, S; Nahn, S; Newman-Holmes, C; O'Dell, V; Pedro, K; Prokofyev, O; Rakness, G; Sexton-Kennedy, E; Soha, A; Spalding, W J; Spiegel, L; Strobbe, N; Taylor, L; Tkaczyk, S; Tran, N V; Uplegger, L; Vaandering, E W; Vernieri, C; Verzocchi, M; Vidal, R; Weber, H A; Whitbeck, A; Acosta, D; Avery, P; Bortignon, P; Bourilkov, D; Carnes, A; Carver, M; Curry, D; Das, S; Field, R D; Furic, I K; Gleyzer, S V; Konigsberg, J; Korytov, A; Kotov, K; Ma, P; Matchev, K; Mei, H; Milenovic, P; Mitselmakher, G; Rank, D; Rossin, R; Shchutska, L; Snowball, M; Sperka, D; Terentyev, N; Thomas, L; Wang, J; Wang, S; Yelton, J; Hewamanage, S; Linn, S; Markowitz, P; Martinez, G; Rodriguez, J L; Ackert, A; Adams, J R; Adams, T; Askew, A; Bein, S; Bochenek, J; Diamond, B; Haas, J; Hagopian, S; Hagopian, V; Johnson, K F; Khatiwada, A; Prosper, H; Weinberg, M; Baarmand, M M; Bhopatkar, V; Colafranceschi, S; Hohlmann, M; Kalakhety, H; Noonan, D; Roy, T; Yumiceva, F; Adams, M R; Apanasevich, L; Berry, D; Betts, R R; Bucinskaite, I; Cavanaugh, R; Evdokimov, O; Gauthier, L; Gerber, C E; Hofman, D J; Kurt, P; O'Brien, C; Sandoval Gonzalez, I D; Turner, P; Varelas, N; Wu, Z; Zakaria, M; Bilki, B; Clarida, W; Dilsiz, K; Durgut, S; Gandrajula, R P; Haytmyradov, M; Khristenko, V; Merlo, J-P; Mermerkaya, H; Mestvirishvili, A; Moeller, A; Nachtman, J; Ogul, H; Onel, Y; Ozok, F; Penzo, A; Snyder, C; Tiras, E; Wetzel, J; Yi, K; Anderson, I; Barnett, B A; Blumenfeld, B; Eminizer, N; Fehling, D; Feng, L; Gritsan, A V; Maksimovic, P; Martin, C; Osherson, M; Roskes, J; Sady, A; Sarica, U; Swartz, M; Xiao, M; Xin, Y; You, C; Baringer, P; Bean, A; Benelli, G; Bruner, C; Kenny, R P; Majumder, D; Malek, M; Murray, M; Sanders, S; Stringer, R; Wang, Q; Ivanov, A; Kaadze, K; Khalil, S; Makouski, M; Maravin, Y; Mohammadi, A; Saini, L K; Skhirtladze, N; Toda, S; Lange, D; Rebassoo, F; Wright, D; Anelli, C; Baden, A; Baron, O; Belloni, A; Calvert, B; Eno, S C; Ferraioli, C; Gomez, J A; Hadley, N J; Jabeen, S; Kellogg, R G; Kolberg, T; Kunkle, J; Lu, Y; Mignerey, A C; Shin, Y H; Skuja, A; Tonjes, M B; Tonwar, S C; Apyan, A; Barbieri, R; Baty, A; Bierwagen, K; Brandt, S; Busza, W; Cali, I A; Demiragli, Z; Di Matteo, L; Gomez Ceballos, G; Goncharov, M; Gulhan, D; Iiyama, Y; Innocenti, G M; Klute, M; Kovalskyi, D; Lai, Y S; Lee, Y-J; Levin, A; Luckey, P D; Marini, A C; Mcginn, C; Mironov, C; Narayanan, S; Niu, X; Paus, C; Roland, C; Roland, G; Salfeld-Nebgen, J; Stephans, G S F; Sumorok, K; Varma, M; Velicanu, D; Veverka, J; Wang, J; Wang, T W; Wyslouch, B; Yang, M; Zhukova, V; Dahmes, B; Evans, A; Finkel, A; Gude, A; Hansen, P; Kalafut, S; Kao, S C; Klapoetke, K; Kubota, Y; Lesko, Z; Mans, J; Nourbakhsh, S; Ruckstuhl, N; Rusack, R; Tambe, N; Turkewitz, J; Acosta, J G; Oliveros, S; Avdeeva, E; Bloom, K; Bose, S; Claes, D R; Dominguez, A; Fangmeier, C; Gonzalez Suarez, R; Kamalieddin, R; Knowlton, D; Kravchenko, I; Meier, F; Monroy, J; Ratnikov, F; Siado, J E; Snow, G R; Alyari, M; Dolen, J; George, J; Godshalk, A; Harrington, C; Iashvili, I; Kaisen, J; Kharchilava, A; Kumar, A; Rappoccio, S; Roozbahani, B; Alverson, G; Barberis, E; Baumgartel, D; Chasco, M; Hortiangtham, A; Massironi, A; Morse, D M; Nash, D; Orimoto, T; Teixeira De Lima, R; Trocino, D; Wang, R-J; Wood, D; Zhang, J; Bhattacharya, S; Hahn, K A; Kubik, A; Low, J F; Mucia, N; Odell, N; Pollack, B; Schmitt, M; Stoynev, S; Sung, K; Trovato, M; Velasco, M; Brinkerhoff, A; Dev, N; Hildreth, M; Jessop, C; Karmgard, D J; Kellams, N; Lannon, K; Marinelli, N; Meng, F; Mueller, C; Musienko, Y; Planer, M; Reinsvold, A; Ruchti, R; Smith, G; Taroni, S; Valls, N; Wayne, M; Wolf, M; Woodard, A; Antonelli, L; Brinson, J; Bylsma, B; Durkin, L S; Flowers, S; Hart, A; Hill, C; Hughes, R; Ji, W; Ling, T Y; Liu, B; Luo, W; Puigh, D; Rodenburg, M; Winer, B L; Wulsin, H W; Driga, O; Elmer, P; Hardenbrook, J; Hebda, P; Koay, S A; Lujan, P; Marlow, D; Medvedeva, T; Mooney, M; Olsen, J; Palmer, C; Piroué, P; Saka, H; Stickland, D; Tully, C; Zuranski, A; Malik, S; Barker, A; Barnes, V E; Benedetti, D; Bortoletto, D; Gutay, L; Jha, M K; Jones, M; Jung, A W; Jung, K; Kumar, A; Miller, D H; Neumeister, N; Radburn-Smith, B C; Shi, X; Shipsey, I; Silvers, D; Sun, J; Svyatkovskiy, A; Wang, F; Xie, W; Xu, L; Parashar, N; Stupak, J; Adair, A; Akgun, B; Chen, Z; Ecklund, K M; Geurts, F J M; Guilbaud, M; Li, W; Michlin, B; Northup, M; Padley, B P; Redjimi, R; Roberts, J; Rorie, J; Tu, Z; Zabel, J; Betchart, B; Bodek, A; de Barbaro, P; Demina, R; Eshaq, Y; Ferbel, T; Galanti, M; Garcia-Bellido, A; Han, J; Harel, A; Hindrichs, O; Khukhunaishvili, A; Petrillo, G; Tan, P; Verzetti, M; Arora, S; Chou, J P; Contreras-Campana, C; Contreras-Campana, E; Ferencek, D; Gershtein, Y; Gray, R; Halkiadakis, E; Hidas, D; Hughes, E; Kaplan, S; Kunnawalkam Elayavalli, R; Lath, A; Nash, K; Panwalkar, S; Park, M; Salur, S; Schnetzer, S; Sheffield, D; Somalwar, S; Stone, R; Thomas, S; Thomassen, P; Walker, M; Foerster, M; Riley, G; Rose, K; Spanier, S; Bouhali, O; Castaneda Hernandez, A; Celik, A; Dalchenko, M; De Mattia, M; Delgado, A; Dildick, S; Eusebi, R; Gilmore, J; Huang, T; Kamon, T; Krutelyov, V; Mueller, R; Osipenkov, I; Pakhotin, Y; Patel, R; Perloff, A; Rose, A; Safonov, A; Tatarinov, A; Ulmer, K A; Akchurin, N; Cowden, C; Damgov, J; Dragoiu, C; Dudero, P R; Faulkner, J; Kunori, S; Lamichhane, K; Lee, S W; Libeiro, T; Undleeb, S; Volobouev, I; Appelt, E; Delannoy, A G; Greene, S; Gurrola, A; Janjam, R; Johns, W; Maguire, C; Mao, Y; Melo, A; Ni, H; Sheldon, P; Tuo, S; Velkovska, J; Xu, Q; Arenton, M W; Cox, B; Francis, B; Goodell, J; Hirosky, R; Ledovskoy, A; Li, H; Lin, C; Neu, C; Sinthuprasith, T; Sun, X; Wang, Y; Wolfe, E; Wood, J; Xia, F; Clarke, C; Harr, R; Karchin, P E; Kottachchi Kankanamge Don, C; Lamichhane, P; Sturdy, J; Belknap, D A; Carlsmith, D; Cepeda, M; Dasu, S; Dodd, L; Duric, S; Gomber, B; Grothe, M; Hall-Wilton, R; Herndon, M; Hervé, A; Klabbers, P; Lanaro, A; Levine, A; Long, K; Loveless, R; Mohapatra, A; Ojalvo, I; Perry, T; Pierro, G A; Polese, G; Ruggles, T; Sarangi, T; Savin, A; Sharma, A; Smith, N; Smith, W H; Taylor, D; Verwilligen, P; Woods, N

2016-04-29

Results on two-particle angular correlations for charged particles produced in pp collisions at a center-of-mass energy of 13 TeV are presented. The data were taken with the CMS detector at the LHC and correspond to an integrated luminosity of about 270  nb^{-1}. The correlations are studied over a broad range of pseudorapidity (|η|<2.4) and over the full azimuth (ϕ) as a function of charged particle multiplicity and transverse momentum (p_{T}). In high-multiplicity events, a long-range (|Δη|>2.0), near-side (Δϕ≈0) structure emerges in the two-particle Δη-Δϕ correlation functions. The magnitude of the correlation exhibits a pronounced maximum in the range 1.0

Kubo formulas for the shear and bulk viscosity relaxation times and the scalar field theory shear τπ calculation

NASA Astrophysics Data System (ADS)

Czajka, Alina; Jeon, Sangyong

2017-06-01

In this paper we provide a quantum field theoretical study on the shear and bulk relaxation times. First, we find Kubo formulas for the shear and the bulk relaxation times, respectively. They are found by examining response functions of the stress-energy tensor. We use general properties of correlation functions and the gravitational Ward identity to parametrize analytical structures of the Green functions describing both sound and diffusion mode. We find that the hydrodynamic limits of the real parts of the respective energy-momentum tensor correlation functions provide us with the method of computing both the shear and bulk viscosity relaxation times. Next, we calculate the shear viscosity relaxation time using the diagrammatic approach in the Keldysh basis for the massless λ ϕ4 theory. We derive a respective integral equation which enables us to compute η τπ and then we extract the shear relaxation time. The relaxation time is shown to be inversely related to the thermal width as it should be.

Do Practical Standard Coupled Cluster Calculations Agree Better than Kohn–Sham Calculations with Currently Available Functionals When Compared to the Best Available Experimental Data for Dissociation Energies of Bonds to 3d Transition Metals?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, Xuefei; Zhang, Wenjing; Tang, Mingsheng

2015-05-12

Coupled-cluster (CC) methods have been extensively used as the high-level approach in quantum electronic structure theory to predict various properties of molecules when experimental results are unavailable. It is often assumed that CC methods, if they include at least up to connected-triple-excitation quasiperturbative corrections to a full treatment of single and double excitations (in particular, CCSD(T)), and a very large basis set, are more accurate than Kohn–Sham (KS) density functional theory (DFT). In the present work, we tested and compared the performance of standard CC and KS methods on bond energy calculations of 20 3d transition metal-containing diatomic molecules againstmore » the most reliable experimental data available, as collected in a database called 3dMLBE20. It is found that, although the CCSD(T) and higher levels CC methods have mean unsigned deviations from experiment that are smaller than most exchange-correlation functionals for metal–ligand bond energies of transition metals, the improvement is less than one standard deviation of the mean unsigned deviation. Furthermore, on average, almost half of the 42 exchange-correlation functionals that we tested are closer to experiment than CCSD(T) with the same extended basis set for the same molecule. The results show that, when both relativistic and core–valence correlation effects are considered, even the very high-level (expensive) CC method with single, double, triple, and perturbative quadruple cluster operators, namely, CCSDT(2)Q, averaged over 20 bond energies, gives a mean unsigned deviation (MUD(20) = 4.7 kcal/mol when one correlates only valence, 3p, and 3s electrons of transition metals and only valence electrons of ligands, or 4.6 kcal/mol when one correlates all core electrons except for 1s shells of transition metals, S, and Cl); and that is similar to some good xc functionals (e.g., B97-1 (MUD(20) = 4.5 kcal/mol) and PW6B95 (MUD(20) = 4.9 kcal/mol)) when the same basis set is used. We found that, for both coupled cluster calculations and KS calculations, the T1 diagnostics correlate the errors better than either the M diagnostics or the B1 DFT-based diagnostics. The potential use of practical standard CC methods as a benchmark theory is further confounded by the finding that CC and DFT methods usually have different signs of the error. We conclude that the available experimental data do not provide a justification for using conventional single-reference CC theory calculations to validate or test xc functionals for systems involving 3d transition metals.« less

Construction and application of a new dual-hybrid random phase approximation.

PubMed

Mezei, Pál D; Csonka, Gábor I; Ruzsinszky, Adrienn; Kállay, Mihály

2015-10-13

The direct random phase approximation (dRPA) combined with Kohn-Sham reference orbitals is among the most promising tools in computational chemistry and applicable in many areas of chemistry and physics. The reason for this is that it scales as N(4) with the system size, which is a considerable advantage over the accurate ab initio wave function methods like standard coupled-cluster. dRPA also yields a considerably more accurate description of thermodynamic and electronic properties than standard density-functional theory methods. It is also able to describe strong static electron correlation effects even in large systems with a small or vanishing band gap missed by common single-reference methods. However, dRPA has several flaws due to its self-correlation error. In order to obtain accurate and precise reaction energies, barriers and noncovalent intra- and intermolecular interactions, we construct a new dual-hybrid dRPA (hybridization of exact and semilocal exchange in both the energy and the orbitals) and test the performance of this new functional on isogyric, isodesmic, hypohomodesmotic, homodesmotic, and hyperhomodesmotic reaction classes. We also use a test set of 14 Diels-Alder reactions, six atomization energies (AE6), 38 hydrocarbon atomization energies, and 100 reaction barrier heights (DBH24, HT-BH38, and NHT-BH38). For noncovalent complexes, we use the NCCE31 and S22 test sets. To test the intramolecular interactions, we use a set of alkane, cysteine, phenylalanine-glycine-glycine tripeptide, and monosaccharide conformers. We also discuss the delocalization and static correlation errors. We show that a universally accurate description of chemical properties can be provided by a large, 75% exact exchange mixing both in the calculation of the reference orbitals and the final energy.

A general method for the derivation of the functional forms of the effective energy terms in coarse-grained energy functions of polymers. I. Backbone potentials of coarse-grained polypeptide chains

NASA Astrophysics Data System (ADS)

Sieradzan, Adam K.; Makowski, Mariusz; Augustynowicz, Antoni; Liwo, Adam

2017-03-01

A general and systematic method for the derivation of the functional expressions for the effective energy terms in coarse-grained force fields of polymer chains is proposed. The method is based on the expansion of the potential of mean force of the system studied in the cluster-cumulant series and expanding the all-atom energy in the Taylor series in the squares of interatomic distances about the squares of the distances between coarse-grained centers, to obtain approximate analytical expressions for the cluster cumulants. The primary degrees of freedom to average about are the angles for collective rotation of the atoms contained in the coarse-grained interaction sites about the respective virtual-bond axes. The approach has been applied to the revision of the virtual-bond-angle, virtual-bond-torsional, and backbone-local-and-electrostatic correlation potentials for the UNited RESidue (UNRES) model of polypeptide chains, demonstrating the strong dependence of the torsional and correlation potentials on virtual-bond angles, not considered in the current UNRES. The theoretical considerations are illustrated with the potentials calculated from the ab initio potential-energy surface of terminally blocked alanine by numerical integration and with the statistical potentials derived from known protein structures. The revised torsional potentials correctly indicate that virtual-bond angles close to 90° result in the preference for the turn and helical structures, while large virtual-bond angles result in the preference for polyproline II and extended backbone geometry. The revised correlation potentials correctly reproduce the preference for the formation of β-sheet structures for large values of virtual-bond angles and for the formation of α-helical structures for virtual-bond angles close to 90°.

Fluctuation Diagnostics of the Electron Self-Energy: Origin of the Pseudogap Physics.

PubMed

Gunnarsson, O; Schäfer, T; LeBlanc, J P F; Gull, E; Merino, J; Sangiovanni, G; Rohringer, G; Toschi, A

2015-06-12

We demonstrate how to identify which physical processes dominate the low-energy spectral functions of correlated electron systems. We obtain an unambiguous classification through an analysis of the equation of motion for the electron self-energy in its charge, spin, and particle-particle representations. Our procedure is then employed to clarify the controversial physics responsible for the appearance of the pseudogap in correlated systems. We illustrate our method by examining the attractive and repulsive Hubbard model in two dimensions. In the latter, spin fluctuations are identified as the origin of the pseudogap, and we also explain why d-wave pairing fluctuations play a marginal role in suppressing the low-energy spectral weight, independent of their actual strength.

Extracting p Λ scattering lengths from heavy ion collisions

NASA Astrophysics Data System (ADS)

Shapoval, V. M.; Erazmus, B.; Lednicky, R.; Sinyukov, Yu. M.

2015-09-01

The source radii previously extracted by the STAR Collaboration from the p -Λ ⊕p ¯-Λ ¯ and p ¯-Λ ⊕p -Λ ¯ correlation functions measured in 10% most central Au+Au collisions at top Relativistic Heavy Ion Collider (RHIC) energy, √{sN N}=200 GeV, differ by a factor of 2. The probable reason for this is the neglect of residual correlation effect in the STAR analysis. In the present paper we analyze baryon correlation functions within the Lednický and Lyuboshitz analytical model, extended to effectively account for the residual correlation contribution. Different analytical approximations for such a contribution are considered. We also use the averaged source radii extracted from hydrokinetic model (HKM) simulations to fit the experimental data. In contrast to the STAR experimental study, the calculations in HKM show both p Λ and p Λ ¯ radii to be quite close, as expected from theoretical considerations. Using the effective Gaussian parametrization of residual correlations we obtain a satisfactory fit to the measured baryon-antibaryon correlation function with the HKM source radius value 3.28 fm. The baryon-antibaryon spin-averaged strong interaction scattering length is also extracted from the fit to the experimental correlation function.

Multiconfiguration Pair-Density Functional Theory Outperforms Kohn-Sham Density Functional Theory and Multireference Perturbation Theory for Ground-State and Excited-State Charge Transfer.

PubMed

Ghosh, Soumen; Sonnenberger, Andrew L; Hoyer, Chad E; Truhlar, Donald G; Gagliardi, Laura

2015-08-11

The correct description of charge transfer in ground and excited states is very important for molecular interactions, photochemistry, electrochemistry, and charge transport, but it is very challenging for Kohn-Sham (KS) density functional theory (DFT). KS-DFT exchange-correlation functionals without nonlocal exchange fail to describe both ground- and excited-state charge transfer properly. We have recently proposed a theory called multiconfiguration pair-density functional theory (MC-PDFT), which is based on a combination of multiconfiguration wave function theory with a new type of density functional called an on-top density functional. Here we have used MC-PDFT to study challenging ground- and excited-state charge-transfer processes by using on-top density functionals obtained by translating KS exchange-correlation functionals. For ground-state charge transfer, MC-PDFT performs better than either the PBE exchange-correlation functional or CASPT2 wave function theory. For excited-state charge transfer, MC-PDFT (unlike KS-DFT) shows qualitatively correct behavior at long-range with great improvement in predicted excitation energies.

gRINN: a tool for calculation of residue interaction energies and protein energy network analysis of molecular dynamics simulations.

PubMed

Serçinoglu, Onur; Ozbek, Pemra

2018-05-25

Atomistic molecular dynamics (MD) simulations generate a wealth of information related to the dynamics of proteins. If properly analyzed, this information can lead to new insights regarding protein function and assist wet-lab experiments. Aiming to identify interactions between individual amino acid residues and the role played by each in the context of MD simulations, we present a stand-alone software called gRINN (get Residue Interaction eNergies and Networks). gRINN features graphical user interfaces (GUIs) and a command-line interface for generating and analyzing pairwise residue interaction energies and energy correlations from protein MD simulation trajectories. gRINN utilizes the features of NAMD or GROMACS MD simulation packages and automatizes the steps necessary to extract residue-residue interaction energies from user-supplied simulation trajectories, greatly simplifying the analysis for the end-user. A GUI, including an embedded molecular viewer, is provided for visualization of interaction energy time-series, distributions, an interaction energy matrix, interaction energy correlations and a residue correlation matrix. gRINN additionally offers construction and analysis of Protein Energy Networks, providing residue-based metrics such as degrees, betweenness-centralities, closeness centralities as well as shortest path analysis. gRINN is free and open to all users without login requirement at http://grinn.readthedocs.io.

Modeling the adiabatic connection in H2.

PubMed

Peach, Michael J G; Teale, Andrew M; Tozer, David J

2007-06-28

Full configuration interaction (FCI) data are used to quantify the accuracy of approximate adiabatic connection (AC) forms in describing the ground state potential energy curve of H2, within spin-restricted density functional theory (DFT). For each internuclear separation R, accurate properties of the AC are determined from large basis set FCI calculations. The parameters in the approximate AC form are then determined so as to reproduce these FCI values exactly, yielding an exchange-correlation energy expressed entirely in terms of FCI-derived quantities. This is combined with other FCI-derived energy components to give the total electronic energy; comparison with the FCI energy quantifies the accuracy of the AC form. Initial calculations focus on a [1/1]-Padé-based form. The potential energy curve determined using the procedure is a notable improvement over those from existing DFT functionals. The accuracy near equilibrium is quantified by calculating the bond length and vibrational wave numbers; errors in the latter are below 0.5%. The molecule dissociates correctly, which can be traced to the use of virtual orbital eigenvalues in the slope in the noninteracting limit, capturing static correlation. At intermediate R, the potential energy curve exhibits an unphysical barrier, similar to that noted previously using the random phase approximation. Alternative forms of the AC are also considered, paying attention to size extensivity and the behavior in the strong-interaction limit; none provide an accurate potential energy curve for all R, although good accuracy can be achieved near equilibrium. The study demonstrates how data from correlated ab initio calculations can provide valuable information about AC forms and highlight areas where further theoretical progress is required.

Extension of the KLI approximation toward the exact optimized effective potential.

PubMed

Iafrate, G J; Krieger, J B

2013-03-07

The integral equation for the optimized effective potential (OEP) is utilized in a compact form from which an accurate OEP solution for the spin-unrestricted exchange-correlation potential, Vxcσ, is obtained for any assumed orbital-dependent exchange-correlation energy functional. The method extends beyond the Krieger-Li-Iafrate (KLI) approximation toward the exact OEP result. The compact nature of the OEP equation arises by replacing the integrals involving the Green's function terms in the traditional OEP equation by an equivalent first-order perturbation theory wavefunction often referred to as the "orbital shift" function. Significant progress is then obtained by solving the equation for the first order perturbation theory wavefunction by use of Dalgarno functions which are determined from well known methods of partial differential equations. The use of Dalgarno functions circumvents the need to explicitly address the Green's functions and the associated problems with "sum over states" numerics; as well, the Dalgarno functions provide ease in dealing with inherent singularities arising from the origin and the zeros of the occupied orbital wavefunctions. The Dalgarno approach for finding a solution to the OEP equation is described herein, and a detailed illustrative example is presented for the special case of a spherically symmetric exchange-correlation potential. For the case of spherical symmetry, the relevant Dalgarno function is derived by direct integration of the appropriate radial equation while utilizing a user friendly method which explicitly treats the singular behavior at the origin and at the nodal singularities arising from the zeros of the occupied states. The derived Dalgarno function is shown to be an explicit integral functional of the exact OEP Vxcσ, thus allowing for the reduction of the OEP equation to a self-consistent integral equation for the exact exchange-correlation potential; the exact solution to this integral equation can be determined by iteration with the natural zeroth order correction given by the KLI exchange-correlation potential. Explicit analytic results are provided to illustrate the first order iterative correction beyond the KLI approximation. The derived correction term to the KLI potential explicitly involves spatially weighted products of occupied orbital densities in any assumed orbital-dependent exchange-correlation energy functional; as well, the correction term is obtained with no adjustable parameters. Moreover, if the equation for the exact optimized effective potential is further iterated, one can obtain the OEP as accurately as desired.

Extension of the KLI approximation toward the exact optimized effective potential

NASA Astrophysics Data System (ADS)

Iafrate, G. J.; Krieger, J. B.

2013-03-01

The integral equation for the optimized effective potential (OEP) is utilized in a compact form from which an accurate OEP solution for the spin-unrestricted exchange-correlation potential, Vxcσ, is obtained for any assumed orbital-dependent exchange-correlation energy functional. The method extends beyond the Krieger-Li-Iafrate (KLI) approximation toward the exact OEP result. The compact nature of the OEP equation arises by replacing the integrals involving the Green's function terms in the traditional OEP equation by an equivalent first-order perturbation theory wavefunction often referred to as the "orbital shift" function. Significant progress is then obtained by solving the equation for the first order perturbation theory wavefunction by use of Dalgarno functions which are determined from well known methods of partial differential equations. The use of Dalgarno functions circumvents the need to explicitly address the Green's functions and the associated problems with "sum over states" numerics; as well, the Dalgarno functions provide ease in dealing with inherent singularities arising from the origin and the zeros of the occupied orbital wavefunctions. The Dalgarno approach for finding a solution to the OEP equation is described herein, and a detailed illustrative example is presented for the special case of a spherically symmetric exchange-correlation potential. For the case of spherical symmetry, the relevant Dalgarno function is derived by direct integration of the appropriate radial equation while utilizing a user friendly method which explicitly treats the singular behavior at the origin and at the nodal singularities arising from the zeros of the occupied states. The derived Dalgarno function is shown to be an explicit integral functional of the exact OEP Vxcσ, thus allowing for the reduction of the OEP equation to a self-consistent integral equation for the exact exchange-correlation potential; the exact solution to this integral equation can be determined by iteration with the natural zeroth order correction given by the KLI exchange-correlation potential. Explicit analytic results are provided to illustrate the first order iterative correction beyond the KLI approximation. The derived correction term to the KLI potential explicitly involves spatially weighted products of occupied orbital densities in any assumed orbital-dependent exchange-correlation energy functional; as well, the correction term is obtained with no adjustable parameters. Moreover, if the equation for the exact optimized effective potential is further iterated, one can obtain the OEP as accurately as desired.

Multireference second order perturbation theory with a simplified treatment of dynamical correlation.

PubMed

Xu, Enhua; Zhao, Dongbo; Li, Shuhua

2015-10-13

A multireference second order perturbation theory based on a complete active space configuration interaction (CASCI) function or density matrix renormalized group (DMRG) function has been proposed. This method may be considered as an approximation to the CAS/A approach with the same reference, in which the dynamical correlation is simplified with blocked correlated second order perturbation theory based on the generalized valence bond (GVB) reference (GVB-BCPT2). This method, denoted as CASCI-BCPT2/GVB or DMRG-BCPT2/GVB, is size consistent and has a similar computational cost as the conventional second order perturbation theory (MP2). We have applied it to investigate a number of problems of chemical interest. These problems include bond-breaking potential energy surfaces in four molecules, the spectroscopic constants of six diatomic molecules, the reaction barrier for the automerization of cyclobutadiene, and the energy difference between the monocyclic and bicyclic forms of 2,6-pyridyne. Our test applications demonstrate that CASCI-BCPT2/GVB can provide comparable results with CASPT2 (second order perturbation theory based on the complete active space self-consistent-field wave function) for systems under study. Furthermore, the DMRG-BCPT2/GVB method is applicable to treat strongly correlated systems with large active spaces, which are beyond the capability of CASPT2.

Microscopic Electron Variations Measured Simultaneously By The Cluster Spacecraft

NASA Astrophysics Data System (ADS)

Buckley, A. M.; Carozzi, T. D.; Gough, M. P.; Beloff, N.

Data is used from the Particle Correlator experiments running on each of the four Cluster spacecraft so as to determine common microscopic behaviour in the elec- tron population observed over the macroscopic Cluster separations. The Cluster par- ticle correlator experiments operate by forming on board Auto Correlation Functions (ACFs) generated from short time series of electron counts obtained, as a function of electron energy, from the PEACE HEEA sensor. The information on the microscopic variation of the electron flux covers the frequency range DC up to 41 kHz (encom- passing typical electron plasma frequencies and electron gyro frequencies and their harmonics), the electron energy range is that covered by the PEACE HEEA sensor (within the range 1 eV to 26 keV). Results are presented of coherent electron struc- tures observed simultaneously by the four spacecraft in the differing plasma interac- tion regions and boundaries encountered by Cluster. As an aid to understanding the plasma interactions, use is made of numerical simulations which model both the un- derlying statistical properties of the electrons and also the manner in which particle correlator experiments operate.

Investigation of the 9B nucleus and its cluster-nucleon correlations

NASA Astrophysics Data System (ADS)

Zhao, Qing; Ren, Zhongzhou; Lyu, Mengjiao; Horiuchi, Hisashi; Funaki, Yasuro; Röpke, Gerd; Schuck, Peter; Tohsaki, Akihiro; Xu, Chang; Yamada, Taiichi; Zhou, Bo

2018-05-01

In order to study the correlations between clusters and nucleons in light nuclei, we formulate a new superposed Tohsaki-Horiuchi-Schuck-Röpke (THSR) wave function which describes both spatially large spreading and cluster-correlated dynamics of valence nucleons. Using this new THSR wave function, the binding energy of 9B is significantly improved in comparison with our previous studies. We calculate the excited states of 9B and obtain an energy spectrum of 9B which is consistent with the experimental results. This includes the prediction of the first 1 /2+ excited state of 9B which is not yet fixed experimentally. We study the proton dynamics in 9B and find that the cluster-proton correlation plays an essential role for the proton dynamics in the ground state of 9B. Furthermore, we discuss the density distribution of the valence proton with special attention to its tail structure. Finally, the resonance nature of excited states of 9B is illustrated comparing root-mean-square radii between the ground and excited states.

Non-empirical exchange-correlation parameterizations based on exact conditions from correlated orbital theory.

PubMed

Haiduke, Roberto Luiz A; Bartlett, Rodney J

2018-05-14

Some of the exact conditions provided by the correlated orbital theory are employed to propose new non-empirical parameterizations for exchange-correlation functionals from Density Functional Theory (DFT). This reparameterization process is based on range-separated functionals with 100% exact exchange for long-range interelectronic interactions. The functionals developed here, CAM-QTP-02 and LC-QTP, show mitigated self-interaction error, correctly predict vertical ionization potentials as the negative of eigenvalues for occupied orbitals, and provide nice excitation energies, even for challenging charge-transfer excited states. Moreover, some improvements are observed for reaction barrier heights with respect to the other functionals belonging to the quantum theory project (QTP) family. Finally, the most important achievement of these new functionals is an excellent description of vertical electron affinities (EAs) of atoms and molecules as the negative of appropriate virtual orbital eigenvalues. In this case, the mean absolute deviations for EAs in molecules are smaller than 0.10 eV, showing that physical interpretation can indeed be ascribed to some unoccupied orbitals from DFT.

Non-empirical exchange-correlation parameterizations based on exact conditions from correlated orbital theory

NASA Astrophysics Data System (ADS)

Haiduke, Roberto Luiz A.; Bartlett, Rodney J.

2018-05-01

Some of the exact conditions provided by the correlated orbital theory are employed to propose new non-empirical parameterizations for exchange-correlation functionals from Density Functional Theory (DFT). This reparameterization process is based on range-separated functionals with 100% exact exchange for long-range interelectronic interactions. The functionals developed here, CAM-QTP-02 and LC-QTP, show mitigated self-interaction error, correctly predict vertical ionization potentials as the negative of eigenvalues for occupied orbitals, and provide nice excitation energies, even for challenging charge-transfer excited states. Moreover, some improvements are observed for reaction barrier heights with respect to the other functionals belonging to the quantum theory project (QTP) family. Finally, the most important achievement of these new functionals is an excellent description of vertical electron affinities (EAs) of atoms and molecules as the negative of appropriate virtual orbital eigenvalues. In this case, the mean absolute deviations for EAs in molecules are smaller than 0.10 eV, showing that physical interpretation can indeed be ascribed to some unoccupied orbitals from DFT.

Semilocal Exchange Energy Functional for Two-Dimensional Quantum Systems: A Step Beyond Generalized Gradient Approximations.

PubMed

Jana, Subrata; Samal, Prasanjit

2017-06-29

Semilocal density functionals for the exchange-correlation energy of electrons are extensively used as they produce realistic and accurate results for finite and extended systems. The choice of techniques plays a crucial role in constructing such functionals of improved accuracy and efficiency. An accurate and efficient semilocal exchange energy functional in two dimensions is constructed by making use of the corresponding hole which is derived based on the density matrix expansion. The exchange hole involved is localized under the generalized coordinate transformation and satisfies all the relevant constraints. Comprehensive testing and excellent performance of the functional is demonstrated versus exact exchange results. The accuracy of results obtained by using the newly constructed functional is quite remarkable as it substantially reduces the errors present in the local and nonempirical exchange functionals proposed so far for two-dimensional quantum systems. The underlying principles involved in the functional construction are physically appealing and hold promise for developing range separated and nonlocal exchange functionals in two dimensions.

Communication: A new class of non-empirical explicit density functionals on the third rung of Jacob's ladder

NASA Astrophysics Data System (ADS)

de Silva, Piotr; Corminboeuf, Clémence

2015-09-01

We construct an orbital-free non-empirical meta-generalized gradient approximation (GGA) functional, which depends explicitly on density through the density overlap regions indicator [P. de Silva and C. Corminboeuf, J. Chem. Theory Comput. 10, 3745 (2014)]. The functional does not depend on either the kinetic energy density or the density Laplacian; therefore, it opens a new class of meta-GGA functionals. By construction, our meta-GGA yields exact exchange and correlation energy for the hydrogen atom and recovers the second order gradient expansion for exchange in the slowly varying limit. We show that for molecular systems, overall performance is better than non-empirical GGAs. For atomization energies, performance is on par with revTPSS, without any dependence on Kohn-Sham orbitals.

Removing the barrier to the calculation of activation energies

DOE PAGES

Mesele, Oluwaseun O.; Thompson, Ward H.

2016-10-06

Approaches for directly calculating the activation energy for a chemical reaction from a simulation at a single temperature are explored with applications to both classical and quantum systems. The activation energy is obtained from a time correlation function that can be evaluated from the same molecular dynamics trajectories or quantum dynamics used to evaluate the rate constant itself and thus requires essentially no extra computational work.

Natural occupation numbers in two-electron quantum rings.

PubMed

Tognetti, Vincent; Loos, Pierre-François

2016-02-07

Natural orbitals (NOs) are central constituents for evaluating correlation energies through efficient approximations. Here, we report the closed-form expression of the NOs of two-electron quantum rings, which are prototypical finite-extension systems and new starting points for the development of exchange-correlation functionals in density functional theory. We also show that the natural occupation numbers for these two-electron paradigms are in general non-vanishing and follow the same power law decay as atomic and molecular two-electron systems.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pribram-Jones, A.; Burke, K.

We show that the adiabatic connection formula of ground-state density functional theory relates the correlation energy to a coupling-constant integral over a purely potential contribution, and is widely used to understand and improve approximations. The corresponding formula for thermal density functional theory is cast as an integral over temperatures instead, ranging upward from the system's physical temperature. We also show how to relate different correlation components to each other, either in terms of temperature or coupling-constant integrations. Lastly, we illustrate our results on the uniform electron gas.

Fractional Ornstein-Uhlenbeck noise

NASA Astrophysics Data System (ADS)

Fa, Kwok Sau

2018-06-01

Fractional Ornstein-Uhlenbeck noise is considered and investigated. The fractional Ornstein-Uhlenbeck noise may be linked with a supercapacitor driven by the white noise, and its correlation function for the stationary state shows monotonic and oscillatory decays. In the case of the oscillatory behavior the correlation function presents behaviors similar to those of the harmonic noise (harmonic oscillator driven by the white noise). For application, the Langevin equation with the harmonic potential driven by the fractional Ornstein-Uhlenbeck noise is considered; the first two moments and mean energy are investigated.

Natural occupation numbers in two-electron quantum rings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tognetti, Vincent, E-mail: vincent.tognetti@univ-rouen.fr; Loos, Pierre-François

2016-02-07

Natural orbitals (NOs) are central constituents for evaluating correlation energies through efficient approximations. Here, we report the closed-form expression of the NOs of two-electron quantum rings, which are prototypical finite-extension systems and new starting points for the development of exchange-correlation functionals in density functional theory. We also show that the natural occupation numbers for these two-electron paradigms are in general non-vanishing and follow the same power law decay as atomic and molecular two-electron systems.

Scalable properties of metal clusters: A comparative study of modern exchange-correlation functionals

NASA Astrophysics Data System (ADS)

Koitz, Ralph; Soini, Thomas M.; Genest, Alexander; Trickey, S. B.; Rösch, Notker

2012-07-01

The performance of eight generalized gradient approximation exchange-correlation (xc) functionals is assessed by a series of scalar relativistic all-electron calculations on octahedral palladium model clusters Pdn with n = 13, 19, 38, 55, 79, 147 and the analogous clusters Aun (for n up through 79). For these model systems, we determined the cohesive energies and average bond lengths of the optimized octahedral structures. We extrapolate these values to the bulk limits and compare with the corresponding experimental values. While the well-established functionals BP, PBE, and PW91 are the most accurate at predicting energies, the more recent forms PBEsol, VMTsol, and VT{84}sol significantly improve the accuracy of geometries. The observed trends are largely similar for both Pd and Au. In the same spirit, we also studied the scalability of the ionization potentials and electron affinities of the Pd clusters, and extrapolated those quantities to estimates of the work function. Overall, the xc functionals can be classified into four distinct groups according to the accuracy of the computed parameters. These results allow a judicious selection of xc approximations for treating transition metal clusters.

Chemical accuracy from quantum Monte Carlo for the benzene dimer.

PubMed

Azadi, Sam; Cohen, R E

2015-09-14

We report an accurate study of interactions between benzene molecules using variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods. We compare these results with density functional theory using different van der Waals functionals. In our quantum Monte Carlo (QMC) calculations, we use accurate correlated trial wave functions including three-body Jastrow factors and backflow transformations. We consider two benzene molecules in the parallel displaced geometry, and find that by highly optimizing the wave function and introducing more dynamical correlation into the wave function, we compute the weak chemical binding energy between aromatic rings accurately. We find optimal VMC and DMC binding energies of -2.3(4) and -2.7(3) kcal/mol, respectively. The best estimate of the coupled-cluster theory through perturbative triplets/complete basis set limit is -2.65(2) kcal/mol [Miliordos et al., J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate that QMC methods give chemical accuracy for weakly bound van der Waals molecular interactions, comparable to results from the best quantum chemistry methods.

Computational study of An-X bonding (An = Th, U; X = p-block-based ligands) in pyrrolic macrocycle-supported complexes from the quantum theory of atoms in molecules and bond energy decomposition analysis.

PubMed

O'Brien, Kieran T P; Kaltsoyannis, Nikolas

2017-01-17

A systematic computational study of organoactinide complexes of the form [LAnX] n+ has been carried out using density functional theory, the quantum theory of atoms in molecules (QTAIM) and Ziegler-Rauk energy decomposition analysis (EDA) methods. The systems studied feature L = trans-calix[2]benzene[2]pyrrolide, An = Th(iv), Th(iii), U(iii) and X = BH 4 , BO 2 C 2 H 4 , Me, N(SiH 3 ) 2 , OPh, CH 3 , NH 2 , OH, F, SiH 3 , PH 2 , SH, Cl, CH 2 Ph, NHPh, OPh, SiH 2 Ph, PHPh 2 , SPh, CPh 3 , NPh 2 , OPh, SiPh 3 PPh 2 , SPh. The PBE0 hybrid functional proved most suitable for geometry optimisations based on comparisons with available experimental data. An-X bond critical point electron densities, energy densities and An-X delocalisation indices, calculated with the PBE functional at the PBE0 geometries, are correlated with An-X bond energies, enthalpies and with the terms in the EDA. Good correlations are found between energies and QTAIM metrics, particularly for the orbital interaction term, provided the X ligand is part of an isoelectronic series and the number of open shell electrons is low (i.e. for the present Th(iv) and Th(iii) systems).

Theoretical study of transition-metal ions bound to benzene

NASA Technical Reports Server (NTRS)

Bauschlicher, Charles W., Jr.; Partridge, Harry; Langhoff, Stephen R.

1992-01-01

Theoretical binding energies are reported for all first-row and selected second-row transition metal ions (M+) bound to benzene. The calculations employ basis sets of at least double-zeta plus polarization quality and account for electron correlation using the modified coupled-pair functional method. While the bending is predominantly electrostatic, the binding energies are significantly increased by electron correlation, because the donation from the metal d orbitals to the benzene pi* orbitals is not well described at the self-consistent-field level. The uncertainties in the computed binding energies are estimated to be about 5 kcal/mol. Although the calculated and experimental binding energies generally agree to within their combined uncertainties, it is likely that the true binding energies lie in the lower portion of the experimental range. This is supported by the very good agreement between the theoretical and recent experimental binding energies for AgC6H6(+).

Optimized Hypernetted-Chain Solutions for Helium -4 Surfaces and Metal Surfaces

NASA Astrophysics Data System (ADS)

Qian, Guo-Xin

This thesis is a study of inhomogeneous Bose systems such as liquid ('4)He slabs and inhomogeneous Fermi systems such as the electron gas in metal films, at zero temperature. Using a Jastrow-type many-body wavefunction, the ground state energy is expressed by means of Bogoliubov-Born-Green-Kirkwood -Yvon and Hypernetted-Chain techniques. For Bose systems, Euler-Lagrange equations are derived for the one- and two -body functions and systematic approximation methods are physically motivated. It is shown that the optimized variational method includes a self-consistent summation of ladder- and ring-diagrams of conventional many-body theory. For Fermi systems, a linear potential model is adopted to generate the optimized Hartree-Fock basis. Euler-Lagrange equations are derived for the two-body correlations which serve to screen the strong bare Coulomb interaction. The optimization of the pair correlation leads to an expression of correlation energy in which the state averaged RPA part is separated. Numerical applications are presented for the density profile and pair distribution function for both ('4)He surfaces and metal surfaces. Both the bulk and surface energies are calculated in good agreement with experiments.

A time-correlation function approach to nuclear dynamical effects in X-ray spectroscopy

NASA Astrophysics Data System (ADS)

Karsten, Sven; Bokarev, Sergey I.; Aziz, Saadullah G.; Ivanov, Sergei D.; Kühn, Oliver

2017-06-01

Modern X-ray spectroscopy has proven itself as a robust tool for probing the electronic structure of atoms in complex environments. Despite working on energy scales that are much larger than those corresponding to nuclear motions, taking nuclear dynamics and the associated nuclear correlations into account may be of importance for X-ray spectroscopy. Recently, we have developed an efficient protocol to account for nuclear dynamics in X-ray absorption and resonant inelastic X-ray scattering spectra [Karsten et al., J. Phys. Chem. Lett. 8, 992 (2017)], based on ground state molecular dynamics accompanied with state-of-the-art calculations of electronic excitation energies and transition dipoles. Here, we present an alternative derivation of the formalism and elaborate on the developed simulation protocol using gas phase and bulk water as examples. The specific spectroscopic features stemming from the nuclear motions are analyzed and traced down to the dynamics of electronic energy gaps and transition dipole correlation functions. The observed tendencies are explained on the basis of a simple harmonic model, and the involved approximations are discussed. The method represents a step forward over the conventional approaches that treat the system in full complexity and provides a reasonable starting point for further improvements.

A time-correlation function approach to nuclear dynamical effects in X-ray spectroscopy.

PubMed

Karsten, Sven; Bokarev, Sergey I; Aziz, Saadullah G; Ivanov, Sergei D; Kühn, Oliver

2017-06-14

Modern X-ray spectroscopy has proven itself as a robust tool for probing the electronic structure of atoms in complex environments. Despite working on energy scales that are much larger than those corresponding to nuclear motions, taking nuclear dynamics and the associated nuclear correlations into account may be of importance for X-ray spectroscopy. Recently, we have developed an efficient protocol to account for nuclear dynamics in X-ray absorption and resonant inelastic X-ray scattering spectra [Karsten et al., J. Phys. Chem. Lett. 8, 992 (2017)], based on ground state molecular dynamics accompanied with state-of-the-art calculations of electronic excitation energies and transition dipoles. Here, we present an alternative derivation of the formalism and elaborate on the developed simulation protocol using gas phase and bulk water as examples. The specific spectroscopic features stemming from the nuclear motions are analyzed and traced down to the dynamics of electronic energy gaps and transition dipole correlation functions. The observed tendencies are explained on the basis of a simple harmonic model, and the involved approximations are discussed. The method represents a step forward over the conventional approaches that treat the system in full complexity and provides a reasonable starting point for further improvements.

Conical intersections of free energy surfaces in solution: Effect of electron correlation on a protonated Schiff base in methanol solution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mori, Toshifumi; Nakano, Katsuhiro; Kato, Shigeki

2010-08-14

The minimum energy conical intersection (MECI) optimization method with taking account of the dynamic electron correlation effect [T. Mori and S. Kato, Chem. Phys. Lett. 476, 97 (2009)] is extended to locate the MECI of nonequilibrium free energy surfaces in solution. A multistate electronic perturbation theory is introduced into the nonequilibrium free energy formula, which is defined as a function of solute and solvation coordinates. The analytical free energy gradient and interstate coupling vectors are derived, and are applied to locate MECIs in solution. The present method is applied to study the cis-trans photoisomerization reaction of a protonated Schiff basemore » molecule (PSB3) in methanol (MeOH) solution. It is found that the effect of dynamic electron correlation largely lowers the energy of S{sub 1} state. We also show that the solvation effect strongly stabilizes the MECI obtained by twisting the terminal C=N bond to become accessible in MeOH solution, whereas the conical intersection is found to be unstable in gas phase. The present study indicates that both electron correlation and solvation effects are important in the photoisomerization reaction of PSB3. The effect of counterion is also examined, and seems to be rather small in solution. The structures of free energy surfaces around MECIs are also discussed.« less

Uniform electron gases. III. Low-density gases on three-dimensional spheres.

PubMed

Agboola, Davids; Knol, Anneke L; Gill, Peter M W; Loos, Pierre-François

2015-08-28

By combining variational Monte Carlo (VMC) and complete-basis-set limit Hartree-Fock (HF) calculations, we have obtained near-exact correlation energies for low-density same-spin electrons on a three-dimensional sphere (3-sphere), i.e., the surface of a four-dimensional ball. In the VMC calculations, we compare the efficacies of two types of one-electron basis functions for these strongly correlated systems and analyze the energy convergence with respect to the quality of the Jastrow factor. The HF calculations employ spherical Gaussian functions (SGFs) which are the curved-space analogs of Cartesian Gaussian functions. At low densities, the electrons become relatively localized into Wigner crystals, and the natural SGF centers are found by solving the Thomson problem (i.e., the minimum-energy arrangement of n point charges) on the 3-sphere for various values of n. We have found 11 special values of n whose Thomson sites are equivalent. Three of these are the vertices of four-dimensional Platonic solids - the hyper-tetrahedron (n = 5), the hyper-octahedron (n = 8), and the 24-cell (n = 24) - and a fourth is a highly symmetric structure (n = 13) which has not previously been reported. By calculating the harmonic frequencies of the electrons around their equilibrium positions, we also find the first-order vibrational corrections to the Thomson energy.

The Portuguese version of the Epilepsy Surgery Inventory (ESI-55): cross-cultural adaptation and evaluation of psychometric properties.

PubMed

Alonso, Neide Barreira; Ciconelli, Rozana Mesquita; da Silva, Tatiana Indelicato; Westphal-Guitti, Ana Carolina; Azevedo, Auro Mauro; da Silva Noffs, Maria Helena; Caboclo, Luís Otávio Sales Ferreira; Sakamoto, Américo Ceiki; Targas Yacubian, Elza Márcia

2006-08-01

The purpose of this study was to develop a Portuguese version of the Epilepsy Surgery Inventory (ESI-55) and to assess its psychometric properties. Sixty patients with temporal lobe epilepsy related to unilateral mesial temporal sclerosis who underwent presurgical evaluation at the Universidade Federal de São Paulo (UNIFESP) formed the sample for this study. The psychometric properties of the ESI-55 included: reliability, validity, and responsiveness. Internal consistency was high in all domains (Cronbach's alpha ranging from 0.76 for Social Function to 0.88 for Physical Function) except Overall Quality of Life (alpha=0.45). Test-retest reliability after 1 week was good, with the intraclass correlation coefficient ranging from 0.79 (Energy/Fatigue) to 0.92 (Role Limitations due to Emotional Problems). Interrater reliability ranged from 0.84 (Cognitive Function) to 0.94 (Role Limitations due to Physical Problems). For construct validity, we verified a high correlation between the ESI-55 and Health Assessment Questionnaire-8 for the Physical Function domain (Pearson linear correlation=-0.84), and a moderate correlation for the Pain domain (P=-0.58), but for the other subscales no correlation was detected. Beck Depression Inventory and ESI-55 domains were highly statistically correlated (ANOVA: P<0.005), but there was no association of the Cognitive Function and Role Limitations due to Memory Problems subscales with neuropsychological evaluation (Pearson coefficient: P>0.05). With respect to demographic characteristics, a statistically significant correlation was observed for the variable educational level (Student t, P<0.005) and ESI-55 scores. There was a high correlation between seizure frequency and ESI-55 domains for clinical variables (ANOVA, P<0.005). Surgical treatment in this series improved health-related quality of life in the seizure-free group in three domains--Health Perception (1.24), Emotional Well-Being (1.32), and Energy/Fatigue (1.48)-as reflected by the standard response mean and the effect size of the sample. Our results support the psychometric properties of the Portuguese version of the ESI-55 as a measure of health-related quality of life.

FIBER AND INTEGRAL OPTICS: Mode composition of radiation in graded-index waveguides with random microbending of the axis

NASA Astrophysics Data System (ADS)

Valyaev, A. B.; Krivoshlykov, S. G.

1989-06-01

It is shown that the problem of investigating the mode composition of a partly coherent radiation beam in a randomly inhomogeneous medium can be reduced to a study of evolution of the energy of individual modes and of the coefficients of correlations between the modes. General expressions are obtained for the coupling coefficients of modes in a parabolic waveguide with a random microbending of the axis and an analysis is made of their evolution as a function of the excitation conditions. An estimate is obtained of the distance in which a steady-state energy distribution between the modes is established. Explicit expressions are obtained for the correlation function in the case when a waveguide is excited by off-axial Gaussian beams or Gauss-Hermite modes.

Ab-initio study of electronic structure and elastic properties of ZrC

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mund, H. S., E-mail: hmoond@gmail.com; Ahuja, B. L.

2016-05-23

The electronic and elastic properties of ZrC have been investigated using the linear combination of atomic orbitals method within the framework of density functional theory. Different exchange-correlation functionals are taken into account within generalized gradient approximation. We have computed energy bands, density of states, elastic constants, bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, lattice parameters and pressure derivative of the bulk modulus by calculating ground state energy of the rock salt structure type ZrC.

The Measurement of the Evaporation Residues Excitation Functions in the Fusion Reactions 144Sm (40Ar,xn) and 166Er(40Ar,xn)

NASA Astrophysics Data System (ADS)

Chernysheva, E. V.; Rodin, A. M.; Belozerov, A. V.; Dmitriev, S. N.; Gulyaev, A. V.; Gulyaeva, A. V.; Itkis, M. G.; Novoselov, A. S.; Oganessian, Yu. Ts.; Salamatin, V. S.; Stepantsov, S. V.; Vedeneev, V. Yu.; Yukhimchuk, S. A.; Krupa, L.; Kliman, J.; Motycak, S.; Sivacek, I.

2015-06-01

The evaporation residues excitation functions for the reactions 40Ar+144Sm→184Hg and 40Ar+166Er→206Rn were measured at the energies below and above the Coulomb barrier (Elab=142-207 MeV) using a mass-separator MASHA. The experimental data were compared with theoretical calculations using a Channel Coupling Model. The influence of experimental beam energy spread on the excitation functions was taking into account. It was found that structure of xn-cross sections correlate strongly with the nuclear structure of colliding nuclei.

Evaluation of Density Functionals and Basis Sets for Carbohydrates

USDA-ARS?s Scientific Manuscript database

Correlated ab initio wave function calculations using MP2/aug-cc-pVTZ model chemistry have been performed for three test sets of gas phase saccharide conformations to provide reference values for their relative energies. The test sets consist of 15 conformers of alpha and beta-D-allopyranose, 15 of ...

Dispersion correction derived from first principles for density functional theory and Hartree-Fock theory.

PubMed

Guidez, Emilie B; Gordon, Mark S

2015-03-12

The modeling of dispersion interactions in density functional theory (DFT) is commonly performed using an energy correction that involves empirically fitted parameters for all atom pairs of the system investigated. In this study, the first-principles-derived dispersion energy from the effective fragment potential (EFP) method is implemented for the density functional theory (DFT-D(EFP)) and Hartree-Fock (HF-D(EFP)) energies. Overall, DFT-D(EFP) performs similarly to the semiempirical DFT-D corrections for the test cases investigated in this work. HF-D(EFP) tends to underestimate binding energies and overestimate intermolecular equilibrium distances, relative to coupled cluster theory, most likely due to incomplete accounting for electron correlation. Overall, this first-principles dispersion correction yields results that are in good agreement with coupled-cluster calculations at a low computational cost.

The neural basis of functional neuroimaging signal with positron and single-photon emission tomography.

PubMed

Sestini, S

2007-07-01

Functional imaging techniques such as positron and single-photon emission tomography exploit the relationship between neural activity, energy demand and cerebral blood flow to functionally map the brain. Despite the fact that neurobiological processes are not completely understood, several results have revealed the signals that trigger the metabolic and vascular changes accompanying variations in neural activity. Advances in this field have demonstrated that release of the major excitatory neurotransmitter glutamate initiates diverse signaling processes between neurons, astrocytes and blood perfusion, and that this signaling is crucial for the occurrence of brain imaging signals. Better understanding of the neural sites of energy consumption and the temporal correlation between energy demand, energy consumption and associated cerebrovascular hemodynamics gives novel insight into the potential of these imaging tools in the study of metabolic neurodegenerative disorders.

Fulde-Ferrell-Larkin-Ovchinnikov correlation and free fluids in the one-dimensional attractive Hubbard model

NASA Astrophysics Data System (ADS)

Cheng, Song; Yu, Yi-Cong; Batchelor, M. T.; Guan, Xi-Wen

2018-03-01

In this Rapid Communication, we show that low-energy macroscopic properties of the one-dimensional (1D) attractive Hubbard model exhibit two fluids of bound pairs and of unpaired fermions. Using the thermodynamic Bethe ansatz equations of the model, we first determine the low-temperature phase diagram and analytically calculate the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing correlation function for the partially polarized phase. We then show that for such an FFLO-like state in the low-density regime the effective chemical potentials of bound pairs and unpaired fermions behave like two free fluids. Consequently, the susceptibility, compressibility, and specific heat obey simple additivity rules, indicating the "free" particle nature of interacting fermions on a 1D lattice. In contrast to the continuum Fermi gases, the correlation critical exponents and thermodynamics of the attractive Hubbard model essentially depend on two lattice interacting parameters. Finally, we study scaling functions, the Wilson ratio and susceptibility, which provide universal macroscopic properties and dimensionless constants of interacting fermions at low energy.

Dissecting the accountability of parameterized and parameter-free single-hybrid and double-hybrid functionals for photophysical properties of TADF-based OLEDs

NASA Astrophysics Data System (ADS)

Alipour, Mojtaba; Karimi, Niloofar

2017-06-01

Organic light emitting diodes (OLEDs) based on thermally activated delayed fluorescence (TADF) emitters are an attractive category of materials that have witnessed a booming development in recent years. In the present contribution, we scrutinize the accountability of parameterized and parameter-free single-hybrid (SH) and double-hybrid (DH) functionals through the two formalisms, full time-dependent density functional theory (TD-DFT) and Tamm-Dancoff approximation (TDA), for the estimation of photophysical properties like absorption energy, emission energy, zero-zero transition energy, and singlet-triplet energy splitting of TADF molecules. According to our detailed analyses on the performance of SHs based on TD-DFT and TDA, the TDA-based parameter-free SH functionals, PBE0 and TPSS0, with one-third of exact-like exchange turned out to be the best performers in comparison to other functionals from various rungs to reproduce the experimental data of the benchmarked set. Such affordable SH approximations can thus be employed to predict and design the TADF molecules with low singlet-triplet energy gaps for OLED applications. From another perspective, considering this point that both the nonlocal exchange and correlation are essential for a more reliable description of large charge-transfer excited states, applicability of the functionals incorporating these terms, namely, parameterized and parameter-free DHs, has also been evaluated. Perusing the role of exact-like exchange, perturbative-like correlation, solvent effects, and other related factors, we find that the parameterized functionals B2π-PLYP and B2GP-PLYP and the parameter-free models PBE-CIDH and PBE-QIDH have respectable performance with respect to others. Lastly, besides the recommendation of reliable computational protocols for the purpose, hopefully this study can pave the way toward further developments of other SHs and DHs for theoretical explorations in the field of OLEDs technology.

Exploring biorthonormal transformations of pair-correlation functions in atomic structure variational calculations

NASA Astrophysics Data System (ADS)

Verdebout, S.; Jönsson, P.; Gaigalas, G.; Godefroid, M.; Froese Fischer, C.

2010-04-01

Multiconfiguration expansions frequently target valence correlation and correlation between valence electrons and the outermost core electrons. Correlation within the core is often neglected. A large orbital basis is needed to saturate both the valence and core-valence correlation effects. This in turn leads to huge numbers of configuration state functions (CSFs), many of which are unimportant. To avoid the problems inherent to the use of a single common orthonormal orbital basis for all correlation effects in the multiconfiguration Hartree-Fock (MCHF) method, we propose to optimize independent MCHF pair-correlation functions (PCFs), bringing their own orthonormal one-electron basis. Each PCF is generated by allowing single- and double-excitations from a multireference (MR) function. This computational scheme has the advantage of using targeted and optimally localized orbital sets for each PCF. These pair-correlation functions are coupled together and with each component of the MR space through a low dimension generalized eigenvalue problem. Nonorthogonal orbital sets being involved, the interaction and overlap matrices are built using biorthonormal transformation of the coupled basis sets followed by a counter-transformation of the PCF expansions. Applied to the ground state of beryllium, the new method gives total energies that are lower than the ones from traditional complete active space (CAS)-MCHF calculations using large orbital active sets. It is fair to say that we now have the possibility to account for, in a balanced way, correlation deep down in the atomic core in variational calculations.

Numerical renormalization group calculation of impurity internal energy and specific heat of quantum impurity models

NASA Astrophysics Data System (ADS)

Merker, L.; Costi, T. A.

2012-08-01

We introduce a method to obtain the specific heat of quantum impurity models via a direct calculation of the impurity internal energy requiring only the evaluation of local quantities within a single numerical renormalization group (NRG) calculation for the total system. For the Anderson impurity model we show that the impurity internal energy can be expressed as a sum of purely local static correlation functions and a term that involves also the impurity Green function. The temperature dependence of the latter can be neglected in many cases, thereby allowing the impurity specific heat Cimp to be calculated accurately from local static correlation functions; specifically via Cimp=(∂Eionic)/(∂T)+(1)/(2)(∂Ehyb)/(∂T), where Eionic and Ehyb are the energies of the (embedded) impurity and the hybridization energy, respectively. The term involving the Green function can also be evaluated in cases where its temperature dependence is non-negligible, adding an extra term to Cimp. For the nondegenerate Anderson impurity model, we show by comparison with exact Bethe ansatz calculations that the results recover accurately both the Kondo induced peak in the specific heat at low temperatures as well as the high-temperature peak due to the resonant level. The approach applies to multiorbital and multichannel Anderson impurity models with arbitrary local Coulomb interactions. An application to the Ohmic two-state system and the anisotropic Kondo model is also given, with comparisons to Bethe ansatz calculations. The approach could also be of interest within other impurity solvers, for example, within quantum Monte Carlo techniques.

Bose-Einstein correlations in p p ,   p Pb , and PbPb collisions at s N N = 0.9 – 7 TeV

DOE PAGES

Sirunyan, A. M.; Tumasyan, A.; Adam, W.; ...

2018-06-14

Here, quantum-statistical (Bose-Einstein) two-particle correlations are measured in pp collisions at √s = 0.9, 2.76, and 7 TeV, as well as in pPb and peripheral PbPb collisions at nucleon-nucleon center-of-mass energies of 5.02 and 2.76 TeV, respectively, using the CMS detector at the Large Hadron Collider. Separate analyses are performed for same-sign unidentified charged particles as well as for same-sign pions and kaons identified via their energy loss in the silicon tracker. The characteristics of the one-, two-, and three-dimensional correlation functions are studied as functions of the pair average transverse momentum (k T) and the charged-particle multiplicity in themore » event. For all systems, the extracted correlation radii steadily increase with the event multiplicity, and decrease with increasing k T. The radii are in the range 1–5 fm, the largest values corresponding to very high multiplicity pPb interactions and to peripheral PbPb collisions with multiplicities similar to those seen in pPb data. It is also observed that the dependencies of the radii on multiplicity and k T largely factorize. At the same multiplicity, the radii are relatively independent of the colliding system and center-of-mass energy.« less

Bose-Einstein correlations in $$pp, p\\mathrm{Pb}$$, and PbPb collisions at $$\\sqrt{{s}_{NN}}=0.9-7$$ TeV

DOE PAGES

Sirunyan, Albert M; et al.

2018-06-15

Quantum-statistical (Bose-Einstein) two-particle correlations are measured in pp collisions at s=0.9, 2.76, and 7 TeV, as well as in pPb and peripheral PbPb collisions at nucleon-nucleon center-of-mass energies of 5.02 and 2.76 TeV, respectively, using the CMS detector at the Large Hadron Collider. Separate analyses are performed for same-sign unidentified charged particles as well as for same-sign pions and kaons identified via their energy loss in the silicon tracker. The characteristics of the one-, two-, and three-dimensional correlation functions are studied as functions of the pair average transverse momentum (kT) and the charged-particle multiplicity in the event. For all systems, the extractedmore » correlation radii steadily increase with the event multiplicity, and decrease with increasing kT. The radii are in the range 1–5 fm, the largest values corresponding to very high multiplicity pPb interactions and to peripheral PbPb collisions with multiplicities similar to those seen in pPb data. It is also observed that the dependencies of the radii on multiplicity and kT largely factorize. At the same multiplicity, the radii are relatively independent of the colliding system and center-of-mass energy.« less

Bose-Einstein correlations in $$pp, p\\mathrm{Pb}$$, and PbPb collisions at $$\\sqrt{{s}_{NN}}=0.9-7$$ TeV

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sirunyan, Albert M; et al.

Quantum-statistical (Bose-Einstein) two-particle correlations are measured in pp collisions at s=0.9, 2.76, and 7 TeV, as well as in pPb and peripheral PbPb collisions at nucleon-nucleon center-of-mass energies of 5.02 and 2.76 TeV, respectively, using the CMS detector at the Large Hadron Collider. Separate analyses are performed for same-sign unidentified charged particles as well as for same-sign pions and kaons identified via their energy loss in the silicon tracker. The characteristics of the one-, two-, and three-dimensional correlation functions are studied as functions of the pair average transverse momentum (kT) and the charged-particle multiplicity in the event. For all systems, the extractedmore » correlation radii steadily increase with the event multiplicity, and decrease with increasing kT. The radii are in the range 1–5 fm, the largest values corresponding to very high multiplicity pPb interactions and to peripheral PbPb collisions with multiplicities similar to those seen in pPb data. It is also observed that the dependencies of the radii on multiplicity and kT largely factorize. At the same multiplicity, the radii are relatively independent of the colliding system and center-of-mass energy.« less

Bose-Einstein correlations in p p ,   p Pb , and PbPb collisions at s N N = 0.9 – 7 TeV

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sirunyan, A. M.; Tumasyan, A.; Adam, W.

Here, quantum-statistical (Bose-Einstein) two-particle correlations are measured in pp collisions at √s = 0.9, 2.76, and 7 TeV, as well as in pPb and peripheral PbPb collisions at nucleon-nucleon center-of-mass energies of 5.02 and 2.76 TeV, respectively, using the CMS detector at the Large Hadron Collider. Separate analyses are performed for same-sign unidentified charged particles as well as for same-sign pions and kaons identified via their energy loss in the silicon tracker. The characteristics of the one-, two-, and three-dimensional correlation functions are studied as functions of the pair average transverse momentum (k T) and the charged-particle multiplicity in themore » event. For all systems, the extracted correlation radii steadily increase with the event multiplicity, and decrease with increasing k T. The radii are in the range 1–5 fm, the largest values corresponding to very high multiplicity pPb interactions and to peripheral PbPb collisions with multiplicities similar to those seen in pPb data. It is also observed that the dependencies of the radii on multiplicity and k T largely factorize. At the same multiplicity, the radii are relatively independent of the colliding system and center-of-mass energy.« less

Full Wave Function Optimization with Quantum Monte Carlo and Its Effect on the Dissociation Energy of FeS.

PubMed

Haghighi Mood, Kaveh; Lüchow, Arne

2017-08-17

Diffusion quantum Monte Carlo calculations with partial and full optimization of the guide function are carried out for the dissociation of the FeS molecule. For the first time, quantum Monte Carlo orbital optimization for transition metal compounds is performed. It is demonstrated that energy optimization of the orbitals of a complete active space wave function in the presence of a Jastrow correlation function is required to obtain agreement with the experimental dissociation energy. Furthermore, it is shown that orbital optimization leads to a 5 Δ ground state, in agreement with experiments but in disagreement with other high-level ab initio wave function calculations which all predict a 5 Σ + ground state. The role of the Jastrow factor in DMC calculations with pseudopotentials is investigated. The results suggest that a large Jastrow factor may improve the DMC accuracy substantially at small additional cost.

Predictive coupled-cluster isomer orderings for some Si{sub n}C{sub m} (m, n ≤ 12) clusters: A pragmatic comparison between DFT and complete basis limit coupled-cluster benchmarks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Byrd, Jason N., E-mail: byrd.jason@ensco.com; ENSCO, Inc., 4849 North Wickham Road, Melbourne, Florida 32940; Lutz, Jesse J., E-mail: jesse.lutz.ctr@afit.edu

The accurate determination of the preferred Si{sub 12}C{sub 12} isomer is important to guide experimental efforts directed towards synthesizing SiC nano-wires and related polymer structures which are anticipated to be highly efficient exciton materials for the opto-electronic devices. In order to definitively identify preferred isomeric structures for silicon carbon nano-clusters, highly accurate geometries, energies, and harmonic zero point energies have been computed using coupled-cluster theory with systematic extrapolation to the complete basis limit for set of silicon carbon clusters ranging in size from SiC{sub 3} to Si{sub 12}C{sub 12}. It is found that post-MBPT(2) correlation energy plays a significant rolemore » in obtaining converged relative isomer energies, suggesting that predictions using low rung density functional methods will not have adequate accuracy. Utilizing the best composite coupled-cluster energy that is still computationally feasible, entailing a 3-4 SCF and coupled-cluster theory with singles and doubles extrapolation with triple-ζ (T) correlation, the closo Si{sub 12}C{sub 12} isomer is identified to be the preferred isomer in the support of previous calculations [X. F. Duan and L. W. Burggraf, J. Chem. Phys. 142, 034303 (2015)]. Additionally we have investigated more pragmatic approaches to obtaining accurate silicon carbide isomer energies, including the use of frozen natural orbital coupled-cluster theory and several rungs of standard and double-hybrid density functional theory. Frozen natural orbitals as a way to compute post-MBPT(2) correlation energy are found to be an excellent balance between efficiency and accuracy.« less

Locating Microseism Sources Using Spurious Arrivals in Intercontinental Noise Correlations

NASA Astrophysics Data System (ADS)

Retailleau, Lise; Boué, Pierre; Stehly, Laurent; Campillo, Michel

2017-10-01

The accuracy of Green's functions retrieved from seismic noise correlations in the microseism frequency band is limited by the uneven distribution of microseism sources at the surface of the Earth. As a result, correlation functions are often biased as compared to the expected Green's functions, and they can include spurious arrivals. These spurious arrivals are seismic arrivals that are visible on the correlation and do not belong to the theoretical impulse response. In this article, we propose to use Rayleigh wave spurious arrivals detected on correlation functions computed between European and United States seismic stations to locate microseism sources in the Atlantic Ocean. We perform a slant stack on a time distance gather of correlations obtained from an array of stations that comprises a regional deployment and a distant station. The arrival times and the apparent slowness of the spurious arrivals lead to the location of their source, which is obtained through a grid search procedure. We discuss improvements in the location through this methodology as compared to classical back projection of microseism energy. This method is interesting because it only requires an array and a distant station on each side of an ocean, conditions that can be met relatively easily.

The self-consistent calculation of pseudo-molecule energy levels, construction of energy level correlation diagrams and an automated computation system for SCF-X(Alpha)-SW calculations

NASA Technical Reports Server (NTRS)

Schlosser, H.

1981-01-01

The self consistent calculation of the electronic energy levels of noble gas pseudomolecules formed when a metal surface is bombarded by noble gas ions is discussed along with the construction of energy level correlation diagrams as a function of interatomic spacing. The self consistent field x alpha scattered wave (SCF-Xalpha-SW) method is utilized. Preliminary results on the Ne-Mg system are given. An interactive x alpha programming system, implemented on the LeRC IBM 370 computer, is described in detail. This automated system makes use of special PROCDEFS (procedure definitions) to minimize the data to be entered manually at a remote terminal. Listings of the special PROCDEFS and of typical input data are given.

A DFT and ab initio benchmarking study of metal-alkane interactions and the activation of carbon-hydrogen bonds.

PubMed

Flener-Lovitt, Charity; Woon, David E; Dunning, Thom H; Girolami, Gregory S

2010-02-04

Density functional theory and ab initio methods have been used to calculate the structures and energies of minima and transition states for the reactions of methane coordinated to a transition metal. The reactions studied are reversible C-H bond activation of the coordinated methane ligand to form a transition metal methyl hydride complex and dissociation of the coordinated methane ligand. The reaction sequence can be summarized as L(x)M(CH(3))H <==> L(x)M(CH(4)) <==> L(x)M + CH(4), where L(x)M is the osmium-containing fragment (C(5)H(5))Os(R(2)PCH(2)PR(2))(+) and R is H or CH(3). Three-center metal-carbon-hydrogen interactions play an important role in this system. Both basis sets and functionals have been benchmarked in this work, including new correlation consistent basis sets for a third transition series element, osmium. Double zeta quality correlation consistent basis sets yield energies close to those from calculations with quadruple-zeta basis sets, with variations that are smaller than the differences between functionals. The energies of important species on the potential energy surface, calculated by using 10 DFT functionals, are compared both to experimental values and to CCSD(T) single point calculations. Kohn-Sham natural bond orbital descriptions are used to understand the differences between functionals. Older functionals favor electrostatic interactions over weak donor-acceptor interactions and, therefore, are not particularly well suited for describing systems--such as sigma-complexes--in which the latter are dominant. Newer kinetic and dispersion-corrected functionals such as MPW1K and M05-2X provide significantly better descriptions of the bonding interactions, as judged by their ability to predict energies closer to CCSD(T) values. Kohn-Sham and natural bond orbitals are used to differentiate between bonding descriptions. Our evaluations of these basis sets and DFT functionals lead us to recommend the use of dispersion corrected functionals in conjunction with double-zeta or larger basis sets with polarization functions for calculations involving weak interactions, such as those found in sigma-complexes with transition metals.

Towards an exact correlated orbital theory for electrons

NASA Astrophysics Data System (ADS)

Bartlett, Rodney J.

2009-12-01

The formal and computational attraction of effective one-particle theories like Hartree-Fock and density functional theory raise the question of how far such approaches can be taken to offer exact results for selected properties of electrons in atoms, molecules, and solids. Some properties can be exactly described within an effective one-particle theory, like principal ionization potentials and electron affinities. This fact can be used to develop equations for a correlated orbital theory (COT) that guarantees a correct one-particle energy spectrum. They are built upon a coupled-cluster based frequency independent self-energy operator presented here, which distinguishes the approach from Dyson theory. The COT also offers an alternative to Kohn-Sham density functional theory (DFT), whose objective is to represent the electronic density exactly as a single determinant, while paying less attention to the energy spectrum. For any estimate of two-electron terms COT offers a litmus test of its accuracy for principal Ip's and Ea's. This feature for approximating the COT equations is illustrated numerically.

Self-consistent many-electron theory of electron work functions and surface potential characteristics for selected metals

NASA Technical Reports Server (NTRS)

Smith, J. R.

1969-01-01

Electron work functions, surface potentials, and electron number density distributions and electric fields in the surface region of 26 metals were calculated from first principles within the free electron model. Calculation proceeded from an expression of the total energy as a functional of the electron number density, including exchange and correlation energies, as well as a first inhomogeneity term. The self-consistent solution was obtained via a variational procedure. Surface barriers were due principally to many-body effects; dipole barriers were small only for some alkali metals, becoming quite large for the transition metals. Surface energies were inadequately described by this model, which neglects atomistic effects. Reasonable results were obtained for electron work functions and surface potential characteristics, maximum electron densities varying by a factor of over 60.

Communication: Near-locality of exchange and correlation density functionals for 1- and 2-electron systems

NASA Astrophysics Data System (ADS)

Sun, Jianwei; Perdew, John P.; Yang, Zenghui; Peng, Haowei

2016-05-01

The uniform electron gas and the hydrogen atom play fundamental roles in condensed matter physics and quantum chemistry. The former has an infinite number of electrons uniformly distributed over the neutralizing positively charged background, and the latter only one electron bound to the proton. The uniform electron gas was used to derive the local spin density approximation to the exchange-correlation functional that undergirds the development of the Kohn-Sham density functional theory. We show here that the ground-state exchange-correlation energies of the hydrogen atom and many other 1- and 2-electron systems are modeled surprisingly well by a different local spin density approximation (LSDA0). LSDA0 is constructed to satisfy exact constraints but agrees surprisingly well with the exact results for a uniform two-electron density in a finite, curved three-dimensional space. We also apply LSDA0 to excited or noded 1-electron densities, where it works less well. Furthermore, we show that the localization of the exact exchange hole for a 1- or 2-electron ground state can be measured by the ratio of the exact exchange energy to its optimal lower bound.

Three-point Green functions in the odd sector of QCD

NASA Astrophysics Data System (ADS)

Kadavý, T.; Kampf, K.; Novotný, J.

2016-11-01

A review of familiar results of the three-point Green functions of currents in the odd-intrinsic parity sector of QCD is presented. Such Green functions include very well-known examples of VVP, VAS or AAP correlators. We also shortly present some of the new results for VVA and AAA Green functions with a discussion of their high-energy behaviour and its relation to the QCD condensates.

Computing many-body wave functions with guaranteed precision: the first-order Møller-Plesset wave function for the ground state of helium atom.

PubMed

Bischoff, Florian A; Harrison, Robert J; Valeev, Edward F

2012-09-14

We present an approach to compute accurate correlation energies for atoms and molecules using an adaptive discontinuous spectral-element multiresolution representation for the two-electron wave function. Because of the exponential storage complexity of the spectral-element representation with the number of dimensions, a brute-force computation of two-electron (six-dimensional) wave functions with high precision was not practical. To overcome the key storage bottlenecks we utilized (1) a low-rank tensor approximation (specifically, the singular value decomposition) to compress the wave function, and (2) explicitly correlated R12-type terms in the wave function to regularize the Coulomb electron-electron singularities of the Hamiltonian. All operations necessary to solve the Schrödinger equation were expressed so that the reconstruction of the full-rank form of the wave function is never necessary. Numerical performance of the method was highlighted by computing the first-order Møller-Plesset wave function of a helium atom. The computed second-order Møller-Plesset energy is precise to ~2 microhartrees, which is at the precision limit of the existing general atomic-orbital-based approaches. Our approach does not assume special geometric symmetries, hence application to molecules is straightforward.

Combining two-body density functionals with multiconfigurational wavefunctions: diatomic molecules

NASA Astrophysics Data System (ADS)

McDouall, Joseph J. W.

The MCSCF method provides a correct zero-order wavefunction for all regions of molecular potential energy surfaces. To obtain quantitative accuracy a proper treatment of the dynamic correlation problem must be implemented. Traditionally this has been achieved through multireference variants of perturbation theory, configuration interaction and coupled cluster theory. The computational cost of such techniques makes them prohibitive for all but the smallest molecular problems. Reported here is an investigation into the efficacy of two-body density functionals in providing the dynamic correlation energy for MCSCF reference states. Tests were made on the two-body density functionals of Colle and Salvetti (CS), Moscardó and San-Fabián (MSF), and Moscardó and Pérez-Jiménez (MPJ5) in predicting the equilibrium bond lengths, harmonic frequencies and dissociation energies of fifteen diatomic molecules (3B2, 3BN, 2BS, 1C2, 2CN, 1CO, 1F2, 1FCl, 1N2, 3NCl, 3O2, 1PN, 3Si2, 3SiO, 3SO) using full valence-shell CASSCF reference wavefunctions. Also studied were modifications of these functionals recently suggested by Miehlich, Stoll and Savin (MSS) and Gräfenstein and Cremer (GC). The results obtained show accuracy comparable with and typically superior to the popular Kohn-Sham BLYP and B3LYP methods. However, the latter methods are not applicable in all regions of a potential energy surface, and even predict incorrect ground states for some systems. The use of two-body density functionals with MCSCF reference states does not share this shortcoming.

Function of a large biarticular hip and knee extensor during walking and running in guinea fowl (Numida meleagris).

PubMed

Carr, Jennifer A; Ellerby, David J; Marsh, Richard L

2011-10-15

Physiological and anatomical evidence suggests that in birds the iliotibialis lateralis pars postacetabularis (ILPO) is functionally important for running. Incorporating regional information, we estimated the mean sarcomere strain trajectory and electromyographic (EMG) amplitude of the ILPO during level and incline walking and running. Using these data and data in the literature of muscle energy use, we examined three hypotheses: (1) active lengthening will occur on the ascending limb of the length-tension curve to avoid potential damage caused by stretch on the descending limb; (2) the active strain cycle will shift to favor active shortening when the birds run uphill and shortening will occur on the plateau and shallow ascending limb of the length-tension curve; and (3) measures of EMG intensity will correlate with energy use when the mechanical function of the muscle is similar. Supporting the first hypothesis, we found that the mean sarcomere lengths at the end of active lengthening during level locomotion were smaller than the predicted length at the start of the plateau of the length-tension curve. Supporting the second hypothesis, the magnitude of active lengthening decreased with increasing slope, whereas active shortening increased. In evaluating the relationship between EMG amplitude and energy use (hypothesis 3), we found that although increases in EMG intensity with speed, slope and loading were positively correlated with muscle energy use, the quantitative relationships between these variables differed greatly under different conditions. The relative changes in EMG intensity and energy use by the muscle probably varied because of changes in the mechanical function of the muscle that altered the ratio of muscle energy use to active muscle volume. Considering the overall function of the cycle of active lengthening and shortening of the fascicles of the ILPO, we conclude that the function of active lengthening is unlikely to be energy conservation and may instead be related to promoting stability at the knee. The work required to lengthen the ILPO during stance is provided by co-contracting knee flexors. We suggest that this potentially energetically expensive co-contraction serves to stabilize the knee in early stance by increasing the mechanical impedance of the joint.

Variational energy principle for compressible, baroclinic flow. 1: First and second variations of total kinetic action

NASA Technical Reports Server (NTRS)

Schmid, L. A.

1977-01-01

The case of a cold gas in the absence of external force fields is considered. Since the only energy involved is kinetic energy, the total kinetic action (i.e., the space-time integral of the kinetic energy density) should serve as the total free-energy functional in this case, and as such should be a local minimum for all possible fluctuations about stable flow. This conjecture is tested by calculating explicit, manifestly covariant expressions for the first and second variations of the total kinetic action in the context of Lagrangian kinematics. The general question of the correlation between physical stability and the convexity of any action integral that can be interpreted as the total free-energy functional of the flow is discussed and illustrated for the cases of rectillinear and rotating shearing flows.

Describing a Strongly Correlated Model System with Density Functional Theory.

PubMed

Kong, Jing; Proynov, Emil; Yu, Jianguo; Pachter, Ruth

2017-07-06

The linear chain of hydrogen atoms, a basic prototype for the transition from a metal to Mott insulator, is studied with a recent density functional theory model functional for nondynamic and strong correlation. The computed cohesive energy curve for the transition agrees well with accurate literature results. The variation of the electronic structure in this transition is characterized with a density functional descriptor that yields the atomic population of effectively localized electrons. These new methods are also applied to the study of the Peierls dimerization of the stretched even-spaced Mott insulator to a chain of H 2 molecules, a different insulator. The transitions among the two insulating states and the metallic state of the hydrogen chain system are depicted in a semiquantitative phase diagram. Overall, we demonstrate the capability of studying strongly correlated materials with a mean-field model at the fundamental level, in contrast to the general pessimistic view on such a feasibility.

Harmonic-phase path-integral approximation of thermal quantum correlation functions

NASA Astrophysics Data System (ADS)

Robertson, Christopher; Habershon, Scott

2018-03-01

We present an approximation to the thermal symmetric form of the quantum time-correlation function in the standard position path-integral representation. By transforming to a sum-and-difference position representation and then Taylor-expanding the potential energy surface of the system to second order, the resulting expression provides a harmonic weighting function that approximately recovers the contribution of the phase to the time-correlation function. This method is readily implemented in a Monte Carlo sampling scheme and provides exact results for harmonic potentials (for both linear and non-linear operators) and near-quantitative results for anharmonic systems for low temperatures and times that are likely to be relevant to condensed phase experiments. This article focuses on one-dimensional examples to provide insights into convergence and sampling properties, and we also discuss how this approximation method may be extended to many-dimensional systems.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, Wenhu; Kotliar, Gabriel; Tsvelik, Alexei M.

Dynamical mean-field theory is used to study the quantum critical point (QCP) in the doped Hubbard model on a square lattice. We characterize the QCP by a universal scaling form of the self-energy and a spin density wave instability at an incommensurate wave vector. The scaling form unifies the low-energy kink and the high-energy waterfall feature in the spectral function, while the spin dynamics includes both the critical incommensurate and high-energy antiferromagnetic paramagnons. Here, we use the frequency-dependent four-point correlation function of spin operators to calculate the momentum-dependent correction to the electron self-energy. Furthermore, by comparing with the calculations basedmore » on the spin-fermion model, our results indicate the frequency dependence of the quasiparticle-paramagnon vertices is an important factor to capture the momentum dependence in quasiparticle scattering.« less

Long-Range Near-Side Angular Correlations in Proton-Proton Interactions in CMS.

ScienceCinema

None

2017-12-09

The CMS Collaboration Results on two-particle angular correlations for charged particles emitted in proton-proton collisions at center of mass energies of 0.9, 2.36 and 7TeV over a broad range of pseudorapidity (?) and azimuthal angle (f) are presented using data collected with the CMS detector at the LHC. Short-range correlations in ??, which are studied in minimum bias events, are characterized using a simple independent cluster parameterization in order to quantify their strength (cluster size) and their extent in ? (cluster decay width). Long-range azimuthal correlations are studied more differentially as a function of charged particle multiplicity and particle transverse momentum using a 980nb-1 data set at 7TeV. In high multiplicity events, a pronounced structure emerges in the two-dimensional correlation function for particles in intermediate pT’s of 1-3GeV/c, 2.0< |??|<4.8 and ?f˜0. This is the ?rst observation of such a ridge-like feature in two-particle correlation functions in pp or p-pbar collisions. EVO Universe, password "seminar"; Phone Bridge ID: 2330444 Password: 5142

Assessing Many-Body Effects of Water Self-Ions. I: OH-(H2O) n Clusters.

PubMed

Egan, Colin K; Paesani, Francesco

2018-04-10

The importance of many-body effects in the hydration of the hydroxide ion (OH - ) is investigated through a systematic analysis of the many-body expansion of the interaction energy carried out at the CCSD(T) level of theory, extrapolated to the complete basis set limit, for the low-lying isomers of OH - (H 2 O) n clusters, with n = 1-5. This is accomplished by partitioning individual fragments extracted from the whole clusters into "groups" that are classified by both the number of OH - and water molecules and the hydrogen bonding connectivity within each fragment. With the aid of the absolutely localized molecular orbital energy decomposition analysis (ALMO-EDA) method, this structure-based partitioning is found to largely correlate with the character of different many-body interactions, such as cooperative and anticooperative hydrogen bonding, within each fragment. This analysis emphasizes the importance of a many-body representation of inductive electrostatics and charge transfer in modeling OH - hydration. Furthermore, the rapid convergence of the many-body expansion of the interaction energy also suggests a rigorous path for the development of analytical potential energy functions capable of describing individual OH - -water many-body terms, with chemical accuracy. Finally, a comparison between the reference CCSD(T) many-body interaction terms with the corresponding values obtained with various exchange-correlation functionals demonstrates that range-separated, dispersion-corrected, hybrid functionals exhibit the highest accuracy, while GGA functionals, with or without dispersion corrections, are inadequate to describe OH - -water interactions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Al-Hamdani, Yasmine S.; Alfè, Dario; von Lilienfeld, O. Anatole

Density functional theory (DFT) studies of weakly interacting complexes have recently focused on the importance of van der Waals dispersion forces, whereas the role of exchange has received far less attention. Here, by exploiting the subtle binding between water and a boron and nitrogen doped benzene derivative (1,2-azaborine) we show how exact exchange can alter the binding conformation within a complex. Benchmark values have been calculated for three orientations of the water monomer on 1,2-azaborine from explicitly correlated quantum chemical methods, and we have also used diffusion quantum Monte Carlo. For a host of popular DFT exchange-correlation functionals we showmore » that the lack of exact exchange leads to the wrong lowest energy orientation of water on 1,2-azaborine. As such, we suggest that a high proportion of exact exchange and the associated improvement in the electronic structure could be needed for the accurate prediction of physisorption sites on doped surfaces and in complex organic molecules. Meanwhile to predict correct absolute interaction energies an accurate description of exchange needs to be augmented by dispersion inclusive functionals, and certain non-local van der Waals functionals (optB88- and optB86b-vdW) perform very well for absolute interaction energies. Through a comparison with water on benzene and borazine (B₃N₃H₆) we show that these results could have implications for the interaction of water with doped graphene surfaces, and suggest a possible way of tuning the interaction energy.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Al-Hamdani, Yasmine S.; Michaelides, Angelos, E-mail: angelos.michaelides@ucl.ac.uk; Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ

Density functional theory (DFT) studies of weakly interacting complexes have recently focused on the importance of van der Waals dispersion forces, whereas the role of exchange has received far less attention. Here, by exploiting the subtle binding between water and a boron and nitrogen doped benzene derivative (1,2-azaborine) we show how exact exchange can alter the binding conformation within a complex. Benchmark values have been calculated for three orientations of the water monomer on 1,2-azaborine from explicitly correlated quantum chemical methods, and we have also used diffusion quantum Monte Carlo. For a host of popular DFT exchange-correlation functionals we showmore » that the lack of exact exchange leads to the wrong lowest energy orientation of water on 1,2-azaborine. As such, we suggest that a high proportion of exact exchange and the associated improvement in the electronic structure could be needed for the accurate prediction of physisorption sites on doped surfaces and in complex organic molecules. Meanwhile to predict correct absolute interaction energies an accurate description of exchange needs to be augmented by dispersion inclusive functionals, and certain non-local van der Waals functionals (optB88- and optB86b-vdW) perform very well for absolute interaction energies. Through a comparison with water on benzene and borazine (B{sub 3}N{sub 3}H{sub 6}) we show that these results could have implications for the interaction of water with doped graphene surfaces, and suggest a possible way of tuning the interaction energy.« less

Probabilistic Density Function Method for Stochastic ODEs of Power Systems with Uncertain Power Input

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Peng; Barajas-Solano, David A.; Constantinescu, Emil

Wind and solar power generators are commonly described by a system of stochastic ordinary differential equations (SODEs) where random input parameters represent uncertainty in wind and solar energy. The existing methods for SODEs are mostly limited to delta-correlated random parameters (white noise). Here we use the Probability Density Function (PDF) method for deriving a closed-form deterministic partial differential equation (PDE) for the joint probability density function of the SODEs describing a power generator with time-correlated power input. The resulting PDE is solved numerically. A good agreement with Monte Carlo Simulations shows accuracy of the PDF method.

Holographic non-Fermi-liquid fixed points.

PubMed

Faulkner, Tom; Iqbal, Nabil; Liu, Hong; McGreevy, John; Vegh, David

2011-04-28

Techniques arising from string theory can be used to study assemblies of strongly interacting fermions. Via this 'holographic duality', various strongly coupled many-body systems are solved using an auxiliary theory of gravity. Simple holographic realizations of finite density exhibit single-particle spectral functions with sharp Fermi surfaces, of a form distinct from those of the Landau theory. The self-energy is given by a correlation function in an infrared (IR) fixed-point theory that is represented by a two-dimensional anti de Sitter space (AdS(2)) region in the dual gravitational description. Here, we describe in detail the gravity calculation of this IR correlation function.

Multiconfiguration Pair-Density Functional Theory and Complete Active Space Second Order Perturbation Theory. Bond Dissociation Energies of FeC, NiC, FeS, NiS, FeSe, and NiSe.

PubMed

Sharkas, Kamal; Gagliardi, Laura; Truhlar, Donald G

2017-12-07

We investigate the performance of multiconfiguration pair-density functional theory (MC-PDFT) and complete active space second-order perturbation theory for computing the bond dissociation energies of the diatomic molecules FeC, NiC, FeS, NiS, FeSe, and NiSe, for which accurate experimental data have become recently available [Matthew, D. J.; Tieu, E.; Morse, M. D. J. Chem. Phys. 2017, 146, 144310-144320]. We use three correlated participating orbital (CPO) schemes (nominal, moderate, and extended) to define the active spaces, and we consider both the complete active space (CAS) and the separated-pair (SP) schemes to specify the configurations included for a given active space. We found that the moderate SP-PDFT scheme with the tPBE on-top density functional has the smallest mean unsigned error (MUE) of the methods considered. This level of theory provides a balanced treatment of the static and dynamic correlation energies for the studied systems. This is encouraging because the method is low in cost even for much more complicated systems.

Block correlated second order perturbation theory with a generalized valence bond reference function.

PubMed

Xu, Enhua; Li, Shuhua

2013-11-07

The block correlated second-order perturbation theory with a generalized valence bond (GVB) reference (GVB-BCPT2) is proposed. In this approach, each geminal in the GVB reference is considered as a "multi-orbital" block (a subset of spin orbitals), and each occupied or virtual spin orbital is also taken as a single block. The zeroth-order Hamiltonian is set to be the summation of the individual Hamiltonians of all blocks (with explicit two-electron operators within each geminal) so that the GVB reference function and all excited configuration functions are its eigenfunctions. The GVB-BCPT2 energy can be directly obtained without iteration, just like the second order Mo̸ller-Plesset perturbation method (MP2), both of which are size consistent. We have applied this GVB-BCPT2 method to investigate the equilibrium distances and spectroscopic constants of 7 diatomic molecules, conformational energy differences of 8 small molecules, and bond-breaking potential energy profiles in 3 systems. GVB-BCPT2 is demonstrated to have noticeably better performance than MP2 for systems with significant multi-reference character, and provide reasonably accurate results for some systems with large active spaces, which are beyond the capability of all CASSCF-based methods.

Adler function and hadronic contribution to the muon g-2 in a nonlocal chiral quark model

NASA Astrophysics Data System (ADS)

Dorokhov, Alexander E.

2004-11-01

The behavior of the vector Adler function at spacelike momenta is studied in the framework of a covariant chiral quark model with instantonlike quark-quark interaction. This function describes the transition between the high-energy asymptotically free region of almost massless current quarks to the low-energy hadronized regime with massive constituent quarks. The model reproduces the Adler function and V-A correlator extracted from the ALEPH and OPAL data on hadronic τ lepton decays, transformed into the Euclidean domain via dispersion relations. The leading order contribution from the hadronic part of the photon vacuum polarization to the anomalous magnetic moment of the muon, ahvp(1)μ, is estimated.

Energy distribution in disordered elastic networks

NASA Astrophysics Data System (ADS)

Plaza, Gustavo R.

2010-09-01

Disordered networks are found in many natural and artificial materials, from gels or cytoskeletal structures to metallic foams or bones. Here, the energy distribution in this type of networks is modeled, taking into account the orientation of the struts. A correlation between the orientation and the energy per unit volume is found and described as a function of the connectivity in the network and the relative bending stiffness of the struts. If one or both parameters have relatively large values, the struts aligned in the loading direction present the highest values of energy. On the contrary, if these have relatively small values, the highest values of energy can be reached in the struts oriented transversally. This result allows explaining in a simple way remodeling processes in biological materials, for example, the remodeling of trabecular bone and the reorganization in the cytoskeleton. Additionally, the correlation between the orientation, the affinity, and the bending-stretching ratio in the network is discussed.

Inclusion of electron correlation for the target wave function in low- to intermediate-energy e-N2 scattering

NASA Technical Reports Server (NTRS)

Weatherford, C. A.; Brown, F. B.; Temkin, A.

1987-01-01

In a recent calculation, an exact exchange method was developed for use in the partial-differential-equation approach to electron-molecule scattering and was applied to e-N2 scattering in the fixed-nuclei approximation with an adiabatic polarization potential at low energies (0-10 eV). Integrated elastic cross sections were calculated and found to be lower than experiment at energies both below and above the Pi(g) resonance. It was speculated at that time that improved experimental agreement could be obtained if a correlated target representation were used in place of the uncorrelated one. The present paper implements this suggestion and demonstrates the improved agreement. These calculations are also extended to higher energies (0-30 eV) so asd to include the Sigma(u) resonance. Some discrepancies among the experiments and between experiment and the various calculations at very low energy are noted.

Stretched hydrogen molecule from a constrained-search density-functional perspective

DOE Office of Scientific and Technical Information (OSTI.GOV)

Valone, Steven M; Levy, Mel

2009-01-01

Constrained-search density functional theory gives valuable insights into the fundamentals of density functional theory. It provides exact results and bounds on the ground- and excited-state density functionals. An important advantage of the theory is that it gives guidance in the construction of functionals. Here they engage constrained search theory to explore issues associated with the functional behavior of 'stretched bonds' in molecular hydrogen. A constrained search is performed with familiar valence bond wavefunctions ordinarily used to describe molecular hydrogen. The effective, one-electron hamiltonian is computed and compared to the corresponding uncorrelated, Hartree-Fock effective hamiltonian. Analysis of the functional suggests themore » need to construct different functionals for the same density and to allow a competition among these functions. As a result the correlation energy functional is composed explicitly of energy gaps from the different functionals.« less

Dependence of mycelial morphology on impeller type and agitation intensity.

PubMed

Jüsten, P; Paul, G C; Nienow, A W; Thomas, C R

1996-12-20

The influence of the agitation conditions on the morphology of Penicillium chrysogenum (freely dispersed and aggregated forms) was examined using radial (Rushton turbines and paddles), axial (pitched blades, propeller, and Prochem Maxflow T), and counterflow impellers (Intermig). Culture broth was taken from a continuous fermentation at steady state and was agitated for 30 min in an ungassed vessel of 1.4-L working volume. The power inputs per unit volume of liquid in the tank, P/V(L), ranged from 0.6 to 6 kW/m(3). Image analysis was used to measure mycelial morphology. To characterize the intensity of the damage caused by different impellers, the mean total hyphal length (freely dispersed form) and the mean projected area (all dispersed types, i.e., also including aggregates) were used. [In this study, breakage of aggregates was taken into account quantitatively for the first time.]At 1.4-L scale and a given P/V(L), changes in the morphology depended significantly on the impeller geometry. However, the morphological data (obtained with different geometries and various P/V(L)) could be correlated on the basis of equal tip speed and two other, less simple, mixing parameters. One is based on the specific energy dissipation rate in the impeller region, which is simply related to P/V(L) and particular impeller geometrical parameters. The other which is developed in this study is based on a combination of the specific energy dissipation rate in the impeller swept volume and the frequency of mycelial circulation through that volume. For convenience, the function arising from this concept is called the "energy dissipation/circulation" function.To test the broader validity of these correlations, scale-up experiments were carried out in mixing tanks of 1.4, 20, and 180 L using a Rushton turbine and broth from a fed-batch fermentation. The energy dissipation/circulation function was a reasonable correlating parameter for hyphal damage over this range of scales, whereas tip speed, P/V(L), and specific energy dissipation rate in the impeller region were poor. Two forms of the energy dissipation/circulation function were considered, one of which additionally allowed for the numbers of vortices behind the blades of each impeller type. Although both forms were successful at correlating the data for the standard impeller designs considered here, there was preliminary evidence that allowing for the vortices would be valuable. (c) 1996 John Wiley & Sons, Inc.

New angles on energy correlation functions

DOE PAGES

Moult, Ian; Necib, Lina; Thaler, Jesse

2016-12-29

Jet substructure observables, designed to identify specific features within jets, play an essential role at the Large Hadron Collider (LHC), both for searching for signals beyond the Standard Model and for testing QCD in extreme phase space regions. In this paper, we systematically study the structure of infrared and collinear safe substructure observables, defining a generalization of the energy correlation functions to probe n-particle correlations within a jet. These generalized correlators provide a flexible basis for constructing new substructure observables optimized for specific purposes. Focusing on three major targets of the jet substructure community — boosted top tagging, boosted W/Z/Hmore » tagging, and quark/gluon discrimination — we use power-counting techniques to identify three new series of powerful discriminants: M i, N i, and U i. The Mi series is designed for use on groomed jets, providing a novel example of observables with improved discrimination power after the removal of soft radiation. The N i series behave parametrically like the N -subjettiness ratio observables, but are defined without respect to subjet axes, exhibiting improved behavior in the unresolved limit. Finally, the U i series improves quark/gluon discrimination by using higher-point correlators to simultaneously probe multiple emissions within a jet. Taken together, these observables broaden the scope for jet substructure studies at the LHC.« less

New angles on energy correlation functions

NASA Astrophysics Data System (ADS)

Moult, Ian; Necib, Lina; Thaler, Jesse

2016-12-01

Jet substructure observables, designed to identify specific features within jets, play an essential role at the Large Hadron Collider (LHC), both for searching for signals beyond the Standard Model and for testing QCD in extreme phase space regions. In this paper, we systematically study the structure of infrared and collinear safe substructure observables, defining a generalization of the energy correlation functions to probe n-particle correlations within a jet. These generalized correlators provide a flexible basis for constructing new substructure observables optimized for specific purposes. Focusing on three major targets of the jet substructure community — boosted top tagging, boosted W/Z/H tagging, and quark/gluon discrimination — we use power-counting techniques to identify three new series of powerful discriminants: M i , N i , and U i . The M i series is designed for use on groomed jets, providing a novel example of observables with improved discrimination power after the removal of soft radiation. The N i series behave parametrically like the N -subjettiness ratio observables, but are defined without respect to subjet axes, exhibiting improved behavior in the unresolved limit. Finally, the U i series improves quark/gluon discrimination by using higher-point correlators to simultaneously probe multiple emissions within a jet. Taken together, these observables broaden the scope for jet substructure studies at the LHC.

On the accuracy of density-functional theory exchange-correlation functionals for H bonds in small water clusters: Benchmarks approaching the complete basis set limit

NASA Astrophysics Data System (ADS)

Santra, Biswajit; Michaelides, Angelos; Scheffler, Matthias

2007-11-01

The ability of several density-functional theory (DFT) exchange-correlation functionals to describe hydrogen bonds in small water clusters (dimer to pentamer) in their global minimum energy structures is evaluated with reference to second order Møller-Plesset perturbation theory (MP2). Errors from basis set incompleteness have been minimized in both the MP2 reference data and the DFT calculations, thus enabling a consistent systematic evaluation of the true performance of the tested functionals. Among all the functionals considered, the hybrid X3LYP and PBE0 functionals offer the best performance and among the nonhybrid generalized gradient approximation functionals, mPWLYP and PBE1W perform best. The popular BLYP and B3LYP functionals consistently underbind and PBE and PW91 display rather variable performance with cluster size.

On the accuracy of density-functional theory exchange-correlation functionals for H bonds in small water clusters: benchmarks approaching the complete basis set limit.

PubMed

Santra, Biswajit; Michaelides, Angelos; Scheffler, Matthias

2007-11-14

The ability of several density-functional theory (DFT) exchange-correlation functionals to describe hydrogen bonds in small water clusters (dimer to pentamer) in their global minimum energy structures is evaluated with reference to second order Moller-Plesset perturbation theory (MP2). Errors from basis set incompleteness have been minimized in both the MP2 reference data and the DFT calculations, thus enabling a consistent systematic evaluation of the true performance of the tested functionals. Among all the functionals considered, the hybrid X3LYP and PBE0 functionals offer the best performance and among the nonhybrid generalized gradient approximation functionals, mPWLYP and PBE1W perform best. The popular BLYP and B3LYP functionals consistently underbind and PBE and PW91 display rather variable performance with cluster size.

Strain coupling of oxygen non-stoichiometry in perovskite thin films

NASA Astrophysics Data System (ADS)

Herklotz, Andreas; Lee, Dongkyu; Guo, Er-Jia; Meyer, Tricia L.; Petrie, Jonathan R.; Lee, Ho Nyung

2017-12-01

The effects of strain and oxygen vacancies on perovskite thin films have been studied in great detail over the past decades and have been treated separately from each other. While epitaxial strain has been realized as a tuning knob to tailor the functional properties of correlated oxides, oxygen vacancies are usually regarded as undesirable and detrimental. In transition metal oxides, oxygen defects strongly modify the properties and functionalities via changes in oxidation states of the transition metals. However, such coupling is not well understood in epitaxial films, but rather deemed as cumbersome or experimental artifact. Only recently it has been recognized that lattice strain and oxygen non-stoichiometry are strongly correlated in a vast number of perovskite systems and that this coupling can be beneficial for information and energy technologies. Recent experimental and theoretical studies have focused on understanding the correlated phenomena between strain and oxygen vacancies for a wide range of perovskite systems. These correlations not only include the direct relationship between elastic strain and the formation energy of oxygen vacancies, but also comprise highly complex interactions such as strain-induced phase transitions due to oxygen vacancy ordering. Therefore, we aim in this review to give a comprehensive overview on the coupling between strain and oxygen vacancies in perovskite oxides and point out the potential applications of the emergent functionalities strongly coupled to oxygen vacancies.

Guaiacol hydrodeoxygenation mechanism on Pt(111): Insights from density functional theory and linear free energy relations

USDA-ARS?s Scientific Manuscript database

In this study density functional theory (DFT) was used to study the adsorption of guaiacol and its initial hydrodeoxygenation (HDO) reactions on Pt(111). Previously reported Brønsted–Evans–Polanyi (BEP) correlations for small open chain molecules are found to be inadequate in estimating the reaction...

Prediction of Iron K-Edge Absorption Spectra Using Time-Dependent Density Functional Theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

George, S.DeBeer; Petrenko, T.; Neese, F.

2009-05-14

Iron K-edge X-ray absorption pre-edge features have been calculated using a time-dependent density functional approach. The influence of functional, solvation, and relativistic effects on the calculated energies and intensities has been examined by correlation of the calculated parameters to experimental data on a series of 10 iron model complexes, which span a range of high-spin and low-spin ferrous and ferric complexes in O{sub h} to T{sub d} geometries. Both quadrupole and dipole contributions to the spectra have been calculated. We find that good agreement between theory and experiment is obtained by using the BP86 functional with the CP(PPP) basis setmore » on the Fe and TZVP one of the remaining atoms. Inclusion of solvation yields a small improvement in the calculated energies. However, the inclusion of scalar relativistic effects did not yield any improved correlation with experiment. The use of these methods to uniquely assign individual spectral transitions and to examine experimental contributions to backbonding is discussed.« less

Influence of Van der Waals interaction on the thermodynamics properties of NaCl

NASA Astrophysics Data System (ADS)

Marcondes, M. L.; Wentzcovitch, R. M.; Assali, L. V. C.

2016-12-01

Equations of state (EoS) are extremely important in several scientific domains. However, many applications require EoS parameters at high pressures and temperatures. Experimental determination of these parameters is limited in such conditions and ab initio calculations have become important in computing them. Density Functional Theory (DFT) with its various approximations for exchange and correlation energy is the method of choice, but lack of a good description of the exchange-correlation energy results in large errors in EoS parameters. It is well known that the alkali halides have been problematic from the onset and the quest for DFT functionals appropriate for such ionic and relatively weakly bonded systems has remained an active topic of research. Here we use DFT + van der Waals functionals to calculate the thermal equation of state and thermodynamic properties of the B1 NaCl phase. Our results show a remarkable improvement over the performance of standard the LDA and GGA functionals. This is hardly surprising given that ions in this system have nearly closed shell configurations.

Estimating energy expenditure from heart rate in older adults: a case for calibration.

PubMed

Schrack, Jennifer A; Zipunnikov, Vadim; Goldsmith, Jeff; Bandeen-Roche, Karen; Crainiceanu, Ciprian M; Ferrucci, Luigi

2014-01-01

Accurate measurement of free-living energy expenditure is vital to understanding changes in energy metabolism with aging. The efficacy of heart rate as a surrogate for energy expenditure is rooted in the assumption of a linear function between heart rate and energy expenditure, but its validity and reliability in older adults remains unclear. To assess the validity and reliability of the linear function between heart rate and energy expenditure in older adults using different levels of calibration. Heart rate and energy expenditure were assessed across five levels of exertion in 290 adults participating in the Baltimore Longitudinal Study of Aging. Correlation and random effects regression analyses assessed the linearity of the relationship between heart rate and energy expenditure and cross-validation models assessed predictive performance. Heart rate and energy expenditure were highly correlated (r=0.98) and linear regardless of age or sex. Intra-person variability was low but inter-person variability was high, with substantial heterogeneity of the random intercept (s.d. =0.372) despite similar slopes. Cross-validation models indicated individual calibration data substantially improves accuracy predictions of energy expenditure from heart rate, reducing the potential for considerable measurement bias. Although using five calibration measures provided the greatest reduction in the standard deviation of prediction errors (1.08 kcals/min), substantial improvement was also noted with two (0.75 kcals/min). These findings indicate standard regression equations may be used to make population-level inferences when estimating energy expenditure from heart rate in older adults but caution should be exercised when making inferences at the individual level without proper calibration.

The scattering of low energy positrons by helium

NASA Technical Reports Server (NTRS)

Humberston, J. W.

1973-01-01

Kohn's variational method is used to calculate the positron-helium scattering length and low energy S-wave phase shifts for a quite realistic Hylleraas type of helium function containing an electron-electron correlation term. The zero energy wavefunction is used to calculate the value of the annihilation rate parameter Z sub eff. All the results are significantly different from those for Drachman's helium model B, but are in better agreement with the available experimental data.

Oxygen reduction on a Pt(111) catalyst in HT-PEM fuel cells by density functional theory

NASA Astrophysics Data System (ADS)

Sun, Hong; Li, Jie; Almheiri, Saif; Xiao, Jianyu

2017-08-01

The oxygen reduction reaction plays an important role in the performance of high-temperature proton exchange membrane (HT-PEM) fuel cells. In this study, a molecular dynamics model, which is based on the density functional theory and couples the system's energy, the exchange-correlation energy functional, the charge density distribution function, and the simplified Kohn-Sham equation, was developed to simulate the oxygen reduction reaction on a Pt(111) surface. Additionally, an electrochemical reaction system on the basis of a four-electron reaction mechanism was also developed for this simulation. The reaction path of the oxygen reduction reaction, the product structure of each reaction step and the system's energy were simulated. It is found that the first step reaction of the first hydrogen ion with the oxygen molecule is the controlling step of the overall reaction. Increasing the operating temperature speeds up the first step reaction rate and slightly decreases its reaction energy barrier. Our results provide insight into the working principles of HT-PEM fuel cells.

Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Analytical gradients.

PubMed

Łazarski, Roman; Burow, Asbjörn Manfred; Grajciar, Lukáš; Sierka, Marek

2016-10-30

A full implementation of analytical energy gradients for molecular and periodic systems is reported in the TURBOMOLE program package within the framework of Kohn-Sham density functional theory using Gaussian-type orbitals as basis functions. Its key component is a combination of density fitting (DF) approximation and continuous fast multipole method (CFMM) that allows for an efficient calculation of the Coulomb energy gradient. For exchange-correlation part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097) is extended to energy gradients. Computational efficiency and asymptotic O(N) scaling behavior of the implementation is demonstrated for various molecular and periodic model systems, with the largest unit cell of hematite containing 640 atoms and 19,072 basis functions. The overall computational effort of energy gradient is comparable to that of the Kohn-Sham matrix formation. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Electronic properties of CdWO{sub 4}: Use of hybrid exchange and correlation functionals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meena, B. S., E-mail: bsmphysics@gmail.com; Mund, H. S.; Ahuja, B. L.

Energy bands, density of states (DOS), Mulliken population (MP) and electron momentum densities (EMDs) of CdWO{sub 4} are presented using hybrid exchange and correlation functionals namely B3LYP, B3PW and PBE0. To validate the present hybrid potentials, theoretical EMDs have been compared with the experimental Compton profile. It is found that LCAO-B3LYP based Compton profile gives a better agreement with experiment than other theoretical profiles. The energy bands and DOS show a wide band gap semiconducting nature of CdWO{sub 4}. The theoretical band gap obtained using B3LYP scheme reconciles well with the available experimental data. In addition, we have also presentedmore » the anisotropies in EMDs along [100], [110] and [001] directions and the bonding effects using the MP data.« less

Lattice QCD Thermodynamics and RHIC-BES Particle Production within Generic Nonextensive Statistics

NASA Astrophysics Data System (ADS)

Tawfik, Abdel Nasser

2018-05-01

The current status of implementing Tsallis (nonextensive) statistics on high-energy physics is briefly reviewed. The remarkably low freezeout-temperature, which apparently fails to reproduce the firstprinciple lattice QCD thermodynamics and the measured particle ratios, etc. is discussed. The present work suggests a novel interpretation for the so-called " Tsallis-temperature". It is proposed that the low Tsallis-temperature is due to incomplete implementation of Tsallis algebra though exponential and logarithmic functions to the high-energy particle-production. Substituting Tsallis algebra into grand-canonical partition-function of the hadron resonance gas model seems not assuring full incorporation of nonextensivity or correlations in that model. The statistics describing the phase-space volume, the number of states and the possible changes in the elementary cells should be rather modified due to interacting correlated subsystems, of which the phase-space is consisting. Alternatively, two asymptotic properties, each is associated with a scaling function, are utilized to classify a generalized entropy for such a system with large ensemble (produced particles) and strong correlations. Both scaling exponents define equivalence classes for all interacting and noninteracting systems and unambiguously characterize any statistical system in its thermodynamic limit. We conclude that the nature of lattice QCD simulations is apparently extensive and accordingly the Boltzmann-Gibbs statistics is fully fulfilled. Furthermore, we found that the ratios of various particle yields at extreme high and extreme low energies of RHIC-BES is likely nonextensive but not necessarily of Tsallis type.

Fully quantum-state resolved study of NO{sub 2} photodissociation. Correlated NO({sup 2}{Pi}{sub {Omega}}, {nu} = 0 J,A) + O({sup 3}P{sub j}) distributions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sanov, A.; Bieler, C.R.; Reisler, H.

1995-09-14

Relative O({sup 3}P{sub j} = 2.1.0) spin-orbit populations correlated with specific NO[{sup 2}{Pi}{sub {Omega}} = {1/2}, 3/2; {nu} = 0; f; {Lambda} = {Pi}(A{prime}), {Pi}(A{double_prime})] product states were obtained following photolysis of NO{sub 2} at excess energies E{sup {+-}} = 390, 425, and 1054 cm{sup -1}. These fully quantum state-resolved measurements were carried out by recording spatial profiles of recoiling NO({sup 2}{Pi}{sub {Omega}}, J, {Lambda}) products using polarized radiation for photolysis and state-selective laser ionization detection. The relative O({sup 3}P{sub j}) populations correlated with each NO({sup 2}{Pi}{sub {Omega}}, J, {Lambda}) state show marked fluctuations at each excess energy as amore » function of rotational state and {Lambda}-doublet component. The relative populations also fluctuate as a function of excess energy. The O({sup 3}P{sub j}) spin-orbit population ratios, when averaged over all measurements, exhibit distributions that are colder than statistical, in agreement with previous results. In particular, we find that, on average, O({sup 3}P{sub 1}):O({sup 3}P{sub 2}) population ratios correlated with the ground NO({sup 2}{Pi}{sub {1/2}}) state are colder than the corresponding ratios correlated with the excited NO({sup 2}{Pi}{sub 3/2}) spin-orbit state. These results are in agreement with the state-specific calculations of Katigiri and Kato. 45 refs., 12 figs., 3 tabs.« less

Wave-function-based approach to quasiparticle bands: Insight into the electronic structure of c-ZnS

NASA Astrophysics Data System (ADS)

Stoyanova, A.; Hozoi, L.; Fulde, P.; Stoll, H.

2011-05-01

Ab initio wave-function-based methods are employed for the study of quasiparticle energy bands of zinc-blende ZnS, with focus on the Zn 3d “semicore” states. The relative energies of these states with respect to the top of the S 3p valence bands appear to be poorly described as compared to experimental values not only within the local density approximation (LDA), but also when many-body corrections within the GW approximation are applied to the LDA or LDA + U mean-field solutions [T. Miyake, P. Zhang, M. L. Cohen, and S. G. Louie, Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.74.245213 74, 245213 (2006)]. In the present study, we show that for the accurate description of the Zn 3d states a correlation treatment based on wave-function methods is needed. Our study rests on a local Hamiltonian approach which rigorously describes the short-range polarization and charge redistribution effects around an extra hole or electron placed into the valence respective conduction bands of semiconductors and insulators. The method also facilitates the computation of electron correlation effects beyond relaxation and polarization. The electron correlation treatment is performed on finite clusters cut off the infinite system. The formalism makes use of localized Wannier functions and embedding potentials derived explicitly from prior periodic Hartree-Fock calculations. The on-site and nearest-neighbor charge relaxation lead to corrections of several eV to the Hartree-Fock band energies and gap. Corrections due to long-range polarization are of the order of 1.0 eV. The dispersion of the Hartree-Fock bands is only slightly affected by electron correlations. We find the Zn 3d “semicore” states to lie ~9.0 eV below the top of the S 3p valence bands, in very good agreement with values from valence-band x-ray photoemission.

Monte Carlo simulations used to calculate the energy deposited in the coronary artery lumen as a function of iodine concentration and photon energy.

PubMed

Hocine, Nora; Meignan, Michel; Masset, Hélène

2018-04-01

To better understand the risks of cumulative medical X-ray investigations and the possible causal role of contrast agent on the coronary artery wall, the correlation between iodinated contrast media and the increase of energy deposited in the coronary artery lumen as a function of iodine concentration and photon energy is investigated. The calculations of energy deposition have been performed using Monte Carlo (MC) simulation codes, namely PENetration and Energy LOss of Positrons and Electrons (PENELOPE) and Monte Carlo N-Particle eXtended (MCNPX). Exposure of a cylinder phantom, artery and a metal stent (AISI 316L) to several X-ray photon beams were simulated. For the energies used in cardiac imaging the energy deposited in the coronary artery lumen increases with the quantity of iodine. Monte Carlo calculations indicate a strong dependence of the energy enhancement factor (EEF) on photon energy and iodine concentration. The maximum value of EEF is equal to 25; this factor is showed for 83 keV and for 400 mg Iodine/mL. No significant impact of the stent is observed on the absorbed dose in the artery for incident X-ray beams with mean energies of 44, 48, 52 and 55 keV. A strong correlation was shown between the increase in the concentration of iodine and the energy deposited in the coronary artery lumen for the energies used in cardiac imaging and over the energy range between 44 and 55 keV. The data provided by this study could be useful for creating new medical imaging protocols to obtain better diagnostic information with a lower level of radiation exposure.

Angular correlations in pair production at the LHC in the parton Reggeization approach

NASA Astrophysics Data System (ADS)

Karpishkov, Anton; Nefedov, Maxim; Saleev, Vladimir

2017-10-01

We calculate angular correlation spectra between beauty (B) and anti-beauty mesons in proton-proton collisions in the leading order approximation of the parton Reggeization approach consistently merged with the next-to-leading order corrections from the emission of additional hard gluon (NLO* approximation). To describe b-quark hadronization we use the universal scale-depended parton-to-meson fragmentation functions extracted from the combined e+e- annihilation data. The Kimber-Martin-Ryskin model for the unintegrated parton distribution functions in a proton is implied. We have obtained good agreement between our predictions and data from the CMS Collaboration at the energy TeV for angular correlations within uncertainties and without free parameters.

Simultaneous analytical optimization of variational parameters in Gaussian-type functions with full configuration interaction of multicomponent molecular orbital method by elimination of translational and rotational motions: application to isotopomers of the hydrogen molecule.

PubMed

Ishimoto, Takayoshi; Tachikawa, Masanori; Nagashima, Umpei

2008-04-28

We have extended the multicomponent molecular orbital (MCMO) method to the full-configuration interaction (full-CI) fully variational molecular orbital method by elimination of translational and rotational motion components from total Hamiltonian. In the MCMO scheme, the quantum effects of protons and deuterons as well as electrons can be directly taken into account. All variational parameters in the full-CI scheme, i.e., exponents and centers (alpha and R) in the Gaussian-type function (GTF) basis set as well as the CI coefficients, are simultaneously optimized by using their analytical gradients. The total energy of the H(2) molecule calculated using the electronic [6s3p2d1f] and nuclear [1s1p1d1f] GTFs is -1.161 726 hartree, which can be compared to the energy of -1.164 025 hartree reported using a 512 term-explicitly correlated GTF calculation. Although the d- and f-type nuclear GTFs contribute to the improvement of energy convergence, the convergence of electron-nucleus correlation energy is slower than that of electron-electron one. The nuclear wave functions are delocalized due to the electron-nucleus correlation effect compared to the result of Hartree-Fock level of MCMO method. In addition, the average internuclear distances of all diatomic molecules are within 0.001 A of the previously reported experimental results. The dipole moment of the HD molecule estimated by our method is 8.4 x 10(-4) D, which is in excellent agreement with the experimental result of (8-10) x 10(-4) D.

Lack of Energy: An Important and Distinct Component of HIV-Related Fatigue and Daytime Function

PubMed Central

Aouizerat, Bradley E.; Gay, Caryl L.; Lerdal, Anners; Portillo, Carmen J.; Lee, Kathryn A.

2012-01-01

Context Fatigue is a prevalent symptom among adults living with human immunodeficiency virus (HIV). There is increasing evidence that fatigue and energy are related, yet distinct constructs. Although HIV-related fatigue has been well studied, little is known about perceived energy and how it relates to fatigue, individual characteristics, and other symptoms. Objectives To describe the experience of perceived energy in adults with HIV and evaluate its relationship to demographic and clinical characteristics as well as symptoms of fatigue, sleep disturbance, anxiety, depression, and daytime function. Methods The design was descriptive, comparative, and correlational. The sample of 318 adults with HIV completed a demographic questionnaire, the Memorial Symptom Assessment Scale, and measures of fatigue, sleep disturbance, anxiety, depressive symptoms, and daytime function. Medical records were reviewed for disease and treatment data. Participants who reported a lack of energy were compared with those who did not on demographic, clinical, and symptom variables. Regression models of perceived energy and its interference with daytime function also were evaluated. Results Perceived lack of energy was highly prevalent (65%) and more strongly related to interference with daytime function than more general measures of fatigue severity, even when controlling for other characteristics and symptoms. Like other aspects of fatigue, lack of energy was associated with sleep disturbance, anxiety, and depressive symptoms. Lack of energy was more strongly related to morning fatigue than to evening fatigue. Conclusion Lack of energy interferes with daytime function and is not just the inverse of fatigue but a distinct perception that differs from fatigue. PMID:22917712

DFT-based method for more accurate adsorption energies: An adaptive sum of energies from RPBE and vdW density functionals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hensley, Alyssa J. R.; Ghale, Kushal; Rieg, Carolin

In recent years, the popularity of density functional theory with periodic boundary conditions (DFT) has surged for the design and optimization of functional materials. However, no single DFT exchange–correlation functional currently available gives accurate adsorption energies on transition metals both when bonding to the surface is dominated by strong covalent or ionic bonding and when it has strong contributions from van der Waals interactions (i.e., dispersion forces). Here we present a new, simple method for accurately predicting adsorption energies on transition-metal surfaces based on DFT calculations, using an adaptively weighted sum of energies from RPBE and optB86b-vdW (or optB88-vdW) densitymore » functionals. This method has been benchmarked against a set of 39 reliable experimental energies for adsorption reactions. Our results show that this method has a mean absolute error and root mean squared error relative to experiments of 13.4 and 19.3 kJ/mol, respectively, compared to 20.4 and 26.4 kJ/mol for the BEEF-vdW functional. For systems with large van der Waals contributions, this method decreases these errors to 11.6 and 17.5 kJ/mol. Furthermore, this method provides predictions of adsorption energies both for processes dominated by strong covalent or ionic bonding and for those dominated by dispersion forces that are more accurate than those of any current standard DFT functional alone.« less

DFT-based method for more accurate adsorption energies: An adaptive sum of energies from RPBE and vdW density functionals

DOE PAGES

Hensley, Alyssa J. R.; Ghale, Kushal; Rieg, Carolin; ...

2017-01-26

In recent years, the popularity of density functional theory with periodic boundary conditions (DFT) has surged for the design and optimization of functional materials. However, no single DFT exchange–correlation functional currently available gives accurate adsorption energies on transition metals both when bonding to the surface is dominated by strong covalent or ionic bonding and when it has strong contributions from van der Waals interactions (i.e., dispersion forces). Here we present a new, simple method for accurately predicting adsorption energies on transition-metal surfaces based on DFT calculations, using an adaptively weighted sum of energies from RPBE and optB86b-vdW (or optB88-vdW) densitymore » functionals. This method has been benchmarked against a set of 39 reliable experimental energies for adsorption reactions. Our results show that this method has a mean absolute error and root mean squared error relative to experiments of 13.4 and 19.3 kJ/mol, respectively, compared to 20.4 and 26.4 kJ/mol for the BEEF-vdW functional. For systems with large van der Waals contributions, this method decreases these errors to 11.6 and 17.5 kJ/mol. Furthermore, this method provides predictions of adsorption energies both for processes dominated by strong covalent or ionic bonding and for those dominated by dispersion forces that are more accurate than those of any current standard DFT functional alone.« less

Conventional and Explicitly Correlated ab Initio Benchmark Study on Water Clusters: Revision of the BEGDB and WATER27 Data Sets.

PubMed

Manna, Debashree; Kesharwani, Manoj K; Sylvetsky, Nitai; Martin, Jan M L

2017-07-11

Benchmark ab initio energies for BEGDB and WATER27 data sets have been re-examined at the MP2 and CCSD(T) levels with both conventional and explicitly correlated (F12) approaches. The basis set convergence of both conventional and explicitly correlated methods has been investigated in detail, both with and without counterpoise corrections. For the MP2 and CCSD-MP2 contributions, rapid basis set convergence observed with explicitly correlated methods is compared to conventional methods. However, conventional, orbital-based calculations are preferred for the calculation of the (T) term, since it does not benefit from F12. CCSD(F12*) converges somewhat faster with the basis set than CCSD-F12b for the CCSD-MP2 term. The performance of various DFT methods is also evaluated for the BEGDB data set, and results show that Head-Gordon's ωB97X-V and ωB97M-V functionals outperform all other DFT functionals. Counterpoise-corrected DSD-PBEP86 and raw DSD-PBEPBE-NL also perform well and are close to MP2 results. In the WATER27 data set, the anionic (deprotonated) water clusters exhibit unacceptably slow basis set convergence with the regular cc-pVnZ-F12 basis sets, which have only diffuse s and p functions. To overcome this, we have constructed modified basis sets, denoted aug-cc-pVnZ-F12 or aVnZ-F12, which have been augmented with diffuse functions on the higher angular momenta. The calculated final dissociation energies of BEGDB and WATER27 data sets are available in the Supporting Information. Our best calculated dissociation energies can be reproduced through n-body expansion, provided one pushes to the basis set and electron correlation limit for the two-body term; for the three-body term, post-MP2 contributions (particularly CCSD-MP2) are important for capturing the three-body dispersion effects. Terms beyond four-body can be adequately captured at the MP2-F12 level.

Peculiarities of the momentum distribution functions of strongly correlated charged fermions

NASA Astrophysics Data System (ADS)

Larkin, A. S.; Filinov, V. S.; Fortov, V. E.

2018-01-01

New numerical version of the Wigner approach to quantum thermodynamics of strongly coupled systems of particles has been developed for extreme conditions, when analytical approximations based on different kinds of perturbation theories cannot be applied. An explicit analytical expression of the Wigner function has been obtained in linear and harmonic approximations. Fermi statistical effects are accounted for by effective pair pseudopotential depending on coordinates, momenta and degeneracy parameter of particles and taking into account Pauli blocking of fermions. A new quantum Monte-Carlo method for calculations of average values of arbitrary quantum operators has been developed. Calculations of the momentum distribution functions and the pair correlation functions of degenerate ideal Fermi gas have been carried out for testing the developed approach. Comparison of the obtained momentum distribution functions of strongly correlated Coulomb systems with the Maxwell-Boltzmann and the Fermi distributions shows the significant influence of interparticle interaction both at small momenta and in high energy quantum ‘tails’.

The dissociation energy of N2

NASA Technical Reports Server (NTRS)

Almloef, Jan; Deleeuw, Bradley J.; Taylor, Peter R.; Bauschlicher, Charles W., Jr.; Siegbahn, Per

1989-01-01

The requirements for very accurate ab initio quantum chemical prediction of dissociation energies are examined using a detailed investigation of the nitrogen molecule. Although agreement with experiment to within 1 kcal/mol is not achieved even with the most elaborate multireference CI (configuration interaction) wave functions and largest basis sets currently feasible, it is possible to obtain agreement to within about 2 kcal/mol, or 1 percent of the dissociation energy. At this level it is necessary to account for core-valence correlation effects and to include up to h-type functions in the basis. The effect of i-type functions, the use of different reference configuration spaces, and basis set superposition error were also investigated. After discussing these results, the remaining sources of error in our best calculations are examined.

Use of the rVV10 Nonlocal Correlation Functional in the B97M-V Density Functional: Defining B97M-rV and Related Functionals [On the Use of the rVV10 Nonlocal Correlation Functional in the B97M-V Density Functional: Defining B97M-rV and Related Functionals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mardirossian, Narbe; Ruiz Pestana, Luis; Womack, James C.

The VV10 and rVV10 nonlocal correlation functionals are consistently implemented and assessed, with the goal of determining if the rVV10 nonlocal correlation functional can replace the VV10 nonlocal correlation functional in the recently developed B97M-V density functional, to give the B97M-rV density functional. Along the way, four density functionals are simultaneously tested: VV10, rVV10, B97M-V, and B97M-rV. An initial assessment is carried out across the S22 data set, and the short-range damping variable, b, is varied for all four density functionals in order to determine the sensitivity of the functionals to the empirical parameter. The results of this test indicatemore » that a value of b = 6 (fortuitously the same as that in B97M-V) is suitable for B97M-rV. The functionals are then compared across an extensive database of interaction energies, and it is demonstrated that B97M-rV either matches or outperforms B97M-V for all of the tests considered. Finally, the optimization of b across the S22 data set is extended to two range-separated hybrid density functionals, ωB97X-V and ωB97M-V, and a value of b = 6.2 is recommended for both ωB97X-rV and ωB97M-rV.« less

Use of the rVV10 Nonlocal Correlation Functional in the B97M-V Density Functional: Defining B97M-rV and Related Functionals [On the Use of the rVV10 Nonlocal Correlation Functional in the B97M-V Density Functional: Defining B97M-rV and Related Functionals

DOE PAGES

Mardirossian, Narbe; Ruiz Pestana, Luis; Womack, James C.; ...

2016-12-06

The VV10 and rVV10 nonlocal correlation functionals are consistently implemented and assessed, with the goal of determining if the rVV10 nonlocal correlation functional can replace the VV10 nonlocal correlation functional in the recently developed B97M-V density functional, to give the B97M-rV density functional. Along the way, four density functionals are simultaneously tested: VV10, rVV10, B97M-V, and B97M-rV. An initial assessment is carried out across the S22 data set, and the short-range damping variable, b, is varied for all four density functionals in order to determine the sensitivity of the functionals to the empirical parameter. The results of this test indicatemore » that a value of b = 6 (fortuitously the same as that in B97M-V) is suitable for B97M-rV. The functionals are then compared across an extensive database of interaction energies, and it is demonstrated that B97M-rV either matches or outperforms B97M-V for all of the tests considered. Finally, the optimization of b across the S22 data set is extended to two range-separated hybrid density functionals, ωB97X-V and ωB97M-V, and a value of b = 6.2 is recommended for both ωB97X-rV and ωB97M-rV.« less

Neutron-neutron angular correlations in spontaneous fission of 252Cf and 240Pu

NASA Astrophysics Data System (ADS)

Verbeke, J. M.; Nakae, L. F.; Vogt, R.

2018-04-01

Background: Angular anisotropy has been observed between prompt neutrons emitted during the fission process. Such an anisotropy arises because the emitted neutrons are boosted along the direction of the parent fragment. Purpose: To measure the neutron-neutron angular correlations from the spontaneous fission of 252Cf and 240Pu oxide samples using a liquid scintillator array capable of pulse-shape discrimination. To compare these correlations to simulations combining the Monte Carlo radiation transport code MCNPX with the fission event generator FREYA. Method: Two different analysis methods were used to study the neutron-neutron correlations with varying energy thresholds. The first is based on setting a light output threshold while the second imposes a time-of-flight cutoff. The second method has the advantage of being truly detector independent. Results: The neutron-neutron correlation modeled by FREYA depends strongly on the sharing of the excitation energy between the two fragments. The measured asymmetry enabled us to adjust the FREYA parameter x in 240Pu, which controls the energy partition between the fragments and is so far inaccessible in other measurements. The 240Pu data in this analysis was the first available to quantify the energy partition for this isotope. The agreement between data and simulation is overall very good for 252Cf(sf ) and 240Pu(sf ) . Conclusions: The asymmetry in the measured neutron-neutron angular distributions can be predicted by FREYA. The shape of the correlation function depends on how the excitation energy is partitioned between the two fission fragments. Experimental data suggest that the lighter fragment is disproportionately excited.

Metal-insulator transition in a doubly orbitally degenerate model with correlated hopping

NASA Astrophysics Data System (ADS)

Didukh, L.; Skorenkyy, Yu.; Dovhopyaty, Yu.; Hankevych, V.

2000-03-01

In the present paper, we propose a doubly orbitally degenerate narrow-band model with correlated hopping. The peculiarity of the model is taking into account the matrix element of electron-electron interaction, which describes intersite hoppings of electrons. In particular, this leads to the concentration dependence of the effective hopping integral. The cases of the strong and weak Hund's coupling are considered. By means of a generalized mean-field approximation the single-particle Green function and quasiparticle energy spectrum are calculated. Metal-insulator transition is studied in the model at different integer values of the electron concentration. With the help of the obtained energy spectrum, we find energy gap width and criteria of metal-insulator transition.

An accurate global potential energy surface, dipole moment surface, and rovibrational frequencies for NH3

NASA Astrophysics Data System (ADS)

Huang, Xinchuan; Schwenke, David W.; Lee, Timothy J.

2008-12-01

A global potential energy surface (PES) that includes short and long range terms has been determined for the NH3 molecule. The singles and doubles coupled-cluster method that includes a perturbational estimate of connected triple excitations and the internally contracted averaged coupled-pair functional electronic structure methods have been used in conjunction with very large correlation-consistent basis sets, including diffuse functions. Extrapolation to the one-particle basis set limit was performed and core correlation and scalar relativistic contributions were included directly, while the diagonal Born-Oppenheimer correction was added. Our best purely ab initio PES, denoted "mixed," is constructed from two PESs which differ in whether the ic-ACPF higher-order correlation correction was added or not. Rovibrational transition energies computed from the mixed PES agree well with experiment and the best previous theoretical studies, but most importantly the quality does not deteriorate even up to 10300cm-1 above the zero-point energy (ZPE). The mixed PES was improved further by empirical refinement using the most reliable J =0-2 rovibrational transitions in the HITRAN 2004 database. Agreement between high-resolution experiment and rovibrational transition energies computed from our refined PES for J =0-6 is excellent. Indeed, the root mean square (rms) error for 13 HITRAN 2004 bands for J =0-2 is 0.023cm-1 and that for each band is always ⩽0.06cm-1. For J =3-5 the rms error is always ⩽0.15cm-1. This agreement means that transition energies computed with our refined PES should be useful in the assignment of new high-resolution NH3 spectra and in correcting mistakes in previous assignments. Ideas for further improvements to our refined PES and for extension to other isotopolog are discussed.

Optimization of an exchange-correlation density functional for water

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fritz, Michelle; Fernández-Serra, Marivi; Institute for Advanced Computational Science, Stony Brook University, Stony Brook, New York 11794-3800

2016-06-14

We describe a method, that we call data projection onto parameter space (DPPS), to optimize an energy functional of the electron density, so that it reproduces a dataset of experimental magnitudes. Our scheme, based on Bayes theorem, constrains the optimized functional not to depart unphysically from existing ab initio functionals. The resulting functional maximizes the probability of being the “correct” parameterization of a given functional form, in the sense of Bayes theory. The application of DPPS to water sheds new light on why density functional theory has performed rather poorly for liquid water, on what improvements are needed, and onmore » the intrinsic limitations of the generalized gradient approximation to electron exchange and correlation. Finally, we present tests of our water-optimized functional, that we call vdW-DF-w, showing that it performs very well for a variety of condensed water systems.« less

Collision cross sections of N2 by H+ impact at keV energies within time-dependent density-functional theory

NASA Astrophysics Data System (ADS)

Yu, W.; Gao, C.-Z.; Zhang, Y.; Zhang, F. S.; Hutton, R.; Zou, Y.; Wei, B.

2018-03-01

We calculate electron capture and ionization cross sections of N2 impacted by the H+ projectile at keV energies. To this end, we employ the time-dependent density-functional theory coupled nonadiabatically to molecular dynamics. To avoid the explicit treatment of the complex density matrix in the calculation of cross sections, we propose an approximate method based on the assumption of constant ionization rate over the period of the projectile passing the absorbing boundary. Our results agree reasonably well with experimental data and semi-empirical results within the measurement uncertainties in the considered energy range. The discrepancies are mainly attributed to the inadequate description of exchange-correlation functional and the crude approximation for constant ionization rate. Although the present approach does not predict the experiments quantitatively for collision energies below 10 keV, it is still helpful to calculate total cross sections of ion-molecule collisions within a certain energy range.

Effect of Finite Computational Domain on Turbulence Scaling Law in Both Physical and Spectral Spaces

NASA Technical Reports Server (NTRS)

Hou, Thomas Y.; Wu, Xiao-Hui; Chen, Shiyi; Zhou, Ye

1998-01-01

The well-known translation between the power law of energy spectrum and that of the correlation function or the second order structure function has been widely used in analyzing random data. Here, we show that the translation is valid only in proper scaling regimes. The regimes of valid translation are different for the correlation function and the structure function. Indeed, they do not overlap. Furthermore, in practice, the power laws exist only for a finite range of scales. We show that this finite range makes the translation inexact even in the proper scaling regime. The error depends on the scaling exponent. The current findings are applicable to data analysis in fluid turbulence and other stochastic systems.

Uniform electron gases. III. Low-density gases on three-dimensional spheres

DOE Office of Scientific and Technical Information (OSTI.GOV)

Agboola, Davids; Knol, Anneke L.; Gill, Peter M. W., E-mail: peter.gill@anu.edu.au

2015-08-28

By combining variational Monte Carlo (VMC) and complete-basis-set limit Hartree-Fock (HF) calculations, we have obtained near-exact correlation energies for low-density same-spin electrons on a three-dimensional sphere (3-sphere), i.e., the surface of a four-dimensional ball. In the VMC calculations, we compare the efficacies of two types of one-electron basis functions for these strongly correlated systems and analyze the energy convergence with respect to the quality of the Jastrow factor. The HF calculations employ spherical Gaussian functions (SGFs) which are the curved-space analogs of Cartesian Gaussian functions. At low densities, the electrons become relatively localized into Wigner crystals, and the natural SGFmore » centers are found by solving the Thomson problem (i.e., the minimum-energy arrangement of n point charges) on the 3-sphere for various values of n. We have found 11 special values of n whose Thomson sites are equivalent. Three of these are the vertices of four-dimensional Platonic solids — the hyper-tetrahedron (n = 5), the hyper-octahedron (n = 8), and the 24-cell (n = 24) — and a fourth is a highly symmetric structure (n = 13) which has not previously been reported. By calculating the harmonic frequencies of the electrons around their equilibrium positions, we also find the first-order vibrational corrections to the Thomson energy.« less

Dynamic dual-energy chest radiography: a potential tool for lung tissue motion monitoring and kinetic study

PubMed Central

Xu, Tong; Ducote, Justin L.; Wong, Jerry T.; Molloi, Sabee

2011-01-01

Dual-energy chest radiography has the potential to provide better diagnosis of lung disease by removing the bone signal from the image. Dynamic dual-energy radiography is now possible with the introduction of digital flat panel detectors. The purpose of this study is to evaluate the feasibility of using dynamic dual-energy chest radiography for functional lung imaging and tumor motion assessment. The dual energy system used in this study can acquire up to 15 frame of dual-energy images per second. A swine animal model was mechanically ventilated and imaged using the dual-energy system. Sequences of soft-tissue images were obtained using dual-energy subtraction. Time subtracted soft-tissue images were shown to be able to provide information on regional ventilation. Motion tracking of a lung anatomic feature (a branch of pulmonary artery) was performed based on an image cross-correlation algorithm. The tracking precision was found to be better than 1 mm. An adaptive correlation model was established between the above tracked motion and an external surrogate signal (temperature within the tracheal tube). This model is used to predict lung feature motion using the continuous surrogate signal and low frame rate dual-energy images (0.1 to 3.0 frames /sec). The average RMS error of the prediction was (1.1 ± 0.3) mm. The dynamic dual-energy was shown to be potentially useful for lung functional imaging such as regional ventilation and kinetic studies. It can also be used for lung tumor motion assessment and prediction during radiation therapy. PMID:21285477

Dynamic dual-energy chest radiography: a potential tool for lung tissue motion monitoring and kinetic study.

PubMed

Xu, Tong; Ducote, Justin L; Wong, Jerry T; Molloi, Sabee

2011-02-21

Dual-energy chest radiography has the potential to provide better diagnosis of lung disease by removing the bone signal from the image. Dynamic dual-energy radiography is now possible with the introduction of digital flat-panel detectors. The purpose of this study is to evaluate the feasibility of using dynamic dual-energy chest radiography for functional lung imaging and tumor motion assessment. The dual-energy system used in this study can acquire up to 15 frames of dual-energy images per second. A swine animal model was mechanically ventilated and imaged using the dual-energy system. Sequences of soft-tissue images were obtained using dual-energy subtraction. Time subtracted soft-tissue images were shown to be able to provide information on regional ventilation. Motion tracking of a lung anatomic feature (a branch of pulmonary artery) was performed based on an image cross-correlation algorithm. The tracking precision was found to be better than 1 mm. An adaptive correlation model was established between the above tracked motion and an external surrogate signal (temperature within the tracheal tube). This model is used to predict lung feature motion using the continuous surrogate signal and low frame rate dual-energy images (0.1-3.0 frames per second). The average RMS error of the prediction was (1.1 ± 0.3) mm. The dynamic dual energy was shown to be potentially useful for lung functional imaging such as regional ventilation and kinetic studies. It can also be used for lung tumor motion assessment and prediction during radiation therapy.

Description of quasiparticle and satellite properties via cumulant expansions of the retarded one-particle Green's function

DOE PAGES

Mayers, Matthew Z.; Hybertsen, Mark S.; Reichman, David R.

2016-08-22

A cumulant-based GW approximation for the retarded one-particle Green's function is proposed, motivated by an exact relation between the improper Dyson self-energy and the cumulant generating function. We explore qualitative aspects of this method within a simple one-electron independent phonon model, where it is seen that the method preserves the energy moment of the spectral weight while also reproducing the exact Green's function in the weak-coupling limit. For the three-dimensional electron gas, this method predicts multiple satellites at the bottom of the band, albeit with inaccurate peak spacing. But, its quasiparticle properties and correlation energies are more accurate than bothmore » previous cumulant methods and standard G0W0. These results point to features that may be exploited within the framework of cumulant-based methods and suggest promising directions for future exploration and improvements of cumulant-based GW approaches.« less

Accurate density functional prediction of molecular electron affinity with the scaling corrected Kohn–Sham frontier orbital energies

NASA Astrophysics Data System (ADS)

Zhang, DaDi; Yang, Xiaolong; Zheng, Xiao; Yang, Weitao

2018-04-01

Electron affinity (EA) is the energy released when an additional electron is attached to an atom or a molecule. EA is a fundamental thermochemical property, and it is closely pertinent to other important properties such as electronegativity and hardness. However, accurate prediction of EA is difficult with density functional theory methods. The somewhat large error of the calculated EAs originates mainly from the intrinsic delocalisation error associated with the approximate exchange-correlation functional. In this work, we employ a previously developed non-empirical global scaling correction approach, which explicitly imposes the Perdew-Parr-Levy-Balduz condition to the approximate functional, and achieve a substantially improved accuracy for the calculated EAs. In our approach, the EA is given by the scaling corrected Kohn-Sham lowest unoccupied molecular orbital energy of the neutral molecule, without the need to carry out the self-consistent-field calculation for the anion.

Mitigating the impact of the DESI fiber assignment on galaxy clustering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burden, Angela; Padmanabhan, Nikhil; Cahn, Robert N.

2017-03-01

We present a simple strategy to mitigate the impact of an incomplete spectroscopic redshift galaxy sample as a result of fiber assignment and survey tiling. The method has been designed for the Dark Energy Spectroscopic Instrument (DESI) galaxy survey but may have applications beyond this. We propose a modification to the usual correlation function that nulls the almost purely angular modes affected by survey incompleteness due to fiber assignment. Predictions of this modified statistic can be calculated given a model of the two point correlation function. The new statistic can be computed with a slight modification to the data cataloguesmore » input to the standard correlation function code and does not incur any additional computational time. Finally we show that the spherically averaged baryon acoustic oscillation signal is not biased by the new statistic.« less

Systematic errors in transport calculations of shear viscosity using the Green-Kubo formalism

NASA Astrophysics Data System (ADS)

Rose, J. B.; Torres-Rincon, J. M.; Oliinychenko, D.; Schäfer, A.; Petersen, H.

2018-05-01

The purpose of this study is to provide a reproducible framework in the use of the Green-Kubo formalism to extract transport coefficients. More specifically, in the case of shear viscosity, we investigate the limitations and technical details of fitting the auto-correlation function to a decaying exponential. This fitting procedure is found to be applicable for systems interacting both through constant and energy-dependent cross-sections, although this is only true for sufficiently dilute systems in the latter case. We find that the optimal fit technique consists in simultaneously fixing the intercept of the correlation function and use a fitting interval constrained by the relative error on the correlation function. The formalism is then applied to the full hadron gas, for which we obtain the shear viscosity to entropy ratio.

Association of specific frequency bands of functional MRI signal oscillations with motor symptoms and depression in Parkinson's disease.

PubMed

Song, Xiaopeng; Hu, Xiao; Zhou, Shuqin; Xu, Yuanyuan; Zhang, Yi; Yuan, Yonggui; Liu, Yijun; Zhu, Huaiqiu; Liu, Weiguo; Gao, Jia-Hong

2015-11-17

A novel empirical mode decomposition method was adopted to investigate the dissociative or interactive neural impact of depression and motor impairments in Parkinson's disease (PD). Resting-state fMRI data of 59 PD subjects were first decomposed into characteristic frequency bands, and the main effects of motor severity and depression and their interaction on the energy of blood-oxygen-level-dependent signal oscillation in specific frequency bands were then evaluated. The results show that the severity of motor symptoms is negatively correlated with the energy in the frequency band of 0.10-0.25 Hz in the bilateral thalamus, but positively correlated with 0.01-0.027 Hz band energy in the bilateral postcentral gyrus. The severity of depression, on the other hand, is positively correlated with the energy of 0.10-0.25 Hz but negatively with 0.01-0.027 Hz in the bilateral subgenual gyrus. Notably, the interaction between motor and depressive symptoms is negatively correlated with the energy of 0.10-0.25 Hz in the substantia nigra, hippocampus, inferior orbitofrontal cortex, and temporoparietal junction, but positively correlated with 0.02-0.05 Hz in the same regions. These findings indicate unique associations of fMRI band signals with motor and depressive symptoms in PD in specific brain regions, which may underscore the neural impact of the comorbidity and the differentiation between the two PD-related disorders.

[Supercomputer investigation of the protein-ligand system low-energy minima].

PubMed

Oferkin, I V; Sulimov, A V; Katkova, E V; Kutov, D K; Grigoriev, F V; Kondakova, O A; Sulimov, V B

2015-01-01

The accuracy of the protein-ligand binding energy calculations and ligand positioning is strongly influenced by the choice of the docking target function. This work demonstrates the evaluation of the five different target functions used in docking: functions based on MMFF94 force field and functions based on PM7 quantum-chemical method accounting or without accounting the implicit solvent model (PCM, COSMO or SGB). For these purposes the ligand positions corresponding to the minima of the target function and the experimentally known ligand positions in the protein active site (crystal ligand positions) were compared. Each function was examined on the same test-set of 16 protein-ligand complexes. The new parallelized docking program FLM based on Monte Carlo search algorithm was developed to perform the comprehensive low-energy minima search and to calculate the protein-ligand binding energy. This study demonstrates that the docking target function based on the MMFF94 force field can be used to detect the crystal or near crystal positions of the ligand by the finding the low-energy local minima spectrum of the target function. The importance of solvent accounting in the docking process for the accurate ligand positioning is also shown. The accuracy of the ligand positioning as well as the correlation between the calculated and experimentally determined protein-ligand binding energies are improved when the MMFF94 force field is substituted by the new PM7 method with implicit solvent accounting.

A Non-Local, Energy-Optimized Kernel: Recovering Second-Order Exchange and Beyond in Extended Systems

NASA Astrophysics Data System (ADS)

Bates, Jefferson; Laricchia, Savio; Ruzsinszky, Adrienn

The Random Phase Approximation (RPA) is quickly becoming a standard method beyond semi-local Density Functional Theory that naturally incorporates weak interactions and eliminates self-interaction error. RPA is not perfect, however, and suffers from self-correlation error as well as an incorrect description of short-ranged correlation typically leading to underbinding. To improve upon RPA we introduce a short-ranged, exchange-like kernel that is one-electron self-correlation free for one and two electron systems in the high-density limit. By tuning the one free parameter in our model to recover an exact limit of the homogeneous electron gas correlation energy we obtain a non-local, energy-optimized kernel that reduces the errors of RPA for both homogeneous and inhomogeneous solids. To reduce the computational cost of the standard kernel-corrected RPA, we also implement RPA renormalized perturbation theory for extended systems, and demonstrate its capability to describe the dominant correlation effects with a low-order expansion in both metallic and non-metallic systems. Furthermore we stress that for norm-conserving implementations the accuracy of RPA and beyond RPA structural properties compared to experiment is inherently limited by the choice of pseudopotential. Current affiliation: King's College London.

A perturbative approach to the redshift space correlation function: beyond the Standard Model

NASA Astrophysics Data System (ADS)

Bose, Benjamin; Koyama, Kazuya

2017-08-01

We extend our previous redshift space power spectrum code to the redshift space correlation function. Here we focus on the Gaussian Streaming Model (GSM). Again, the code accommodates a wide range of modified gravity and dark energy models. For the non-linear real space correlation function used in the GSM we use the Fourier transform of the RegPT 1-loop matter power spectrum. We compare predictions of the GSM for a Vainshtein screened and Chameleon screened model as well as GR. These predictions are compared to the Fourier transform of the Taruya, Nishimichi and Saito (TNS) redshift space power spectrum model which is fit to N-body data. We find very good agreement between the Fourier transform of the TNS model and the GSM predictions, with <= 6% deviations in the first two correlation function multipoles for all models for redshift space separations in 50Mpch <= s <= 180Mpc/h. Excellent agreement is found in the differences between the modified gravity and GR multipole predictions for both approaches to the redshift space correlation function, highlighting their matched ability in picking up deviations from GR. We elucidate the timeliness of such non-standard templates at the dawn of stage-IV surveys and discuss necessary preparations and extensions needed for upcoming high quality data.

Analytical expressions for the log-amplitude correlation function of a plane wave through anisotropic atmospheric refractive turbulence.

PubMed

Gudimetla, V S Rao; Holmes, Richard B; Smith, Carey; Needham, Gregory

2012-05-01

The effect of anisotropic Kolmogorov turbulence on the log-amplitude correlation function for plane-wave fields is investigated using analysis, numerical integration, and simulation. A new analytical expression for the log-amplitude correlation function is derived for anisotropic Kolmogorov turbulence. The analytic results, based on the Rytov approximation, agree well with a more general wave-optics simulation based on the Fresnel approximation as well as with numerical evaluations, for low and moderate strengths of turbulence. The new expression reduces correctly to previously published analytic expressions for isotropic turbulence. The final results indicate that, as asymmetry becomes greater, the Rytov variance deviates from that given by the standard formula. This deviation becomes greater with stronger turbulence, up to moderate turbulence strengths. The anisotropic effects on the log-amplitude correlation function are dominant when the separation of the points is within the Fresnel length. In the direction of stronger turbulence, there is an enhanced dip in the correlation function at a separation close to the Fresnel length. The dip is diminished in the weak-turbulence axis, suggesting that energy redistribution via focusing and defocusing is dominated by the strong-turbulence axis. The new analytical expression is useful when anisotropy is observed in relevant experiments. © 2012 Optical Society of America

The relationship between change in apathy and changes in cognition and functional outcomes in currently non-depressed SSRI-treated patients with major depressive disorder.

PubMed

Rothschild, Anthony J; Raskin, Joel; Wang, Chia-Ning; Marangell, Lauren B; Fava, Maurizio

2014-01-01

Apathy in the context of treated major depressive disorder (MDD) is a frequently observed phenomenon in clinical practice. This study aimed to assess the validity of the Rothschild Scale for Antidepressant Tachyphylaxis® (RSAT) and the Massachusetts General Hospital Cognitive and Physical Functioning Questionnaire (CPFQ) for measuring apathy, and to assess the relationship between apathy and possible contributing factors, in patients with MDD and residual apathy in the absence of depressed mood. The underlying structure and validity of the RSAT and CPFQ were assessed via factor analysis and correlation with the Apathy Evaluation Scale-Clinician rated version (AES-C) in 483 patients who had previously responded to treatment with a selective serotonin reuptake inhibitor. The relationship between apathy and contributing variables was investigated via structural equation modeling. Correlation and regression analyses were conducted to examine the relationship between the Sheehan Disability Scale (SDS) and the RSAT, CPFQ, and AES-C. The RSAT and CPFQ were validated with the AES-C with respect to energy and motivation. The latent variable "Energy and Interest", based on the energy, motivation, and interest items (RSAT and CPFQ), was a major contributing factor to apathy. Improvements in function (SDS) were significantly correlated with, and predicted by, improvements in apathy and cognitive and physical functioning (assessed by the RSAT, CPFQ, and AES-C). These analyses provide further information on apathy and its assessment in the context of treated MDD. A better understanding of apathy will aid further investigation of this phenomenon and, ultimately, determination of the most appropriate approach for its clinical management. © 2013.

Quantum critical point revisited by dynamical mean-field theory

NASA Astrophysics Data System (ADS)

Xu, Wenhu; Kotliar, Gabriel; Tsvelik, Alexei M.

2017-03-01

Dynamical mean-field theory is used to study the quantum critical point (QCP) in the doped Hubbard model on a square lattice. The QCP is characterized by a universal scaling form of the self-energy and a spin density wave instability at an incommensurate wave vector. The scaling form unifies the low-energy kink and the high-energy waterfall feature in the spectral function, while the spin dynamics includes both the critical incommensurate and high-energy antiferromagnetic paramagnons. We use the frequency-dependent four-point correlation function of spin operators to calculate the momentum-dependent correction to the electron self-energy. By comparing with the calculations based on the spin-fermion model, our results indicate the frequency dependence of the quasiparticle-paramagnon vertices is an important factor to capture the momentum dependence in quasiparticle scattering.

Quantum critical point revisited by dynamical mean-field theory

DOE PAGES

Xu, Wenhu; Kotliar, Gabriel; Tsvelik, Alexei M.

2017-03-31

Dynamical mean-field theory is used to study the quantum critical point (QCP) in the doped Hubbard model on a square lattice. We characterize the QCP by a universal scaling form of the self-energy and a spin density wave instability at an incommensurate wave vector. The scaling form unifies the low-energy kink and the high-energy waterfall feature in the spectral function, while the spin dynamics includes both the critical incommensurate and high-energy antiferromagnetic paramagnons. Here, we use the frequency-dependent four-point correlation function of spin operators to calculate the momentum-dependent correction to the electron self-energy. Furthermore, by comparing with the calculations basedmore » on the spin-fermion model, our results indicate the frequency dependence of the quasiparticle-paramagnon vertices is an important factor to capture the momentum dependence in quasiparticle scattering.« less

Correlating molecular spectroscopy and molecular chemometrics to explore carbohydrate functional groups and utilization of coproducts from biofuel and biobrewing processing.

PubMed

Chen, Limei; Zhang, Xuewei; Yu, Peiqiang

2014-06-04

Dried distillers grains with solubles (DDGS) was coproducts from bioethanol and biobrewing industry. It was an excellent resource of protein and energy feedstuff in China. Conventional studies often focus on traditional nutritional profiles. To data, there is little research on molecular structure-nutrition interaction of carbohydrate in coproducts. In this study, five kinds of corn-grain based DDGS and two kinds of barley-grain based DDGS were collected from different manufactures in the north of China. They were coded as "1, 2, 3, 4, 5, 6, and 7", respectively. The primary purposes of this project were to investigate the molecular structure-nutrition interaction of carbohydrate in coproducts, in terms of (1) carbohydrate-related chemical composition and nutrient profiles, (2) predicted values for energy in coproducts for animal, and (3) in situ digestion of dry matter. The result showed that acid detergent fiber content in corn DDGS and barley DDGS had negative correlation with structural carbohydrate peak area, cellulose compounds, and carbohydrate component peaks (first, second, and total peak area), which were measured with molecular spectroscopy. The correlation between carbohydrate peak area (second and total) and digestible fiber (tdNDF) were negative. There were no correlation between carbohydrate spectral intensities and energy values, carbohydrate subfractions partitioned by CNCPS system, and in situ rumen degradation. The results indicate that carbohydrate spectral profiles (functional groups) are associated with the carbohydrate nutritive values in coproducts from biofuel and biobrewing processing.

Detector response function of an energy-resolved CdTe single photon counting detector.

PubMed

Liu, Xin; Lee, Hyoung Koo

2014-01-01

While spectral CT using single photon counting detector has shown a number of advantages in diagnostic imaging, knowledge of the detector response function of an energy-resolved detector is needed to correct the signal bias and reconstruct the image more accurately. The objective of this paper is to study the photo counting detector response function using laboratory sources, and investigate the signal bias correction method. Our approach is to model the detector response function over the entire diagnostic energy range (20 keV

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lepori, Francesca; Viel, Matteo; Baccigalupi, Carlo

We investigate the Alcock Paczy'nski (AP) test applied to the Baryon Acoustic Oscillation (BAO) feature in the galaxy correlation function. By using a general formalism that includes relativistic effects, we quantify the importance of the linear redshift space distortions and gravitational lensing corrections to the galaxy number density fluctuation. We show that redshift space distortions significantly affect the shape of the correlation function, both in radial and transverse directions, causing different values of galaxy bias to induce offsets up to 1% in the AP test. On the other hand, we find that the lensing correction around the BAO scale modifiesmore » the amplitude but not the shape of the correlation function and therefore does not introduce any systematic effect. Furthermore, we investigate in details how the AP test is sensitive to redshift binning: a window function in transverse direction suppresses correlations and shifts the peak position toward smaller angular scales. We determine the correction that should be applied in order to account for this effect, when performing the test with data from three future planned galaxy redshift surveys: Euclid, the Dark Energy Spectroscopic Instrument (DESI) and the Square Kilometer Array (SKA).« less

Signals of dynamical and statistical process from IMF-IMF correlation function

NASA Astrophysics Data System (ADS)

Pagano, E. V.; Acosta, L.; Auditore, L.; Baran, V.; Cap, T.; Cardella, G.; Colonna, M.; De Luca, S.; De Filippo, E.; Dell'Aquila, D.; Francalanza, L.; Gnoffo, B.; Lanzalone, G.; Lombardo, I.; Maiolino, C.; Martorana, N. S.; Norella, S.; Pagano, A.; Papa, M.; Piasecki, E.; Pirrone, S.; Politi, G.; Porto, F.; Quattrocchi, L.; Rizzo, F.; Rosato, E.; Russotto, P.; Siwek-Wilczyńska, K.; Trifiro, A.; Trimarchi, M.; Verde, G.; Vigilante, M.; Wilczyńsky, J.

2017-11-01

In this paper we briefly discuss about a novel application of the IMF-IMF correlation function to the physical case of binary massive projectile-like (PLF) splitting for dynamical and statistical breakup/fission in heavy ion collisions at Fermi energy. Theoretical simulations are also shown for comparisons with the data. These preliminary results have been obtained for the reverse kinematics reaction 124Sn + 64Ni at 35 AMeV that was studied using the forward part of CHIMERA detector. In that reaction a strong competition between a dynamical and a statistical components and its evolution with the charge asymmetry of the binary break up was already shown. In this work we show that the IMF-IMF correlation function can be used to pin down the timescale of the fragments production in binary fission-like phenomena. We also made simulations with the CoMDII model in order to compare to the experimental IMF-IMF correlation function. In future we plan to extend these studies to different reaction mechanisms and nuclear systems and to compare with different theoretical transport simulations.

Extraction of jet properties from two particle azimuthal correlations in proton-proton and gold+gold collisions at center of mass energy = 200 GeV

NASA Astrophysics Data System (ADS)

Constantin, Paul

Two particle azimuthal correlation functions measured in pp and AuAu collisions at sNN = 200 GeV at midrapidity with the central arms of the PHENIX detector are analyzed in order to extract the properties of hadronic jets produced in QCD vacuum and highly excited QCD media, like the jet shape parameters jT and kT, the jet conditional yields (number of associated hadrons per high pT trigger hadron) and the jet fragmentation function. The analysis of pp data starts with the measurement of the vacuum fragmentation function from which the pT dependence of the mean fragmentation momentum fraction is extracted. We obtain a constant value of = 0.74 +/- 0.02 for pT above 3 GeV/c. Soft (non-perturbative) parton fragmentation becomes significant below 3 GeV/c and the slope of the fragmentation function is pT dependent in this region. Gaussian fits to jet induced azimuthal correlations are employed to measure the mean jet fragmentation transverse momentum <| jTy|> = 359 +/- 11 (stat) +/- 6 (syst) MeV/c and the mean partonic transverse momentum <|k Ty|> = 964 +/- 49 (stat) +/- 16 (syst) MeV/c. The analysis of AuAu data is based on azimuthal correlation functions between charged hadrons in the 1.5--3 GeV/c and 3--5 GeV/c pT regions in five classes of collision centrality. The mean jet fragmentation transverse momentum <|jTy|> is centrality independent and consistent with the value in pp data mentioned above. A strong broadening with the centrality of the extracted mean partonic transverse momentum <|kTy|> (multiplied by ) is observed. This is an important finding because hadronic jet quenching through energy loss is expected to be accompanied by a broadening effect. Another important finding is that the jet conditional yields in both the near (Deltaφ ˜ 0) and away (Deltaφ ˜ pi) regions exhibit a slightly raising trend with centrality. This was also expected to accompany the jet quenching found at higher pT based on simple energy conservation considerations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burke, K.; Smith, J. C.; Grabowski, P. E.

Universal exact conditions guided the construction of most ground-state density functional approximations in use today. Here, we derive the relation between the entropy and Mermin free energy density functionals for thermal density functional theory. Both the entropy and sum of kinetic and electron-electron repulsion functionals are shown to be monotonically increasing with temperature, while the Mermin functional is concave downwards. Analogous relations are found for both exchange and correlation. The importance of these conditions is illustrated in two extremes: the Hubbard dimer and the uniform gas.

Electron Transport and Nonlinear Optical Properties of Substituted Aryldimesityl Boranes: A DFT Study

PubMed Central

Pandith, Altaf Hussain; Islam, Nasarul

2014-01-01

A comprehensive theoretical study was carried out on a series of aryldimesityl borane (DMB) derivatives using Density Functional theory. Optimized geometries and electronic parameters like electron affinity, reorganization energy, frontiers molecular contours, polarizability and hyperpolarizability have been calculated by employing B3PW91/6-311++G (d, p) level of theory. Our results show that the Hammett function and geometrical parameters correlates well with the reorganization energies and hyperpolarizability for the series of DMB derivatives studied in this work. The orbital energy study reveals that the electron releasing substituents increase the LUMO energies and electron withdrawing substituents decrease the LUMO energies, reflecting the electron transport character of aryldimesityl borane derivatives. From frontier molecular orbitals diagram it is evident that mesityl rings act as the donor, while the phenylene and Boron atom appear as acceptors in these systems. The calculated hyperpolarizability of secondary amine derivative of DMB is 40 times higher than DMB (1). The electronic excitation contributions to the hyperpolarizability studied by using TDDFT calculation shows that hyperpolarizability correlates well with dipole moment in ground and excited state and excitation energy in terms of the two-level model. Thus the results of these calculations can be helpful in designing the DMB derivatives for efficient electron transport and nonlinear optical material by appropriate substitution with electron releasing or withdrawing substituents on phenyl ring of DMB system. PMID:25479382

On the accuracy of density functional theory and wave function methods for calculating vertical ionization energies

DOE Office of Scientific and Technical Information (OSTI.GOV)

McKechnie, Scott; Booth, George H.; Cohen, Aron J.

The best practice in computational methods for determining vertical ionization energies (VIEs) is assessed, via reference to experimentally determined VIEs that are corroborated by highly accurate coupled-cluster calculations. These reference values are used to benchmark the performance of density-functional theory (DFT) and wave function methods: Hartree-Fock theory (HF), second-order Møller-Plesset perturbation theory (MP2) and Electron Propagator Theory (EPT). The core test set consists of 147 small molecules. An extended set of six larger molecules, from benzene to hexacene, is also considered to investigate the dependence of the results on molecule size. The closest agreement with experiment is found for ionizationmore » energies obtained from total energy diff calculations. In particular, DFT calculations using exchange-correlation functionals with either a large amount of exact exchange or long-range correction perform best. The results from these functionals are also the least sensitive to an increase in molecule size. In general, ionization energies calculated directly from the orbital energies of the neutral species are less accurate and more sensitive to an increase in molecule size. For the single-calculation approach, the EPT calculations are in closest agreement for both sets of molecules. For the orbital energies from DFT functionals, only those with long-range correction give quantitative agreement with dramatic failing for all other functionals considered. The results offer a practical hierarchy of approximations for the calculation of vertical ionization energies. In addition, the experimental and computational reference values can be used as a standardized set of benchmarks, against which other approximate methods can be compared.« less

Beam Energy Dependence of the Third Harmonic of Azimuthal Correlations in Au +Au Collisions at RHIC

NASA Astrophysics Data System (ADS)

Adamczyk, L.; Adkins, J. K.; Agakishiev, G.; Aggarwal, M. M.; Ahammed, Z.; Alekseev, I.; Aparin, A.; Arkhipkin, D.; Aschenauer, E. C.; Attri, A.; Averichev, G. S.; Bai, X.; Bairathi, V.; Bellwied, R.; Bhasin, A.; Bhati, A. K.; Bhattarai, P.; Bielcik, J.; Bielcikova, J.; Bland, L. C.; Bordyuzhin, I. G.; Bouchet, J.; Brandenburg, J. D.; Brandin, A. V.; Bunzarov, I.; Butterworth, J.; Caines, H.; Calderón de la Barca Sánchez, M.; Campbell, J. M.; Cebra, D.; Chakaberia, I.; Chaloupka, P.; Chang, Z.; Chatterjee, A.; Chattopadhyay, S.; Chen, J. H.; Chen, X.; Cheng, J.; Cherney, M.; Christie, W.; Contin, G.; Crawford, H. J.; Das, S.; De Silva, L. C.; Debbe, R. R.; Dedovich, T. G.; Deng, J.; Derevschikov, A. A.; di Ruzza, B.; Didenko, L.; Dilks, C.; Dong, X.; Drachenberg, J. L.; Draper, J. E.; Du, C. M.; Dunkelberger, L. E.; Dunlop, J. C.; Efimov, L. G.; Engelage, J.; Eppley, G.; Esha, R.; Evdokimov, O.; Eyser, O.; Fatemi, R.; Fazio, S.; Federic, P.; Fedorisin, J.; Feng, Z.; Filip, P.; Fisyak, Y.; Flores, C. E.; Fulek, L.; Gagliardi, C. A.; Garand, D.; Geurts, F.; Gibson, A.; Girard, M.; Greiner, L.; Grosnick, D.; Gunarathne, D. S.; Guo, Y.; Gupta, S.; Gupta, A.; Guryn, W.; Hamad, A. I.; Hamed, A.; Haque, R.; Harris, J. W.; He, L.; Heppelmann, S.; Heppelmann, S.; Hirsch, A.; Hoffmann, G. W.; Horvat, S.; Huang, T.; Huang, X.; Huang, B.; Huang, H. Z.; Huck, P.; Humanic, T. J.; Igo, G.; Jacobs, W. W.; Jang, H.; Jentsch, A.; Jia, J.; Jiang, K.; Judd, E. G.; Kabana, S.; Kalinkin, D.; Kang, K.; Kauder, K.; Ke, H. W.; Keane, D.; Kechechyan, A.; Khan, Z. H.; Kikoła, D. P.; Kisel, I.; Kisiel, A.; Kochenda, L.; Koetke, D. D.; Kosarzewski, L. K.; Kraishan, A. F.; Kravtsov, P.; Krueger, K.; Kumar, L.; Lamont, M. A. C.; Landgraf, J. M.; Landry, K. D.; Lauret, J.; Lebedev, A.; Lednicky, R.; Lee, J. H.; Li, X.; Li, C.; Li, X.; Li, Y.; Li, W.; Lin, T.; Lisa, M. A.; Liu, F.; Ljubicic, T.; Llope, W. J.; Lomnitz, M.; Longacre, R. S.; Luo, X.; Ma, R.; Ma, G. L.; Ma, Y. G.; Ma, L.; Magdy, N.; Majka, R.; Manion, A.; Margetis, S.; Markert, C.; Matis, H. S.; McDonald, D.; McKinzie, S.; Meehan, K.; Mei, J. C.; Minaev, N. G.; Mioduszewski, S.; Mishra, D.; Mohanty, B.; Mondal, M. M.; Morozov, D. A.; Mustafa, M. K.; Nandi, B. K.; Nasim, Md.; Nayak, T. K.; Nigmatkulov, G.; Niida, T.; Nogach, L. V.; Noh, S. Y.; Novak, J.; Nurushev, S. B.; Odyniec, G.; Ogawa, A.; Oh, K.; Okorokov, V. A.; Olvitt, D.; Page, B. S.; Pak, R.; Pan, Y. X.; Pandit, Y.; Panebratsev, Y.; Pawlik, B.; Pei, H.; Perkins, C.; Pile, P.; Pluta, J.; Poniatowska, K.; Porter, J.; Posik, M.; Poskanzer, A. M.; Pruthi, N. K.; Putschke, J.; Qiu, H.; Quintero, A.; Ramachandran, S.; Raniwala, S.; Raniwala, R.; Ray, R. L.; Ritter, H. G.; Roberts, J. B.; Rogachevskiy, O. V.; Romero, J. L.; Ruan, L.; Rusnak, J.; Rusnakova, O.; Sahoo, N. R.; Sahu, P. K.; Sakrejda, I.; Salur, S.; Sandweiss, J.; Sarkar, A.; Schambach, J.; Scharenberg, R. P.; Schmah, A. M.; Schmidke, W. B.; Schmitz, N.; Seger, J.; Seyboth, P.; Shah, N.; Shahaliev, E.; Shanmuganathan, P. V.; Shao, M.; Sharma, A.; Sharma, B.; Sharma, M. K.; Shen, W. Q.; Shi, Z.; Shi, S. S.; Shou, Q. Y.; Sichtermann, E. P.; Sikora, R.; Simko, M.; Singha, S.; Skoby, M. J.; Smirnov, N.; Smirnov, D.; Solyst, W.; Song, L.; Sorensen, P.; Spinka, H. M.; Srivastava, B.; Stanislaus, T. D. S.; Stepanov, M.; Stock, R.; Strikhanov, M.; Stringfellow, B.; Sumbera, M.; Summa, B.; Sun, Z.; Sun, X. M.; Sun, Y.; Surrow, B.; Svirida, D. N.; Tang, Z.; Tang, A. H.; Tarnowsky, T.; Tawfik, A.; Thäder, J.; Thomas, J. H.; Timmins, A. R.; Tlusty, D.; Todoroki, T.; Tokarev, M.; Trentalange, S.; Tribble, R. E.; Tribedy, P.; Tripathy, S. K.; Tsai, O. D.; Ullrich, T.; Underwood, D. G.; Upsal, I.; Van Buren, G.; van Nieuwenhuizen, G.; Vandenbroucke, M.; Varma, R.; Vasiliev, A. N.; Vertesi, R.; Videbæk, F.; Vokal, S.; Voloshin, S. A.; Vossen, A.; Wang, F.; Wang, G.; Wang, J. S.; Wang, H.; Wang, Y.; Wang, Y.; Webb, G.; Webb, J. C.; Wen, L.; Westfall, G. D.; Wieman, H.; Wissink, S. W.; Witt, R.; Wu, Y.; Xiao, Z. G.; Xie, W.; Xie, G.; Xin, K.; Xu, Y. F.; Xu, Q. H.; Xu, N.; Xu, H.; Xu, Z.; Xu, J.; Yang, S.; Yang, Y.; Yang, Y.; Yang, C.; Yang, Y.; Yang, Q.; Ye, Z.; Ye, Z.; Yepes, P.; Yi, L.; Yip, K.; Yoo, I.-K.; Yu, N.; Zbroszczyk, H.; Zha, W.; Zhang, X. P.; Zhang, Y.; Zhang, J.; Zhang, J.; Zhang, S.; Zhang, S.; Zhang, Z.; Zhang, J. B.; Zhao, J.; Zhong, C.; Zhou, L.; Zhu, X.; Zoulkarneeva, Y.; Zyzak, M.; STAR Collaboration

2016-03-01

We present results from a harmonic decomposition of two-particle azimuthal correlations measured with the STAR detector in Au +Au collisions for energies ranging from √{sN N }=7.7 to 200 GeV. The third harmonic v32{2 }=⟨cos 3 (ϕ1-ϕ2)⟩ , where ϕ1-ϕ2 is the angular difference in azimuth, is studied as a function of the pseudorapidity difference between particle pairs Δ η =η1-η2 . Nonzero v32{2 } is directly related to the previously observed large-Δ η narrow-Δ ϕ ridge correlations and has been shown in models to be sensitive to the existence of a low viscosity quark gluon plasma phase. For sufficiently central collisions, v32{2 } persist down to an energy of 7.7 GeV, suggesting that quark gluon plasma may be created even in these low energy collisions. In peripheral collisions at these low energies, however, v32{2 } is consistent with zero. When scaled by the pseudorapidity density of charged-particle multiplicity per participating nucleon pair, v32{2 } for central collisions shows a minimum near √{sN N }=20 GeV .

Stopping dynamics of ions passing through correlated honeycomb clusters

NASA Astrophysics Data System (ADS)

Balzer, Karsten; Schlünzen, Niclas; Bonitz, Michael

2016-12-01

A combined nonequilibrium Green functions-Ehrenfest dynamics approach is developed that allows for a time-dependent study of the energy loss of a charged particle penetrating a strongly correlated system at zero and finite temperatures. Numerical results are presented for finite inhomogeneous two-dimensional Fermi-Hubbard models, where the many-electron dynamics in the target are treated fully quantum mechanically and the motion of the projectile is treated classically. The simulations are based on the solution of the two-time Dyson (Keldysh-Kadanoff-Baym) equations using the second-order Born, third-order, and T -matrix approximations of the self-energy. As application, we consider protons and helium nuclei with a kinetic energy between 1 and 500 keV/u passing through planar fragments of the two-dimensional honeycomb lattice and, in particular, examine the influence of electron-electron correlations on the energy exchange between projectile and electron system. We investigate the time dependence of the projectile's kinetic energy (stopping power), the electron density, the double occupancy, and the photoemission spectrum. Finally, we show that, for a suitable choice of the Hubbard model parameters, the results for the stopping power are in fair agreement with ab initio simulations for particle irradiation of single-layer graphene.

Diffuse Waves and Energy Densities Near Boundaries

NASA Astrophysics Data System (ADS)

Sanchez-Sesma, F. J.; Rodriguez-Castellanos, A.; Campillo, M.; Perton, M.; Luzon, F.; Perez-Ruiz, J. A.

2007-12-01

Green function can be retrieved from averaging cross correlations of motions within a diffuse field. In fact, it has been shown that for an elastic inhomogeneous, anisotropic medium under equipartitioned, isotropic illumination, the average cross correlations are proportional to the imaginary part of Green function. For instance coda waves are due to multiple scattering and their intensities follow diffusive regimes. Coda waves and the noise sample the medium and effectively carry information along their paths. In this work we explore the consequences of assuming both source and receiver at the same point. From the observable side, the autocorrelation is proportional to the energy density at a given point. On the other hand, the imaginary part of the Green function at the source itself is finite because the singularity of Green function is restricted to the real part. The energy density at a point is proportional with the trace of the imaginary part of Green function tensor at the source itself. The Green function availability may allow establishing the theoretical energy density of a seismic diffuse field generated by a background equipartitioned excitation. We study an elastic layer with free surface and overlaying a half space and compute the imaginary part of the Green function for various depths. We show that the resulting spectrum is indeed closely related to the layer dynamic response and the corresponding resonant frequencies are revealed. One implication of present findings lies in the fact that spatial variations may be useful in detecting the presence of a target by its signature in the distribution of diffuse energy. These results may be useful in assessing the seismic response of a given site if strong ground motions are scarce. It suffices having a reasonable illumination from micro earthquakes and noise. We consider that the imaginary part of Green function at the source is a spectral signature of the site. The relative importance of the peaks of this energy spectrum, ruling out non linear effects, may influence the seismic response for future earthquakes. Partial supports from DGAPA-UNAM, Project IN114706, Mexico; from Proyect MCyT CGL2005-05500-C02/BTE, Spain; from project DyETI of INSU-CNRS, France, and from the Instituto Mexicano del Petróleo are greatly appreciated.

Progress in calculating the potential energy surface of H3+.

PubMed

Adamowicz, Ludwik; Pavanello, Michele

2012-11-13

The most accurate electronic structure calculations are performed using wave function expansions in terms of basis functions explicitly dependent on the inter-electron distances. In our recent work, we use such basis functions to calculate a highly accurate potential energy surface (PES) for the H(3)(+) ion. The functions are explicitly correlated Gaussians, which include inter-electron distances in the exponent. Key to obtaining the high accuracy in the calculations has been the use of the analytical energy gradient determined with respect to the Gaussian exponential parameters in the minimization of the Rayleigh-Ritz variational energy functional. The effective elimination of linear dependences between the basis functions and the automatic adjustment of the positions of the Gaussian centres to the changing molecular geometry of the system are the keys to the success of the computational procedure. After adiabatic and relativistic corrections are added to the PES and with an effective accounting of the non-adiabatic effects in the calculation of the rotational/vibrational states, the experimental H(3)(+) rovibrational spectrum is reproduced at the 0.1 cm(-1) accuracy level up to 16,600 cm(-1) above the ground state.

Effect of the nonlocal exchange on the performance of the orbital-dependent correlation functionals from second-order perturbation theory.

PubMed

Schweigert, Igor V; Bartlett, Rodney J

2008-09-28

Adding a fraction of the nonlocal exchange operator to the local orbital-dependent exchange potential improves the many-body perturbation expansion based on the Kohn-Sham determinant. The effect of such a hybrid scheme on the performance of the orbital-dependent correlation functional from the second-order perturbation theory (PT2H) is investigated numerically. A small fraction of the nonlocal exchange is often sufficient to ensure the existence of the self-consistent solution for the PT2H potential. In the He and Be atoms, including 37% of the nonlocal exchange leads to the correlation energies and electronic densities that are very close to the exact ones. In molecules, varying the fraction of the nonlocal exchange may result in the PT2H energy closely reproducing the CCSD(T) value; however such a fraction depends on the system and does not always result in an accurate electronic density. We also numerically verify that the "semicanonical" perturbation series includes most of the beneficial effects of the nonlocal exchange without sacrificing the locality of the exchange potential.

The standard mean-field treatment of inter-particle attraction in classical DFT is better than one might expect

NASA Astrophysics Data System (ADS)

Archer, Andrew J.; Chacko, Blesson; Evans, Robert

2017-07-01

In classical density functional theory (DFT), the part of the Helmholtz free energy functional arising from attractive inter-particle interactions is often treated in a mean-field or van der Waals approximation. On the face of it, this is a somewhat crude treatment as the resulting functional generates the simple random phase approximation (RPA) for the bulk fluid pair direct correlation function. We explain why using standard mean-field DFT to describe inhomogeneous fluid structure and thermodynamics is more accurate than one might expect based on this observation. By considering the pair correlation function g(x) and structure factor S(k) of a one-dimensional model fluid, for which exact results are available, we show that the mean-field DFT, employed within the test-particle procedure, yields results much superior to those from the RPA closure of the bulk Ornstein-Zernike equation. We argue that one should not judge the quality of a DFT based solely on the approximation it generates for the bulk pair direct correlation function.

Linear-scaling explicitly correlated treatment of solids: periodic local MP2-F12 method.

PubMed

Usvyat, Denis

2013-11-21

Theory and implementation of the periodic local MP2-F12 method in the 3*A fixed-amplitude ansatz is presented. The method is formulated in the direct space, employing local representation for the occupied, virtual, and auxiliary orbitals in the form of Wannier functions (WFs), projected atomic orbitals (PAOs), and atom-centered Gaussian-type orbitals, respectively. Local approximations are introduced, restricting the list of the explicitly correlated pairs, as well as occupied, virtual, and auxiliary spaces in the strong orthogonality projector to the pair-specific domains on the basis of spatial proximity of respective orbitals. The 4-index two-electron integrals appearing in the formalism are approximated via the direct-space density fitting technique. In this procedure, the fitting orbital spaces are also restricted to local fit-domains surrounding the fitted densities. The formulation of the method and its implementation exploits the translational symmetry and the site-group symmetries of the WFs. Test calculations are performed on LiH crystal. The results show that the periodic LMP2-F12 method substantially accelerates basis set convergence of the total correlation energy, and even more so the correlation energy differences. The resulting energies are quite insensitive to the resolution-of-the-identity domain sizes and the quality of the auxiliary basis sets. The convergence with the orbital domain size is somewhat slower, but still acceptable. Moreover, inclusion of slightly more diffuse functions, than those usually used in the periodic calculations, improves the convergence of the LMP2-F12 correlation energy with respect to both the size of the PAO-domains and the quality of the orbital basis set. At the same time, the essentially diffuse atomic orbitals from standard molecular basis sets, commonly utilized in molecular MP2-F12 calculations, but problematic in the periodic context, are not necessary for LMP2-F12 treatment of crystals.

Vicinage effect in the energy loss of H2 dimers: Experiment and calculations based on time-dependent density-functional theory

NASA Astrophysics Data System (ADS)

Koval, N. E.; Borisov, A. G.; Rosa, L. F. S.; Stori, E. M.; Dias, J. F.; Grande, P. L.; Sánchez-Portal, D.; Muiño, R. Díez

2017-06-01

We present a combined theoretical and experimental study of the energy loss of H2+ molecular ions interacting with thin oxide and carbon films. As a result of quantum mechanical interference of the target electrons, the energy loss of a molecular projectile differs from the sum of the energy losses of individual atomic projectiles. This difference is known as the vicinage effect. Calculations based on the time-dependent density functional theory allow the first-principles description of the dynamics of target excitations produced by the correlated motion of the nucleons forming the molecule. We investigate in detail the dependence of the vicinage effect on the speed and charge state of the projectile and find an excellent agreement between calculated and measured data.

A comparison of the coupled cluster and internally contracted averaged coupled-pair functional levels of theory for the calculation of the MCH2(+) binding energies for M = Sc to Cu

NASA Technical Reports Server (NTRS)

Bauschlicher, Charles W., Jr.; Partridge, Harry; Scuseria, Gustavo E.

1992-01-01

The correlation contribution to the M-C binding energy for the MCH2(+) systems can exceed 100 kcal/mol. At the self-consistent field (SCF) level, these systems can be more than 50 kcal/mol above the fragment energies. In spite of the poor zeroth-order reference, the coupled cluster single and double excitation method with a perturbational estimate of triple excitations, CCSD(T), method is shown to provide an accurate description of these systems. The maximum difference between the CCSD(T) and internally contracted averaged coupled-pair functional binding energies is 1.5 kcal/mol for CrCH2(+), with the remaining systems agreeing to within 1.0 kcal/mol.

Interdependence of different symmetry energy elements

NASA Astrophysics Data System (ADS)

Mondal, C.; Agrawal, B. K.; De, J. N.; Samaddar, S. K.; Centelles, M.; Viñas, X.

2017-08-01

Relations between the nuclear symmetry energy coefficient and its density derivatives are derived. The relations hold for a class of interactions with quadratic momentum dependence and a power-law density dependence. The structural connection between the different symmetry energy elements as obtained seems to be followed by almost all reasonable nuclear energy density functionals, both relativistic and nonrelativistic, suggesting a universality in the correlation structure. This, coupled with known values of some well-accepted constants related to nuclear matter, helps in constraining values of different density derivatives of the nuclear symmetry energy, shedding light on the isovector part of the nuclear interaction.

Estimate of oxygen consumption and intracellular zinc concentration of human spermatozoa in relation to motility.

PubMed

Henkel, Ralf R; Defosse, Kerstin; Koyro, Hans-Wilhelm; Weissmann, Norbert; Schill, Wolf-Bernhard

2003-03-01

To investigate the human sperm oxygen/energy consumption and zinc content in relation to motility. In washed spermatozoa from 67 ejaculates, the oxygen consumption was determined. Following calculation of the total oxygen consumed by the Ideal Gas Law, the energy consumption of spermatozoa was calculated. In addition, the zinc content of the sperm was determined using an atomic absorption spectrometer. The resulting data were correlated to the vitality and motility. The oxygen consumption averaged 0.24 micromol/10(6) sperm x 24h, 0.28 micromol/10(6) live sperm x 24h and 0.85 micromol/10(6) live motile sperm x 24h. Further calculations revealed that sperm motility was the most energy consuming process (164.31 mJ/10(6) motile spermatozoa x 24h), while the oxygen consumption of the total spermatozoa was 46.06 mJ/10(6) spermatozoa x 24h. The correlation of the oxygen/energy consumption and zinc content with motility showed significant negative correlations (r= -0.759; P<0.0001 and r=-0.441; P<0.0001, respectively). However, when correlating sperm energy consumption with the zinc content, a significant positive relation (r=0.323; P=0.01) was observed. Poorly motile sperm are actually wasting the available energy. Moreover, our data clearly support the "Geometric Clutch Model" of the axoneme function and demonstrate the importance of the outer dense fibers for the generation of sperm motility, especially progressive motility.

Coupled π π , K K ¯ scattering in P -wave and the ρ resonance from lattice QCD

DOE PAGES

Wilson, David J.; Briceño, Raúl A.; Dudek, Jozef J.; ...

2015-11-02

In this study, we determine elastic and coupled-channel amplitudes for isospin-1 meson-meson scattering inmore » $P$-wave, by calculating correlation functions using lattice QCD with light quark masses such that $$m_\\pi = 236$$ MeV in a cubic volume of $$\\sim (4 \\,\\mathrm{fm})^3$$. Variational analyses of large matrices of correlation functions computed using operator constructions resembling $$\\pi\\pi$$, $$K\\overline{K}$$ and $$q\\bar{q}$$, in several moving frames and several lattice irreducible representations, leads to discrete energy spectra from which scattering amplitudes are extracted. In the elastic $$\\pi\\pi$$ scattering region we obtain a detailed energy-dependence for the phase-shift, corresponding to a $$\\rho$$ resonance, and we extend the analysis into the coupled-channel $$K\\overline{K}$$ region for the first time, finding a small coupling between the channels.« less

Correlation between protein secondary structure, backbone bond angles, and side-chain orientations.

PubMed

Lundgren, Martin; Niemi, Antti J

2012-08-01

We investigate the fine structure of the sp3 hybridized covalent bond geometry that governs the tetrahedral architecture around the central C(α) carbon of a protein backbone, and for this we develop new visualization techniques to analyze high-resolution x-ray structures in the Protein Data Bank. We observe that there is a correlation between the deformations of the ideal tetrahedral symmetry and the local secondary structure of the protein. We propose a universal coarse-grained energy function to describe the ensuing side-chain geometry in terms of the C(β) carbon orientations. The energy function can model the side-chain geometry with a subatomic precision. As an example we construct the C(α)-C(β) structure of HP35 chicken villin headpiece. We obtain a configuration that deviates less than 0.4 Å in root-mean-square distance from the experimental x-ray structure.

Electronic properties of III-nitride semiconductors: A first-principles investigation using the Tran-Blaha modified Becke-Johnson potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Araujo, Rafael B., E-mail: rafaelbna@gmail.com; Almeida, J. S. de, E-mail: jailton-almeida@hotmail.com; Ferreira da Silva, A.

In this work, we use density functional theory to investigate the influence of semilocal exchange and correlation effects on the electronic properties of III-nitride semiconductors considering zinc-blende and wurtzite crystal structures. We find that the inclusion of such effects through the use of the Tran-Blaha modified Becke-Johnson potential yields an excellent description of the electronic structures of these materials giving energy band gaps which are systematically larger than the ones obtained with standard functionals such as the generalized gradient approximation. The discrepancy between the experimental and theoretical band gaps is then significantly reduced with semilocal exchange and correlation effects. However,more » the effective masses are overestimated in the zinc-blende nitrides, but no systematic trend is found in the wurtzite compounds. New results for energy band gaps and effective masses of zinc-blende and wurtzite indium nitrides are presented.« less

Mitochondrial respiratory efficiency is positively correlated with human sperm motility.

PubMed

Ferramosca, Alessandra; Provenzano, Sara Pinto; Coppola, Lamberto; Zara, Vincenzo

2012-04-01

To correlate sperm mitochondrial respiratory efficiency with variations in sperm motility and with sperm morphologic anomalies. Sperm mitochondrial respiratory activity was evaluated with a polarographic assay of oxygen consumption carried out in hypotonically-treated sperm cells. A possible relationship among sperm mitochondrial respiratory efficiency, sperm motility, and morphologic anomalies was investigated. Mitochondrial respiratory efficiency was positively correlated with sperm motility and negatively correlated with the percentage of immotile spermatozoa. Moreover, midpiece defects impaired mitochondrial functionality. Our data indicate that an increase in sperm motility requires a parallel increase in mitochondrial respiratory capacity, thereby supporting the fundamental role played by mitochondrial oxidative phosphorylation in sperm motility of normozoospermic subjects. These results are of physiopathological relevance because they suggest that disturbances of sperm mitochondrial function and of energy production could be responsible for asthenozoospermia. Copyright © 2012 Elsevier Inc. All rights reserved.

Comparative studies of the spectroscopy of CuCl2: DFT versus standard ab initio approaches

NASA Astrophysics Data System (ADS)

Ramírez-Solís, A.; Poteau, R.; Vela, A.; Daudey, J. P.

2005-04-01

The XΠg2-Σg +2, XΠg2-Δg2, XΠg2-Σu +2, XΠg2-Πu2 transitions on CuCl2 have been studied using several exchange-correlation functionals from the various types of density functional theory (DFT) approaches like local density approximation (LDA), generalized gradient approximation (GGA), hybrid and meta-GGA. The results are compared with the experience and with those coming from the most sophisticated nondynamic and dynamic electronic correlation treatments using the same relativistic effective core potentials and especially developed basis sets to study the electronic structure of the five lowest states and the corresponding vertical and adiabatic transition energies. The calculated transition energies for three of the hybrid functionals (B3LYP, B97-2, and PBE0) are in very good agreement with the benchmark ab initio results and experimental figures. All of the other functionals largely overestimate the XΠg2-Σg +2 and XΠg2-Δg2 transition energies, many of them even placing the Δg2 ligand field state above the charge transfer Πu2 and Σu +2 states. The relative weight of the Hartree-Fock exchange in the definition of the functional used appears to play a key role in the accurate description of the ΛSΣ density defined by the orientation of the 3d hole (σ, π, or δ) on Cu in the field of both chlorine atoms, but no simple connection of this weight with the quality of the spectra has been found. Mulliken charges and spin densities are carefully analyzed; a possible link between the extent of spin density on the metal for the XΠg2 state and the performance of the various functionals was observed, suggesting that those that lead to the largest values (close to 0.65) are the ones that best reproduce these four transitions. Most functionals lead to a remarkably low ionicity for the three ligand field states even for the best performing functionals, compared to the complete active space (SCF) (21, 14) ab initio values. These findings show that not only large variational ab initio calculations can produce reliable spectroscopic results for extremely complex systems where delicate electronic correlation effects have to be carefully dealt with. However, those functionals that were recently shown to perform best for a series of molecular properties [J. Chem. Phys. 121 3405 (2004)] are not the ones that produce the best transition energies for this complex case.

Direct work function measurement by gas phase photoelectron spectroscopy and its application on PbS nanoparticles.

PubMed

Axnanda, Stephanus; Scheele, Marcus; Crumlin, Ethan; Mao, Baohua; Chang, Rui; Rani, Sana; Faiz, Mohamed; Wang, Suidong; Alivisatos, A Paul; Liu, Zhi

2013-01-01

Work function is a fundamental property of a material's surface. It is playing an ever more important role in engineering new energy materials and efficient energy devices, especially in the field of photovoltaic devices, catalysis, semiconductor heterojunctions, nanotechnology, and electrochemistry. Using ambient pressure X-ray photoelectron spectroscopy (APXPS), we have measured the binding energies of core level photoelectrons of Ar gas in the vicinity of several reference materials with known work functions (Au(111), Pt(111), graphite) and PbS nanoparticles. We demonstrate an unambiguously negative correlation between the work functions of reference samples and the binding energies of Ar 2p core level photoelectrons detected from the Ar gas near the sample surface region. Using this experimentally determined linear relationship between the surface work function and Ar gas core level photoelectron binding energy, we can measure the surface work function of different materials under different gas environments. To demonstrate the potential applications of this ambient pressure XPS technique in nanotechnology and solar energy research, we investigate the work functions of PbS nanoparticles with various capping ligands: methoxide, mercaptopropionic acid, and ethanedithiol. Significant Fermi level position changes are observed for PbS nanoparticles when the nanoparticle size and capping ligands are varied. The corresponding changes in the valence band maximum illustrate that an efficient quantum dot solar cell design has to take into account the electrochemical effect of the capping ligand as well.

Large Deviations in Weakly Interacting Boundary Driven Lattice Gases

NASA Astrophysics Data System (ADS)

van Wijland, Frédéric; Rácz, Zoltán

2005-01-01

One-dimensional, boundary-driven lattice gases with local interactions are studied in the weakly interacting limit. The density profiles and the correlation functions are calculated to first order in the interaction strength for zero-range and short-range processes differing only in the specifics of the detailed-balance dynamics. Furthermore, the effective free-energy (large-deviation function) and the integrated current distribution are also found to this order. From the former, we find that the boundary drive generates long-range correlations only for the short-range dynamics while the latter provides support to an additivity principle recently proposed by Bodineau and Derrida.

Classical Wigner method with an effective quantum force: application to reaction rates.

PubMed

Poulsen, Jens Aage; Li, Huaqing; Nyman, Gunnar

2009-07-14

We construct an effective "quantum force" to be used in the classical molecular dynamics part of the classical Wigner method when determining correlation functions. The quantum force is obtained by estimating the most important short time separation of the Feynman paths that enter into the expression for the correlation function. The evaluation of the force is then as easy as classical potential energy evaluations. The ideas are tested on three reaction rate problems. The resulting transmission coefficients are in much better agreement with accurate results than transmission coefficients from the ordinary classical Wigner method.

Algorithms for calculating mass-velocity and Darwin relativistic corrections with n-electron explicitly correlated Gaussians with shifted centers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stanke, Monika, E-mail: monika@fizyka.umk.pl; Palikot, Ewa, E-mail: epalikot@doktorant.umk.pl; Adamowicz, Ludwik, E-mail: ludwik@email.arizona.edu

2016-05-07

Algorithms for calculating the leading mass-velocity (MV) and Darwin (D) relativistic corrections are derived for electronic wave functions expanded in terms of n-electron explicitly correlated Gaussian functions with shifted centers and without pre-exponential angular factors. The algorithms are implemented and tested in calculations of MV and D corrections for several points on the ground-state potential energy curves of the H{sub 2} and LiH molecules. The algorithms are general and can be applied in calculations of systems with an arbitrary number of electrons.

Coded aperture imaging with self-supporting uniformly redundant arrays

DOEpatents

Fenimore, Edward E.

1983-01-01

A self-supporting uniformly redundant array pattern for coded aperture imaging. The present invention utilizes holes which are an integer times smaller in each direction than holes in conventional URA patterns. A balance correlation function is generated where holes are represented by 1's, nonholes are represented by -1's, and supporting area is represented by 0's. The self-supporting array can be used for low energy applications where substrates would greatly reduce throughput. The balance correlation response function for the self-supporting array pattern provides an accurate representation of the source of nonfocusable radiation.

Heisenberg symmetry and collective modes of one dimensional unitary correlated fermions

NASA Astrophysics Data System (ADS)

Abhinav, Kumar; Chandrasekhar, B.; Vyas, Vivek M.; Panigrahi, Prasanta K.

2017-02-01

The correlated fermionic many-particle system, near infinite scattering length, reveals an underlying Heisenberg symmetry in one dimension, as compared to an SO (2 , 1) symmetry in two dimensions. This facilitates an exact map from the interacting to the non-interacting system, both with and without a harmonic trap, and explains the short-distance scaling behavior of the wave-function. Taking advantage of the phenomenological Calogero-Sutherland-type interaction, motivated by the density functional approach, we connect the ground-state energy shift, to many-body correlation effect. For the excited states, modes at integral values of the harmonic frequency ω are predicted in one dimension, in contrast to the breathing modes with frequency 2ω in two dimensions.

Description of a Generalized Analytical Model for the Micro-dosimeter Response

NASA Technical Reports Server (NTRS)

Badavi, Francis F.; Stewart-Sloan, Charlotte R.; Xapsos, Michael A.; Shinn, Judy L.; Wilson, John W.; Hunter, Abigail

2007-01-01

An analytical prediction capability for space radiation in Low Earth Orbit (LEO), correlated with the Space Transportation System (STS) Shuttle Tissue Equivalent Proportional Counter (TEPC) measurements, is presented. The model takes into consideration the energy loss straggling and chord length distribution of the TEPC detector, and is capable of predicting energy deposition fluctuations in a micro-volume by incoming ions through both direct and indirect ionic events. The charged particle transport calculations correlated with STS 56, 51, 110 and 114 flights are accomplished by utilizing the most recent version (2005) of the Langley Research Center (LaRC) deterministic ionized particle transport code High charge (Z) and Energy TRaNsport WZETRN), which has been extensively validated with laboratory beam measurements and available space flight data. The agreement between the TEPC model prediction (response function) and the TEPC measured differential and integral spectra in lineal energy (y) domain is promising.

Wind energy system time-domain (WEST) analyzers

NASA Technical Reports Server (NTRS)

Dreier, M. E.; Hoffman, J. A.

1981-01-01

A portable analyzer which simulates in real time the complex nonlinear dynamics of horizontal axis wind energy systems was constructed. Math models for an aeroelastic rotor featuring nonlinear aerodynamic and inertial terms were implemented with high speed digital controllers and analog calculation. This model was combined with other math models of elastic supports, control systems, a power train and gimballed rotor kinematics. A stroboscopic display system graphically depicting distributed blade loads, motion, and other aerodynamic functions on a cathode ray tube is included. Limited correlation efforts showed good comparison between the results of this analyzer and other sophisticated digital simulations. The digital simulation results were successfully correlated with test data.

Integrated and spectral energy flows of the GLAS GCM

NASA Technical Reports Server (NTRS)

Tennebaum, J.

1981-01-01

Methods to analyze the generation, transport, and dissipation of energy to study geophysical fluid flows are discussed. Energetics analyses are pursued in several directions: (1) the longitudinal and time dependence on the energy flow to the stratosphere was examined as a function of geographical sector; (2) strong and weak energy flows were correlated by medium range forecasts; (3) the one dimensional spectral results (Fourier services around latitude circles) were extended to spherical harmonics over a global domain; (4) the validity of vertical velocities derived from mass convergence was examined for their effect on the conversion of eddy available potential energy to eddy kinetic energy.

Exact conditions on the temperature dependence of density functionals

DOE PAGES

Burke, K.; Smith, J. C.; Grabowski, P. E.; ...

2016-05-15

Universal exact conditions guided the construction of most ground-state density functional approximations in use today. Here, we derive the relation between the entropy and Mermin free energy density functionals for thermal density functional theory. Both the entropy and sum of kinetic and electron-electron repulsion functionals are shown to be monotonically increasing with temperature, while the Mermin functional is concave downwards. Analogous relations are found for both exchange and correlation. The importance of these conditions is illustrated in two extremes: the Hubbard dimer and the uniform gas.

Energy dependence of the ridge in high multiplicity proton-proton collisions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dusling, Kevin; Tribedy, Prithwish; Venugopalan, Raju

2016-01-27

In this study, we demonstrate that the recent measurement of azimuthally collimated, long-range rapidity (“ridge”) correlations in √s=13 TeV proton-proton (p+p) collisions by the ATLAS Collaboration at the LHC are in agreement with expectations from the color glass condensate effective theory of high-energy QCD. The observation that the integrated near-side yield as a function of multiplicity is independent of collision energy is a natural consequence of the fact that multiparticle production is driven by a single semihard saturation scale in the color glass condensate framework. We argue further that the azimuthal structure of these recent ATLAS ridge measurements strongly constrainsmore » hydrodynamic interpretations of such correlations in high-multiplicity p+p collisions.« less

Modelling the angular correlation function and its full covariance in photometric galaxy surveys

NASA Astrophysics Data System (ADS)

Crocce, Martín; Cabré, Anna; Gaztañaga, Enrique

2011-06-01

Near-future cosmology will see the advent of wide-area photometric galaxy surveys, such as the Dark Energy Survey (DES), that extend to high redshifts (z˜ 1-2) but give poor radial distance resolution. In such cases splitting the data into redshift bins and using the angular correlation function w(θ), or the Cℓ power spectrum, will become the standard approach to extracting cosmological information or to studying the nature of dark energy through the baryon acoustic oscillations (BAO) probe. In this work we present a detailed model for w(θ) at large scales as a function of redshift and binwidth, including all relevant effects, namely non-linear gravitational clustering, bias, redshift space distortions and photo-z uncertainties. We also present a model for the full covariance matrix, characterizing the angular correlation measurements, that takes into account the same effects as for w(θ) and also the possibility of a shot-noise component and partial sky coverage. Provided with a large-volume N-body simulation from the MICE collaboration, we built several ensembles of mock redshift bins with a sky coverage and depth typical of forthcoming photometric surveys. The model for the angular correlation and the one for the covariance matrix agree remarkably well with the mock measurements in all configurations. The prospects for a full shape analysis of w(θ) at BAO scales in forthcoming photometric surveys such as DES are thus very encouraging.

Observation of Noise Correlated by the Hawking Effect in a Water Tank.

PubMed

Euvé, L-P; Michel, F; Parentani, R; Philbin, T G; Rousseaux, G

2016-09-16

We measured the power spectrum and two-point correlation function for the randomly fluctuating free surface on the downstream side of a stationary flow with a maximum Froude number F_{max}≈0.85 reached above a localized obstacle. On such a flow the scattering of incident long wavelength modes is analogous to that responsible for black hole radiation (the Hawking effect). Our measurements of the noise show a clear correlation between pairs of modes of opposite energies. We also measure the scattering coefficients by applying the same analysis of correlations to waves produced by a wave maker.

Basis convergence of range-separated density-functional theory.

PubMed

Franck, Odile; Mussard, Bastien; Luppi, Eleonora; Toulouse, Julien

2015-02-21

Range-separated density-functional theory (DFT) is an alternative approach to Kohn-Sham density-functional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functional theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Møller-Plesset correlation energy of four systems (He, Ne, N2, and H2O) with cardinal number X of the Dunning basis sets cc - p(C)V XZ and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-functional theory based on an exponential formula.

Computational and Theoretical Investigations of Strongly Correlated Fermions in Optical Lattices

DTIC Science & Technology

2013-08-29

and two-particle spectral functions across the disorder - driven superconductor - insulator transition". 22. Invited speaker, \\Fermions in Optical...energy gaps across the disorder - driven superconductor - insulator transition", October 7, 2010, Harvard. 27. Seminar on \\Probing Quantum Phases of...Perimeter Institute, November 14, 2011. 37. Seminar on \\Single and two-particle energy gaps across the disorder - driven superconductor - insulator transition

Comparison of the quadratic configuration interaction and coupled cluster approaches to electron correlation including the effect of triple excitations

NASA Technical Reports Server (NTRS)

Taylor, Peter R.; Lee, Timothy J.; Rendell, Alistair P.

1990-01-01

The recently proposed quadratic configuration interaction (QCI) method is compared with the more rigorous coupled cluster (CC) approach for a variety of chemical systems. Some of these systems are well represented by a single-determinant reference function and others are not. The finite order singles and doubles correlation energy, the perturbational triples correlation energy, and a recently devised diagnostic for estimating the importance of multireference effects are considered. The spectroscopic constants of CuH, the equilibrium structure of cis-(NO)2 and the binding energies of Be3, Be4, Mg3, and Mg4 were calculated using both approaches. The diagnostic for estimating multireference character clearly demonstrates that the QCI method becomes less satisfactory than the CC approach as non-dynamical correlation becomes more important, in agreement with a perturbational analysis of the two methods and the numerical estimates of the triple excitation energies they yield. The results for CuH show that the differences between the two methods become more apparent as the chemical systems under investigation becomes more multireference in nature and the QCI results consequently become less reliable. Nonetheless, when the system of interest is dominated by a single reference determinant both QCI and CC give very similar results.

Extremely correlated Fermi liquid theory of the t-J model in 2 dimensions: low energy properties

NASA Astrophysics Data System (ADS)

Shastry, B. Sriram; Mai, Peizhi

2018-01-01

Low energy properties of the metallic state of the two-dimensional t-J model are presented for second neighbor hopping with hole-doping (t\\prime ≤slant 0) and electron-doping (t\\prime > 0), with various superexchange energy J. We use a closed set of equations for the Greens functions obtained from the extremely correlated Fermi liquid theory. These equations reproduce the known low energies features of the large U Hubbard model in infinite dimensions. The density and temperature dependent quasiparticle weight, decay rate and the peak spectral heights over the Brillouin zone are calculated. We also calculate the resistivity, Hall conductivity, Hall number and cotangent Hall angle. The spectral features display high thermal sensitivity at modest T for density n≳ 0.8, implying a suppression of the effective Fermi-liquid temperature by two orders of magnitude relative to the bare bandwidth. The cotangent Hall angle exhibits a T 2 behavior at low T, followed by an interesting kink at higher T. The Hall number exhibits strong renormalization due to correlations. Flipping the sign of t\\prime changes the curvature of the resistivity versus T curves between convex and concave. Our results provide a natural route for understanding the observed difference in the temperature dependent resistivity of strongly correlated electron-doped and hole-doped matter.

Semiclassical wave packet treatment of scattering resonances: application to the delta zero-point energy effect in recombination reactions.

PubMed

Vetoshkin, Evgeny; Babikov, Dmitri

2007-09-28

For the first time Feshbach-type resonances important in recombination reactions are characterized using the semiclassical wave packet method. This approximation allows us to determine the energies, lifetimes, and wave functions of the resonances and also to observe a very interesting correlation between them. Most important is that this approach permits description of a quantum delta-zero-point energy effect in recombination reactions and reproduces the anomalous rates of ozone formation.

Relaxation of a High-Energy Quasiparticle in a One-Dimensional Bose Gas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tan, Shina; Glazman, Leonid I.; Pustilnik, Michael

2010-08-27

We evaluate the relaxation rate of high-energy quasiparticles in a weakly interacting one-dimensional Bose gas. Unlike in higher dimensions, the rate is a nonmonotonic function of temperature, with a maximum at the crossover to the state of suppressed density fluctuations. At the maximum, the relaxation rate may significantly exceed its zero-temperature value. We also find the dependence of the differential inelastic scattering rate on the transferred energy. This rate yields information about temperature dependence of local pair correlations.

Quartic scaling MP2 for solids: A highly parallelized algorithm in the plane wave basis

NASA Astrophysics Data System (ADS)

Schäfer, Tobias; Ramberger, Benjamin; Kresse, Georg

2017-03-01

We present a low-complexity algorithm to calculate the correlation energy of periodic systems in second-order Møller-Plesset (MP2) perturbation theory. In contrast to previous approximation-free MP2 codes, our implementation possesses a quartic scaling, O ( N 4 ) , with respect to the system size N and offers an almost ideal parallelization efficiency. The general issue that the correlation energy converges slowly with the number of basis functions is eased by an internal basis set extrapolation. The key concept to reduce the scaling is to eliminate all summations over virtual orbitals which can be elegantly achieved in the Laplace transformed MP2 formulation using plane wave basis sets and fast Fourier transforms. Analogously, this approach could allow us to calculate second order screened exchange as well as particle-hole ladder diagrams with a similar low complexity. Hence, the presented method can be considered as a step towards systematically improved correlation energies.

Big Data Meets Quantum Chemistry Approximations: The Δ-Machine Learning Approach.

PubMed

Ramakrishnan, Raghunathan; Dral, Pavlo O; Rupp, Matthias; von Lilienfeld, O Anatole

2015-05-12

Chemically accurate and comprehensive studies of the virtual space of all possible molecules are severely limited by the computational cost of quantum chemistry. We introduce a composite strategy that adds machine learning corrections to computationally inexpensive approximate legacy quantum methods. After training, highly accurate predictions of enthalpies, free energies, entropies, and electron correlation energies are possible, for significantly larger molecular sets than used for training. For thermochemical properties of up to 16k isomers of C7H10O2 we present numerical evidence that chemical accuracy can be reached. We also predict electron correlation energy in post Hartree-Fock methods, at the computational cost of Hartree-Fock, and we establish a qualitative relationship between molecular entropy and electron correlation. The transferability of our approach is demonstrated, using semiempirical quantum chemistry and machine learning models trained on 1 and 10% of 134k organic molecules, to reproduce enthalpies of all remaining molecules at density functional theory level of accuracy.

Accelerating the two-point and three-point galaxy correlation functions using Fourier transforms

NASA Astrophysics Data System (ADS)

Slepian, Zachary; Eisenstein, Daniel J.

2016-01-01

Though Fourier transforms (FTs) are a common technique for finding correlation functions, they are not typically used in computations of the anisotropy of the two-point correlation function (2PCF) about the line of sight in wide-angle surveys because the line-of-sight direction is not constant on the Cartesian grid. Here we show how FTs can be used to compute the multipole moments of the anisotropic 2PCF. We also show how FTs can be used to accelerate the 3PCF algorithm of Slepian & Eisenstein. In both cases, these FT methods allow one to avoid the computational cost of pair counting, which scales as the square of the number density of objects in the survey. With the upcoming large data sets of Dark Energy Spectroscopic Instrument, Euclid, and Large Synoptic Survey Telescope, FT techniques will therefore offer an important complement to simple pair or triplet counts.

Finite-size effects on current correlation functions

NASA Astrophysics Data System (ADS)

Chen, Shunda; Zhang, Yong; Wang, Jiao; Zhao, Hong

2014-02-01

We study why the calculation of current correlation functions (CCFs) still suffers from finite-size effects even when the periodic boundary condition is taken. Two important one-dimensional, momentum-conserving systems are investigated as examples. Intriguingly, it is found that the state of a system recurs in the sense of microcanonical ensemble average, and such recurrence may result in oscillations in CCFs. Meanwhile, we find that the sound mode collisions induce an extra time decay in a current so that its correlation function decays faster (slower) in a smaller (larger) system. Based on these two unveiled mechanisms, a procedure for correctly evaluating the decay rate of a CCF is proposed, with which our analysis suggests that the global energy CCF decays as ˜t-2/3 in the diatomic hard-core gas model and in a manner close to ˜t-1/2 in the Fermi-Pasta-Ulam-β model.

Hidden correlations entailed by q-non additivity render the q-monoatomic gas highly non trivial

NASA Astrophysics Data System (ADS)

Plastino, A.; Rocca, M. C.

2018-01-01

It ts known that Tsallis' q-non-additivity entails hidden correlations. It has also been shown that even for a monoatomic gas, both the q-partition function Z and the mean energy 〈 U 〉 diverge and, in particular, exhibit poles for certain values of the Tsallis non additivity parameter q. This happens because Z and 〈 U 〉 both depend on a Γ-function. This Γ, in turn, depends upon the spatial dimension ν. We encounter three different regimes according to the argument A of the Γ-function. (1) A > 0, (2) A < 0 and Γ > 0 outside the poles. (3) A displays poles and the physics is obtained via dimensional regularization. In cases (2) and (3) one discovers gravitational effects and quartets of particles. Moreover, bound states and gravitational effects emerge as a consequence of the hidden q-correlations.

Thermodynamically accessible titanium clusters TiN, N = 2-32.

PubMed

Lazauskas, Tomas; Sokol, Alexey A; Buckeridge, John; Catlow, C Richard A; Escher, Susanne G E T; Farrow, Matthew R; Mora-Fonz, David; Blum, Volker W; Phaahla, Tshegofatso M; Chauke, Hasani R; Ngoepe, Phuti E; Woodley, Scott M

2018-05-10

We have performed a genetic algorithm search on the tight-binding interatomic potential energy surface (PES) for small TiN (N = 2-32) clusters. The low energy candidate clusters were further refined using density functional theory (DFT) calculations with the PBEsol exchange-correlation functional and evaluated with the PBEsol0 hybrid functional. The resulting clusters were analysed in terms of their structural features, growth mechanism and surface area. The results suggest a growth mechanism that is based on forming coordination centres by interpenetrating icosahedra, icositetrahedra and Frank-Kasper polyhedra. We identify centres of coordination, which act as centres of bulk nucleation in medium sized clusters and determine the morphological features of the cluster.

Statistical against dynamical PLF fission as seen by the IMF-IMF correlation functions and comparisons with CoMD model

NASA Astrophysics Data System (ADS)

Pagano, E. V.; Acosta, L.; Auditore, L.; Cap, T.; Cardella, G.; Colonna, M.; De Filippo, E.; Geraci, E.; Gnoffo, B.; Lanzalone, G.; Maiolino, C.; Martorana, N.; Pagano, A.; Papa, M.; Piasecki, E.; Pirrone, S.; Politi, G.; Porto, F.; Quattrocchi, L.; Rizzo, F.; Russotto, P.; Trifiro’, A.; Trimarchi, M.; Siwek-Wilczynska, K.

2018-05-01

In nuclear reactions at Fermi energies two and multi particles intensity interferometry correlation methods are powerful tools in order to pin down the characteristic time scale of the emission processes. In this paper we summarize an improved application of the fragment-fragment correlation function in the specific physics case of heavy projectile-like (PLF) binary massive splitting in two fragments of intermediate mass(IMF). Results are shown for the reverse kinematics reaction 124 Sn+64 Ni at 35 AMeV that has been investigated by using the forward part of CHIMERA multi-detector. The analysis was performed as a function of the charge asymmetry of the observed couples of IMF. We show a coexistence of dynamical and statistical components as a function of the charge asymmetry. Transport CoMD simulations are compared with the data in order to pin down the timescale of the fragments production and the relevant ingredients of the in medium effective interaction used in the transport calculations.

Communication: The description of strong correlation within self-consistent Green's function second-order perturbation theory

NASA Astrophysics Data System (ADS)

Phillips, Jordan J.; Zgid, Dominika

2014-06-01

We report an implementation of self-consistent Green's function many-body theory within a second-order approximation (GF2) for application with molecular systems. This is done by iterative solution of the Dyson equation expressed in matrix form in an atomic orbital basis, where the Green's function and self-energy are built on the imaginary frequency and imaginary time domain, respectively, and fast Fourier transform is used to efficiently transform these quantities as needed. We apply this method to several archetypical examples of strong correlation, such as a H32 finite lattice that displays a highly multireference electronic ground state even at equilibrium lattice spacing. In all cases, GF2 gives a physically meaningful description of the metal to insulator transition in these systems, without resorting to spin-symmetry breaking. Our results show that self-consistent Green's function many-body theory offers a viable route to describing strong correlations while remaining within a computationally tractable single-particle formalism.

Perturbation theory corrections to the two-particle reduced density matrix variational method.

PubMed

Juhasz, Tamas; Mazziotti, David A

2004-07-15

In the variational 2-particle-reduced-density-matrix (2-RDM) method, the ground-state energy is minimized with respect to the 2-particle reduced density matrix, constrained by N-representability conditions. Consider the N-electron Hamiltonian H(lambda) as a function of the parameter lambda where we recover the Fock Hamiltonian at lambda=0 and we recover the fully correlated Hamiltonian at lambda=1. We explore using the accuracy of perturbation theory at small lambda to correct the 2-RDM variational energies at lambda=1 where the Hamiltonian represents correlated atoms and molecules. A key assumption in the correction is that the 2-RDM method will capture a fairly constant percentage of the correlation energy for lambda in (0,1] because the nonperturbative 2-RDM approach depends more significantly upon the nature rather than the strength of the two-body Hamiltonian interaction. For a variety of molecules we observe that this correction improves the 2-RDM energies in the equilibrium bonding region, while the 2-RDM energies at stretched or nearly dissociated geometries, already highly accurate, are not significantly changed. At equilibrium geometries the corrected 2-RDM energies are similar in accuracy to those from coupled-cluster singles and doubles (CCSD), but at nonequilibrium geometries the 2-RDM energies are often dramatically more accurate as shown in the bond stretching and dissociation data for water and nitrogen. (c) 2004 American Institute of Physics.

Second order Møller-Plesset and coupled cluster singles and doubles methods with complex basis functions for resonances in electron-molecule scattering

DOE PAGES

White, Alec F.; Epifanovsky, Evgeny; McCurdy, C. William; ...

2017-06-21

The method of complex basis functions is applied to molecular resonances at correlated levels of theory. Møller-Plesset perturbation theory at second order and equation-of-motion electron attachment coupled-cluster singles and doubles (EOM-EA-CCSD) methods based on a non-Hermitian self-consistent-field reference are used to compute accurate Siegert energies for shape resonances in small molecules including N 2 - , CO - , CO 2 - , and CH 2 O - . Analytic continuation of complex θ-trajectories is used to compute Siegert energies, and the θ-trajectories of energy differences are found to yield more consistent results than those of total energies.more » Furthermore, the ability of such methods to accurately compute complex potential energy surfaces is investigated, and the possibility of using EOM-EA-CCSD for Feshbach resonances is explored in the context of e-helium scattering.« less

Second order Møller-Plesset and coupled cluster singles and doubles methods with complex basis functions for resonances in electron-molecule scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

White, Alec F.; Epifanovsky, Evgeny; McCurdy, C. William

The method of complex basis functions is applied to molecular resonances at correlated levels of theory. Møller-Plesset perturbation theory at second order and equation-of-motion electron attachment coupled-cluster singles and doubles (EOM-EA-CCSD) methods based on a non-Hermitian self-consistent-field reference are used to compute accurate Siegert energies for shape resonances in small molecules including N 2 - , CO - , CO 2 - , and CH 2 O - . Analytic continuation of complex θ-trajectories is used to compute Siegert energies, and the θ-trajectories of energy differences are found to yield more consistent results than those of total energies.more » Furthermore, the ability of such methods to accurately compute complex potential energy surfaces is investigated, and the possibility of using EOM-EA-CCSD for Feshbach resonances is explored in the context of e-helium scattering.« less

Correlation of particle-induced displacement damage in silicon

NASA Astrophysics Data System (ADS)

Summers, G. P.; Dale, C. J.; Burke, E. A.; Wolicki, E. A.; Marshall, P. W.

1987-12-01

The effects of displacement damage caused in several types of silicon bipolar transistors by protons, deuterons, helium ions, and by 1-MeV-equivalent neutrons are considered. Measurements are compared to calculations of the nonionizing energy deposition in silicon as a function of particle type and energy. Measurements were made of displacement damage factors for 2N2222A and 2N2907A switching transistors, and for 2N3055, 2N6678, and 2N6547 power transistors, as a function of collector current using 3.7-175-MeV protons, 4.3-37-MeV deuterons, and 16.8-65-MeV helium ions. Long-term ionization effects on the value of the displacement damage factors were taken into account. In calculating the energy dependence of the nonionizing energy deposition, Rutherford, nuclear elastic, and nuclear inelastic interactions, and Lindhard energy partition were considered.

The energy separation between the classical and nonclassical isomers of protonated acetylene - An extensive study in one- and n-particle space saturation

NASA Technical Reports Server (NTRS)

Lindh, Roland; Rice, Julia E.; Lee, Timothy J.

1991-01-01

The energy separation between the classical and nonclassical forms of protonated acetylene has been reinvestigated in light of the recent experimentally deduced lower bound to this value of 6.0 kcal/mol. The objective of the present study is to use state-of-the-art ab initio quantum mechanical methods to establish this energy difference to within chemical accuracy (i.e., about 1 kcal/mol). The one-particle basis sets include up to g-type functions and the electron correlation methods include single and double excitation coupled-cluster (CCSD), the CCSD(T) extension, multireference configuration interaction, and the averaged coupled-pair functional methods. A correction for zero-point vibrational energies has also been included, yielding a best estimate for the energy difference between the classical and nonclassical forms of 3.7 + or - 1.3 kcal/mol.

Analytic functions for potential energy curves, dipole moments, and transition dipole moments of LiRb molecule.

PubMed

You, Yang; Yang, Chuan-Lu; Wang, Mei-Shan; Ma, Xiao-Guang; Liu, Wen-Wang; Wang, Li-Zhi

2016-01-15

The analytic potential energy functions (APEFs) of the X(1)Σ(+), 2(1)Σ(+), a(3)Σ(+), and 2(3)Σ(+) states of the LiRb molecule are obtained using Morse long-range potential energy function with damping function and nonlinear least-squares method. These calculations were based on the potential energy curves (PECs) calculated using the multi-reference configuration interaction (MRCI) method. The reliability of the APEFs is confirmed using the curves of their first and second derivatives. By using the obtained APEFs, the rotational and vibrational energy levels of the states are determined by solving the Schrödinger equation of nuclear movement. The spectroscopic parameters, which are deduced using Dunham expansion, and the obtained rotational and vibrational levels are compared with the reported theoretical and experimental values. The correlation effect of the electrons of the inner shell remarkably improves the results compared with the experimental spectroscopic parameters. For the first time, the APEFs for the dipole moments and transition dipole moments of the states have been determined based on the curves obtained from the MRCI calculations. Copyright © 2015 Elsevier B.V. All rights reserved.

Correlating ion energies and CF{sub 2} surface production during fluorocarbon plasma processing of silicon

DOE Office of Scientific and Technical Information (OSTI.GOV)

Martin, Ina T.; Zhou Jie; Fisher, Ellen R.

2006-07-01

Ion energy distribution (IED) measurements are reported for ions in the plasma molecular beam source of the imaging of radicals interacting with surfaces (IRIS) apparatus. The IEDs and relative intensities of nascent ions in C{sub 3}F{sub 8} and C{sub 4}F{sub 8} plasma molecular beams were measured using a Hiden PSM003 mass spectrometer mounted on the IRIS main chamber. The IEDs are complex and multimodal, with mean ion energies ranging from 29 to 92 eV. Integrated IEDs provided relative ion intensities as a function of applied rf power and source pressure. Generally, higher applied rf powers and lower source pressures resultedmore » in increased ion intensities and mean ion energies. Most significantly, a comparison to CF{sub 2} surface interaction measurements previously made in our laboratories reveals that mean ion energies are directly and linearly correlated to CF{sub 2} surface production in these systems.« less

The effect of a hot, spherical scattering cloud on quasi-periodic oscillation behavior

NASA Astrophysics Data System (ADS)

Bussard, R. W.; Weisskopf, M. C.; Elsner, R. F.; Shibazaki, N.

1988-04-01

A Monte Carlo technique is used to investigate the effects of a hot electron scattering cloud surrounding a time-dependent X-ray source. Results are presented for the time-averaged emergent energy spectra and the mean residence time in the cloud as a function of energy. Moreover, after Fourier transforming the scattering Green's function, it is shown how the cloud affects both the observed power spectrum of a time-dependent source and the cross spectrum (Fourier transform of a cross correlation between energy bands). It is found that the power spectra intrinsic to the source are related to those observed by a relatively simple frequency-dependent multiplicative factor (a transmission function). The cloud can severely attenuate high frequencies in the power spectra, depending on optical depth, and, at lower frequencies, the transmission function has roughly a Lorentzian shape. It is also found that if the intrinsic energy spectrum is constant in time, the phase of the cross spectrum is determined entirely by scattering. Finally, the implications of the results for studies of the X-ray quasi-periodic oscillators are discussed.

Estimate of the Coulomb correlation energy in CeAg2Ge2 from inverse photoemission and high resolution photoemission spectroscopy

NASA Astrophysics Data System (ADS)

Banik, Soma; Arya, A.; Bendounan, Azzedine; Maniraj, M.; Thamizhavel, A.; Vobornik, I.; Dhar, S. K.; Deb, S. K.

2014-08-01

The occupied and the unoccupied electronic structure of CeAg2Ge2 single crystal has been studied using high resolution photoemission and inverse photoemission spectroscopy, respectively. High resolution photoemission reveals the clear signature of Ce 4f states in the occupied electronic structure which was not observed clearly in our earlier studies. The Coulomb correlation energy in this system has been determined experimentally from the position of the 4f states above and below the Fermi level. Theoretically, the correlation energy has been determined by using the first principles density functional calculations within the generalized gradient approximations taking into account the strong intra-atomic (on-site) interaction Hubbard Ueff term. The calculated valence band shows minor changes in the spectral shape with increasing Ueff due to the fact that the density of Ce 4f state is narrow in the occupied part and is hybridized with the Ce 5d, Ag 4d and Ge 4p states. On the other hand, substantial changes are observed in the spectral shape of the calculated conduction band with increasing Ueff since the density of Ce 4f state is very large in the unoccupied part, compared to other states. The estimated value of correlation energy for CeAg2Ge2 from the experiment and the theory is ≈ 4.2 eV. The resonant photoemission data are analyzed in the framework of the single-impurity Anderson model which further confirms the presence of the Coulomb correlation energy and small hybridization in this system.

Study of the low energy spectrum of titanium by using QMC methods

NASA Astrophysics Data System (ADS)

Buendía, E.; Caballero, M. A.; Gálvez, F. J.

2018-02-01

We study the ground state and the low energy excited states of Ti. Each variational wave function is a product of a Jastrow correlation factor by a model function obtained within the parameterized optimized effective potential (POEP) framework by using a configuration mixing. Near degeneracy effects between the orbitals 4s and 4p, as well as excitations to the 3d orbital due to the strong competition between 4s and 3d orbitals in transition metal atoms are taken into account. All electron calculations have been carried out by using quantum Monte Carlo techniques, variational and diffusion.

Communication: Water on hexagonal boron nitride from diffusion Monte Carlo

DOE Office of Scientific and Technical Information (OSTI.GOV)

Al-Hamdani, Yasmine S.; Ma, Ming; Michaelides, Angelos, E-mail: angelos.michaelides@ucl.ac.uk

2015-05-14

Despite a recent flurry of experimental and simulation studies, an accurate estimate of the interaction strength of water molecules with hexagonal boron nitride is lacking. Here, we report quantum Monte Carlo results for the adsorption of a water monomer on a periodic hexagonal boron nitride sheet, which yield a water monomer interaction energy of −84 ± 5 meV. We use the results to evaluate the performance of several widely used density functional theory (DFT) exchange correlation functionals and find that they all deviate substantially. Differences in interaction energies between different adsorption sites are however better reproduced by DFT.

Properties of real metallic surfaces: Effects of density functional semilocality and van der Waals nonlocality

PubMed Central

Patra, Abhirup; Bates, Jefferson E.; Sun, Jianwei; Perdew, John P.

2017-01-01

We have computed the surface energies, work functions, and interlayer surface relaxations of clean (111), (100), and (110) surfaces of Al, Cu, Ru, Rh, Pd, Ag, Pt, and Au. We interpret the surface energy from liquid metal measurements as the mean of the solid-state surface energies over these three lowest-index crystal faces. We compare experimental (and random phase approximation) reference values to those of a family of nonempirical semilocal density functionals, from the basic local density approximation (LDA) to our most advanced general purpose meta-generalized gradient approximation, strongly constrained and appropriately normed (SCAN). The closest agreement is achieved by the simplest density functional LDA, and by the most sophisticated one, SCAN+rVV10 (Vydrov–Van Voorhis 2010). The long-range van der Waals interaction, incorporated through rVV10, increases the surface energies by about 10%, and increases the work functions by about 3%. LDA works for metal surfaces through two known error cancellations. The Perdew–Burke–Ernzerhof generalized gradient approximation tends to underestimate both surface energies (by about 24%) and work functions (by about 4%), yielding the least-accurate results. The amount by which a functional underestimates these surface properties correlates with the extent to which it neglects van der Waals attraction at intermediate and long range. Qualitative arguments are given for the signs of the van der Waals contributions to the surface energy and work function. A standard expression for the work function in Kohn–Sham (KS) theory is shown to be valid in generalized KS theory. Interlayer relaxations from different functionals are in reasonable agreement with one another, and usually with experiment. PMID:29042509

A reference-modified density functional theory: An application to solvation free-energy calculations for a Lennard-Jones solution.

PubMed

Sumi, Tomonari; Maruyama, Yutaka; Mitsutake, Ayori; Koga, Kenichiro

2016-06-14

In the conventional classical density functional theory (DFT) for simple fluids, an ideal gas is usually chosen as the reference system because there is a one-to-one correspondence between the external field and the density distribution function, and the exact intrinsic free-energy functional is available for the ideal gas. In this case, the second-order density functional Taylor series expansion of the excess intrinsic free-energy functional provides the hypernetted-chain (HNC) approximation. Recently, it has been shown that the HNC approximation significantly overestimates the solvation free energy (SFE) for an infinitely dilute Lennard-Jones (LJ) solution, especially when the solute particles are several times larger than the solvent particles [T. Miyata and J. Thapa, Chem. Phys. Lett. 604, 122 (2014)]. In the present study, we propose a reference-modified density functional theory as a systematic approach to improve the SFE functional as well as the pair distribution functions. The second-order density functional Taylor series expansion for the excess part of the intrinsic free-energy functional in which a hard-sphere fluid is introduced as the reference system instead of an ideal gas is applied to the LJ pure and infinitely dilute solution systems and is proved to remarkably improve the drawbacks of the HNC approximation. Furthermore, the third-order density functional expansion approximation in which a factorization approximation is applied to the triplet direct correlation function is examined for the LJ systems. We also show that the third-order contribution can yield further refinements for both the pair distribution function and the excess chemical potential for the pure LJ liquids.

Excitons and Davydov splitting in sexithiophene from first-principles many-body Green's function theory

NASA Astrophysics Data System (ADS)

Leng, Xia; Yin, Huabing; Liang, Dongmei; Ma, Yuchen

2015-09-01

Organic semiconductors have promising and broad applications in optoelectronics. Understanding their electronic excited states is important to help us control their spectroscopic properties and performance of devices. There have been a large amount of experimental investigations on spectroscopies of organic semiconductors, but theoretical calculation from first principles on this respect is still limited. Here, we use density functional theory (DFT) and many-body Green's function theory, which includes the GW method and Bethe-Salpeter equation, to study the electronic excited-state properties and spectroscopies of one prototypical organic semiconductor, sexithiophene. The exciton energies of sexithiophene in both the gas and bulk crystalline phases are very sensitive to the exchange-correlation functionals used in DFT for ground-state structure relaxation. We investigated the influence of dynamical screening in the electron-hole interaction on exciton energies, which is found to be very pronounced for triplet excitons and has to be taken into account in first principles calculations. In the sexithiophene single crystal, the energy of the lowest triplet exciton is close to half the energy of the lowest singlet one. While lower-energy singlet and triplet excitons are intramolecular Frenkel excitons, higher-energy excitons are of intermolecular charge-transfer type. The calculated optical absorption spectra and Davydov splitting are in good agreement with experiments.

Effects of van der Waals Interactions in the Adsorption of Isooctane and Ethanol on Fe(100) Surfaces

PubMed Central

2014-01-01

van der Waals (vdW) forces play a fundamental role in the structure and behavior of diverse systems. Because of development of functionals that include nonlocal correlation, it is possible to study the effects of vdW interactions in systems of industrial and tribological interest. Here we simulated within the framework of density functional theory (DFT) the adsorption of isooctane (2,2,4-trimethylpentane) and ethanol on an Fe(100) surface, employing various exchange–correlation functionals to take vdW forces into account. In particular, this paper discusses the effect of vdW forces on the magnitude of adsorption energies, equilibrium geometries, and their role in the binding mechanism. According to our calculations, vdW interactions increase the adsorption energies and reduce the equilibrium distances. Nevertheless, they do not influence the spatial configuration of the adsorbed molecules. Their effect on the electronic density is a nonisotropic, delocalized accumulation of charge between the molecule and the slab. In conclusion, vdW forces are essential for the adsorption of isooctane and ethanol on a bcc Fe(100) surface. PMID:25126156

A perturbative approach to the redshift space correlation function: beyond the Standard Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bose, Benjamin; Koyama, Kazuya, E-mail: benjamin.bose@port.ac.uk, E-mail: kazuya.koyama@port.ac.uk

We extend our previous redshift space power spectrum code to the redshift space correlation function. Here we focus on the Gaussian Streaming Model (GSM). Again, the code accommodates a wide range of modified gravity and dark energy models. For the non-linear real space correlation function used in the GSM we use the Fourier transform of the RegPT 1-loop matter power spectrum. We compare predictions of the GSM for a Vainshtein screened and Chameleon screened model as well as GR. These predictions are compared to the Fourier transform of the Taruya, Nishimichi and Saito (TNS) redshift space power spectrum model whichmore » is fit to N-body data. We find very good agreement between the Fourier transform of the TNS model and the GSM predictions, with ≤ 6% deviations in the first two correlation function multipoles for all models for redshift space separations in 50Mpc h ≤ s ≤ 180Mpc/ h . Excellent agreement is found in the differences between the modified gravity and GR multipole predictions for both approaches to the redshift space correlation function, highlighting their matched ability in picking up deviations from GR. We elucidate the timeliness of such non-standard templates at the dawn of stage-IV surveys and discuss necessary preparations and extensions needed for upcoming high quality data.« less

Accurate Energies and Orbital Description in Semi-Local Kohn-Sham DFT

NASA Astrophysics Data System (ADS)

Lindmaa, Alexander; Kuemmel, Stephan; Armiento, Rickard

2015-03-01

We present our progress on a scheme in semi-local Kohn-Sham density-functional theory (KS-DFT) for improving the orbital description while still retaining the level of accuracy of the usual semi-local exchange-correlation (xc) functionals. DFT is a widely used tool for first-principles calculations of properties of materials. A given task normally requires a balance of accuracy and computational cost, which is well achieved with semi-local DFT. However, commonly used semi-local xc functionals have important shortcomings which often can be attributed to features of the corresponding xc potential. One shortcoming is an overly delocalized representation of localized orbitals. Recently a semi-local GGA-type xc functional was constructed to address these issues, however, it has the trade-off of lower accuracy of the total energy. We discuss the source of this error in terms of a surplus energy contribution in the functional that needs to be accounted for, and offer a remedy for this issue which formally stays within KS-DFT, and, which does not harshly increase the computational effort. The end result is a scheme that combines accurate total energies (e.g., relaxed geometries) with an improved orbital description (e.g., improved band structure).

Stable isomers and electronic, vibrational, and optical properties of WS2 nano-clusters: A first-principles study

NASA Astrophysics Data System (ADS)

Hafizi, Roohollah; Hashemifar, S. Javad; Alaei, Mojtaba; Jangrouei, MohammadReza; Akbarzadeh, Hadi

2016-12-01

In this paper, we employ an evolutionary algorithm along with the full-potential density functional theory (DFT) computations to perform a comprehensive search for the stable structures of stoichiometric (WS2)n nano-clusters (n = 1 - 9), within three different exchange-correlation functionals. Our results suggest that n = 5 and 8 are possible candidates for the low temperature magic sizes of WS2 nano-clusters while at temperatures above 500 Kelvin, n = 7 exhibits a comparable relative stability with n = 8. The electronic properties and energy gap of the lowest energy isomers were computed within several schemes, including semilocal Perdew-Burke-Ernzerhof and Becke-Lee-Yang-Parr functionals, hybrid B3LYP functional, many body based DFT+GW approach, ΔSCF method, and time dependent DFT calculations. Vibrational spectra of the lowest lying isomers, computed by the force constant method, are used to address IR spectra and thermal free energy of the clusters. Time dependent density functional calculation in a real time domain is applied to determine the full absorption spectra and optical gap of the lowest energy isomers of the WS2 nano-clusters.

The ACS Survey of Galactic Globular Clusters. VIII. Effects of Environment on Globular Cluster Global Mass Functions

NASA Astrophysics Data System (ADS)

Paust, Nathaniel E. Q.; Reid, I. Neill; Piotto, Giampaolo; Aparicio, Antonio; Anderson, Jay; Sarajedini, Ata; Bedin, Luigi R.; Chaboyer, Brian; Dotter, Aaron; Hempel, Maren; Majewski, Steven; Marín-Franch, A.; Milone, Antonino; Rosenberg, Alfred; Siegel, Michael

2010-02-01

We have used observations obtained as part of the Hubble Space Telescope/ACS Survey of Galactic Globular Clusters to construct global present-day mass functions for 17 globular clusters utilizing multi-mass King models to extrapolate from our observations to the global cluster behavior. The global present-day mass functions for these clusters are well matched by power laws from the turnoff, ≈0.8 M sun, to 0.2-0.3 M sun on the lower main sequence. The slopes of those power-law fits, α, have been correlated with an extensive set of intrinsic and extrinsic cluster properties to investigate which parameters may influence the form of the present-day mass function. We do not confirm previous suggestions of correlations between α and either metallicity or Galactic location. However, we do find a strong statistical correlation with the related parameters central surface brightness, μ V , and inferred central density, ρ0. The correlation is such that clusters with denser cores (stronger binding energy) tend to have steeper mass functions (a higher proportion of low-mass stars), suggesting that dynamical evolution due to external interactions may have played a key role in determining α. Thus, the present-day mass function may owe more to nurture than to nature. Detailed modeling of external dynamical effects is therefore a requisite for determining the initial mass function for Galactic globular clusters.

Contact angle of sessile drops in Lennard-Jones systems.

PubMed

Becker, Stefan; Urbassek, Herbert M; Horsch, Martin; Hasse, Hans

2014-11-18

Molecular dynamics simulations are used for studying the contact angle of nanoscale sessile drops on a planar solid wall in a system interacting via the truncated and shifted Lennard-Jones potential. The entire range between total wetting and dewetting is investigated by varying the solid-fluid dispersive interaction energy. The temperature is varied between the triple point and the critical temperature. A correlation is obtained for the contact angle in dependence of the temperature and the dispersive interaction energy. Size effects are studied by varying the number of fluid particles at otherwise constant conditions, using up to 150,000 particles. For particle numbers below 10,000, a decrease of the contact angle is found. This is attributed to a dependence of the solid-liquid surface tension on the droplet size. A convergence to a constant contact angle is observed for larger system sizes. The influence of the wall model is studied by varying the density of the wall. The effective solid-fluid dispersive interaction energy at a contact angle of θ = 90° is found to be independent of temperature and to decrease linearly with the solid density. A correlation is developed that describes the contact angle as a function of the dispersive interaction, the temperature, and the solid density. The density profile of the sessile drop and the surrounding vapor phase is described by a correlation combining a sigmoidal function and an oscillation term.

mBEEF-vdW: Robust fitting of error estimation density functionals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lundgaard, Keld T.; Wellendorff, Jess; Voss, Johannes

Here, we propose a general-purpose semilocal/nonlocal exchange-correlation functional approximation, named mBEEF-vdW. The exchange is a meta generalized gradient approximation, and the correlation is a semilocal and nonlocal mixture, with the Rutgers-Chalmers approximation for van der Waals (vdW) forces. The functional is fitted within the Bayesian error estimation functional (BEEF) framework. We improve the previously used fitting procedures by introducing a robust MM-estimator based loss function, reducing the sensitivity to outliers in the datasets. To more reliably determine the optimal model complexity, we furthermore introduce a generalization of the bootstrap 0.632 estimator with hierarchical bootstrap sampling and geometric mean estimator overmore » the training datasets. Using this estimator, we show that the robust loss function leads to a 10% improvement in the estimated prediction error over the previously used least-squares loss function. The mBEEF-vdW functional is benchmarked against popular density functional approximations over a wide range of datasets relevant for heterogeneous catalysis, including datasets that were not used for its training. Overall, we find that mBEEF-vdW has a higher general accuracy than competing popular functionals, and it is one of the best performing functionals on chemisorption systems, surface energies, lattice constants, and dispersion. We also show the potential-energy curve of graphene on the nickel(111) surface, where mBEEF-vdW matches the experimental binding length. mBEEF-vdW is currently available in gpaw and other density functional theory codes through Libxc, version 3.0.0.« less

mBEEF-vdW: Robust fitting of error estimation density functionals

DOE PAGES

Lundgaard, Keld T.; Wellendorff, Jess; Voss, Johannes; ...

2016-06-15

Here, we propose a general-purpose semilocal/nonlocal exchange-correlation functional approximation, named mBEEF-vdW. The exchange is a meta generalized gradient approximation, and the correlation is a semilocal and nonlocal mixture, with the Rutgers-Chalmers approximation for van der Waals (vdW) forces. The functional is fitted within the Bayesian error estimation functional (BEEF) framework. We improve the previously used fitting procedures by introducing a robust MM-estimator based loss function, reducing the sensitivity to outliers in the datasets. To more reliably determine the optimal model complexity, we furthermore introduce a generalization of the bootstrap 0.632 estimator with hierarchical bootstrap sampling and geometric mean estimator overmore » the training datasets. Using this estimator, we show that the robust loss function leads to a 10% improvement in the estimated prediction error over the previously used least-squares loss function. The mBEEF-vdW functional is benchmarked against popular density functional approximations over a wide range of datasets relevant for heterogeneous catalysis, including datasets that were not used for its training. Overall, we find that mBEEF-vdW has a higher general accuracy than competing popular functionals, and it is one of the best performing functionals on chemisorption systems, surface energies, lattice constants, and dispersion. We also show the potential-energy curve of graphene on the nickel(111) surface, where mBEEF-vdW matches the experimental binding length. mBEEF-vdW is currently available in gpaw and other density functional theory codes through Libxc, version 3.0.0.« less

The structure and energetics of Cr(CO)6 and Cr(CO)5

NASA Technical Reports Server (NTRS)

Barnes, Leslie A.; Liu, Bowen; Lindh, Roland

1992-01-01

The geometric structure of Cr(CO)6 is optimized at the modified coupled pair functional (MCPF), single and double excitation coupled-cluster (CCSD) and CCSD(T) levels of theory (including a perturbational estimate for connected triple excitations), and the force constants for the totally symmetric representation are determined. The geometry of Cr(CO)5 is partially optimized at the MCPF, CCSD, and CCSD(T) levels of theory. Comparison with experimental data shows that the CCSD(T) method gives the best results for the structures and force constants, and that remaining errors are probably due to deficiencies in the one-particle basis sets used for CO. The total binding energies of Cr(CO)6 and Cr(CO)5 are also determined at the MCPF, CCSD, and CCSD(T) levels of theory. The CCSD(T) method gives a much larger total binding energy than either the MCPF or CCSD methods. An analysis of the basis set superposition error (BSSE) at the MCPF level of treatment points out limitations in the one-particle basis used. Calculations using larger basis sets reduce the BSSE, but the total binding energy of Cr(CO)6 is still significantly smaller than the experimental value, although the first CO bond dissociation energy of Cr(CO)6 is well described. An investigation of 3s3p correlation reveals only a small effect. In the largest basis set, the total CO binding energy of Cr(CO)6 is estimated to be 140 kcal/mol at the CCSD(T) level of theory, or about 86 percent of the experimental value. The remaining discrepancy between the experimental and theoretical value is probably due to limitations in the one-particle basis, rather than limitations in the correlation treatment. In particular an additional d function and an f function on each C and O are needed to obtain quantitative results. This is underscored by the fact that even using a very large primitive set (1042 primitive functions contracted to 300 basis functions), the superposition error for the total binding energy of Cr(CO)6 is 22 kcal/mol at the MCPF level of treatment.

An Energy-Independent Pro-longevity Function of Triacylglycerol in Yeast

PubMed Central

Hall, Kevin W.; Deng, Xiexiong; Li, Pan; Benning, Christoph; Williams, Barry L.; Kuo, Min-Hao

2016-01-01

Intracellular triacylglycerol (TAG) is a ubiquitous energy storage lipid also involved in lipid homeostasis and signaling. Comparatively, little is known about TAG’s role in other cellular functions. Here we show a pro-longevity function of TAG in the budding yeast Saccharomyces cerevisiae. In yeast strains derived from natural and laboratory environments a correlation between high levels of TAG and longer chronological lifespan was observed. Increased TAG abundance through the deletion of TAG lipases prolonged chronological lifespan of laboratory strains, while diminishing TAG biosynthesis shortened lifespan without apparently affecting vegetative growth. TAG-mediated lifespan extension was independent of several other known stress response factors involved in chronological aging. Because both lifespan regulation and TAG metabolism are conserved, this cellular pro-longevity function of TAG may extend to other organisms. PMID:26907989

Proton-proton elastic scattering excitation functions at intermediate energies

NASA Astrophysics Data System (ADS)

Rohdjess, H.

1998-05-01

Polarized and unpolarized proton-proton elastic scattering is investigated with the EDDA-experiment at the Cooler Synchrotron COSY at Jülich to significantly improve the world data base in the beam energy range 500-2500 MeV. Measurements during beam acceleration with thin internal targets and a large acceptance detector provide excitation functions over a broad angular and energy range with unprecedented internal consistency. Data taking with an unpolarized CH2 fiber target and an unpolarized beam have been completed and the derived differential cross sections are presented and compared to a recent phase shift analysis. With a polarized atomic beam target newly installed in COSY and a polarized COSY beam—currently under development—the measurements will be extended to analyzing powers and spin correlation parameters.

Stochastic Gravity: Theory and Applications.

PubMed

Hu, Bei Lok; Verdaguer, Enric

2004-01-01

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operatorvalued) stress-energy bi-tensor which describes the fluctuations of quantum matter fields in curved spacetimes. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open systems concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise, and decoherence. We then focus on the properties of the stress-energy bi-tensor. We obtain a general expression for the noise kernel of a quantum field defined at two distinct points in an arbitrary curved spacetime as products of covariant derivatives of the quantum field's Green function. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime. We offer an analytical solution of the Einstein-Langevin equation and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole (enclosed in a box). We derive a fluctuation-dissipation relation between the fluctuations in the radiation and the dissipative dynamics of metric fluctuations.

Renormalized Energy Concentration in Random Matrices

NASA Astrophysics Data System (ADS)

Borodin, Alexei; Serfaty, Sylvia

2013-05-01

We define a "renormalized energy" as an explicit functional on arbitrary point configurations of constant average density in the plane and on the real line. The definition is inspired by ideas of Sandier and Serfaty (From the Ginzburg-Landau model to vortex lattice problems, 2012; 1D log-gases and the renormalized energy, 2013). Roughly speaking, it is obtained by subtracting two leading terms from the Coulomb potential on a growing number of charges. The functional is expected to be a good measure of disorder of a configuration of points. We give certain formulas for its expectation for general stationary random point processes. For the random matrix β-sine processes on the real line ( β = 1,2,4), and Ginibre point process and zeros of Gaussian analytic functions process in the plane, we compute the expectation explicitly. Moreover, we prove that for these processes the variance of the renormalized energy vanishes, which shows concentration near the expected value. We also prove that the β = 2 sine process minimizes the renormalized energy in the class of determinantal point processes with translation invariant correlation kernels.

Magnetic helicity generation in the frame of Kazantsev model

NASA Astrophysics Data System (ADS)

Yushkov, Egor V.; Lukin, Alexander S.

2017-11-01

Using a magnetic dynamo model, suggested by Kazantsev (J. Exp. Theor. Phys. 1968, vol. 26, p. 1031), we study the small-scale helicity generation in a turbulent electrically conducting fluid. We obtain the asymptotic dependencies of dynamo growth rate and magnetic correlation functions on magnetic Reynolds numbers. Special attention is devoted to the comparison of a longitudinal correlation function and a function of magnetic helicity for various conditions of asymmetric turbulent flows. We compare the analytical solutions on small scales with numerical results, calculated by an iterative algorithm on non-uniform grids. We show that the exponential growth of current helicity is simultaneous with the magnetic energy for Reynolds numbers larger than some critical value and estimate this value for various types of asymmetry.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tokár, K.; Derian, R.; Mitas, L.

Using explicitly correlated fixed-node quantum Monte Carlo and density functional theory (DFT) methods, we study electronic properties, ground-state multiplets, ionization potentials, electron affinities, and low-energy fragmentation channels of charged half-sandwich and multidecker vanadium-benzene systems with up to 3 vanadium atoms, including both anions and cations. It is shown that, particularly in anions, electronic correlations play a crucial role; these effects are not systematically captured with any commonly used DFT functionals such as gradient corrected, hybrids, and range-separated hybrids. On the other hand, tightly bound cations can be described qualitatively by DFT. A comparison of DFT and quantum Monte Carlo providesmore » an in-depth understanding of the electronic structure and properties of these correlated systems. The calculations also serve as a benchmark study of 3d molecular anions that require a balanced many-body description of correlations at both short- and long-range distances.« less

Converting conformational changes to electrostatic energy in molecular motors: The energetics of ATP synthase.

PubMed

Strajbl, Marek; Shurki, Avital; Warshel, Arieh

2003-12-09

F1-ATPase is the catalytic component of the ATP synthase molecular machine responsible for most of the uphill synthesis of ATP in living systems. The enormous advances in biochemical and structural studies of this machine provide an opportunity for detailed understanding of the nature of its rotary mechanism. However, further quantitative progress in this direction requires development of reliable ways of translating the observed structural changes to the corresponding energies. This requirement is particularly challenging because we are dealing with a large system that couples major structural changes with a chemical process. The present work provides such a structure-function correlation by using the linear response approximation to describe the rotary mechanism. This approach allows one to evaluate the energy of transitions between different conformational states by considering only the changes in the corresponding electrostatic energies of the ligands. The relevant energetics are also obtained by calculating the linear response approximation-based free energies of transferring the ligands from water to the different sites of F1-ATPase in their different conformational states. We also use the empirical valence bond approach to evaluate the actual free-energy profile for the ATP synthesis in the different conformational states of the system. Integrating the information from the different approaches provides a semiquantitative structure-function correlation for F1-ATPase. It is found that the conformational changes are converted to changes in the electrostatic interaction between the protein and its ligands, which drives the ATP synthesis.

Index of mechanical work in gait of children with cerebral palsy.

PubMed

Dziuba, Alicja Katarzyna; Tylkowska, Małgorzata; Jaroszczuk, Sebastian

2014-01-01

The pathological gait of children with cerebral palsy involves higher mechanical work, which limits their ability to function properly in society. Mechanical work is directly related to walking speed and, although a number of studies have been carried out in this field, few of them analysed the effect of the speed. The study aimed to develop standards for mechanical work during gait of children with cerebral palsy depending on the walking speed. The study covered 18 children with cerebral palsy and 14 healthy children. The BTS Smart software and the author's software were used to evaluate mechanical work, kinetic, potential and rotational energy connected with motion of the children body during walk. Compared to healthy subjects, mechanical work in children with cerebral palsy increases with the degree of disability. It can be expressed as a linear function of walking speed and shows strong and statistically significant correlations with walking gait. A negative statistically significant correlation between the degree of disability and walking speed can be observed. The highest contribution to the total mechanical energy during gait is from mechanical energy of the feet. Instantaneous value of rotational energy is 700 times lower than the instantaneous mechanical energy. An increase in walking speed causes the increase in the effect of the index of kinetic energy on total mechanical work. The method described can provide an objective supplementation for doctors and physical therapists to perform a simple and immediate diagnosis without much technical knowledge.

Comparing Geant4 hadronic models for the WENDI-II rem meter response function.

PubMed

Vanaudenhove, T; Dubus, A; Pauly, N

2013-01-01

The WENDI-II rem meter is one of the most popular neutron dosemeters used to assess a useful quantity of radiation protection, namely the ambient dose equivalent. This is due to its high sensitivity and its energy response that approximately follows the conversion function between neutron fluence and ambient dose equivalent in the range of thermal to 5 GeV. The simulation of the WENDI-II response function with the Geant4 toolkit is then perfectly suited to compare low- and high-energy hadronic models provided by this Monte Carlo code. The results showed that the thermal treatment of hydrogen in polyethylene for neutron <4 eV has a great influence over the whole detector range. Above 19 MeV, both Bertini Cascade and Binary Cascade models show a good correlation with the results found in the literature, while low-energy parameterised models are not suitable for this application.

Nuclear quantum shape-phase transitions in odd-mass systems

NASA Astrophysics Data System (ADS)

Quan, S.; Li, Z. P.; Vretenar, D.; Meng, J.

2018-03-01

Microscopic signatures of nuclear ground-state shape-phase transitions in odd-mass Eu isotopes are explored starting from excitation spectra and collective wave functions obtained by diagonalization of a core-quasiparticle coupling Hamiltonian based on energy density functionals. As functions of the physical control parameter—the number of nucleons—theoretical low-energy spectra, two-neutron separation energies, charge isotope shifts, spectroscopic quadrupole moments, and E 2 reduced transition matrix elements accurately reproduce available data and exhibit more-pronounced discontinuities at neutron number N =90 compared with the adjacent even-even Sm and Gd isotopes. The enhancement of the first-order quantum phase transition in odd-mass systems can be attributed to a shape polarization effect of the unpaired proton which, at the critical neutron number, starts predominantly coupling to Gd core nuclei that are characterized by larger quadrupole deformation and weaker proton pairing correlations compared with the corresponding Sm isotopes.

Crystal structure optimisation using an auxiliary equation of state

NASA Astrophysics Data System (ADS)

Jackson, Adam J.; Skelton, Jonathan M.; Hendon, Christopher H.; Butler, Keith T.; Walsh, Aron

2015-11-01

Standard procedures for local crystal-structure optimisation involve numerous energy and force calculations. It is common to calculate an energy-volume curve, fitting an equation of state around the equilibrium cell volume. This is a computationally intensive process, in particular, for low-symmetry crystal structures where each isochoric optimisation involves energy minimisation over many degrees of freedom. Such procedures can be prohibitive for non-local exchange-correlation functionals or other "beyond" density functional theory electronic structure techniques, particularly where analytical gradients are not available. We present a simple approach for efficient optimisation of crystal structures based on a known equation of state. The equilibrium volume can be predicted from one single-point calculation and refined with successive calculations if required. The approach is validated for PbS, PbTe, ZnS, and ZnTe using nine density functionals and applied to the quaternary semiconductor Cu2ZnSnS4 and the magnetic metal-organic framework HKUST-1.

Energy decomposition analysis of single bonds within Kohn-Sham density functional theory.

PubMed

Levine, Daniel S; Head-Gordon, Martin

2017-11-28

An energy decomposition analysis (EDA) for single chemical bonds is presented within the framework of Kohn-Sham density functional theory based on spin projection equations that are exact within wave function theory. Chemical bond energies can then be understood in terms of stabilization caused by spin-coupling augmented by dispersion, polarization, and charge transfer in competition with destabilizing Pauli repulsions. The EDA reveals distinguishing features of chemical bonds ranging across nonpolar, polar, ionic, and charge-shift bonds. The effect of electron correlation is assessed by comparison with Hartree-Fock results. Substituent effects are illustrated by comparing the C-C bond in ethane against that in bis(diamantane), and dispersion stabilization in the latter is quantified. Finally, three metal-metal bonds in experimentally characterized compounds are examined: a [Formula: see text]-[Formula: see text] dimer, the [Formula: see text]-[Formula: see text] bond in dizincocene, and the Mn-Mn bond in dimanganese decacarbonyl.

Enabling Computational Nanotechnology through JavaGenes in a Cycle Scavenging Environment

NASA Technical Reports Server (NTRS)

Globus, Al; Menon, Madhu; Srivastava, Deepak; Biegel, Bryan A. (Technical Monitor)

2002-01-01

A genetic algorithm procedure is developed and implemented for fitting parameters for many-body inter-atomic force field functions for simulating nanotechnology atomistic applications using portable Java on cycle-scavenged heterogeneous workstations. Given a physics based analytic functional form for the force field, correlated parameters in a multi-dimensional environment are typically chosen to fit properties given either by experiments and/or by higher accuracy quantum mechanical simulations. The implementation automates this tedious procedure using an evolutionary computing algorithm operating on hundreds of cycle-scavenged computers. As a proof of concept, we demonstrate the procedure for evaluating the Stillinger-Weber (S-W) potential by (a) reproducing the published parameters for Si using S-W energies in the fitness function, and (b) evolving a "new" set of parameters using semi-empirical tightbinding energies in the fitness function. The "new" parameters are significantly better suited for Si cluster energies and forces as compared to even the published S-W potential.

Ab initio study on the ground and low-lying states of BAlk (Alk = Li, Na, K) molecules.

PubMed

Xiao, Ke-La; Yang, Chuan-Lu; Wang, Mei-Shan; Ma, Xiao-Guang; Liu, Wen-Wang

2014-10-02

The potential energy curves (PECs) and dipole moment functions of (1)Π, (3)Π, (1)Σ(+), and (3)Σ(+) states of BAlk (Alk = Li, Na, K) are calculated using multireference configuration interaction method and large all-electron basis sets. The effects of inner-shell correlation electron for BAlk are considered. The ro-vibrational energy levels are obtained by solving the Schrödinger equation of nuclear motion based on the ab initio PECs. The spectroscopic parameters are determined from the ro-vibrational levels with Dunham expansion. The PECs are fitted into analytical potential energy functions using the Morse long-range potential function. The dipole moment functions for the states of BAlk are presented. The transition dipole moments for (1)Σ(+) → (1)Π and (3)Σ(+) → (3)Π states of BAlk are obtained. The interactions between the outermost electron of Alk and B 2p electrons for (1)Π, (3)Π, (1)Σ(+), and (3)Σ(+) states are also analyzed, respectively.

Global Patch Matching

NASA Astrophysics Data System (ADS)

Huang, X.; Hu, K.; Ling, X.; Zhang, Y.; Lu, Z.; Zhou, G.

2017-09-01

This paper introduces a novel global patch matching method that focuses on how to remove fronto-parallel bias and obtain continuous smooth surfaces with assuming that the scenes covered by stereos are piecewise continuous. Firstly, simple linear iterative cluster method (SLIC) is used to segment the base image into a series of patches. Then, a global energy function, which consists of a data term and a smoothness term, is built on the patches. The data term is the second-order Taylor expansion of correlation coefficients, and the smoothness term is built by combing connectivity constraints and the coplanarity constraints are combined to construct the smoothness term. Finally, the global energy function can be built by combining the data term and the smoothness term. We rewrite the global energy function in a quadratic matrix function, and use least square methods to obtain the optimal solution. Experiments on Adirondack stereo and Motorcycle stereo of Middlebury benchmark show that the proposed method can remove fronto-parallel bias effectively, and produce continuous smooth surfaces.

Violation of the continuity equation in the Krieger-Li-Iafrate approximation for current-density functional theory

NASA Astrophysics Data System (ADS)

Siegmund, Marc; Pankratov, Oleg

2011-01-01

We show that the exchange-correlation scalar and vector potentials obtained from the optimized effective potential (OEP) equations and from the Krieger-Li-Iafrate (KLI) approximation for the current-density functional theory (CDFT) change under a gauge transformation such that the energy functional remains invariant. This alone does not assure, however, the theory’s compliance with the continuity equation. Using the model of a quantum ring with a broken angular symmetry which is penetrated by a magnetic flux we demonstrate that the physical current density calculated with the exact-exchange CDFT in the KLI approximation violates the continuity condition. In contrast, the current found from a solution of the full OEP equations satisfies this condition. We argue that the continuity violation stems from the fact that the KLI potentials are not (in general) the exact functional derivatives of a gauge-invariant exchange-correlation functional.