Time-dependent density-functional tight-binding method with the third-order expansion of electron density

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

Nishimoto, Yoshio, E-mail: nishimoto.yoshio@fukui.kyoto-u.ac.jp

2015-09-07

We develop a formalism for the calculation of excitation energies and excited state gradients for the self-consistent-charge density-functional tight-binding method with the third-order contributions of a Taylor series of the density functional theory energy with respect to the fluctuation of electron density (time-dependent density-functional tight-binding (TD-DFTB3)). The formulation of the excitation energy is based on the existing time-dependent density functional theory and the older TD-DFTB2 formulae. The analytical gradient is computed by solving Z-vector equations, and it requires one to calculate the third-order derivative of the total energy with respect to density matrix elements due to the inclusion of themore » third-order contributions. The comparison of adiabatic excitation energies for selected small and medium-size molecules using the TD-DFTB2 and TD-DFTB3 methods shows that the inclusion of the third-order contributions does not affect excitation energies significantly. A different set of parameters, which are optimized for DFTB3, slightly improves the prediction of adiabatic excitation energies statistically. The application of TD-DFTB for the prediction of absorption and fluorescence energies of cresyl violet demonstrates that TD-DFTB3 reproduced the experimental fluorescence energy quite well.« less

Time-dependent density-functional tight-binding method with the third-order expansion of electron density.

PubMed

Nishimoto, Yoshio

2015-09-07

We develop a formalism for the calculation of excitation energies and excited state gradients for the self-consistent-charge density-functional tight-binding method with the third-order contributions of a Taylor series of the density functional theory energy with respect to the fluctuation of electron density (time-dependent density-functional tight-binding (TD-DFTB3)). The formulation of the excitation energy is based on the existing time-dependent density functional theory and the older TD-DFTB2 formulae. The analytical gradient is computed by solving Z-vector equations, and it requires one to calculate the third-order derivative of the total energy with respect to density matrix elements due to the inclusion of the third-order contributions. The comparison of adiabatic excitation energies for selected small and medium-size molecules using the TD-DFTB2 and TD-DFTB3 methods shows that the inclusion of the third-order contributions does not affect excitation energies significantly. A different set of parameters, which are optimized for DFTB3, slightly improves the prediction of adiabatic excitation energies statistically. The application of TD-DFTB for the prediction of absorption and fluorescence energies of cresyl violet demonstrates that TD-DFTB3 reproduced the experimental fluorescence energy quite well.

Finite Temperature Densities via the S-Function Method with Application to Electron Screening in Plasmas

NASA Astrophysics Data System (ADS)

Watrous, Mitchell James

1997-12-01

A new approach to the Green's-function method for the calculation of equilibrium densities within the finite temperature, Kohn-Sham formulation of density functional theory is presented, which extends the method to all temperatures. The contour of integration in the complex energy plane is chosen such that the density is given by a sum of Green's function differences evaluated at the Matsubara frequencies, rather than by the calculation and summation of Kohn-Sham single-particle wave functions. The Green's functions are written in terms of their spectral representation and are calculated as the solutions of their defining differential equations. These differential equations are boundary value problems as opposed to the standard eigenvalue problems. For large values of the complex energy, the differential equations are further simplified from second to first-order by writing the Green's functions in terms of logarithmic derivatives. An asymptotic expression for the Green's functions is derived, which allows the sum over Matsubara poles to be approximated. The method is applied to the screening of nuclei by electrons in finite temperature plasmas. To demonstrate the method's utility, and to illustrate its advantages, the results of previous wave function type calculations for protons and neon nuclei are reproduced. The method is also used to formulate a new screening model for fusion reactions in the solar core, and the predicted reaction rate enhancements factors are compared with existing models.

Trunk density profile estimates from dual X-ray absorptiometry.

PubMed

Wicke, Jason; Dumas, Geneviève A; Costigan, Patrick A

2008-01-01

Accurate body segment parameters are necessary to estimate joint loads when using biomechanical models. Geometric methods can provide individualized data for these models but the accuracy of the geometric methods depends on accurate segment density estimates. The trunk, which is important in many biomechanical models, has the largest variability in density along its length. Therefore, the objectives of this study were to: (1) develop a new method for modeling trunk density profiles based on dual X-ray absorptiometry (DXA) and (2) develop a trunk density function for college-aged females and males that can be used in geometric methods. To this end, the density profiles of 25 females and 24 males were determined by combining the measurements from a photogrammetric method and DXA readings. A discrete Fourier transformation was then used to develop the density functions for each sex. The individual density and average density profiles compare well with the literature. There were distinct differences between the profiles of two of participants (one female and one male), and the average for their sex. It is believed that the variations in these two participants' density profiles were a result of the amount and distribution of fat they possessed. Further studies are needed to support this possibility. The new density functions eliminate the uniform density assumption associated with some geometric models thus providing more accurate trunk segment parameter estimates. In turn, more accurate moments and forces can be estimated for the kinetic analyses of certain human movements.

Implementation and benchmark of a long-range corrected functional in the density functional based tight-binding method

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

Lutsker, V.; Niehaus, T. A., E-mail: thomas.niehaus@physik.uni-regensburg.de; Aradi, B.

2015-11-14

Bridging the gap between first principles methods and empirical schemes, the density functional based tight-binding method (DFTB) has become a versatile tool in predictive atomistic simulations over the past years. One of the major restrictions of this method is the limitation to local or gradient corrected exchange-correlation functionals. This excludes the important class of hybrid or long-range corrected functionals, which are advantageous in thermochemistry, as well as in the computation of vibrational, photoelectron, and optical spectra. The present work provides a detailed account of the implementation of DFTB for a long-range corrected functional in generalized Kohn-Sham theory. We apply themore » method to a set of organic molecules and compare ionization potentials and electron affinities with the original DFTB method and higher level theory. The new scheme cures the significant overpolarization in electric fields found for local DFTB, which parallels the functional dependence in first principles density functional theory (DFT). At the same time, the computational savings with respect to full DFT calculations are not compromised as evidenced by numerical benchmark data.« 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.

Course 4: Density Functional Theory, Methods, Techniques, and Applications

NASA Astrophysics Data System (ADS)

Chrétien, S.; Salahub, D. R.

Contents 1 Introduction 2 Density functional theory 2.1 Hohenberg and Kohn theorems 2.2 Levy's constrained search 2.3 Kohn-Sham method 3 Density matrices and pair correlation functions 4 Adiabatic connection or coupling strength integration 5 Comparing and constrasting KS-DFT and HF-CI 6 Preparing new functionals 7 Approximate exchange and correlation functionals 7.1 The Local Spin Density Approximation (LSDA) 7.2 Gradient Expansion Approximation (GEA) 7.3 Generalized Gradient Approximation (GGA) 7.4 meta-Generalized Gradient Approximation (meta-GGA) 7.5 Hybrid functionals 7.6 The Optimized Effective Potential method (OEP) 7.7 Comparison between various approximate functionals 8 LAP correlation functional 9 Solving the Kohn-Sham equations 9.1 The Kohn-Sham orbitals 9.2 Coulomb potential 9.3 Exchange-correlation potential 9.4 Core potential 9.5 Other choices and sources of error 9.6 Functionality 10 Applications 10.1 Ab initio molecular dynamics for an alanine dipeptide model 10.2 Transition metal clusters: The ecstasy, and the agony... 10.3 The conversion of acetylene to benzene on Fe clusters 11 Conclusions

Spin-Multiplet Components and Energy Splittings by Multistate Density Functional Theory.

PubMed

Grofe, Adam; Chen, Xin; Liu, Wenjian; Gao, Jiali

2017-10-05

Kohn-Sham density functional theory has been tremendously successful in chemistry and physics. Yet, it is unable to describe the energy degeneracy of spin-multiplet components with any approximate functional. This work features two contributions. (1) We present a multistate density functional theory (MSDFT) to represent spin-multiplet components and to determine multiplet energies. MSDFT is a hybrid approach, taking advantage of both wave function theory and density functional theory. Thus, the wave functions, electron densities and energy density-functionals for ground and excited states and for different components are treated on the same footing. The method is illustrated on valence excitations of atoms and molecules. (2) Importantly, a key result is that for cases in which the high-spin components can be determined separately by Kohn-Sham density functional theory, the transition density functional in MSDFT (which describes electronic coupling) can be defined rigorously. The numerical results may be explored to design and optimize transition density functionals for configuration coupling in multiconfigurational DFT.

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.

Shape information from a critical point analysis of calculated electron density maps: application to DNA-drug systems

NASA Astrophysics Data System (ADS)

Leherte, L.; Allen, F. H.; Vercauteren, D. P.

1995-04-01

A computational method is described for mapping the volume within the DNA double helix accessible to a groove-binding antibiotic, netropsin. Topological critical point analysis is used to locate maxima in electron density maps reconstructed from crystallographically determined atomic coordinates. The peaks obtained in this way are represented as ellipsoids with axes related to local curvature of the electron density function. Combining the ellipsoids produces a single electron density function which can be probed to estimate effective volumes of the interacting species. Close complementarity between host and ligand in this example shows the method to be a good representation of the electron density function at various resolutions; while at the atomic level the ellipsoid method gives results which are in close agreement with those from the conventional, spherical, van der Waals approach.

Shape information from a critical point analysis of calculated electron density maps: Application to DNA-drug systems

NASA Astrophysics Data System (ADS)

Leherte, Laurence; Allen, Frank H.

1994-06-01

A computational method is described for mapping the volume within the DNA double helix accessible to the groove-binding antibiotic netropsin. Topological critical point analysis is used to locate maxima in electron density maps reconstructed from crystallographically determined atomic coordinates. The peaks obtained in this way are represented as ellipsoids with axes related to local curvature of the electron density function. Combining the ellipsoids produces a single electron density function which can be probed to estimate effective volumes of the interacting species. Close complementarity between host and ligand in this example shows the method to give a good representation of the electron density function at various resolutions. At the atomic level, the ellipsoid method gives results which are in close agreement with those from the conventional spherical van der Waals approach.

Generation of Stationary Non-Gaussian Time Histories with a Specified Cross-spectral Density

DOE PAGES

Smallwood, David O.

1997-01-01

The paper reviews several methods for the generation of stationary realizations of sampled time histories with non-Gaussian distributions and introduces a new method which can be used to control the cross-spectral density matrix and the probability density functions (pdfs) of the multiple input problem. Discussed first are two methods for the specialized case of matching the auto (power) spectrum, the skewness, and kurtosis using generalized shot noise and using polynomial functions. It is then shown that the skewness and kurtosis can also be controlled by the phase of a complex frequency domain description of the random process. The general casemore » of matching a target probability density function using a zero memory nonlinear (ZMNL) function is then covered. Next methods for generating vectors of random variables with a specified covariance matrix for a class of spherically invariant random vectors (SIRV) are discussed. Finally the general case of matching the cross-spectral density matrix of a vector of inputs with non-Gaussian marginal distributions is presented.« less

Characterizing bonding patterns in diradicals and triradicals by density-based wave function analysis: A uniform approach

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

Orms, Natalie; Rehn, Dirk; Dreuw, Andreas

Density-based wave function analysis enables unambiguous comparisons of electronic structure computed by different methods and removes ambiguity of orbital choices. Here, we use this tool to investigate the performance of different spin-flip methods for several prototypical diradicals and triradicals. In contrast to previous calibration studies that focused on energy gaps between high and low spin-states, we focus on the properties of the underlying wave functions, such as the number of effectively unpaired electrons. Comparison of different density functional and wave function theory results provides insight into the performance of the different methods when applied to strongly correlated systems such asmore » polyradicals. We also show that canonical molecular orbitals for species like large copper-containing diradicals fail to correctly represent the underlying electronic structure due to highly non-Koopmans character, while density-based analysis of the same wave function delivers a clear picture of bonding pattern.« less

Characterizing bonding patterns in diradicals and triradicals by density-based wave function analysis: A uniform approach

DOE PAGES

Orms, Natalie; Rehn, Dirk; Dreuw, Andreas; ...

2017-12-21

Density-based wave function analysis enables unambiguous comparisons of electronic structure computed by different methods and removes ambiguity of orbital choices. Here, we use this tool to investigate the performance of different spin-flip methods for several prototypical diradicals and triradicals. In contrast to previous calibration studies that focused on energy gaps between high and low spin-states, we focus on the properties of the underlying wave functions, such as the number of effectively unpaired electrons. Comparison of different density functional and wave function theory results provides insight into the performance of the different methods when applied to strongly correlated systems such asmore » polyradicals. We also show that canonical molecular orbitals for species like large copper-containing diradicals fail to correctly represent the underlying electronic structure due to highly non-Koopmans character, while density-based analysis of the same wave function delivers a clear picture of bonding pattern.« less

Multivariate spline methods in surface fitting

NASA Technical Reports Server (NTRS)

Guseman, L. F., Jr. (Principal Investigator); Schumaker, L. L.

1984-01-01

The use of spline functions in the development of classification algorithms is examined. In particular, a method is formulated for producing spline approximations to bivariate density functions where the density function is decribed by a histogram of measurements. The resulting approximations are then incorporated into a Bayesiaan classification procedure for which the Bayes decision regions and the probability of misclassification is readily computed. Some preliminary numerical results are presented to illustrate the method.

Electron-boson spectral density function of correlated multiband systems obtained from optical data: Ba0.6K0.4Fe2As2 and LiFeAs.

PubMed

Hwang, Jungseek

2016-03-31

We introduce an approximate method which can be used to simulate the optical conductivity data of correlated multiband systems for normal and superconducting cases by taking advantage of a reversed process in comparison to a usual optical data analysis, which has been used to extract the electron-boson spectral density function from measured optical spectra of single-band systems, like cuprates. We applied this method to optical conductivity data of two multiband pnictide systems (Ba0.6K0.4Fe2As2 and LiFeAs) and obtained the electron-boson spectral density functions. The obtained electron-boson spectral density consists of a sharp mode and a broad background. The obtained spectral density functions of the multiband systems show similar properties as those of cuprates in several aspects. We expect that our method helps to reveal the nature of strong correlations in the multiband pnictide superconductors.

Metal-ligand delocalization and spin density in the CuCl{sub 2} and [CuCl{sub 4}]{sup 2−} molecules: Some insights from wave function theory

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

Giner, Emmanuel, E-mail: gnrmnl@unife.it; Angeli, Celestino, E-mail: anc@unife.it

2015-09-28

The aim of this paper is to unravel the physical phenomena involved in the calculation of the spin density of the CuCl{sub 2} and [CuCl{sub 4}]{sup 2−} systems using wave function methods. Various types of wave functions are used here, both variational and perturbative, to analyse the effects impacting the spin density. It is found that the spin density on the chlorine ligands strongly depends on the mixing between two types of valence bond structures. It is demonstrated that the main difficulties found in most of the previous studies based on wave function methods come from the fact that eachmore » valence bond structure requires a different set of molecular orbitals and that using a unique set of molecular orbitals in a variational procedure leads to the removal of one of them from the wave function. Starting from these results, a method to compute the spin density at a reasonable computational cost is proposed.« less

A Safari Through Density Functional Theory

NASA Astrophysics Data System (ADS)

Dreizler, Reiner M.; Lüdde, Cora S.

Density functional theory is widely used to treat quantum many body problems in many areas of physics and related fields. A brief survey of this method covering foundations, functionals and applications is presented here.

Electronic Coupling Calculations for Bridge-Mediated Charge Transfer Using Constrained Density Functional Theory (CDFT) and Effective Hamiltonian Approaches at the Density Functional Theory (DFT) and Fragment-Orbital Density Functional Tight Binding (FODFTB) Level

DOE PAGES

Gillet, Natacha; Berstis, Laura; Wu, Xiaojing; ...

2016-09-09

In this paper, four methods to calculate charge transfer integrals in the context of bridge-mediated electron transfer are tested. These methods are based on density functional theory (DFT). We consider two perturbative Green's function effective Hamiltonian methods (first, at the DFT level of theory, using localized molecular orbitals; second, applying a tight-binding DFT approach, using fragment orbitals) and two constrained DFT implementations with either plane-wave or local basis sets. To assess the performance of the methods for through-bond (TB)-dominated or through-space (TS)-dominated transfer, different sets of molecules are considered. For through-bond electron transfer (ET), several molecules that were originally synthesizedmore » by Paddon-Row and co-workers for the deduction of electronic coupling values from photoemission and electron transmission spectroscopies, are analyzed. The tested methodologies prove to be successful in reproducing experimental data, the exponential distance decay constant and the superbridge effects arising from interference among ET pathways. For through-space ET, dedicated p-stacked systems with heterocyclopentadiene molecules were created and analyzed on the basis of electronic coupling dependence on donor-acceptor distance, structure of the bridge, and ET barrier height. The inexpensive fragment-orbital density functional tight binding (FODFTB) method gives similar results to constrained density functional theory (CDFT) and both reproduce the expected exponential decay of the coupling with donor-acceptor distances and the number of bridging units. Finally, these four approaches appear to give reliable results for both TB and TS ET and present a good alternative to expensive ab initio methodologies for large systems involving long-range charge transfers.« less

Electronic Coupling Calculations for Bridge-Mediated Charge Transfer Using Constrained Density Functional Theory (CDFT) and Effective Hamiltonian Approaches at the Density Functional Theory (DFT) and Fragment-Orbital Density Functional Tight Binding (FODFTB) Level

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

Gillet, Natacha; Berstis, Laura; Wu, Xiaojing

In this paper, four methods to calculate charge transfer integrals in the context of bridge-mediated electron transfer are tested. These methods are based on density functional theory (DFT). We consider two perturbative Green's function effective Hamiltonian methods (first, at the DFT level of theory, using localized molecular orbitals; second, applying a tight-binding DFT approach, using fragment orbitals) and two constrained DFT implementations with either plane-wave or local basis sets. To assess the performance of the methods for through-bond (TB)-dominated or through-space (TS)-dominated transfer, different sets of molecules are considered. For through-bond electron transfer (ET), several molecules that were originally synthesizedmore » by Paddon-Row and co-workers for the deduction of electronic coupling values from photoemission and electron transmission spectroscopies, are analyzed. The tested methodologies prove to be successful in reproducing experimental data, the exponential distance decay constant and the superbridge effects arising from interference among ET pathways. For through-space ET, dedicated p-stacked systems with heterocyclopentadiene molecules were created and analyzed on the basis of electronic coupling dependence on donor-acceptor distance, structure of the bridge, and ET barrier height. The inexpensive fragment-orbital density functional tight binding (FODFTB) method gives similar results to constrained density functional theory (CDFT) and both reproduce the expected exponential decay of the coupling with donor-acceptor distances and the number of bridging units. Finally, these four approaches appear to give reliable results for both TB and TS ET and present a good alternative to expensive ab initio methodologies for large systems involving long-range charge transfers.« less

Electronic Coupling Calculations for Bridge-Mediated Charge Transfer Using Constrained Density Functional Theory (CDFT) and Effective Hamiltonian Approaches at the Density Functional Theory (DFT) and Fragment-Orbital Density Functional Tight Binding (FODFTB) Level.

PubMed

Gillet, Natacha; Berstis, Laura; Wu, Xiaojing; Gajdos, Fruzsina; Heck, Alexander; de la Lande, Aurélien; Blumberger, Jochen; Elstner, Marcus

2016-10-11

In this article, four methods to calculate charge transfer integrals in the context of bridge-mediated electron transfer are tested. These methods are based on density functional theory (DFT). We consider two perturbative Green's function effective Hamiltonian methods (first, at the DFT level of theory, using localized molecular orbitals; second, applying a tight-binding DFT approach, using fragment orbitals) and two constrained DFT implementations with either plane-wave or local basis sets. To assess the performance of the methods for through-bond (TB)-dominated or through-space (TS)-dominated transfer, different sets of molecules are considered. For through-bond electron transfer (ET), several molecules that were originally synthesized by Paddon-Row and co-workers for the deduction of electronic coupling values from photoemission and electron transmission spectroscopies, are analyzed. The tested methodologies prove to be successful in reproducing experimental data, the exponential distance decay constant and the superbridge effects arising from interference among ET pathways. For through-space ET, dedicated π-stacked systems with heterocyclopentadiene molecules were created and analyzed on the basis of electronic coupling dependence on donor-acceptor distance, structure of the bridge, and ET barrier height. The inexpensive fragment-orbital density functional tight binding (FODFTB) method gives similar results to constrained density functional theory (CDFT) and both reproduce the expected exponential decay of the coupling with donor-acceptor distances and the number of bridging units. These four approaches appear to give reliable results for both TB and TS ET and present a good alternative to expensive ab initio methodologies for large systems involving long-range charge transfers.

A density matrix-based method for the linear-scaling calculation of dynamic second- and third-order properties at the Hartree-Fock and Kohn-Sham density functional theory levels.

PubMed

Kussmann, Jörg; Ochsenfeld, Christian

2007-11-28

A density matrix-based time-dependent self-consistent field (D-TDSCF) method for the calculation of dynamic polarizabilities and first hyperpolarizabilities using the Hartree-Fock and Kohn-Sham density functional theory approaches is presented. The D-TDSCF method allows us to reduce the asymptotic scaling behavior of the computational effort from cubic to linear for systems with a nonvanishing band gap. The linear scaling is achieved by combining a density matrix-based reformulation of the TDSCF equations with linear-scaling schemes for the formation of Fock- or Kohn-Sham-type matrices. In our reformulation only potentially linear-scaling matrices enter the formulation and efficient sparse algebra routines can be employed. Furthermore, the corresponding formulas for the first hyperpolarizabilities are given in terms of zeroth- and first-order one-particle reduced density matrices according to Wigner's (2n+1) rule. The scaling behavior of our method is illustrated for first exemplary calculations with systems of up to 1011 atoms and 8899 basis functions.

A Tomographic Method for the Reconstruction of Local Probability Density Functions

NASA Technical Reports Server (NTRS)

Sivathanu, Y. R.; Gore, J. P.

1993-01-01

A method of obtaining the probability density function (PDF) of local properties from path integrated measurements is described. The approach uses a discrete probability function (DPF) method to infer the PDF of the local extinction coefficient from measurements of the PDFs of the path integrated transmittance. The local PDFs obtained using the method are compared with those obtained from direct intrusive measurements in propylene/air and ethylene/air diffusion flames. The results of this comparison are good.

Analysis of the photophysical properties of zearalenone using density functional theory

USDA-ARS?s Scientific Manuscript database

The intrinsic photophysical properties of the resorcylic acid moiety of zearalenone offer a convenient label free method to determine zearalenone levels in contaminated agricultural products. Density functional theory and steady-state fluorescence methods were applied to investigate the role of stru...

Magnetic exchange couplings from constrained density functional theory: an efficient approach utilizing analytic derivatives.

PubMed

Phillips, Jordan J; Peralta, Juan E

2011-11-14

We introduce a method for evaluating magnetic exchange couplings based on the constrained density functional theory (C-DFT) approach of Rudra, Wu, and Van Voorhis [J. Chem. Phys. 124, 024103 (2006)]. Our method shares the same physical principles as C-DFT but makes use of the fact that the electronic energy changes quadratically and bilinearly with respect to the constraints in the range of interest. This allows us to use coupled perturbed Kohn-Sham spin density functional theory to determine approximately the corrections to the energy of the different spin configurations and construct a priori the relevant energy-landscapes obtained by constrained spin density functional theory. We assess this methodology in a set of binuclear transition-metal complexes and show that it reproduces very closely the results of C-DFT. This demonstrates a proof-of-concept for this method as a potential tool for studying a number of other molecular phenomena. Additionally, routes to improving upon the limitations of this method are discussed. © 2011 American Institute of Physics

Multicomponent density functional theory embedding formulation.

PubMed

Culpitt, Tanner; Brorsen, Kurt R; Pak, Michael V; Hammes-Schiffer, Sharon

2016-07-28

Multicomponent density functional theory (DFT) methods have been developed to treat two types of particles, such as electrons and nuclei, quantum mechanically at the same level. In the nuclear-electronic orbital (NEO) approach, all electrons and select nuclei, typically key protons, are treated quantum mechanically. For multicomponent DFT methods developed within the NEO framework, electron-proton correlation functionals based on explicitly correlated wavefunctions have been designed and used in conjunction with well-established electronic exchange-correlation functionals. Herein a general theory for multicomponent embedded DFT is developed to enable the accurate treatment of larger systems. In the general theory, the total electronic density is separated into two subsystem densities, denoted as regular and special, and different electron-proton correlation functionals are used for these two electronic densities. In the specific implementation, the special electron density is defined in terms of spatially localized Kohn-Sham electronic orbitals, and electron-proton correlation is included only for the special electron density. The electron-proton correlation functional depends on only the special electron density and the proton density, whereas the electronic exchange-correlation functional depends on the total electronic density. This scheme includes the essential electron-proton correlation, which is a relatively local effect, as well as the electronic exchange-correlation for the entire system. This multicomponent DFT-in-DFT embedding theory is applied to the HCN and FHF(-) molecules in conjunction with two different electron-proton correlation functionals and three different electronic exchange-correlation functionals. The results illustrate that this approach provides qualitatively accurate nuclear densities in a computationally tractable manner. The general theory is also easily extended to other types of partitioning schemes for multicomponent systems.

Multicomponent density functional theory embedding formulation

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

Culpitt, Tanner; Brorsen, Kurt R.; Pak, Michael V.

Multicomponent density functional theory (DFT) methods have been developed to treat two types of particles, such as electrons and nuclei, quantum mechanically at the same level. In the nuclear-electronic orbital (NEO) approach, all electrons and select nuclei, typically key protons, are treated quantum mechanically. For multicomponent DFT methods developed within the NEO framework, electron-proton correlation functionals based on explicitly correlated wavefunctions have been designed and used in conjunction with well-established electronic exchange-correlation functionals. Herein a general theory for multicomponent embedded DFT is developed to enable the accurate treatment of larger systems. In the general theory, the total electronic density ismore » separated into two subsystem densities, denoted as regular and special, and different electron-proton correlation functionals are used for these two electronic densities. In the specific implementation, the special electron density is defined in terms of spatially localized Kohn-Sham electronic orbitals, and electron-proton correlation is included only for the special electron density. The electron-proton correlation functional depends on only the special electron density and the proton density, whereas the electronic exchange-correlation functional depends on the total electronic density. This scheme includes the essential electron-proton correlation, which is a relatively local effect, as well as the electronic exchange-correlation for the entire system. This multicomponent DFT-in-DFT embedding theory is applied to the HCN and FHF{sup −} molecules in conjunction with two different electron-proton correlation functionals and three different electronic exchange-correlation functionals. The results illustrate that this approach provides qualitatively accurate nuclear densities in a computationally tractable manner. The general theory is also easily extended to other types of partitioning schemes for multicomponent systems.« less

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.

Multiple Point Dynamic Gas Density Measurements Using Molecular Rayleigh Scattering

NASA Technical Reports Server (NTRS)

Seasholtz, Richard; Panda, Jayanta

1999-01-01

A nonintrusive technique for measuring dynamic gas density properties is described. Molecular Rayleigh scattering is used to measure the time-history of gas density simultaneously at eight spatial locations at a 50 kHz sampling rate. The data are analyzed using the Welch method of modified periodograms to reduce measurement uncertainty. Cross-correlations, power spectral density functions, cross-spectral density functions, and coherence functions may be obtained from the data. The technique is demonstrated using low speed co-flowing jets with a heated inner jet.

Ensemble density variational methods with self- and ghost-interaction-corrected functionals

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

Pastorczak, Ewa; Pernal, Katarzyna, E-mail: pernalk@gmail.com

2014-05-14

Ensemble density functional theory (DFT) offers a way of predicting excited-states energies of atomic and molecular systems without referring to a density response function. Despite a significant theoretical work, practical applications of the proposed approximations have been scarce and they do not allow for a fair judgement of the potential usefulness of ensemble DFT with available functionals. In the paper, we investigate two forms of ensemble density functionals formulated within ensemble DFT framework: the Gross, Oliveira, and Kohn (GOK) functional proposed by Gross et al. [Phys. Rev. A 37, 2809 (1988)] alongside the orbital-dependent eDFT form of the functional introducedmore » by Nagy [J. Phys. B 34, 2363 (2001)] (the acronym eDFT proposed in analogy to eHF – ensemble Hartree-Fock method). Local and semi-local ground-state density functionals are employed in both approaches. Approximate ensemble density functionals contain not only spurious self-interaction but also the so-called ghost-interaction which has no counterpart in the ground-state DFT. We propose how to correct the GOK functional for both kinds of interactions in approximations that go beyond the exact-exchange functional. Numerical applications lead to a conclusion that functionals free of the ghost-interaction by construction, i.e., eDFT, yield much more reliable results than approximate self- and ghost-interaction-corrected GOK functional. Additionally, local density functional corrected for self-interaction employed in the eDFT framework yields excitations energies of the accuracy comparable to that of the uncorrected semi-local eDFT functional.« less

Quantum mechanical/molecular mechanical/continuum style solvation model: time-dependent density functional theory.

PubMed

Thellamurege, Nandun M; Cui, Fengchao; Li, Hui

2013-08-28

A combined quantum mechanical/molecular mechanical/continuum (QM/MMpol/C) style method is developed for time-dependent density functional theory (TDDFT, including long-range corrected TDDFT) method, induced dipole polarizable force field, and induced surface charge continuum model. Induced dipoles and induced charges are included in the TDDFT equations to solve for the transition energies, relaxed density, and transition density. Analytic gradient is derived and implemented for geometry optimization and molecular dynamics simulation. QM/MMpol/C style DFT and TDDFT methods are used to study the hydrogen bonding of the photoactive yellow protein chromopore in ground state and excited state.

The trust-region self-consistent field method in Kohn-Sham density-functional theory.

PubMed

Thøgersen, Lea; Olsen, Jeppe; Köhn, Andreas; Jørgensen, Poul; Sałek, Paweł; Helgaker, Trygve

2005-08-15

The trust-region self-consistent field (TRSCF) method is extended to the optimization of the Kohn-Sham energy. In the TRSCF method, both the Roothaan-Hall step and the density-subspace minimization step are replaced by trust-region optimizations of local approximations to the Kohn-Sham energy, leading to a controlled, monotonic convergence towards the optimized energy. Previously the TRSCF method has been developed for optimization of the Hartree-Fock energy, which is a simple quadratic function in the density matrix. However, since the Kohn-Sham energy is a nonquadratic function of the density matrix, the local energy functions must be generalized for use with the Kohn-Sham model. Such a generalization, which contains the Hartree-Fock model as a special case, is presented here. For comparison, a rederivation of the popular direct inversion in the iterative subspace (DIIS) algorithm is performed, demonstrating that the DIIS method may be viewed as a quasi-Newton method, explaining its fast local convergence. In the global region the convergence behavior of DIIS is less predictable. The related energy DIIS technique is also discussed and shown to be inappropriate for the optimization of the Kohn-Sham energy.

Invited Paper - Density functional theory: coverage of dynamic and non-dynamic electron correlation effects

NASA Astrophysics Data System (ADS)

Cremer, Dieter

The electron correlation effects covered by density functional theory (DFT) can be assessed qualitatively by comparing DFT densities ρ(r) with suitable reference densities obtained with wavefunction theory (WFT) methods that cover typical electron correlation effects. The analysis of difference densities ρ(DFT)-ρ(WFT) reveals that LDA and GGA exchange (X) functionals mimic non-dynamic correlation effects in an unspecified way. It is shown that these long range correlation effects are caused by the self-interaction error (SIE) of standard X functionals. Self-interaction corrected (SIC) DFT exchange gives, similar to exact exchange, for the bonding region a delocalized exchange hole, and does not cover any correlation effects. Hence, the exchange SIE is responsible for the fact that DFT densities often resemble MP4 or MP2 densities. The correlation functional changes X-only DFT densities in a manner observed when higher order coupling effects between lower order N-electron correlation effects are included. Hybrid functionals lead to changes in the density similar to those caused by SICDFT, which simply reflects the fact that hybrid functionals have been developed to cover part of the SIE and its long range correlation effects in a balanced manner. In the case of spin-unrestricted DFT (UDFT), non-dynamic electron correlation effects enter the calculation both via the X functional and via the wavefunction, which may cause a double-counting of correlation effects. The use of UDFT in the form of permuted orbital and broken-symmetry DFT (PO-UDFT, BS-UDFT) can lead to reasonable descriptions of multireference systems provided certain conditions are fulfilled. More reliable, however, is a combination of DFT and WFT methods, which makes the routine description of multireference systems possible. The development of such methods implies a separation of dynamic and non-dynamic correlation effects. Strategies for accomplishing this goal are discussed in general and tested in practice for CAS (complete active space)-DFT.

A Modeling and Data Analysis of Laser Beam Propagation in the Maritime Domain

DTIC Science & Technology

2015-05-18

approach to computing pdfs is the Kernel Density Method (Reference [9] has an intro - duction to the method), which we will apply to compute the pdf of our...The project has two parts to it: 1) we present a computational analysis of different probability density function approximation techniques; and 2) we... computational analysis of different probability density function approximation techniques; and 2) we introduce preliminary steps towards developing a

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.

DFTB3: Extension of the self-consistent-charge density-functional tight-binding method (SCC-DFTB).

PubMed

Gaus, Michael; Cui, Qiang; Elstner, Marcus

2012-04-10

The self-consistent-charge density-functional tight-binding method (SCC-DFTB) is an approximate quantum chemical method derived from density functional theory (DFT) based on a second-order expansion of the DFT total energy around a reference density. In the present study we combine earlier extensions and improve them consistently with, first, an improved Coulomb interaction between atomic partial charges, and second, the complete third-order expansion of the DFT total energy. These modifications lead us to the next generation of the DFTB methodology called DFTB3, which substantially improves the description of charged systems containing elements C, H, N, O, and P, especially regarding hydrogen binding energies and proton affinities. As a result, DFTB3 is particularly applicable to biomolecular systems. Remaining challenges and possible solutions are also briefly discussed.

The calculations of small molecular conformation energy differences by density functional method

NASA Astrophysics Data System (ADS)

Topol, I. A.; Burt, S. K.

1993-03-01

The differences in the conformational energies for the gauche (G) and trans(T) conformers of 1,2-difluoroethane and for myo-and scyllo-conformer of inositol have been calculated by local density functional method (LDF approximation) with geometry optimization using different sets of calculation parameters. It is shown that in the contrast to Hartree—Fock methods, density functional calculations reproduce the correct sign and value of the gauche effect for 1,2-difluoroethane and energy difference for both conformers of inositol. The results of normal vibrational analysis for1,2-difluoroethane showed that harmonic frequencies calculated in LDF approximation agree with experimental data with the accuracy typical for scaled large basis set Hartree—Fock calculations.

Density-functional expansion methods: evaluation of LDA, GGA, and meta-GGA functionals and different integral approximations.

PubMed

Giese, Timothy J; York, Darrin M

2010-12-28

We extend the Kohn-Sham potential energy expansion (VE) to include variations of the kinetic energy density and use the VE formulation with a 6-31G* basis to perform a "Jacob's ladder" comparison of small molecule properties using density functionals classified as being either LDA, GGA, or meta-GGA. We show that the VE reproduces standard Kohn-Sham DFT results well if all integrals are performed without further approximation, and there is no substantial improvement in using meta-GGA functionals relative to GGA functionals. The advantages of using GGA versus LDA functionals becomes apparent when modeling hydrogen bonds. We furthermore examine the effect of using integral approximations to compute the zeroth-order energy and first-order matrix elements, and the results suggest that the origin of the short-range repulsive potential within self-consistent charge density-functional tight-binding methods mainly arises from the approximations made to the first-order matrix elements.

Exchange-correlation energies of atoms from efficient density functionals: influence of the electron density

DOE PAGES

Tao, Jianmin; Ye, Lin -Hui; Duan, Yuhua

2017-11-20

The primary goal of Kohn–Sham density functional theory is to evaluate the exchange-correlation contribution to electronic properties. However, the accuracy of a density functional can be affected by the electron density. Here we apply the nonempirical Tao–Mo (TM) semilocal functional to study the influence of the electron density on the exchange and correlation energies of atoms and ions, and compare the results with the commonly used nonempirical semilocal functionals local spin-density approximation (LSDA), Perdew–Burke–Ernzerhof (PBE), Tao–Perdew–Staroverov–Scuseria (TPSS), and hybrid functional PBE0. We find that the spin-restricted Hartree–Fock density yields the exchange and correlation energies in good agreement with the Optimizedmore » Effective Potential method, particularly for spherical atoms and ions. However, the errors of these semilocal and hybrid functionals become larger for self-consistent densities. We further find that the quality of the electron density have greater effect on the exchange-correlation energies of kinetic energy density-dependent meta-GGA functionals TPSS and TM than on those of the LSDA and GGA, and therefore, should have greater influence on the performance of meta-GGA functionals. Lastly, we show that the influence of the density quality on PBE0 is slightly reduced, compared to that of PBE, due to the exact mixing.« less

Exchange-correlation energies of atoms from efficient density functionals: influence of the electron density

NASA Astrophysics Data System (ADS)

Tao, Jianmin; Ye, Lin-Hui; Duan, Yuhua

2017-12-01

The primary goal of Kohn-Sham density functional theory is to evaluate the exchange-correlation contribution to electronic properties. However, the accuracy of a density functional can be affected by the electron density. Here we apply the nonempirical Tao-Mo (TM) semilocal functional to study the influence of the electron density on the exchange and correlation energies of atoms and ions, and compare the results with the commonly used nonempirical semilocal functionals local spin-density approximation (LSDA), Perdew-Burke-Ernzerhof (PBE), Tao-Perdew-Staroverov-Scuseria (TPSS), and hybrid functional PBE0. We find that the spin-restricted Hartree-Fock density yields the exchange and correlation energies in good agreement with the Optimized Effective Potential method, particularly for spherical atoms and ions. However, the errors of these semilocal and hybrid functionals become larger for self-consistent densities. We further find that the quality of the electron density have greater effect on the exchange-correlation energies of kinetic energy density-dependent meta-GGA functionals TPSS and TM than on those of the LSDA and GGA, and therefore, should have greater influence on the performance of meta-GGA functionals. Finally, we show that the influence of the density quality on PBE0 is slightly reduced, compared to that of PBE, due to the exact mixing.

Exchange-correlation energies of atoms from efficient density functionals: influence of the electron density

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

Tao, Jianmin; Ye, Lin -Hui; Duan, Yuhua

The primary goal of Kohn–Sham density functional theory is to evaluate the exchange-correlation contribution to electronic properties. However, the accuracy of a density functional can be affected by the electron density. Here we apply the nonempirical Tao–Mo (TM) semilocal functional to study the influence of the electron density on the exchange and correlation energies of atoms and ions, and compare the results with the commonly used nonempirical semilocal functionals local spin-density approximation (LSDA), Perdew–Burke–Ernzerhof (PBE), Tao–Perdew–Staroverov–Scuseria (TPSS), and hybrid functional PBE0. We find that the spin-restricted Hartree–Fock density yields the exchange and correlation energies in good agreement with the Optimizedmore » Effective Potential method, particularly for spherical atoms and ions. However, the errors of these semilocal and hybrid functionals become larger for self-consistent densities. We further find that the quality of the electron density have greater effect on the exchange-correlation energies of kinetic energy density-dependent meta-GGA functionals TPSS and TM than on those of the LSDA and GGA, and therefore, should have greater influence on the performance of meta-GGA functionals. Lastly, we show that the influence of the density quality on PBE0 is slightly reduced, compared to that of PBE, due to the exact mixing.« less

Unsupervised Learning and Pattern Recognition of Biological Data Structures with Density Functional Theory and Machine Learning.

PubMed

Chen, Chien-Chang; Juan, Hung-Hui; Tsai, Meng-Yuan; Lu, Henry Horng-Shing

2018-01-11

By introducing the methods of machine learning into the density functional theory, we made a detour for the construction of the most probable density function, which can be estimated by learning relevant features from the system of interest. Using the properties of universal functional, the vital core of density functional theory, the most probable cluster numbers and the corresponding cluster boundaries in a studying system can be simultaneously and automatically determined and the plausibility is erected on the Hohenberg-Kohn theorems. For the method validation and pragmatic applications, interdisciplinary problems from physical to biological systems were enumerated. The amalgamation of uncharged atomic clusters validated the unsupervised searching process of the cluster numbers and the corresponding cluster boundaries were exhibited likewise. High accurate clustering results of the Fisher's iris dataset showed the feasibility and the flexibility of the proposed scheme. Brain tumor detections from low-dimensional magnetic resonance imaging datasets and segmentations of high-dimensional neural network imageries in the Brainbow system were also used to inspect the method practicality. The experimental results exhibit the successful connection between the physical theory and the machine learning methods and will benefit the clinical diagnoses.

Theoretical investigation of cyromazine tautomerism using density functional theory and Møller–Plesset perturbation theory methods

USDA-ARS?s Scientific Manuscript database

A computational chemistry analysis of six unique tautomers of cyromazine, a pesticide used for fly control, was performed with density functional theory (DFT) and canonical second order Møller–Plesset perturbation theory (MP2) methods to gain insight into the contributions of molecular structure to ...

Raman Optical Activity Spectra from Density Functional Perturbation Theory and Density-Functional-Theory-Based Molecular Dynamics.

PubMed

Luber, Sandra

2017-03-14

We describe the calculation of Raman optical activity (ROA) tensors from density functional perturbation theory, which has been implemented into the CP2K software package. Using the mixed Gaussian and plane waves method, ROA spectra are evaluated in the double-harmonic approximation. Moreover, an approach for the calculation of ROA spectra by means of density functional theory-based molecular dynamics is derived and used to obtain an ROA spectrum via time correlation functions, which paves the way for the calculation of ROA spectra taking into account anharmonicities and dynamic effects at ambient conditions.

Scaling within the spectral function approach

NASA Astrophysics Data System (ADS)

Sobczyk, J. E.; Rocco, N.; Lovato, A.; Nieves, J.

2018-03-01

Scaling features of the nuclear electromagnetic response functions unveil aspects of nuclear dynamics that are crucial for interpreting neutrino- and electron-scattering data. In the large momentum-transfer regime, the nucleon-density response function defines a universal scaling function, which is independent of the nature of the probe. In this work, we analyze the nucleon-density response function of 12C, neglecting collective excitations. We employ particle and hole spectral functions obtained within two distinct many-body methods, both widely used to describe electroweak reactions in nuclei. We show that the two approaches provide compatible nucleon-density scaling functions that for large momentum transfers satisfy first-kind scaling. Both methods yield scaling functions characterized by an asymmetric shape, although less pronounced than that of experimental scaling functions. This asymmetry, only mildly affected by final state interactions, is mostly due to nucleon-nucleon correlations, encoded in the continuum component of the hole spectral function.

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.

Conjugate-gradient optimization method for orbital-free density functional calculations.

PubMed

Jiang, Hong; Yang, Weitao

2004-08-01

Orbital-free density functional theory as an extension of traditional Thomas-Fermi theory has attracted a lot of interest in the past decade because of developments in both more accurate kinetic energy functionals and highly efficient numerical methodology. In this paper, we developed a conjugate-gradient method for the numerical solution of spin-dependent extended Thomas-Fermi equation by incorporating techniques previously used in Kohn-Sham calculations. The key ingredient of the method is an approximate line-search scheme and a collective treatment of two spin densities in the case of spin-dependent extended Thomas-Fermi problem. Test calculations for a quartic two-dimensional quantum dot system and a three-dimensional sodium cluster Na216 with a local pseudopotential demonstrate that the method is accurate and efficient. (c) 2004 American Institute of Physics.

A comparison of different methods to implement higher order derivatives of density functionals

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

van Dam, Hubertus J.J.

Density functional theory is the dominant approach in electronic structure methods today. To calculate properties higher order derivatives of the density functionals are required. These derivatives might be implemented manually,by automatic differentiation, or by symbolic algebra programs. Different authors have cited different reasons for using the particular method of their choice. This paper presents work where all three approaches were used and the strengths and weaknesses of each approach are considered. It is found that all three methods produce code that is suffficiently performanted for practical applications, despite the fact that our symbolic algebra generated code and our automatic differentiationmore » code still have scope for significant optimization. The automatic differentiation approach is the best option for producing readable and maintainable code.« less

Assessment of Ab Initio and Density Functional Theory Methods for the Excitations of Donor-Acceptor Complexes: The Case of the Benzene-Tetracyanoethylene Model.

PubMed

Xu, Peng; Zhang, Cai-Rong; Wang, Wei; Gong, Ji-Jun; Liu, Zi-Jiang; Chen, Hong-Shan

2018-04-10

The understanding of the excited-state properties of electron donors, acceptors and their interfaces in organic optoelectronic devices is a fundamental issue for their performance optimization. In order to obtain a balanced description of the different excitation types for electron-donor-acceptor systems, including the singlet charge transfer (CT), local excitations, and triplet excited states, several ab initio and density functional theory (DFT) methods for excited-state calculations were evaluated based upon the selected model system of benzene-tetracyanoethylene (B-TCNE) complexes. On the basis of benchmark calculations of the equation-of-motion coupled-cluster with single and double excitations method, the arithmetic mean of the absolute errors and standard errors of the electronic excitation energies for the different computational methods suggest that the M11 functional in DFT is superior to the other tested DFT functionals, and time-dependent DFT (TDDFT) with the Tamm-Dancoff approximation improves the accuracy of the calculated excitation energies relative to that of the full TDDFT. The performance of the M11 functional underlines the importance of kinetic energy density, spin-density gradient, and range separation in the development of novel DFT functionals. According to the TDDFT results, the performances of the different TDDFT methods on the CT properties of the B-TCNE complexes were also analyzed.

Performance assessment of density functional methods with Gaussian and Slater basis sets using 7σ orbital momentum distributions of N2O

NASA Astrophysics Data System (ADS)

Wang, Feng; Pang, Wenning; Duffy, Patrick

2012-12-01

Performance of a number of commonly used density functional methods in chemistry (B3LYP, Bhandh, BP86, PW91, VWN, LB94, PBe0, SAOP and X3LYP and the Hartree-Fock (HF) method) has been assessed using orbital momentum distributions of the 7σ orbital of nitrous oxide (NNO), which models electron behaviour in a chemically significant region. The density functional methods are combined with a number of Gaussian basis sets (Pople's 6-31G*, 6-311G**, DGauss TZVP and Dunning's aug-cc-pVTZ as well as even-tempered Slater basis sets, namely, et-DZPp, et-QZ3P, et-QZ+5P and et-pVQZ). Orbital momentum distributions of the 7σ orbital in the ground electronic state of NNO, which are obtained from a Fourier transform into momentum space from single point electronic calculations employing the above models, are compared with experimental measurement of the same orbital from electron momentum spectroscopy (EMS). The present study reveals information on performance of (a) the density functional methods, (b) Gaussian and Slater basis sets, (c) combinations of the density functional methods and basis sets, that is, the models, (d) orbital momentum distributions, rather than a group of specific molecular properties and (e) the entire region of chemical significance of the orbital. It is found that discrepancies of this orbital between the measured and the calculated occur in the small momentum region (i.e. large r region). In general, Slater basis sets achieve better overall performance than the Gaussian basis sets. Performance of the Gaussian basis sets varies noticeably when combining with different Vxc functionals, but Dunning's augcc-pVTZ basis set achieves the best performance for the momentum distributions of this orbital. The overall performance of the B3LYP and BP86 models is similar to newer models such as X3LYP and SAOP. The present study also demonstrates that the combinations of the density functional methods and the basis sets indeed make a difference in the quality of the calculated orbitals.

Computing thermal Wigner densities with the phase integration method

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

Beutier, J.; Borgis, D.; Vuilleumier, R.

2014-08-28

We discuss how the Phase Integration Method (PIM), recently developed to compute symmetrized time correlation functions [M. Monteferrante, S. Bonella, and G. Ciccotti, Mol. Phys. 109, 3015 (2011)], can be adapted to sampling/generating the thermal Wigner density, a key ingredient, for example, in many approximate schemes for simulating quantum time dependent properties. PIM combines a path integral representation of the density with a cumulant expansion to represent the Wigner function in a form calculable via existing Monte Carlo algorithms for sampling noisy probability densities. The method is able to capture highly non-classical effects such as correlation among the momenta andmore » coordinates parts of the density, or correlations among the momenta themselves. By using alternatives to cumulants, it can also indicate the presence of negative parts of the Wigner density. Both properties are demonstrated by comparing PIM results to those of reference quantum calculations on a set of model problems.« less

Computing thermal Wigner densities with the phase integration method.

PubMed

Beutier, J; Borgis, D; Vuilleumier, R; Bonella, S

2014-08-28

We discuss how the Phase Integration Method (PIM), recently developed to compute symmetrized time correlation functions [M. Monteferrante, S. Bonella, and G. Ciccotti, Mol. Phys. 109, 3015 (2011)], can be adapted to sampling/generating the thermal Wigner density, a key ingredient, for example, in many approximate schemes for simulating quantum time dependent properties. PIM combines a path integral representation of the density with a cumulant expansion to represent the Wigner function in a form calculable via existing Monte Carlo algorithms for sampling noisy probability densities. The method is able to capture highly non-classical effects such as correlation among the momenta and coordinates parts of the density, or correlations among the momenta themselves. By using alternatives to cumulants, it can also indicate the presence of negative parts of the Wigner density. Both properties are demonstrated by comparing PIM results to those of reference quantum calculations on a set of model problems.

Study on the Electronic Transport Properties of Zigzag GaN Nanotubes

NASA Astrophysics Data System (ADS)

Li, Enling; Wang, Xiqiang; Hou, Liping; Zhao, Danna; Dai, Yuanbin; Wang, Xuewen

2011-02-01

The electronic transport properties of zigzag GaN nanotubes (n, 0) (4 <= n <= 9) have been calculated using the density functional theory and non-equilibrium Green's functions method. Firstly, the density functional theory (DFT) is used to optimize and calculate the electronic structure of GaNNTs (n, 0) (4<=n<=9). Secondly, DFT and non-equilibrium Green function (NEGF) method are also used to predict the electronic transport properties of GaNNTs two-probe system. The results showed: there is a corresponding relation between the electronic transport properties and the valley of state density of each GaNNT. In addition, the volt-ampere curve of GaNNT is approximately linear.

Basis convergence of range-separated density-functional theory

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

Franck, Odile, E-mail: odile.franck@etu.upmc.fr; Mussard, Bastien, E-mail: bastien.mussard@upmc.fr; CNRS, UMR 7616, Laboratoire de Chimie Théorique, F-75005 Paris

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. Wemore » 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, N{sub 2}, and H{sub 2}O) 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.« less

Electron-Ion Dynamics with Time-Dependent Density Functional Theory: Towards Predictive Solar Cell Modeling: Final Technical Report

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

Maitra, Neepa

2016-07-14

This project investigates the accuracy of currently-used functionals in time-dependent density functional theory, which is today routinely used to predict and design materials and computationally model processes in solar energy conversion. The rigorously-based electron-ion dynamics method developed here sheds light on traditional methods and overcomes challenges those methods have. The fundamental research undertaken here is important for building reliable and practical methods for materials discovery. The ultimate goal is to use these tools for the computational design of new materials for solar cell devices of high efficiency.

Extension of the self-consistent-charge density-functional tight-binding method: third-order expansion of the density functional theory total energy and introduction of a modified effective coulomb interaction.

PubMed

Yang, Yang; Yu, Haibo; York, Darrin; Cui, Qiang; Elstner, Marcus

2007-10-25

The standard self-consistent-charge density-functional-tight-binding (SCC-DFTB) method (Phys. Rev. B 1998, 58, 7260) is derived by a second-order expansion of the density functional theory total energy expression, followed by an approximation of the charge density fluctuations by charge monopoles and an effective damped Coulomb interaction between the atomic net charges. The central assumptions behind this effective charge-charge interaction are the inverse relation of atomic size and chemical hardness and the use of a fixed chemical hardness parameter independent of the atomic charge state. While these approximations seem to be unproblematic for many covalently bound systems, they are quantitatively insufficient for hydrogen-bonding interactions and (anionic) molecules with localized net charges. Here, we present an extension of the SCC-DFTB method to incorporate third-order terms in the charge density fluctuations, leading to chemical hardness parameters that are dependent on the atomic charge state and a modification of the Coulomb scaling to improve the electrostatic treatment within the second-order terms. These modifications lead to a significant improvement in the description of hydrogen-bonding interactions and proton affinities of biologically relevant molecules.

A MATLAB implementation of the minimum relative entropy method for linear inverse problems

NASA Astrophysics Data System (ADS)

Neupauer, Roseanna M.; Borchers, Brian

2001-08-01

The minimum relative entropy (MRE) method can be used to solve linear inverse problems of the form Gm= d, where m is a vector of unknown model parameters and d is a vector of measured data. The MRE method treats the elements of m as random variables, and obtains a multivariate probability density function for m. The probability density function is constrained by prior information about the upper and lower bounds of m, a prior expected value of m, and the measured data. The solution of the inverse problem is the expected value of m, based on the derived probability density function. We present a MATLAB implementation of the MRE method. Several numerical issues arise in the implementation of the MRE method and are discussed here. We present the source history reconstruction problem from groundwater hydrology as an example of the MRE implementation.

Combination of complex momentum representation and Green's function methods in relativistic mean-field theory

NASA Astrophysics Data System (ADS)

Shi, Min; Niu, Zhong-Ming; Liang, Haozhao

2018-06-01

We have combined the complex momentum representation method with the Green's function method in the relativistic mean-field framework to establish the RMF-CMR-GF approach. This new approach is applied to study the halo structure of 74Ca. All the continuum level density of concerned resonant states are calculated accurately without introducing any unphysical parameters, and they are independent of the choice of integral contour. The important single-particle wave functions and densities for the halo phenomenon in 74Ca are discussed in detail.

Density matrix renormalization group with efficient dynamical electron correlation through range separation

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

Hedegård, Erik Donovan, E-mail: erik.hedegard@phys.chem.ethz.ch; Knecht, Stefan; Reiher, Markus, E-mail: markus.reiher@phys.chem.ethz.ch

2015-06-14

We present a new hybrid multiconfigurational method based on the concept of range-separation that combines the density matrix renormalization group approach with density functional theory. This new method is designed for the simultaneous description of dynamical and static electron-correlation effects in multiconfigurational electronic structure problems.

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.

Deconvolution of Stark broadened spectra for multi-point density measurements in a flow Z-pinch

DOE PAGES

Vogman, G. V.; Shumlak, U.

2011-10-13

Stark broadened emission spectra, once separated from other broadening effects, provide a convenient non-perturbing means of making plasma density measurements. A deconvolution technique has been developed to measure plasma densities in the ZaP flow Z-pinch experiment. The ZaP experiment uses sheared flow to mitigate MHD instabilities. The pinches exhibit Stark broadened emission spectra, which are captured at 20 locations using a multi-chord spectroscopic system. Spectra that are time- and chord-integrated are well approximated by a Voigt function. The proposed method simultaneously resolves plasma electron density and ion temperature by deconvolving the spectral Voigt profile into constituent functions: a Gaussian functionmore » associated with instrument effects and Doppler broadening by temperature; and a Lorentzian function associated with Stark broadening by electron density. The method uses analytic Fourier transforms of the constituent functions to fit the Voigt profile in the Fourier domain. The method is discussed and compared to a basic least-squares fit. The Fourier transform fitting routine requires fewer fitting parameters and shows promise in being less susceptible to instrumental noise and to contamination from neighboring spectral lines. The method is evaluated and tested using simulated lines and is applied to experimental data for the 229.69 nm C III line from multiple chords to determine plasma density and temperature across the diameter of the pinch. As a result, these measurements are used to gain a better understanding of Z-pinch equilibria.« less

Deconvolution of Stark broadened spectra for multi-point density measurements in a flow Z-pinch

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

Vogman, G. V.; Shumlak, U.

2011-10-15

Stark broadened emission spectra, once separated from other broadening effects, provide a convenient non-perturbing means of making plasma density measurements. A deconvolution technique has been developed to measure plasma densities in the ZaP flow Z-pinch experiment. The ZaP experiment uses sheared flow to mitigate MHD instabilities. The pinches exhibit Stark broadened emission spectra, which are captured at 20 locations using a multi-chord spectroscopic system. Spectra that are time- and chord-integrated are well approximated by a Voigt function. The proposed method simultaneously resolves plasma electron density and ion temperature by deconvolving the spectral Voigt profile into constituent functions: a Gaussian functionmore » associated with instrument effects and Doppler broadening by temperature; and a Lorentzian function associated with Stark broadening by electron density. The method uses analytic Fourier transforms of the constituent functions to fit the Voigt profile in the Fourier domain. The method is discussed and compared to a basic least-squares fit. The Fourier transform fitting routine requires fewer fitting parameters and shows promise in being less susceptible to instrumental noise and to contamination from neighboring spectral lines. The method is evaluated and tested using simulated lines and is applied to experimental data for the 229.69 nm C III line from multiple chords to determine plasma density and temperature across the diameter of the pinch. These measurements are used to gain a better understanding of Z-pinch equilibria.« less

Magnetic exchange couplings from noncollinear perturbation theory: dinuclear CuII complexes.

PubMed

Phillips, Jordan J; Peralta, Juan E

2014-08-07

To benchmark the performance of a new method based on noncollinear coupled-perturbed density functional theory [J. Chem. Phys. 138, 174115 (2013)], we calculate the magnetic exchange couplings in a series of triply bridged ferromagnetic dinuclear Cu(II) complexes that have been recently synthesized [Phys. Chem. Chem. Phys. 15, 1966 (2013)]. We find that for any basis-set the couplings from our noncollinear coupled-perturbed methodology are practically identical to those of spin-projected energy-differences when a hybrid density functional approximation is employed. This demonstrates that our methodology properly recovers a Heisenberg description for these systems, and is robust in its predictive power of magnetic couplings. Furthermore, this indicates that the failure of density functional theory to capture the subtle variation of the exchange couplings in these complexes is not simply an artifact of broken-symmetry methods, but rather a fundamental weakness of current approximate density functionals for the description of magnetic couplings.

Hyperfine coupling constants of the nitrogen and phosphorus atoms: A challenge for exact-exchange density-functional and post-Hartree-Fock methods

NASA Astrophysics Data System (ADS)

Kaupp, Martin; Arbuznikov, Alexei V.; Heßelmann, Andreas; Görling, Andreas

2010-05-01

The isotropic hyperfine coupling constants of the free N(S4) and P(S4) atoms have been evaluated with high-level post-Hartree-Fock and density-functional methods. The phosphorus hyperfine coupling presents a significant challenge to both types of methods. With large basis sets, MP2 and coupled-cluster singles and doubles calculations give much too small values for the phosphorus atom. Triple excitations are needed in coupled-cluster calculations to achieve reasonable agreement with experiment. None of the standard density functionals reproduce even the correct sign of this hyperfine coupling. Similarly, the computed hyperfine couplings depend crucially on the self-consistent treatment in exact-exchange density-functional theory within the optimized effective potential (OEP) method. Well-balanced auxiliary and orbital basis sets are needed for basis-expansion exact-exchange-only OEP approaches to come close to Hartree-Fock or numerical OEP data. Results from the localized Hartree-Fock and Krieger-Li-Iafrate approximations deviate notably from exact OEP data in spite of very similar total energies. Of the functionals tested, only full exact-exchange methods augmented by a correlation functional gave at least the correct sign of the P(S4) hyperfine coupling but with too low absolute values. The subtle interplay between the spin-polarization contributions of the different core shells has been analyzed, and the influence of even very small changes in the exchange-correlation potential could be identified.

Grand canonical electronic density-functional theory: Algorithms and applications to electrochemistry

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

Sundararaman, Ravishankar; Goddard, III, William A.; Arias, Tomas A.

First-principles calculations combining density-functional theory and continuum solvation models enable realistic theoretical modeling and design of electrochemical systems. When a reaction proceeds in such systems, the number of electrons in the portion of the system treated quantum mechanically changes continuously, with a balancing charge appearing in the continuum electrolyte. A grand-canonical ensemble of electrons at a chemical potential set by the electrode potential is therefore the ideal description of such systems that directly mimics the experimental condition. We present two distinct algorithms: a self-consistent field method and a direct variational free energy minimization method using auxiliary Hamiltonians (GC-AuxH), to solvemore » the Kohn-Sham equations of electronic density-functional theory directly in the grand canonical ensemble at fixed potential. Both methods substantially improve performance compared to a sequence of conventional fixed-number calculations targeting the desired potential, with the GC-AuxH method additionally exhibiting reliable and smooth exponential convergence of the grand free energy. Lastly, we apply grand-canonical density-functional theory to the under-potential deposition of copper on platinum from chloride-containing electrolytes and show that chloride desorption, not partial copper monolayer formation, is responsible for the second voltammetric peak.« less

Grand canonical electronic density-functional theory: Algorithms and applications to electrochemistry.

PubMed

Sundararaman, Ravishankar; Goddard, William A; Arias, Tomas A

2017-03-21

First-principles calculations combining density-functional theory and continuum solvation models enable realistic theoretical modeling and design of electrochemical systems. When a reaction proceeds in such systems, the number of electrons in the portion of the system treated quantum mechanically changes continuously, with a balancing charge appearing in the continuum electrolyte. A grand-canonical ensemble of electrons at a chemical potential set by the electrode potential is therefore the ideal description of such systems that directly mimics the experimental condition. We present two distinct algorithms: a self-consistent field method and a direct variational free energy minimization method using auxiliary Hamiltonians (GC-AuxH), to solve the Kohn-Sham equations of electronic density-functional theory directly in the grand canonical ensemble at fixed potential. Both methods substantially improve performance compared to a sequence of conventional fixed-number calculations targeting the desired potential, with the GC-AuxH method additionally exhibiting reliable and smooth exponential convergence of the grand free energy. Finally, we apply grand-canonical density-functional theory to the under-potential deposition of copper on platinum from chloride-containing electrolytes and show that chloride desorption, not partial copper monolayer formation, is responsible for the second voltammetric peak.

Grand canonical electronic density-functional theory: Algorithms and applications to electrochemistry

DOE PAGES

Sundararaman, Ravishankar; Goddard, III, William A.; Arias, Tomas A.

2017-03-16

First-principles calculations combining density-functional theory and continuum solvation models enable realistic theoretical modeling and design of electrochemical systems. When a reaction proceeds in such systems, the number of electrons in the portion of the system treated quantum mechanically changes continuously, with a balancing charge appearing in the continuum electrolyte. A grand-canonical ensemble of electrons at a chemical potential set by the electrode potential is therefore the ideal description of such systems that directly mimics the experimental condition. We present two distinct algorithms: a self-consistent field method and a direct variational free energy minimization method using auxiliary Hamiltonians (GC-AuxH), to solvemore » the Kohn-Sham equations of electronic density-functional theory directly in the grand canonical ensemble at fixed potential. Both methods substantially improve performance compared to a sequence of conventional fixed-number calculations targeting the desired potential, with the GC-AuxH method additionally exhibiting reliable and smooth exponential convergence of the grand free energy. Lastly, we apply grand-canonical density-functional theory to the under-potential deposition of copper on platinum from chloride-containing electrolytes and show that chloride desorption, not partial copper monolayer formation, is responsible for the second voltammetric peak.« less

Benchmark study of ionization potentials and electron affinities of armchair single-walled carbon nanotubes using density functional theory

NASA Astrophysics Data System (ADS)

Zhou, Bin; Hu, Zhubin; Jiang, Yanrong; He, Xiao; Sun, Zhenrong; Sun, Haitao

2018-05-01

The intrinsic parameters of carbon nanotubes (CNTs) such as ionization potential (IP) and electron affinity (EA) are closely related to their unique properties and associated applications. In this work, we demonstrated the success of optimal tuning method based on range-separated (RS) density functionals for both accurate and efficient prediction of vertical IPs and electron affinities (EAs) of a series of armchair single-walled carbon nanotubes C20n H20 (n  =  2–6) compared to the high-level IP/EA equation-of-motion coupled-cluster method with single and double substitutions (IP/EA-EOM-CCSD). Notably, the resulting frontier orbital energies (–ε HOMO and –ε LUMO) from the tuning method exhibit an excellent approximation to the corresponding IPs and EAs, that significantly outperform other conventional density functionals. In addition, it is suggested that the RS density functionals that possess both a fixed amount of exact exchange in the short-range and a correct long-range asymptotic behavior are suitable for calculating electronic structures of finite-sized CNTs. Next the performance of density functionals for description of various molecular properties such as chemical potential, hardness and electrophilicity are assessed as a function of tube length. Thanks to the efficiency and accuracy of this tuning method, the related behaviors of much longer armchair single-walled CNTs until C200H20 were studied. Lastly, the present work is proved to provide an efficient theoretical tool for future materials design and reliable characterization of other interesting properties of CNT-based systems.

Effective scheme for partitioning covalent bonds in density-functional embedding theory: From molecules to extended covalent systems.

PubMed

Huang, Chen; Muñoz-García, Ana Belén; Pavone, Michele

2016-12-28

Density-functional embedding theory provides a general way to perform multi-physics quantum mechanics simulations of large-scale materials by dividing the total system's electron density into a cluster's density and its environment's density. It is then possible to compute the accurate local electronic structures and energetics of the embedded cluster with high-level methods, meanwhile retaining a low-level description of the environment. The prerequisite step in the density-functional embedding theory is the cluster definition. In covalent systems, cutting across the covalent bonds that connect the cluster and its environment leads to dangling bonds (unpaired electrons). These represent a major obstacle for the application of density-functional embedding theory to study extended covalent systems. In this work, we developed a simple scheme to define the cluster in covalent systems. Instead of cutting covalent bonds, we directly split the boundary atoms for maintaining the valency of the cluster. With this new covalent embedding scheme, we compute the dehydrogenation energies of several different molecules, as well as the binding energy of a cobalt atom on graphene. Well localized cluster densities are observed, which can facilitate the use of localized basis sets in high-level calculations. The results are found to converge faster with the embedding method than the other multi-physics approach ONIOM. This work paves the way to perform the density-functional embedding simulations of heterogeneous systems in which different types of chemical bonds are present.

A very efficient approach to compute the first-passage probability density function in a time-changed Brownian model: Applications in finance

NASA Astrophysics Data System (ADS)

Ballestra, Luca Vincenzo; Pacelli, Graziella; Radi, Davide

2016-12-01

We propose a numerical method to compute the first-passage probability density function in a time-changed Brownian model. In particular, we derive an integral representation of such a density function in which the integrand functions must be obtained solving a system of Volterra equations of the first kind. In addition, we develop an ad-hoc numerical procedure to regularize and solve this system of integral equations. The proposed method is tested on three application problems of interest in mathematical finance, namely the calculation of the survival probability of an indebted firm, the pricing of a single-knock-out put option and the pricing of a double-knock-out put option. The results obtained reveal that the novel approach is extremely accurate and fast, and performs significantly better than the finite difference method.

Final Technical Report [Scalable methods for electronic excitations and optical responses of nanostructures: mathematics to algorithms to observables

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

Saad, Yousef

2014-03-19

The master project under which this work is funded had as its main objective to develop computational methods for modeling electronic excited-state and optical properties of various nanostructures. The specific goals of the computer science group were primarily to develop effective numerical algorithms in Density Functional Theory (DFT) and Time Dependent Density Functional Theory (TDDFT). There were essentially four distinct stated objectives. The first objective was to study and develop effective numerical algorithms for solving large eigenvalue problems such as those that arise in Density Functional Theory (DFT) methods. The second objective was to explore so-called linear scaling methods ormore » Methods that avoid diagonalization. The third was to develop effective approaches for Time-Dependent DFT (TDDFT). Our fourth and final objective was to examine effective solution strategies for other problems in electronic excitations, such as the GW/Bethe-Salpeter method, and quantum transport problems.« less

van der Waals forces in density functional theory: a review of the vdW-DF method.

PubMed

Berland, Kristian; Cooper, Valentino R; Lee, Kyuho; Schröder, Elsebeth; Thonhauser, T; Hyldgaard, Per; Lundqvist, Bengt I

2015-06-01

A density functional theory (DFT) that accounts for van der Waals (vdW) interactions in condensed matter, materials physics, chemistry, and biology is reviewed. The insights that led to the construction of the Rutgers-Chalmers van der Waals density functional (vdW-DF) are presented with the aim of giving a historical perspective, while also emphasizing more recent efforts which have sought to improve its accuracy. In addition to technical details, we discuss a range of recent applications that illustrate the necessity of including dispersion interactions in DFT. This review highlights the value of the vdW-DF method as a general-purpose method, not only for dispersion bound systems, but also in densely packed systems where these types of interactions are traditionally thought to be negligible.

Explicit polarization (X-Pol) potential using ab initio molecular orbital theory and density functional theory.

PubMed

Song, Lingchun; Han, Jaebeom; Lin, Yen-lin; Xie, Wangshen; Gao, Jiali

2009-10-29

The explicit polarization (X-Pol) method has been examined using ab initio molecular orbital theory and density functional theory. The X-Pol potential was designed to provide a novel theoretical framework for developing next-generation force fields for biomolecular simulations. Importantly, the X-Pol potential is a general method, which can be employed with any level of electronic structure theory. The present study illustrates the implementation of the X-Pol method using ab initio Hartree-Fock theory and hybrid density functional theory. The computational results are illustrated by considering a set of bimolecular complexes of small organic molecules and ions with water. The computed interaction energies and hydrogen bond geometries are in good accord with CCSD(T) calculations and B3LYP/aug-cc-pVDZ optimizations.

Optimization of Layer Densities for Spacecraft Multilayered Insulation Systems

NASA Technical Reports Server (NTRS)

Johnson, W. L.

2009-01-01

Numerous tests of various multilayer insulation systems have indicated that there are optimal densities for these systems. However, the only method of calculating this optimal density was by a complex physics based algorithm developed by McIntosh. In the 1970's much data were collected on the performance of these insulation systems with many different variables analyzed. All formulas generated included number of layers and layer density as geometric variables in solving for the heat flux, none of them was in a differentiable form for a single geometric variable. It was recently discovered that by converting the equations from heat flux to thermal conductivity using Fourier's Law, the equations became functions of layer density, temperatures, and material properties only. The thickness and number of layers of the blanket were merged into a layer density. These equations were then differentiated with respect to layer density. By setting the first derivative equal to zero, and solving for the layer density, the critical layer density was determined. Taking a second derivative showed that the critical layer density is a minimum in the function and thus the optimum density for minimal heat leak, this is confirmed by plotting the original function. This method was checked and validated using test data from the Multipurpose Hydrogen Testbed which was designed using McIntosh's algorithm.

Irreducible Green's functions method for a quantum dot coupled to metallic and superconducting leads

NASA Astrophysics Data System (ADS)

Górski, Grzegorz; Kucab, Krzysztof

2017-05-01

Using irreducible Green's functions (IGF) method we analyse the Coulomb interaction dependence of the spectral functions and the transport properties of a quantum dot coupled to isotropic superconductor and metallic leads (SC-QD-N). The irreducible Green's functions method is the modification of classical equation of motion technique. The IGF scheme is based on differentiation of double-time Green's functions, both over the primary and secondary times. The IGF method allows to obtain the spectral functions for equilibrium and non-equilibrium impurity Anderson model used for SC-QD-N system. By the numerical computations, we show the change of spectral and the anomalous densities under the influence of the Coulomb interactions. The observed sign change of the anomalous spectral density can be used as the criterion of the SC singlet-Kondo singlet transition.

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.

Radiometric analysis of photographic data by the effective exposure method

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

Constantine, B J

1972-04-01

The effective exposure method provides for radiometric analysis of photographic data. A three-dimensional model, where density is a function of energy and wavelength, is postulated to represent the film response function. Calibration exposures serve to eliminate the other factors which affect image density. The effective exposure causing an image can be determined by comparing the image density with that of a calibration exposure. If the relative spectral distribution of the source is known, irradiance and/or radiance can be unfolded from the effective exposure expression.

Bypassing the malfunction junction in warm dense matter simulations

NASA Astrophysics Data System (ADS)

Cangi, Attila; Pribram-Jones, Aurora

2015-03-01

Simulation of warm dense matter requires computational methods that capture both quantum and classical behavior efficiently under high-temperature and high-density conditions. The state-of-the-art approach to model electrons and ions under those conditions is density functional theory molecular dynamics, but this method's computational cost skyrockets as temperatures and densities increase. We propose finite-temperature potential functional theory as an in-principle-exact alternative that suffers no such drawback. In analogy to the zero-temperature theory developed previously, we derive an orbital-free free energy approximation through a coupling-constant formalism. Our density approximation and its associated free energy approximation demonstrate the method's accuracy and efficiency. A.C. has been partially supported by NSF Grant CHE-1112442. A.P.J. is supported by DOE Grant DE-FG02-97ER25308.

Scanning tunneling microscopy current from localized basis orbital density functional theory

NASA Astrophysics Data System (ADS)

Gustafsson, Alexander; Paulsson, Magnus

2016-03-01

We present a method capable of calculating elastic scanning tunneling microscopy (STM) currents from localized atomic orbital density functional theory (DFT). To overcome the poor accuracy of the localized orbital description of the wave functions far away from the atoms, we propagate the wave functions, using the total DFT potential. From the propagated wave functions, the Bardeen's perturbative approach provides the tunneling current. To illustrate the method we investigate carbon monoxide adsorbed on a Cu(111) surface and recover the depression/protrusion observed experimentally with normal/CO-functionalized STM tips. The theory furthermore allows us to discuss the significance of s - and p -wave tips.

A low-density culture method of cerebellar granule neurons with paracrine support applicable for the study of neuronal morphogenesis.

PubMed

Kubota, Kenta; Seno, Takeshi; Konishi, Yoshiyuki

2013-11-20

Cerebellar granule neuronal cultures have been used to study the molecular mechanisms underlying neuronal functions, including neuronal morphogenesis. However, a limitation of this system is the difficulty to analyze isolated neurons because these are required to be maintained at a high density. Therefore, in the present study, we aimed to develop a simple and cost-effective method for culturing low-density cerebellar granule neurons. Cerebellar granule cells at two different densities (low- and high-density) were co-cultivated in order for the low-density culture to be supported by the paracrine signals from the high-density culture. This method enabled morphology analysis of isolated cerebellar granule neurons without astrocytic feeder cultures or supplements such as B27. Using this method, we investigated the function of a polarity factor. Studies using hippocampal neurons suggested that glycogen synthase kinase-3 (GSK-3) is an essential regulator of neuronal polarity, and inhibition of GSK-3 results in the formation of multiple axons. Pharmacological inhibitors for GSK-3 (6-bromoindirubin-3'-oxime and lithium chloride) did not cause the formation of multiple axons of cerebellar granule neurons but significantly reduced their length. Consistent results were obtained by introducing kinase-dead form of GSK-3 beta (K85A). These results indicated that GSK-3 is not directly involved in the control of neuronal polarity in cerebellar granule neurons. Overall, this study provides a simple method for culturing low-density cerebellar granule neurons and insights in to the neuronal-type dependent function of GSK-3 in neuronal morphogenesis. © 2013 Elsevier B.V. All rights reserved.

Performance of wave function and density functional methods for water hydrogen bond spin-spin coupling constants.

PubMed

García de la Vega, J M; Omar, S; San Fabián, J

2017-04-01

Spin-spin coupling constants in water monomer and dimer have been calculated using several wave function and density functional-based methods. CCSD, MCSCF, and SOPPA wave functions methods yield similar results, specially when an additive approach is used with the MCSCF. Several functionals have been used to analyze their performance with the Jacob's ladder and a set of functionals with different HF exchange were tested. Functionals with large HF exchange appropriately predict 1 J O H , 2 J H H and 2h J O O couplings, while 1h J O H is better calculated with functionals that include a reduced fraction of HF exchange. Accurate functionals for 1 J O H and 2 J H H have been tested in a tetramer water model. The hydrogen bond effects on these intramolecular couplings are additive when they are calculated by SOPPA(CCSD) wave function and DFT methods. Graphical Abstract Evaluation of the additive effect of the hydrogen bond on spin-spin coupling constants of water using WF and DFT methods.

Simulations of Spray Reacting Flows in a Single Element LDI Injector With and Without Invoking an Eulerian Scalar PDF Method

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Liu, Nan-Suey

2012-01-01

This paper presents the numerical simulations of the Jet-A spray reacting flow in a single element lean direct injection (LDI) injector by using the National Combustion Code (NCC) with and without invoking the Eulerian scalar probability density function (PDF) method. The flow field is calculated by using the Reynolds averaged Navier-Stokes equations (RANS and URANS) with nonlinear turbulence models, and when the scalar PDF method is invoked, the energy and compositions or species mass fractions are calculated by solving the equation of an ensemble averaged density-weighted fine-grained probability density function that is referred to here as the averaged probability density function (APDF). A nonlinear model for closing the convection term of the scalar APDF equation is used in the presented simulations and will be briefly described. Detailed comparisons between the results and available experimental data are carried out. Some positive findings of invoking the Eulerian scalar PDF method in both improving the simulation quality and reducing the computing cost are observed.

Surveillance system and method having an adaptive sequential probability fault detection test

NASA Technical Reports Server (NTRS)

Herzog, James P. (Inventor); Bickford, Randall L. (Inventor)

2005-01-01

System and method providing surveillance of an asset such as a process and/or apparatus by providing training and surveillance procedures that numerically fit a probability density function to an observed residual error signal distribution that is correlative to normal asset operation and then utilizes the fitted probability density function in a dynamic statistical hypothesis test for providing improved asset surveillance.

Surveillance system and method having an adaptive sequential probability fault detection test

NASA Technical Reports Server (NTRS)

Bickford, Randall L. (Inventor); Herzog, James P. (Inventor)

2006-01-01

System and method providing surveillance of an asset such as a process and/or apparatus by providing training and surveillance procedures that numerically fit a probability density function to an observed residual error signal distribution that is correlative to normal asset operation and then utilizes the fitted probability density function in a dynamic statistical hypothesis test for providing improved asset surveillance.

Surveillance System and Method having an Adaptive Sequential Probability Fault Detection Test

NASA Technical Reports Server (NTRS)

Bickford, Randall L. (Inventor); Herzog, James P. (Inventor)

2008-01-01

System and method providing surveillance of an asset such as a process and/or apparatus by providing training and surveillance procedures that numerically fit a probability density function to an observed residual error signal distribution that is correlative to normal asset operation and then utilizes the fitted probability density function in a dynamic statistical hypothesis test for providing improved asset surveillance.

Enhanced local tomography

DOEpatents

Katsevich, Alexander J.; Ramm, Alexander G.

1996-01-01

Local tomography is enhanced to determine the location and value of a discontinuity between a first internal density of an object and a second density of a region within the object. A beam of radiation is directed in a predetermined pattern through the region of the object containing the discontinuity. Relative attenuation data of the beam is determined within the predetermined pattern having a first data component that includes attenuation data through the region. In a first method for evaluating the value of the discontinuity, the relative attenuation data is inputted to a local tomography function .function..sub..LAMBDA. to define the location S of the density discontinuity. The asymptotic behavior of .function..sub..LAMBDA. is determined in a neighborhood of S, and the value for the discontinuity is estimated from the asymptotic behavior of .function..sub..LAMBDA.. In a second method for evaluating the value of the discontinuity, a gradient value for a mollified local tomography function .gradient..function..sub..LAMBDA..epsilon. (x.sub.ij) is determined along the discontinuity; and the value of the jump of the density across the discontinuity curve (or surface) S is estimated from the gradient values.

Free-energy-based lattice Boltzmann model for the simulation of multiphase flows with density contrast.

PubMed

Shao, J Y; Shu, C; Huang, H B; Chew, Y T

2014-03-01

A free-energy-based phase-field lattice Boltzmann method is proposed in this work to simulate multiphase flows with density contrast. The present method is to improve the Zheng-Shu-Chew (ZSC) model [Zheng, Shu, and Chew, J. Comput. Phys. 218, 353 (2006)] for correct consideration of density contrast in the momentum equation. The original ZSC model uses the particle distribution function in the lattice Boltzmann equation (LBE) for the mean density and momentum, which cannot properly consider the effect of local density variation in the momentum equation. To correctly consider it, the particle distribution function in the LBE must be for the local density and momentum. However, when the LBE of such distribution function is solved, it will encounter a severe numerical instability. To overcome this difficulty, a transformation, which is similar to the one used in the Lee-Lin (LL) model [Lee and Lin, J. Comput. Phys. 206, 16 (2005)] is introduced in this work to change the particle distribution function for the local density and momentum into that for the mean density and momentum. As a result, the present model still uses the particle distribution function for the mean density and momentum, and in the meantime, considers the effect of local density variation in the LBE as a forcing term. Numerical examples demonstrate that both the present model and the LL model can correctly simulate multiphase flows with density contrast, and the present model has an obvious improvement over the ZSC model in terms of solution accuracy. In terms of computational time, the present model is less efficient than the ZSC model, but is much more efficient than the LL model.

What correlation effects are covered by density functional theory?

NASA Astrophysics Data System (ADS)

He, Yuan; Grafenstein, Jurgen; Kraka, Elfi; Cremer, Dieter

The electron density distribution rho(r) generated by a DFT calculation was systematically studied by comparison with a series of reference densities obtained by wavefunction theory (WFT) methods that cover typical electron correlation effects. As a sensitive indicator for correlation effects the dipole moment of the CO molecule was used. The analysis reveals that typical LDA and GGA exchange functionals already simulate effects that are actually reminiscent of pair and three-electron correlation effects covered by MP2, MP4, and CCSD(T) in WFT. Correlation functionals contract the density towards the bond and the valence region thus taking negative charge out of the van der Waals region. It is shown that these improvements are relevant for the description of van der Waals interactions. Similar to certain correlated single-determinant WFT methods, BLYP and other GGA functionals underestimate ionic terms needed for a correct description of polar bonds. This is compensated for in hybrid functionals by mixing in HF exchange. The balanced mixing of local and non-local exchange and correlation effects leads to the correct description of polar bonds as in the B3LYP description of the CO molecule. The density obtained with B3LYP is closer to CCSD and CCSD(T) than to MP2 or MP4, which indicates that the B3LYP hybrid functional mimics those pair and three-electron correlation effects, which in WFT are only covered by coupled cluster methods.

An open-source framework for analyzing N-electron dynamics. II. Hybrid density functional theory/configuration interaction methodology.

PubMed

Hermann, Gunter; Pohl, Vincent; Tremblay, Jean Christophe

2017-10-30

In this contribution, we extend our framework for analyzing and visualizing correlated many-electron dynamics to non-variational, highly scalable electronic structure method. Specifically, an explicitly time-dependent electronic wave packet is written as a linear combination of N-electron wave functions at the configuration interaction singles (CIS) level, which are obtained from a reference time-dependent density functional theory (TDDFT) calculation. The procedure is implemented in the open-source Python program detCI@ORBKIT, which extends the capabilities of our recently published post-processing toolbox (Hermann et al., J. Comput. Chem. 2016, 37, 1511). From the output of standard quantum chemistry packages using atom-centered Gaussian-type basis functions, the framework exploits the multideterminental structure of the hybrid TDDFT/CIS wave packet to compute fundamental one-electron quantities such as difference electronic densities, transient electronic flux densities, and transition dipole moments. The hybrid scheme is benchmarked against wave function data for the laser-driven state selective excitation in LiH. It is shown that all features of the electron dynamics are in good quantitative agreement with the higher-level method provided a judicious choice of functional is made. Broadband excitation of a medium-sized organic chromophore further demonstrates the scalability of the method. In addition, the time-dependent flux densities unravel the mechanistic details of the simulated charge migration process at a glance. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

A new quasi-relativistic approach for density functional theory based on the normalized elimination of the small component

NASA Astrophysics Data System (ADS)

Filatov, Michael; Cremer, Dieter

2002-01-01

A recently developed variationally stable quasi-relativistic method, which is based on the low-order approximation to the method of normalized elimination of the small component, was incorporated into density functional theory (DFT). The new method was tested for diatomic molecules involving Ag, Cd, Au, and Hg by calculating equilibrium bond lengths, vibrational frequencies, and dissociation energies. The method is easy to implement into standard quantum chemical programs and leads to accurate results for the benchmark systems studied.

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

San Fabián, J.; Omar, S.; García de la Vega, J. M., E-mail: garcia.delavega@uam.es

The effect of a fraction of Hartree-Fock exchange on the calculated spin-spin coupling constants involving fluorine through a hydrogen bond is analyzed in detail. Coupling constants calculated using wavefunction methods are revisited in order to get high-level calculations using the same basis set. Accurate MCSCF results are obtained using an additive approach. These constants and their contributions are used as a reference for density functional calculations. Within the density functional theory, the Hartree-Fock exchange functional is split in short- and long-range using a modified version of the Coulomb-attenuating method with the SLYP functional as well as with the original B3LYP.more » Results support the difficulties for calculating hydrogen bond coupling constants using density functional methods when fluorine nuclei are involved. Coupling constants are very sensitive to the Hartree-Fock exchange and it seems that, contrary to other properties, it is important to include this exchange for short-range interactions. Best functionals are tested in two different groups of complexes: those related with anionic clusters of type [F(HF){sub n}]{sup −} and those formed by difluoroacetylene and either one or two hydrogen fluoride molecules.« less

Extended screened exchange functional derived from transcorrelated density functional theory.

PubMed

Umezawa, Naoto

2017-09-14

We propose a new formulation of the correlation energy functional derived from the transcorrelated method in use in density functional theory (TC-DFT). An effective Hamiltonian, H TC , is introduced by a similarity transformation of a many-body Hamiltonian, H, with respect to a complex function F: H TC =1FHF. It is proved that an expectation value of H TC for a normalized single Slater determinant, D n , corresponds to the total energy: E[n] = ⟨Ψ n |H|Ψ n ⟩/⟨Ψ n |Ψ n ⟩ = ⟨D n |H TC |D n ⟩ under the two assumptions: (1) The electron density nr associated with a trial wave function Ψ n = D n F is v-representable and (2) Ψ n and D n give rise to the same electron density nr. This formulation, therefore, provides an alternative expression of the total energy that is useful for the development of novel correlation energy functionals. By substituting a specific function for F, we successfully derived a model correlation energy functional, which resembles the functional form of the screened exchange method. The proposed functional, named the extended screened exchange (ESX) functional, is described within two-body integrals and is parametrized for a numerically exact correlation energy of the homogeneous electron gas. The ESX functional does not contain any ingredients of (semi-)local functionals and thus is totally free from self-interactions. The computational cost for solving the self-consistent-field equation is comparable to that of the Hartree-Fock method. We apply the ESX functional to electronic structure calculations for a solid silicon, H - ion, and small atoms. The results demonstrate that the TC-DFT formulation is promising for the systematic improvement of the correlation energy functional.

Multi-Paradigm Multi-Scale Simulations for Fuel Cell Catalysts and Membranes

DTIC Science & Technology

2006-01-01

transfer studies on model systems. . Applying newly developed density functionals QM ( X3LYP ) for estimating the thermodynamics and kinetic energy...Density functional theory methods We have used many QM methods to probe chemical reaction mechanisms and find that the B3LYP and X3LYP [6] flavors of DFT...carried out QM calculations on the surface reactivity of the Pt and PtRu anode catalysts. This QM uses a new ab initio DFT-GGA method ( X3LYP ) [6

A second-order unconstrained optimization method for canonical-ensemble density-functional methods

NASA Astrophysics Data System (ADS)

Nygaard, Cecilie R.; Olsen, Jeppe

2013-03-01

A second order converging method of ensemble optimization (SOEO) in the framework of Kohn-Sham Density-Functional Theory is presented, where the energy is minimized with respect to an ensemble density matrix. It is general in the sense that the number of fractionally occupied orbitals is not predefined, but rather it is optimized by the algorithm. SOEO is a second order Newton-Raphson method of optimization, where both the form of the orbitals and the occupation numbers are optimized simultaneously. To keep the occupation numbers between zero and two, a set of occupation angles is defined, from which the occupation numbers are expressed as trigonometric functions. The total number of electrons is controlled by a built-in second order restriction of the Newton-Raphson equations, which can be deactivated in the case of a grand-canonical ensemble (where the total number of electrons is allowed to change). To test the optimization method, dissociation curves for diatomic carbon are produced using different functionals for the exchange-correlation energy. These curves show that SOEO favors symmetry broken pure-state solutions when using functionals with exact exchange such as Hartree-Fock and Becke three-parameter Lee-Yang-Parr. This is explained by an unphysical contribution to the exact exchange energy from interactions between fractional occupations. For functionals without exact exchange, such as local density approximation or Becke Lee-Yang-Parr, ensemble solutions are favored at interatomic distances larger than the equilibrium distance. Calculations on the chromium dimer are also discussed. They show that SOEO is able to converge to ensemble solutions for systems that are more complicated than diatomic carbon.

van der Waals forces in density functional theory: a review of the vdW-DF method

DOE PAGES

Berland, Kristian; Cooper, Valentino R.; Lee, Kyuho; ...

2015-05-15

We review a density functional theory (DFT) that accounts for van der Waals (vdW) interactions in condensed matter, materials physics, chemistry, and biology. The insights that led to the construction of the Rutgers–Chalmers van der Waals density functional (vdW-DF) are presented with the aim of giving a historical perspective, while also emphasizing more recent efforts which have sought to improve its accuracy. In addition to technical details, we discuss a range of recent applications that illustrate the necessity of including dispersion interactions in DFT. This review highlights the value of the vdW-DF method as a general-purpose method, not only formore » dispersion bound systems, but also in densely packed systems where these types of interactions are traditionally thought to be negligible.« less

Density function theory study of the adsorption and dissociation of carbon monoxide on tungsten nanoparticles.

PubMed

Weng, Meng-Hsiung; Ju, Shin-Pon; Chen, Hsin-Tsung; Chen, Hui-Lung; Lu, Jian-Ming; Lin, Ken-Huang; Lin, Jenn-Sen; Hsieh, Jin-Yuan; Yang, Hsi-Wen

2013-02-01

The adsorption and dissociation properties of carbon monoxide (CO) molecule on tungsten W(n) (n = 10-15) nanoparticles have been investigated by density-functional theory (DFT) calculations. The lowest-energy structures for W(n) (n = 10-15) nanoparticles are found by the basin-hopping method and big-bang method with the modified tight-binding many-body potential. We calculated the corresponding adsorption energies, C-O bond lengths and dissociation barriers for adsorption of CO on nanoparticles. The electronic properties of CO on nanoparticles are studied by the analysis of density of state and charge density. The characteristic of CO on W(n) nanoparticles are also compared with that of W bulk.

Thermodynamically constrained correction to ab initio equations of state

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

French, Martin; Mattsson, Thomas R.

2014-07-07

We show how equations of state generated by density functional theory methods can be augmented to match experimental data without distorting the correct behavior in the high- and low-density limits. The technique is thermodynamically consistent and relies on knowledge of the density and bulk modulus at a reference state and an estimation of the critical density of the liquid phase. We apply the method to four materials representing different classes of solids: carbon, molybdenum, lithium, and lithium fluoride. It is demonstrated that the corrected equations of state for both the liquid and solid phases show a significantly reduced dependence ofmore » the exchange-correlation functional used.« less

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.

Gaussian windows: A tool for exploring multivariate data

NASA Technical Reports Server (NTRS)

Jaeckel, Louis A.

1990-01-01

Presented here is a method for interactively exploring a large set of quantitative multivariate data, in order to estimate the shape of the underlying density function. It is assumed that the density function is more or less smooth, but no other specific assumptions are made concerning its structure. The local structure of the data in a given region may be examined by viewing the data through a Gaussian window, whose location and shape are chosen by the user. A Gaussian window is defined by giving each data point a weight based on a multivariate Gaussian function. The weighted sample mean and sample covariance matrix are then computed, using the weights attached to the data points. These quantities are used to compute an estimate of the shape of the density function in the window region. The local structure of the data is described by a method similar to the method of principal components. By taking many such local views of the data, we can form an idea of the structure of the data set. The method is applicable in any number of dimensions. The method can be used to find and describe simple structural features such as peaks, valleys, and saddle points in the density function, and also extended structures in higher dimensions. With some practice, we can apply our geometrical intuition to these structural features in any number of dimensions, so that we can think about and describe the structure of the data. Since the computations involved are relatively simple, the method can easily be implemented on a small computer.

Psi4 1.1: An Open-Source Electronic Structure Program Emphasizing Automation, Advanced Libraries, and Interoperability.

PubMed

Parrish, Robert M; Burns, Lori A; Smith, Daniel G A; Simmonett, Andrew C; DePrince, A Eugene; Hohenstein, Edward G; Bozkaya, Uğur; Sokolov, Alexander Yu; Di Remigio, Roberto; Richard, Ryan M; Gonthier, Jérôme F; James, Andrew M; McAlexander, Harley R; Kumar, Ashutosh; Saitow, Masaaki; Wang, Xiao; Pritchard, Benjamin P; Verma, Prakash; Schaefer, Henry F; Patkowski, Konrad; King, Rollin A; Valeev, Edward F; Evangelista, Francesco A; Turney, Justin M; Crawford, T Daniel; Sherrill, C David

2017-07-11

Psi4 is an ab initio electronic structure program providing methods such as Hartree-Fock, density functional theory, configuration interaction, and coupled-cluster theory. The 1.1 release represents a major update meant to automate complex tasks, such as geometry optimization using complete-basis-set extrapolation or focal-point methods. Conversion of the top-level code to a Python module means that Psi4 can now be used in complex workflows alongside other Python tools. Several new features have been added with the aid of libraries providing easy access to techniques such as density fitting, Cholesky decomposition, and Laplace denominators. The build system has been completely rewritten to simplify interoperability with independent, reusable software components for quantum chemistry. Finally, a wide range of new theoretical methods and analyses have been added to the code base, including functional-group and open-shell symmetry adapted perturbation theory, density-fitted coupled cluster with frozen natural orbitals, orbital-optimized perturbation and coupled-cluster methods (e.g., OO-MP2 and OO-LCCD), density-fitted multiconfigurational self-consistent field, density cumulant functional theory, algebraic-diagrammatic construction excited states, improvements to the geometry optimizer, and the "X2C" approach to relativistic corrections, among many other improvements.

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.

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.

Adsorbate Diffusion on Transition Metal Nanoparticles

DTIC Science & Technology

2015-01-01

different sizes and shapes using density functional theory calculations. We show that nanoparticles bind adsorbates more strongly than the...structure theoretical methods, a quantitative study with accurate density functional theory (DFT) calculations is still missing. Here, we perform a...functional theory . The projector augmented wave (PAW) potentials29,30 were used for electron- ion interactions and the generalized gradient approximation

Total-energy Assisted Tight-binding Method Based on Local Density Approximation of Density Functional Theory

NASA Astrophysics Data System (ADS)

Fujiwara, Takeo; Nishino, Shinya; Yamamoto, Susumu; Suzuki, Takashi; Ikeda, Minoru; Ohtani, Yasuaki

2018-06-01

A novel tight-binding method is developed, based on the extended Hückel approximation and charge self-consistency, with referring the band structure and the total energy of the local density approximation of the density functional theory. The parameters are so adjusted by computer that the result reproduces the band structure and the total energy, and the algorithm for determining parameters is established. The set of determined parameters is applicable to a variety of crystalline compounds and change of lattice constants, and, in other words, it is transferable. Examples are demonstrated for Si crystals of several crystalline structures varying lattice constants. Since the set of parameters is transferable, the present tight-binding method may be applicable also to molecular dynamics simulations of large-scale systems and long-time dynamical processes.

The maximum entropy method of moments and Bayesian probability theory

NASA Astrophysics Data System (ADS)

Bretthorst, G. Larry

2013-08-01

The problem of density estimation occurs in many disciplines. For example, in MRI it is often necessary to classify the types of tissues in an image. To perform this classification one must first identify the characteristics of the tissues to be classified. These characteristics might be the intensity of a T1 weighted image and in MRI many other types of characteristic weightings (classifiers) may be generated. In a given tissue type there is no single intensity that characterizes the tissue, rather there is a distribution of intensities. Often this distributions can be characterized by a Gaussian, but just as often it is much more complicated. Either way, estimating the distribution of intensities is an inference problem. In the case of a Gaussian distribution, one must estimate the mean and standard deviation. However, in the Non-Gaussian case the shape of the density function itself must be inferred. Three common techniques for estimating density functions are binned histograms [1, 2], kernel density estimation [3, 4], and the maximum entropy method of moments [5, 6]. In the introduction, the maximum entropy method of moments will be reviewed. Some of its problems and conditions under which it fails will be discussed. Then in later sections, the functional form of the maximum entropy method of moments probability distribution will be incorporated into Bayesian probability theory. It will be shown that Bayesian probability theory solves all of the problems with the maximum entropy method of moments. One gets posterior probabilities for the Lagrange multipliers, and, finally, one can put error bars on the resulting estimated density function.

Discontinuous Galerkin finite element method for solving population density functions of cortical pyramidal and thalamic neuronal populations.

PubMed

Huang, Chih-Hsu; Lin, Chou-Ching K; Ju, Ming-Shaung

2015-02-01

Compared with the Monte Carlo method, the population density method is efficient for modeling collective dynamics of neuronal populations in human brain. In this method, a population density function describes the probabilistic distribution of states of all neurons in the population and it is governed by a hyperbolic partial differential equation. In the past, the problem was mainly solved by using the finite difference method. In a previous study, a continuous Galerkin finite element method was found better than the finite difference method for solving the hyperbolic partial differential equation; however, the population density function often has discontinuity and both methods suffer from a numerical stability problem. The goal of this study is to improve the numerical stability of the solution using discontinuous Galerkin finite element method. To test the performance of the new approach, interaction of a population of cortical pyramidal neurons and a population of thalamic neurons was simulated. The numerical results showed good agreement between results of discontinuous Galerkin finite element and Monte Carlo methods. The convergence and accuracy of the solutions are excellent. The numerical stability problem could be resolved using the discontinuous Galerkin finite element method which has total-variation-diminishing property. The efficient approach will be employed to simulate the electroencephalogram or dynamics of thalamocortical network which involves three populations, namely, thalamic reticular neurons, thalamocortical neurons and cortical pyramidal neurons. Copyright © 2014 Elsevier Ltd. All rights reserved.

Study regarding the density evolution of messages and the characteristic functions associated of a LDPC code

NASA Astrophysics Data System (ADS)

Drăghici, S.; Proştean, O.; Răduca, E.; Haţiegan, C.; Hălălae, I.; Pădureanu, I.; Nedeloni, M.; (Barboni Haţiegan, L.

2017-01-01

In this paper a method with which a set of characteristic functions are associated to a LDPC code is shown and also functions that represent the evolution density of messages that go along the edges of a Tanner graph. Graphic representations of the density evolution are shown respectively the study and simulation of likelihood threshold that render asymptotic boundaries between which there are decodable codes were made using MathCad V14 software.

Universal functions of nuclear proximity potential for Skyrme nucleus-nucleus interaction in a semiclassical approach

NASA Astrophysics Data System (ADS)

Gupta, Raj K.; Singh, Dalip; Kumar, Raj; Greiner, Walter

2009-07-01

The universal function of the nuclear proximity potential is obtained for the Skyrme nucleus-nucleus interaction in the semiclassical extended Thomas-Fermi (ETF) approach. This is obtained as a sum of the spin-orbit-density-independent and spin-orbit-density-dependent parts of the Hamiltonian density, since the two terms behave differently, the spin-orbit-density-independent part mainly attractive and the spin-orbit-density-dependent part mainly repulsive. The semiclassical expansions of kinetic energy density and spin-orbit density are allowed up to second order, and the two-parameter Fermi density, with its parameters fitted to experiments, is used for the nuclear density. The universal functions or the resulting nuclear proximity potential reproduce the 'exact' Skyrme nucleus-nucleus interaction potential in the semiclassical approach, within less than ~1 MeV of difference, both at the maximum attraction and in the surface region. An application of the resulting interaction potential to fusion excitation functions shows clearly that the parameterized universal functions of nuclear proximity potential substitute completely the 'exact' potential in the Skyrme energy density formalism based on the semiclassical ETF method, including also the modifications of interaction barriers at sub-barrier energies in terms of modifying the constants of the universal functions.

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.

Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density Matrix

DOE PAGES

Smallwood, D. O.

1996-01-01

It is shown that the usual method for estimating the coherence functions (ordinary, partial, and multiple) for a general multiple-input! multiple-output problem can be expressed as a modified form of Cholesky decomposition of the cross-spectral density matrix of the input and output records. The results can be equivalently obtained using singular value decomposition (SVD) of the cross-spectral density matrix. Using SVD suggests a new form of fractional coherence. The formulation as a SVD problem also suggests a way to order the inputs when a natural physical order of the inputs is absent.

First principle study of transport properties of a graphene nano structure

NASA Astrophysics Data System (ADS)

Kumar, Naveen; Sharma, Munish; Sharma, Jyoti Dhar; Ahluwalia, P. K.

2013-06-01

The first principle quantum transport calculations have been performed for graphene using Tran SIESTA which calculates transport properties using nonequilibrium Green's function method in conjunction with density-functional theory. Transmission functions, electron density of states and current-voltage characteristic have been calculated for a graphene nano structure using graphene electrodes. Transmission function, density of states and projected density of states show a discrete band structure which varies with applied voltage. The value of current is very low for applied voltage between 0.0 V to 5.0 V and lies in the range of pico ampere. In the V-I characteristic current shows non-linear fluctuating pattern with increase in voltage.

Microscopically based energy density functionals for nuclei using the density matrix expansion. II. Full optimization and validation

NASA Astrophysics Data System (ADS)

Navarro Pérez, R.; Schunck, N.; Dyhdalo, A.; Furnstahl, R. J.; Bogner, S. K.

2018-05-01

Background: Energy density functional methods provide a generic framework to compute properties of atomic nuclei starting from models of nuclear potentials and the rules of quantum mechanics. Until now, the overwhelming majority of functionals have been constructed either from empirical nuclear potentials such as the Skyrme or Gogny forces, or from systematic gradient-like expansions in the spirit of the density functional theory for atoms. Purpose: We seek to obtain a usable form of the nuclear energy density functional that is rooted in the modern theory of nuclear forces. We thus consider a functional obtained from the density matrix expansion of local nuclear potentials from chiral effective field theory. We propose a parametrization of this functional carefully calibrated and validated on selected ground-state properties that is suitable for large-scale calculations of nuclear properties. Methods: Our energy functional comprises two main components. The first component is a non-local functional of the density and corresponds to the direct part (Hartree term) of the expectation value of local chiral potentials on a Slater determinant. Contributions to the mean field and the energy of this term are computed by expanding the spatial, finite-range components of the chiral potential onto Gaussian functions. The second component is a local functional of the density and is obtained by applying the density matrix expansion to the exchange part (Fock term) of the expectation value of the local chiral potential. We apply the UNEDF2 optimization protocol to determine the coupling constants of this energy functional. Results: We obtain a set of microscopically constrained functionals for local chiral potentials from leading order up to next-to-next-to-leading order with and without three-body forces and contributions from Δ excitations. These functionals are validated on the calculation of nuclear and neutron matter, nuclear mass tables, single-particle shell structure in closed-shell nuclei, and the fission barrier of 240Pu. Quantitatively, they perform noticeably better than the more phenomenological Skyrme functionals. Conclusions: The inclusion of higher-order terms in the chiral perturbation expansion seems to produce a systematic improvement in predicting nuclear binding energies while the impact on other observables is not really significant. This result is especially promising since all the fits have been performed at the single-reference level of the energy density functional approach, where important collective correlations such as center-of-mass correction, rotational correction, or zero-point vibrational energies have not been taken into account yet.

Self-consistent DFT +U method for real-space time-dependent density functional theory calculations

NASA Astrophysics Data System (ADS)

Tancogne-Dejean, Nicolas; Oliveira, Micael J. T.; Rubio, Angel

2017-12-01

We implemented various DFT+U schemes, including the Agapito, Curtarolo, and Buongiorno Nardelli functional (ACBN0) self-consistent density-functional version of the DFT +U method [Phys. Rev. X 5, 011006 (2015), 10.1103/PhysRevX.5.011006] within the massively parallel real-space time-dependent density functional theory (TDDFT) code octopus. We further extended the method to the case of the calculation of response functions with real-time TDDFT+U and to the description of noncollinear spin systems. The implementation is tested by investigating the ground-state and optical properties of various transition-metal oxides, bulk topological insulators, and molecules. Our results are found to be in good agreement with previously published results for both the electronic band structure and structural properties. The self-consistent calculated values of U and J are also in good agreement with the values commonly used in the literature. We found that the time-dependent extension of the self-consistent DFT+U method yields improved optical properties when compared to the empirical TDDFT+U scheme. This work thus opens a different theoretical framework to address the nonequilibrium properties of correlated systems.

Molecular properties via a subsystem density functional theory formulation: a common framework for electronic embedding.

PubMed

Höfener, Sebastian; Gomes, André Severo Pereira; Visscher, Lucas

2012-01-28

In this article, we present a consistent derivation of a density functional theory (DFT) based embedding method which encompasses wave-function theory-in-DFT (WFT-in-DFT) and the DFT-based subsystem formulation of response theory (DFT-in-DFT) by Neugebauer [J. Neugebauer, J. Chem. Phys. 131, 084104 (2009)] as special cases. This formulation, which is based on the time-averaged quasi-energy formalism, makes use of the variation Lagrangian techniques to allow the use of non-variational (in particular: coupled cluster) wave-function-based methods. We show how, in the time-independent limit, we naturally obtain expressions for the ground-state DFT-in-DFT and WFT-in-DFT embedding via a local potential. We furthermore provide working equations for the special case in which coupled cluster theory is used to obtain the density and excitation energies of the active subsystem. A sample application is given to demonstrate the method. © 2012 American Institute of Physics

Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations.

PubMed

Li, Q; He, Y L; Wang, Y; Tao, W Q

2007-11-01

A coupled double-distribution-function lattice Boltzmann method is developed for the compressible Navier-Stokes equations. Different from existing thermal lattice Boltzmann methods, this method can recover the compressible Navier-Stokes equations with a flexible specific-heat ratio and Prandtl number. In the method, a density distribution function based on a multispeed lattice is used to recover the compressible continuity and momentum equations, while the compressible energy equation is recovered by an energy distribution function. The energy distribution function is then coupled to the density distribution function via the thermal equation of state. In order to obtain an adjustable specific-heat ratio, a constant related to the specific-heat ratio is introduced into the equilibrium energy distribution function. Two different coupled double-distribution-function lattice Boltzmann models are also proposed in the paper. Numerical simulations are performed for the Riemann problem, the double-Mach-reflection problem, and the Couette flow with a range of specific-heat ratios and Prandtl numbers. The numerical results are found to be in excellent agreement with analytical and/or other solutions.

Theory of melting at high pressures: Amending density functional theory with quantum Monte Carlo

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

Shulenburger, L.; Desjarlais, M. P.; Mattsson, T. R.

We present an improved first-principles description of melting under pressure based on thermodynamic integration comparing Density Functional Theory (DFT) and quantum Monte Carlo (QMC) treatments of the system. The method is applied to address the longstanding discrepancy between density functional theory (DFT) calculations and diamond anvil cell (DAC) experiments on the melting curve of xenon, a noble gas solid where van der Waals binding is challenging for traditional DFT methods. The calculations show excellent agreement with data below 20 GPa and that the high-pressure melt curve is well described by a Lindemann behavior up to at least 80 GPa, amore » finding in stark contrast to DAC data.« less

Theory of melting at high pressures: Amending density functional theory with quantum Monte Carlo

DOE PAGES

Shulenburger, L.; Desjarlais, M. P.; Mattsson, T. R.

2014-10-01

We present an improved first-principles description of melting under pressure based on thermodynamic integration comparing Density Functional Theory (DFT) and quantum Monte Carlo (QMC) treatments of the system. The method is applied to address the longstanding discrepancy between density functional theory (DFT) calculations and diamond anvil cell (DAC) experiments on the melting curve of xenon, a noble gas solid where van der Waals binding is challenging for traditional DFT methods. The calculations show excellent agreement with data below 20 GPa and that the high-pressure melt curve is well described by a Lindemann behavior up to at least 80 GPa, amore » finding in stark contrast to DAC data.« less

SU-G-JeP2-02: A Unifying Multi-Atlas Approach to Electron Density Mapping Using Multi-Parametric MRI for Radiation Treatment Planning

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

Ren, S; Tianjin University, Tianjin; Hara, W

Purpose: MRI has a number of advantages over CT as a primary modality for radiation treatment planning (RTP). However, one key bottleneck problem still remains, which is the lack of electron density information in MRI. In the work, a reliable method to map electron density is developed by leveraging the differential contrast of multi-parametric MRI. Methods: We propose a probabilistic Bayesian approach for electron density mapping based on T1 and T2-weighted MRI, using multiple patients as atlases. For each voxel, we compute two conditional probabilities: (1) electron density given its image intensity on T1 and T2-weighted MR images, and (2)more » electron density given its geometric location in a reference anatomy. The two sources of information (image intensity and spatial location) are combined into a unifying posterior probability density function using the Bayesian formalism. The mean value of the posterior probability density function provides the estimated electron density. Results: We evaluated the method on 10 head and neck patients and performed leave-one-out cross validation (9 patients as atlases and remaining 1 as test). The proposed method significantly reduced the errors in electron density estimation, with a mean absolute HU error of 138, compared with 193 for the T1-weighted intensity approach and 261 without density correction. For bone detection (HU>200), the proposed method had an accuracy of 84% and a sensitivity of 73% at specificity of 90% (AUC = 87%). In comparison, the AUC for bone detection is 73% and 50% using the intensity approach and without density correction, respectively. Conclusion: The proposed unifying method provides accurate electron density estimation and bone detection based on multi-parametric MRI of the head with highly heterogeneous anatomy. This could allow for accurate dose calculation and reference image generation for patient setup in MRI-based radiation treatment planning.« less

Assessing Density Functionals Using Many Body Theory for Hybrid Perovskites

NASA Astrophysics Data System (ADS)

Bokdam, Menno; Lahnsteiner, Jonathan; Ramberger, Benjamin; Schäfer, Tobias; Kresse, Georg

2017-10-01

Which density functional is the "best" for structure simulations of a particular material? A concise, first principles, approach to answer this question is presented. The random phase approximation (RPA)—an accurate many body theory—is used to evaluate various density functionals. To demonstrate and verify the method, we apply it to the hybrid perovskite MAPbI3 , a promising new solar cell material. The evaluation is done by first creating finite temperature ensembles for small supercells using RPA molecular dynamics, and then evaluating the variance between the RPA and various approximate density functionals for these ensembles. We find that, contrary to recent suggestions, van der Waals functionals do not improve the description of the material, whereas hybrid functionals and the strongly constrained appropriately normed (SCAN) density functional yield very good agreement with the RPA. Finally, our study shows that in the room temperature tetragonal phase of MAPbI3 , the molecules are preferentially parallel to the shorter lattice vectors but reorientation on ps time scales is still possible.

Generalized-active-space pair-density functional theory: an efficient method to study large, strongly correlated, conjugated systems.

PubMed

Ghosh, Soumen; Cramer, Christopher J; Truhlar, Donald G; Gagliardi, Laura

2017-04-01

Predicting ground- and excited-state properties of open-shell organic molecules by electronic structure theory can be challenging because an accurate treatment has to correctly describe both static and dynamic electron correlation. Strongly correlated systems, i.e. , systems with near-degeneracy correlation effects, are particularly troublesome. Multiconfigurational wave function methods based on an active space are adequate in principle, but it is impractical to capture most of the dynamic correlation in these methods for systems characterized by many active electrons. We recently developed a new method called multiconfiguration pair-density functional theory (MC-PDFT), that combines the advantages of wave function theory and density functional theory to provide a more practical treatment of strongly correlated systems. Here we present calculations of the singlet-triplet gaps in oligoacenes ranging from naphthalene to dodecacene. Calculations were performed for unprecedently large orbitally optimized active spaces of 50 electrons in 50 orbitals, and we test a range of active spaces and active space partitions, including four kinds of frontier orbital partitions. We show that MC-PDFT can predict the singlet-triplet splittings for oligoacenes consistent with the best available and much more expensive methods, and indeed MC-PDFT may constitute the benchmark against which those other models should be compared, given the absence of experimental data.

Determination of Charge-Carrier Mobility in Disordered Thin-Film Solar Cells as a Function of Current Density

NASA Astrophysics Data System (ADS)

Mäckel, Helmut; MacKenzie, Roderick C. I.

2018-03-01

Charge-carrier mobility is a fundamental material parameter, which plays an important role in determining solar-cell efficiency. The higher the mobility, the less time a charge carrier will spend in a device and the less likely it is that it will be lost to recombination. Despite the importance of this physical property, it is notoriously difficult to measure accurately in disordered thin-film solar cells under operating conditions. We, therefore, investigate a method previously proposed in the literature for the determination of mobility as a function of current density. The method is based on a simple analytical model that relates the mobility to carrier density and transport resistance. By revising the theoretical background of the method, we clearly demonstrate what type of mobility can be extracted (constant mobility or effective mobility of electrons and holes). We generalize the method to any combination of measurements that is able to determine the mean electron and hole carrier density, and the transport resistance at a given current density. We explore the robustness of the method by simulating typical organic solar-cell structures with a variety of physical properties, including unbalanced mobilities, unbalanced carrier densities, and for high or low carrier trapping rates. The simulations reveal that near VOC and JSC , the method fails due to the limitation of determining the transport resistance. However, away from these regions (and, importantly, around the maximum power point), the method can accurately determine charge-carrier mobility. In the presence of strong carrier trapping, the method overestimates the effective mobility due to an underestimation of the carrier density.

Excited-state absorption in tetrapyridyl porphyrins: comparing real-time and quadratic-response time-dependent density functional theory

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

Bowman, David N.; Asher, Jason C.; Fischer, Sean A.

2017-01-01

Threemeso-substituted tetrapyridyl porphyrins (free base, Ni(ii), and Cu(ii)) were investigated for their optical limiting (OL) capabilities using real-time (RT-), linear-response (LR-), and quadratic-response (QR-) time-dependent density functional theory (TDDFT) methods.

Analytical excited state forces for the time-dependent density-functional tight-binding method.

PubMed

Heringer, D; Niehaus, T A; Wanko, M; Frauenheim, Th

2007-12-01

An analytical formulation for the geometrical derivatives of excitation energies within the time-dependent density-functional tight-binding (TD-DFTB) method is presented. The derivation is based on the auxiliary functional approach proposed in [Furche and Ahlrichs, J Chem Phys 2002, 117, 7433]. To validate the quality of the potential energy surfaces provided by the method, adiabatic excitation energies, excited state geometries, and harmonic vibrational frequencies were calculated for a test set of molecules in excited states of different symmetry and multiplicity. According to the results, the TD-DFTB scheme surpasses the performance of configuration interaction singles and the random phase approximation but has a lower quality than ab initio time-dependent density-functional theory. As a consequence of the special form of the approximations made in TD-DFTB, the scaling exponent of the method can be reduced to three, similar to the ground state. The low scaling prefactor and the satisfactory accuracy of the method makes TD-DFTB especially suitable for molecular dynamics simulations of dozens of atoms as well as for the computation of luminescence spectra of systems containing hundreds of atoms. (c) 2007 Wiley Periodicals, Inc.

Matching-pursuit/split-operator-Fourier-transform computations of thermal correlation functions.

PubMed

Chen, Xin; Wu, Yinghua; Batista, Victor S

2005-02-08

A rigorous and practical methodology for evaluating thermal-equilibrium density matrices, finite-temperature time-dependent expectation values, and time-correlation functions is described. The method involves an extension of the matching-pursuit/split-operator-Fourier-transform method to the solution of the Bloch equation via imaginary-time propagation of the density matrix and the evaluation of Heisenberg time-evolution operators through real-time propagation in dynamically adaptive coherent-state representations.

Excitation energies from range-separated time-dependent density and density matrix functional theory.

PubMed

Pernal, Katarzyna

2012-05-14

Time-dependent density functional theory (TD-DFT) in the adiabatic formulation exhibits known failures when applied to predicting excitation energies. One of them is the lack of the doubly excited configurations. On the other hand, the time-dependent theory based on a one-electron reduced density matrix functional (time-dependent density matrix functional theory, TD-DMFT) has proven accurate in determining single and double excitations of H(2) molecule if the exact functional is employed in the adiabatic approximation. We propose a new approach for computing excited state energies that relies on functionals of electron density and one-electron reduced density matrix, where the latter is applied in the long-range region of electron-electron interactions. A similar approach has been recently successfully employed in predicting ground state potential energy curves of diatomic molecules even in the dissociation limit, where static correlation effects are dominating. In the paper, a time-dependent functional theory based on the range-separation of electronic interaction operator is rigorously formulated. To turn the approach into a practical scheme the adiabatic approximation is proposed for the short- and long-range components of the coupling matrix present in the linear response equations. In the end, the problem of finding excitation energies is turned into an eigenproblem for a symmetric matrix. Assignment of obtained excitations is discussed and it is shown how to identify double excitations from the analysis of approximate transition density matrix elements. The proposed method used with the short-range local density approximation (srLDA) and the long-range Buijse-Baerends density matrix functional (lrBB) is applied to H(2) molecule (at equilibrium geometry and in the dissociation limit) and to Be atom. The method accounts for double excitations in the investigated systems but, unfortunately, the accuracy of some of them is poor. The quality of the other excitations is in general much better than that offered by TD-DFT-LDA or TD-DMFT-BB approximations if the range-separation parameter is properly chosen. The latter remains an open problem.

High throughput nonparametric probability density estimation.

PubMed

Farmer, Jenny; Jacobs, Donald

2018-01-01

In high throughput applications, such as those found in bioinformatics and finance, it is important to determine accurate probability distribution functions despite only minimal information about data characteristics, and without using human subjectivity. Such an automated process for univariate data is implemented to achieve this goal by merging the maximum entropy method with single order statistics and maximum likelihood. The only required properties of the random variables are that they are continuous and that they are, or can be approximated as, independent and identically distributed. A quasi-log-likelihood function based on single order statistics for sampled uniform random data is used to empirically construct a sample size invariant universal scoring function. Then a probability density estimate is determined by iteratively improving trial cumulative distribution functions, where better estimates are quantified by the scoring function that identifies atypical fluctuations. This criterion resists under and over fitting data as an alternative to employing the Bayesian or Akaike information criterion. Multiple estimates for the probability density reflect uncertainties due to statistical fluctuations in random samples. Scaled quantile residual plots are also introduced as an effective diagnostic to visualize the quality of the estimated probability densities. Benchmark tests show that estimates for the probability density function (PDF) converge to the true PDF as sample size increases on particularly difficult test probability densities that include cases with discontinuities, multi-resolution scales, heavy tails, and singularities. These results indicate the method has general applicability for high throughput statistical inference.

High throughput nonparametric probability density estimation

PubMed Central

Farmer, Jenny

2018-01-01

In high throughput applications, such as those found in bioinformatics and finance, it is important to determine accurate probability distribution functions despite only minimal information about data characteristics, and without using human subjectivity. Such an automated process for univariate data is implemented to achieve this goal by merging the maximum entropy method with single order statistics and maximum likelihood. The only required properties of the random variables are that they are continuous and that they are, or can be approximated as, independent and identically distributed. A quasi-log-likelihood function based on single order statistics for sampled uniform random data is used to empirically construct a sample size invariant universal scoring function. Then a probability density estimate is determined by iteratively improving trial cumulative distribution functions, where better estimates are quantified by the scoring function that identifies atypical fluctuations. This criterion resists under and over fitting data as an alternative to employing the Bayesian or Akaike information criterion. Multiple estimates for the probability density reflect uncertainties due to statistical fluctuations in random samples. Scaled quantile residual plots are also introduced as an effective diagnostic to visualize the quality of the estimated probability densities. Benchmark tests show that estimates for the probability density function (PDF) converge to the true PDF as sample size increases on particularly difficult test probability densities that include cases with discontinuities, multi-resolution scales, heavy tails, and singularities. These results indicate the method has general applicability for high throughput statistical inference. PMID:29750803

Density functional Gaussian-type-orbital approach to theoretical study of nitric oxide dimers

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

Jursic, B.S.; Zdravkovski, Z.

Structure and total energies of the cis NO dimer, the trans NO dimer, and the NO monomer were calculated by ab initio methods (UHF, UMP2, and MP3) and density functional theory methods (LSDA and BLYP) with different basis sets [from 3-21G* to 6-311++(3df,3pd)]. The system is especially hard to model because two NO molecules are weakly associated in a dimer that has very long N-N bond. The results obtained by different methods are compared and the necessity of correlational methods for studying these systems is discussed.

Method for obtaining electron energy-density functions from Langmuir-probe data using a card-programmable calculator

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

Longhurst, G.R.

This paper presents a method for obtaining electron energy density functions from Langmuir probe data taken in cool, dense plasmas where thin-sheath criteria apply and where magnetic effects are not severe. Noise is filtered out by using regression of orthogonal polynomials. The method requires only a programmable calculator (TI-59 or equivalent) to implement and can be used for the most general, nonequilibrium electron energy distribution plasmas. Data from a mercury ion source analyzed using this method are presented and compared with results for the same data using standard numerical techniques.

A Density Functional Approach to Polarizable Models: A Kim-Gordon-Response Density Interaction Potential for Molecular Simulations

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

Tabacchi, G; Hutter, J; Mundy, C

2005-04-07

A combined linear response--frozen electron density model has been implemented in a molecular dynamics scheme derived from an extended Lagrangian formalism. This approach is based on a partition of the electronic charge distribution into a frozen region described by Kim-Gordon theory, and a response contribution determined by the instaneous ionic configuration of the system. The method is free from empirical pair-potentials and the parameterization protocol involves only calculations on properly chosen subsystems. They apply this method to a series of alkali halides in different physical phases and are able to reproduce experimental structural and thermodynamic properties with an accuracy comparablemore » to Kohn-Sham density functional calculations.« less

An improved probabilistic approach for linking progenitor and descendant galaxy populations using comoving number density

NASA Astrophysics Data System (ADS)

Wellons, Sarah; Torrey, Paul

2017-06-01

Galaxy populations at different cosmic epochs are often linked by cumulative comoving number density in observational studies. Many theoretical works, however, have shown that the cumulative number densities of tracked galaxy populations not only evolve in bulk, but also spread out over time. We present a method for linking progenitor and descendant galaxy populations which takes both of these effects into account. We define probability distribution functions that capture the evolution and dispersion of galaxy populations in number density space, and use these functions to assign galaxies at redshift zf probabilities of being progenitors/descendants of a galaxy population at another redshift z0. These probabilities are used as weights for calculating distributions of physical progenitor/descendant properties such as stellar mass, star formation rate or velocity dispersion. We demonstrate that this probabilistic method provides more accurate predictions for the evolution of physical properties than the assumption of either a constant number density or an evolving number density in a bin of fixed width by comparing predictions against galaxy populations directly tracked through a cosmological simulation. We find that the constant number density method performs least well at recovering galaxy properties, the evolving method density slightly better and the probabilistic method best of all. The improvement is present for predictions of stellar mass as well as inferred quantities such as star formation rate and velocity dispersion. We demonstrate that this method can also be applied robustly and easily to observational data, and provide a code package for doing so.

Generalized local emission tomography

DOEpatents

Katsevich, Alexander J.

1998-01-01

Emission tomography enables locations and values of internal isotope density distributions to be determined from radiation emitted from the whole object. In the method for locating the values of discontinuities, the intensities of radiation emitted from either the whole object or a region of the object containing the discontinuities are inputted to a local tomography function .function..sub..LAMBDA..sup.(.PHI.) to define the location S of the isotope density discontinuity. The asymptotic behavior of .function..sub..LAMBDA..sup.(.PHI.) is determined in a neighborhood of S, and the value for the discontinuity is estimated from the asymptotic behavior of .function..sub..LAMBDA..sup.(.PHI.) knowing pointwise values of the attenuation coefficient within the object. In the method for determining the location of the discontinuity, the intensities of radiation emitted from an object are inputted to a local tomography function .function..sub..LAMBDA..sup.(.PHI.) to define the location S of the density discontinuity and the location .GAMMA. of the attenuation coefficient discontinuity. Pointwise values of the attenuation coefficient within the object need not be known in this case.

Estimation of the four-wave mixing noise probability-density function by the multicanonical Monte Carlo method.

PubMed

Neokosmidis, Ioannis; Kamalakis, Thomas; Chipouras, Aristides; Sphicopoulos, Thomas

2005-01-01

The performance of high-powered wavelength-division multiplexed (WDM) optical networks can be severely degraded by four-wave-mixing- (FWM-) induced distortion. The multicanonical Monte Carlo method (MCMC) is used to calculate the probability-density function (PDF) of the decision variable of a receiver, limited by FWM noise. Compared with the conventional Monte Carlo method previously used to estimate this PDF, the MCMC method is much faster and can accurately estimate smaller error probabilities. The method takes into account the correlation between the components of the FWM noise, unlike the Gaussian model, which is shown not to provide accurate results.

Three statistical models for estimating length of stay.

PubMed Central

Selvin, S

1977-01-01

The probability density functions implied by three methods of collecting data on the length of stay in an institution are derived. The expected values associated with these density functions are used to calculate unbiased estimates of the expected length of stay. Two of the methods require an assumption about the form of the underlying distribution of length of stay; the third method does not. The three methods are illustrated with hypothetical data exhibiting the Poisson distribution, and the third (distribution-independent) method is used to estimate the length of stay in a skilled nursing facility and in an intermediate care facility for patients enrolled in California's MediCal program. PMID:914532

Three statistical models for estimating length of stay.

PubMed

Selvin, S

1977-01-01

The probability density functions implied by three methods of collecting data on the length of stay in an institution are derived. The expected values associated with these density functions are used to calculate unbiased estimates of the expected length of stay. Two of the methods require an assumption about the form of the underlying distribution of length of stay; the third method does not. The three methods are illustrated with hypothetical data exhibiting the Poisson distribution, and the third (distribution-independent) method is used to estimate the length of stay in a skilled nursing facility and in an intermediate care facility for patients enrolled in California's MediCal program.

A review of contemporary methods for the presentation of scientific uncertainty.

PubMed

Makinson, K A; Hamby, D M; Edwards, J A

2012-12-01

Graphic methods for displaying uncertainty are often the most concise and informative way to communicate abstract concepts. Presentation methods currently in use for the display and interpretation of scientific uncertainty are reviewed. Numerous subjective and objective uncertainty display methods are presented, including qualitative assessments, node and arrow diagrams, standard statistical methods, box-and-whisker plots,robustness and opportunity functions, contribution indexes, probability density functions, cumulative distribution functions, and graphical likelihood functions.

Optical spectrum of proflavine and its ions

NASA Astrophysics Data System (ADS)

Bonaca, A.; Bilalbegović, G.

2010-06-01

Motivated by possible astrophysical and biological applications we calculate visible and near UV spectral lines of proflavine (C13H11N3, 3,6-diaminoacridine) in vacuum, as well as its anion, cation, and dication. The pseudopotential density functional and time-dependent density functional methods are used. We find a good agreement in spectral line positions calculated by two real-time propagation methods and the Lanczos chain method. Spectra of proflavine and its ions show characteristic UV lines which are good candidates for a detection of these molecules in interstellar space and various biological processes.

Spectroscopic and time-dependent density functional theory investigation of the photophysical properties of zearalenone and its analogs

USDA-ARS?s Scientific Manuscript database

Structures of the mycotoxin zearalenone and its analogs were investigated using density functional theory methods to gain insight into the ground state and excited state properties related to detection. Zearalenone is an estrogenic mycotoxin that can occur in agricultural commodities, and ultraviole...

Identification of Stochastically Perturbed Autonomous Systems from Temporal Sequences of Probability Density Functions

NASA Astrophysics Data System (ADS)

Nie, Xiaokai; Luo, Jingjing; Coca, Daniel; Birkin, Mark; Chen, Jing

2018-03-01

The paper introduces a method for reconstructing one-dimensional iterated maps that are driven by an external control input and subjected to an additive stochastic perturbation, from sequences of probability density functions that are generated by the stochastic dynamical systems and observed experimentally.

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

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.

Modelling population distribution using remote sensing imagery and location-based data

NASA Astrophysics Data System (ADS)

Song, J.; Prishchepov, A. V.

2017-12-01

Detailed spatial distribution of population density is essential for city studies such as urban planning, environmental pollution and city emergency, even estimate pressure on the environment and human exposure and risks to health. However, most of the researches used census data as the detailed dynamic population distribution are difficult to acquire, especially in microscale research. This research describes a method using remote sensing imagery and location-based data to model population distribution at the function zone level. Firstly, urban functional zones within a city were mapped by high-resolution remote sensing images and POIs. The workflow of functional zones extraction includes five parts: (1) Urban land use classification. (2) Segmenting images in built-up area. (3) Identification of functional segments by POIs. (4) Identification of functional blocks by functional segmentation and weight coefficients. (5) Assessing accuracy by validation points. The result showed as Fig.1. Secondly, we applied ordinary least square and geographically weighted regression to assess spatial nonstationary relationship between light digital number (DN) and population density of sampling points. The two methods were employed to predict the population distribution over the research area. The R²of GWR model were in the order of 0.7 and typically showed significant variations over the region than traditional OLS model. The result showed as Fig.2.Validation with sampling points of population density demonstrated that the result predicted by the GWR model correlated well with light value. The result showed as Fig.3. Results showed: (1) Population density is not linear correlated with light brightness using global model. (2) VIIRS night-time light data could estimate population density integrating functional zones at city level. (3) GWR is a robust model to map population distribution, the adjusted R2 of corresponding GWR models were higher than the optimal OLS models, confirming that GWR models demonstrate better prediction accuracy. So this method provide detailed population density information for microscale citizen studies.

Resolution-of-identity stochastic time-dependent configuration interaction for dissipative electron dynamics in strong fields.

PubMed

Klinkusch, Stefan; Tremblay, Jean Christophe

2016-05-14

In this contribution, we introduce a method for simulating dissipative, ultrafast many-electron dynamics in intense laser fields. The method is based on the norm-conserving stochastic unraveling of the dissipative Liouville-von Neumann equation in its Lindblad form. The N-electron wave functions sampling the density matrix are represented in the basis of singly excited configuration state functions. The interaction with an external laser field is treated variationally and the response of the electronic density is included to all orders in this basis. The coupling to an external environment is included via relaxation operators inducing transition between the configuration state functions. Single electron ionization is represented by irreversible transition operators from the ionizing states to an auxiliary continuum state. The method finds its efficiency in the representation of the operators in the interaction picture, where the resolution-of-identity is used to reduce the size of the Hamiltonian eigenstate basis. The zeroth-order eigenstates can be obtained either at the configuration interaction singles level or from a time-dependent density functional theory reference calculation. The latter offers an alternative to explicitly time-dependent density functional theory which has the advantage of remaining strictly valid for strong field excitations while improving the description of the correlation as compared to configuration interaction singles. The method is tested on a well-characterized toy system, the excitation of the low-lying charge transfer state in LiCN.

Resolution-of-identity stochastic time-dependent configuration interaction for dissipative electron dynamics in strong fields

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

Klinkusch, Stefan; Tremblay, Jean Christophe

In this contribution, we introduce a method for simulating dissipative, ultrafast many-electron dynamics in intense laser fields. The method is based on the norm-conserving stochastic unraveling of the dissipative Liouville-von Neumann equation in its Lindblad form. The N-electron wave functions sampling the density matrix are represented in the basis of singly excited configuration state functions. The interaction with an external laser field is treated variationally and the response of the electronic density is included to all orders in this basis. The coupling to an external environment is included via relaxation operators inducing transition between the configuration state functions. Single electronmore » ionization is represented by irreversible transition operators from the ionizing states to an auxiliary continuum state. The method finds its efficiency in the representation of the operators in the interaction picture, where the resolution-of-identity is used to reduce the size of the Hamiltonian eigenstate basis. The zeroth-order eigenstates can be obtained either at the configuration interaction singles level or from a time-dependent density functional theory reference calculation. The latter offers an alternative to explicitly time-dependent density functional theory which has the advantage of remaining strictly valid for strong field excitations while improving the description of the correlation as compared to configuration interaction singles. The method is tested on a well-characterized toy system, the excitation of the low-lying charge transfer state in LiCN.« less

The non-Gaussian joint probability density function of slope and elevation for a nonlinear gravity wave field. [in ocean surface

NASA Technical Reports Server (NTRS)

Huang, N. E.; Long, S. R.; Bliven, L. F.; Tung, C.-C.

1984-01-01

On the basis of the mapping method developed by Huang et al. (1983), an analytic expression for the non-Gaussian joint probability density function of slope and elevation for nonlinear gravity waves is derived. Various conditional and marginal density functions are also obtained through the joint density function. The analytic results are compared with a series of carefully controlled laboratory observations, and good agreement is noted. Furthermore, the laboratory wind wave field observations indicate that the capillary or capillary-gravity waves may not be the dominant components in determining the total roughness of the wave field. Thus, the analytic results, though derived specifically for the gravity waves, may have more general applications.

Density scaling for multiplets

NASA Astrophysics Data System (ADS)

Nagy, Á.

2011-02-01

Generalized Kohn-Sham equations are presented for lowest-lying multiplets. The way of treating non-integer particle numbers is coupled with an earlier method of the author. The fundamental quantity of the theory is the subspace density. The Kohn-Sham equations are similar to the conventional Kohn-Sham equations. The difference is that the subspace density is used instead of the density and the Kohn-Sham potential is different for different subspaces. The exchange-correlation functional is studied using density scaling. It is shown that there exists a value of the scaling factor ζ for which the correlation energy disappears. Generalized OPM and Krieger-Li-Iafrate (KLI) methods incorporating correlation are presented. The ζKLI method, being as simple as the original KLI method, is proposed for multiplets.

Extended polarization in 3rd order SCC-DFTB from chemical potential equilization

PubMed Central

Kaminski, Steve; Giese, Timothy J.; Gaus, Michael; York, Darrin M.; Elstner, Marcus

2012-01-01

In this work we augment the approximate density functional method SCC-DFTB (DFTB3) with the chemical potential equilization (CPE) approach in order to improve the performance for molecular electronic polarizabilities. The CPE method, originally implemented for NDDO type methods by Giese and York, has been shown to emend minimal basis methods wrt response properties significantly, and has been applied to SCC-DFTB recently. CPE allows to overcome this inherent limitation of minimal basis methods by supplying an additional response density. The systematic underestimation is thereby corrected quantitatively without the need to extend the atomic orbital basis, i.e. without increasing the overall computational cost significantly. Especially the dependency of polarizability as a function of molecular charge state was significantly improved from the CPE extension of DFTB3. The empirical parameters introduced by the CPE approach were optimized for 172 organic molecules in order to match the results from density functional methods (DFT) methods using large basis sets. However, the first order derivatives of molecular polarizabilities, as e.g. required to compute Raman activities, are not improved by the current CPE implementation, i.e. Raman spectra are not improved. PMID:22894819

Video shot boundary detection using region-growing-based watershed method

NASA Astrophysics Data System (ADS)

Wang, Jinsong; Patel, Nilesh; Grosky, William

2004-10-01

In this paper, a novel shot boundary detection approach is presented, based on the popular region growing segmentation method - Watershed segmentation. In image processing, gray-scale pictures could be considered as topographic reliefs, in which the numerical value of each pixel of a given image represents the elevation at that point. Watershed method segments images by filling up basins with water starting at local minima, and at points where water coming from different basins meet, dams are built. In our method, each frame in the video sequences is first transformed from the feature space into the topographic space based on a density function. Low-level features are extracted from frame to frame. Each frame is then treated as a point in the feature space. The density of each point is defined as the sum of the influence functions of all neighboring data points. The height function that is originally used in Watershed segmentation is then replaced by inverting the density at the point. Thus, all the highest density values are transformed into local minima. Subsequently, Watershed segmentation is performed in the topographic space. The intuitive idea under our method is that frames within a shot are highly agglomerative in the feature space and have higher possibilities to be merged together, while those frames between shots representing the shot changes are not, hence they have less density values and are less likely to be clustered by carefully extracting the markers and choosing the stopping criterion.

Density functional theory for d- and f-electron materials and compounds

DOE PAGES

Mattson, Ann E.; Wills, John M.

2016-02-12

Here, the fundamental requirements for a computationally tractable Density Functional Theory-based method for relativistic f- and (nonrelativistic) d-electron materials and compounds are presented. The need for basing the Kohn–Sham equations on the Dirac equation is discussed. The full Dirac scheme needs exchange-correlation functionals in terms of four-currents, but ordinary functionals, using charge density and spin-magnetization, can be used in an approximate Dirac treatment. The construction of a functional that includes the additional confinement physics needed for these materials is illustrated using the subsystem-functional scheme. If future studies show that a full Dirac, four-current based, exchange-correlation functional is needed, the subsystemmore » functional scheme is one of the few schemes that can still be used for constructing functional approximations.« less

Eddy current loss analysis of open-slot fault-tolerant permanent-magnet machines based on conformal mapping method

NASA Astrophysics Data System (ADS)

Ji, Jinghua; Luo, Jianhua; Lei, Qian; Bian, Fangfang

2017-05-01

This paper proposed an analytical method, based on conformal mapping (CM) method, for the accurate evaluation of magnetic field and eddy current (EC) loss in fault-tolerant permanent-magnet (FTPM) machines. The aim of modulation function, applied in CM method, is to change the open-slot structure into fully closed-slot structure, whose air-gap flux density is easy to calculate analytically. Therefore, with the help of Matlab Schwarz-Christoffel (SC) Toolbox, both the magnetic flux density and EC density of FTPM machine are obtained accurately. Finally, time-stepped transient finite-element method (FEM) is used to verify the theoretical analysis, showing that the proposed method is able to predict the magnetic flux density and EC loss precisely.

Modeling of nanoscale liquid mixture transport by density functional hydrodynamics

NASA Astrophysics Data System (ADS)

Dinariev, Oleg Yu.; Evseev, Nikolay V.

2017-06-01

Modeling of multiphase compositional hydrodynamics at nanoscale is performed by means of density functional hydrodynamics (DFH). DFH is the method based on density functional theory and continuum mechanics. This method has been developed by the authors over 20 years and used for modeling in various multiphase hydrodynamic applications. In this paper, DFH was further extended to encompass phenomena inherent in liquids at nanoscale. The new DFH extension is based on the introduction of external potentials for chemical components. These potentials are localized in the vicinity of solid surfaces and take account of the van der Waals forces. A set of numerical examples, including disjoining pressure, film precursors, anomalous rheology, liquid in contact with heterogeneous surface, capillary condensation, and forward and reverse osmosis, is presented to demonstrate modeling capabilities.

Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem

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

Pribram-Jones, Aurora; Grabowski, Paul E.; Burke, Kieron

We present that the van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. Finally, this produces a natural method for generating new thermal exchange-correlation approximations.

Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem

DOE PAGES

Pribram-Jones, Aurora; Grabowski, Paul E.; Burke, Kieron

2016-06-08

We present that the van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. Finally, this produces a natural method for generating new thermal exchange-correlation approximations.

Simplified Computation for Nonparametric Windows Method of Probability Density Function Estimation.

PubMed

Joshi, Niranjan; Kadir, Timor; Brady, Michael

2011-08-01

Recently, Kadir and Brady proposed a method for estimating probability density functions (PDFs) for digital signals which they call the Nonparametric (NP) Windows method. The method involves constructing a continuous space representation of the discrete space and sampled signal by using a suitable interpolation method. NP Windows requires only a small number of observed signal samples to estimate the PDF and is completely data driven. In this short paper, we first develop analytical formulae to obtain the NP Windows PDF estimates for 1D, 2D, and 3D signals, for different interpolation methods. We then show that the original procedure to calculate the PDF estimate can be significantly simplified and made computationally more efficient by a judicious choice of the frame of reference. We have also outlined specific algorithmic details of the procedures enabling quick implementation. Our reformulation of the original concept has directly demonstrated a close link between the NP Windows method and the Kernel Density Estimator.

One-dimensional continuum electronic structure with the density-matrix renormalization group and its implications for density-functional theory.

PubMed

Stoudenmire, E M; Wagner, Lucas O; White, Steven R; Burke, Kieron

2012-08-03

We extend the density matrix renormalization group to compute exact ground states of continuum many-electron systems in one dimension with long-range interactions. We find the exact ground state of a chain of 100 strongly correlated artificial hydrogen atoms. The method can be used to simulate 1D cold atom systems and to study density-functional theory in an exact setting. To illustrate, we find an interacting, extended system which is an insulator but whose Kohn-Sham system is metallic.

Cluster perturbation theory for calculation of electronic properties of ensembles of metal nanoclusters

NASA Astrophysics Data System (ADS)

Zhumagulov, Yaroslav V.; Krasavin, Andrey V.; Kashurnikov, Vladimir A.

2018-05-01

The method is developed for calculation of electronic properties of an ensemble of metal nanoclusters with the use of cluster perturbation theory. This method is applied to the system of gold nanoclusters. The Greens function of single nanocluster is obtained by ab initio calculations within the framework of the density functional theory, and then is used in Dyson equation to group nanoclusters together and to compute the Greens function as well as the electron density of states of the whole ensemble. The transition from insulator state of a single nanocluster to metallic state of bulk gold is observed.

Influence of the volume and density functions within geometric models for estimating trunk inertial parameters.

PubMed

Wicke, Jason; Dumas, Genevieve A

2010-02-01

The geometric method combines a volume and a density function to estimate body segment parameters and has the best opportunity for developing the most accurate models. In the trunk, there are many different tissues that greatly differ in density (e.g., bone versus lung). Thus, the density function for the trunk must be particularly sensitive to capture this diversity, such that accurate inertial estimates are possible. Three different models were used to test this hypothesis by estimating trunk inertial parameters of 25 female and 24 male college-aged participants. The outcome of this study indicates that the inertial estimates for the upper and lower trunk are most sensitive to the volume function and not very sensitive to the density function. Although it appears that the uniform density function has a greater influence on inertial estimates in the lower trunk region than in the upper trunk region, this is likely due to the (overestimated) density value used. When geometric models are used to estimate body segment parameters, care must be taken in choosing a model that can accurately estimate segment volumes. Researchers wanting to develop accurate geometric models should focus on the volume function, especially in unique populations (e.g., pregnant or obese individuals).

Hartree and Exchange in Ensemble Density Functional Theory: Avoiding the Nonuniqueness Disaster.

PubMed

Gould, Tim; Pittalis, Stefano

2017-12-15

Ensemble density functional theory is a promising method for the efficient and accurate calculation of excitations of quantum systems, at least if useful functionals can be developed to broaden its domain of practical applicability. Here, we introduce a guaranteed single-valued "Hartree-exchange" ensemble density functional, E_{Hx}[n], in terms of the right derivative of the universal ensemble density functional with respect to the coupling constant at vanishing interaction. We show that E_{Hx}[n] is straightforwardly expressible using block eigenvalues of a simple matrix [Eq. (14)]. Specialized expressions for E_{Hx}[n] from the literature, including those involving superpositions of Slater determinants, can now be regarded as originating from the unifying picture presented here. We thus establish a clear and practical description for Hartree and exchange in ensemble systems.

Statistical properties of a filtered Poisson process with additive random noise: distributions, correlations and moment estimation

NASA Astrophysics Data System (ADS)

Theodorsen, A.; E Garcia, O.; Rypdal, M.

2017-05-01

Filtered Poisson processes are often used as reference models for intermittent fluctuations in physical systems. Such a process is here extended by adding a noise term, either as a purely additive term to the process or as a dynamical term in a stochastic differential equation. The lowest order moments, probability density function, auto-correlation function and power spectral density are derived and used to identify and compare the effects of the two different noise terms. Monte-Carlo studies of synthetic time series are used to investigate the accuracy of model parameter estimation and to identify methods for distinguishing the noise types. It is shown that the probability density function and the three lowest order moments provide accurate estimations of the model parameters, but are unable to separate the noise types. The auto-correlation function and the power spectral density also provide methods for estimating the model parameters, as well as being capable of identifying the noise type. The number of times the signal crosses a prescribed threshold level in the positive direction also promises to be able to differentiate the noise type.

Two-dimensional molecular line transfer for a cometary coma

NASA Astrophysics Data System (ADS)

Szutowicz, S.

2017-09-01

In the proposed axisymmetric model of the cometary coma the gas density profile is described by an angular density function. Three methods for treating two-dimensional radiative transfer are compared: the Large Velocity Gradient (LVG) (the Sobolev method), Accelerated Lambda Iteration (ALI) and accelerated Monte Carlo (MC).

Systematic theoretical investigation of the zero-field splitting in Gd(III) complexes: Wave function and density functional approaches

NASA Astrophysics Data System (ADS)

Khan, Shehryar; Kubica-Misztal, Aleksandra; Kruk, Danuta; Kowalewski, Jozef; Odelius, Michael

2015-01-01

The zero-field splitting (ZFS) of the electronic ground state in paramagnetic ions is a sensitive probe of the variations in the electronic and molecular structure with an impact on fields ranging from fundamental physical chemistry to medical applications. A detailed analysis of the ZFS in a series of symmetric Gd(III) complexes is presented in order to establish the applicability and accuracy of computational methods using multiconfigurational complete-active-space self-consistent field wave functions and of density functional theory calculations. The various computational schemes are then applied to larger complexes Gd(III)DOTA(H2O)-, Gd(III)DTPA(H2O)2-, and Gd(III)(H2O)83+ in order to analyze how the theoretical results compare to experimentally derived parameters. In contrast to approximations based on density functional theory, the multiconfigurational methods produce results for the ZFS of Gd(III) complexes on the correct order of magnitude.

A density functional theory study of the influence of exchange-correlation functionals on the properties of FeAs.

PubMed

Griffin, Sinéad M; Spaldin, Nicola A

2017-06-01

We use density functional theory within the local density approximation (LDA), LDA  +  U, generalised gradient approximation (GGA), GGA  +  U, and hybrid-functional methods to calculate the properties of iron monoarsenide. FeAs, which forms in the MnP structure, is of current interest for potential spintronic applications as well as being the parent compound for the pnictide superconductors. We compare the calculated structural, magnetic and electronic properties obtained using the different functionals to each other and to experiment, and investigate the origin of a recently reported magnetic spiral. Our results indicate the appropriateness or otherwise of the various functionals for describing FeAs and the related Fe-pnictide superconductors.

Numerical methods for the inverse problem of density functional theory

DOE PAGES

Jensen, Daniel S.; Wasserman, Adam

2017-07-17

Here, the inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the numerical methods for solving each problem are substantially different. We examine both problems in this tutorial with a special emphasis on the algorithms and error analysis needed for solving the inverse problem. Two inversion methods based on partial differential equation constrained optimization and constrained variational ideas are introduced. We compare and contrast several different inversion methods applied to one-dimensional finite and periodic modelmore » systems.« less

Numerical methods for the inverse problem of density functional theory

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

Jensen, Daniel S.; Wasserman, Adam

Here, the inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the numerical methods for solving each problem are substantially different. We examine both problems in this tutorial with a special emphasis on the algorithms and error analysis needed for solving the inverse problem. Two inversion methods based on partial differential equation constrained optimization and constrained variational ideas are introduced. We compare and contrast several different inversion methods applied to one-dimensional finite and periodic modelmore » systems.« less

Density functional theory calculations of 95Mo NMR parameters in solid-state compounds.

PubMed

Cuny, Jérôme; Furet, Eric; Gautier, Régis; Le Pollès, Laurent; Pickard, Chris J; d'Espinose de Lacaillerie, Jean-Baptiste

2009-12-21

The application of periodic density functional theory-based methods to the calculation of (95)Mo electric field gradient (EFG) and chemical shift (CS) tensors in solid-state molybdenum compounds is presented. Calculations of EFG tensors are performed using the projector augmented-wave (PAW) method. Comparison of the results with those obtained using the augmented plane wave + local orbitals (APW+lo) method and with available experimental values shows the reliability of the approach for (95)Mo EFG tensor calculation. CS tensors are calculated using the recently developed gauge-including projector augmented-wave (GIPAW) method. This work is the first application of the GIPAW method to a 4d transition-metal nucleus. The effects of ultra-soft pseudo-potential parameters, exchange-correlation functionals and structural parameters are precisely examined. Comparison with experimental results allows the validation of this computational formalism.

Fast and accurate quantum molecular dynamics of dense plasmas across temperature regimes

DOE PAGES

Sjostrom, Travis; Daligault, Jerome

2014-10-10

Here, we develop and implement a new quantum molecular dynamics approximation that allows fast and accurate simulations of dense plasmas from cold to hot conditions. The method is based on a carefully designed orbital-free implementation of density functional theory. The results for hydrogen and aluminum are in very good agreement with Kohn-Sham (orbital-based) density functional theory and path integral Monte Carlo calculations for microscopic features such as the electron density as well as the equation of state. The present approach does not scale with temperature and hence extends to higher temperatures than is accessible in the Kohn-Sham method and lowermore » temperatures than is accessible by path integral Monte Carlo calculations, while being significantly less computationally expensive than either of those two methods.« less

Band-gap corrected density functional theory calculations for InAs/GaSb type II superlattices

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

Wang, Jianwei; Zhang, Yong

2014-12-07

We performed pseudopotential based density functional theory (DFT) calculations for GaSb/InAs type II superlattices (T2SLs), with bandgap errors from the local density approximation mitigated by applying an empirical method to correct the bulk bandgaps. Specifically, this work (1) compared the calculated bandgaps with experimental data and non-self-consistent atomistic methods; (2) calculated the T2SL band structures with varying structural parameters; (3) investigated the interfacial effects associated with the no-common-atom heterostructure; and (4) studied the strain effect due to lattice mismatch between the two components. This work demonstrates the feasibility of applying the DFT method to more exotic heterostructures and defect problemsmore » related to this material system.« less

Modulation Based on Probability Density Functions

NASA Technical Reports Server (NTRS)

Williams, Glenn L.

2009-01-01

A proposed method of modulating a sinusoidal carrier signal to convey digital information involves the use of histograms representing probability density functions (PDFs) that characterize samples of the signal waveform. The method is based partly on the observation that when a waveform is sampled (whether by analog or digital means) over a time interval at least as long as one half cycle of the waveform, the samples can be sorted by frequency of occurrence, thereby constructing a histogram representing a PDF of the waveform during that time interval.

Computing rates of Markov models of voltage-gated ion channels by inverting partial differential equations governing the probability density functions of the conducting and non-conducting states.

PubMed

Tveito, Aslak; Lines, Glenn T; Edwards, Andrew G; McCulloch, Andrew

2016-07-01

Markov models are ubiquitously used to represent the function of single ion channels. However, solving the inverse problem to construct a Markov model of single channel dynamics from bilayer or patch-clamp recordings remains challenging, particularly for channels involving complex gating processes. Methods for solving the inverse problem are generally based on data from voltage clamp measurements. Here, we describe an alternative approach to this problem based on measurements of voltage traces. The voltage traces define probability density functions of the functional states of an ion channel. These probability density functions can also be computed by solving a deterministic system of partial differential equations. The inversion is based on tuning the rates of the Markov models used in the deterministic system of partial differential equations such that the solution mimics the properties of the probability density function gathered from (pseudo) experimental data as well as possible. The optimization is done by defining a cost function to measure the difference between the deterministic solution and the solution based on experimental data. By evoking the properties of this function, it is possible to infer whether the rates of the Markov model are identifiable by our method. We present applications to Markov model well-known from the literature. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

Internal wave energy flux from density perturbations in nonlinear stratifications

NASA Astrophysics Data System (ADS)

Lee, Frank M.; Allshouse, Michael R.; Swinney, Harry L.; Morrison, P. J.

2017-11-01

Tidal flow over the topography at the bottom of the ocean, whose density varies with depth, generates internal gravity waves that have a significant impact on the energy budget of the ocean. Thus, understanding the energy flux (J = p v) is important, but it is difficult to measure simultaneously the pressure and velocity perturbation fields, p and v . In a previous work, a Green's-function-based method was developed to calculate the instantaneous p, v , and thus J , given a density perturbation field for a constant buoyancy frequency N. Here we extend the previous analytic Green's function work to include nonuniform N profiles, namely the tanh-shaped and linear cases, because background density stratifications that occur in the ocean and some experiments are nonlinear. In addition, we present a finite-difference method for the general case where N has an arbitrary profile. Each method is validated against numerical simulations. The methods we present can be applied to measured density perturbation data by using our MATLAB graphical user interface EnergyFlux. PJM was supported by the U.S. Department of Energy Contract DE-FG05-80ET-53088. HLS and MRA were supported by ONR Grant No. N000141110701.

Angle-dependent strong-field molecular ionization rates with tuned range-separated time-dependent density functional theory.

PubMed

Sissay, Adonay; Abanador, Paul; Mauger, François; Gaarde, Mette; Schafer, Kenneth J; Lopata, Kenneth

2016-09-07

Strong-field ionization and the resulting electronic dynamics are important for a range of processes such as high harmonic generation, photodamage, charge resonance enhanced ionization, and ionization-triggered charge migration. Modeling ionization dynamics in molecular systems from first-principles can be challenging due to the large spatial extent of the wavefunction which stresses the accuracy of basis sets, and the intense fields which require non-perturbative time-dependent electronic structure methods. In this paper, we develop a time-dependent density functional theory approach which uses a Gaussian-type orbital (GTO) basis set to capture strong-field ionization rates and dynamics in atoms and small molecules. This involves propagating the electronic density matrix in time with a time-dependent laser potential and a spatial non-Hermitian complex absorbing potential which is projected onto an atom-centered basis set to remove ionized charge from the simulation. For the density functional theory (DFT) functional we use a tuned range-separated functional LC-PBE*, which has the correct asymptotic 1/r form of the potential and a reduced delocalization error compared to traditional DFT functionals. Ionization rates are computed for hydrogen, molecular nitrogen, and iodoacetylene under various field frequencies, intensities, and polarizations (angle-dependent ionization), and the results are shown to quantitatively agree with time-dependent Schrödinger equation and strong-field approximation calculations. This tuned DFT with GTO method opens the door to predictive all-electron time-dependent density functional theory simulations of ionization and ionization-triggered dynamics in molecular systems using tuned range-separated hybrid functionals.

Angle-dependent strong-field molecular ionization rates with tuned range-separated time-dependent density functional theory

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

Sissay, Adonay; Abanador, Paul; Mauger, François

2016-09-07

Strong-field ionization and the resulting electronic dynamics are important for a range of processes such as high harmonic generation, photodamage, charge resonance enhanced ionization, and ionization-triggered charge migration. Modeling ionization dynamics in molecular systems from first-principles can be challenging due to the large spatial extent of the wavefunction which stresses the accuracy of basis sets, and the intense fields which require non-perturbative time-dependent electronic structure methods. In this paper, we develop a time-dependent density functional theory approach which uses a Gaussian-type orbital (GTO) basis set to capture strong-field ionization rates and dynamics in atoms and small molecules. This involves propagatingmore » the electronic density matrix in time with a time-dependent laser potential and a spatial non-Hermitian complex absorbing potential which is projected onto an atom-centered basis set to remove ionized charge from the simulation. For the density functional theory (DFT) functional we use a tuned range-separated functional LC-PBE*, which has the correct asymptotic 1/r form of the potential and a reduced delocalization error compared to traditional DFT functionals. Ionization rates are computed for hydrogen, molecular nitrogen, and iodoacetylene under various field frequencies, intensities, and polarizations (angle-dependent ionization), and the results are shown to quantitatively agree with time-dependent Schrödinger equation and strong-field approximation calculations. This tuned DFT with GTO method opens the door to predictive all-electron time-dependent density functional theory simulations of ionization and ionization-triggered dynamics in molecular systems using tuned range-separated hybrid functionals.« less

Exact density functional and wave function embedding schemes based on orbital localization

NASA Astrophysics Data System (ADS)

Hégely, Bence; Nagy, Péter R.; Ferenczy, György G.; Kállay, Mihály

2016-08-01

Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.

Quantum Crystallography: Density Matrix-Density Functional Theory and the X-Ray Diffraction Experiment

NASA Astrophysics Data System (ADS)

Soirat, Arnaud J. A.

Density Matrix Theory is a Quantum Mechanical formalism in which the wavefunction is eliminated and its role taken over by reduced density matrices. The interest of this is that, it allows one, in principle, to calculate any electronic property of a physical system, without having to solve the Schrodinger equation, using only two entities much simpler than an N-body wavefunction: first and second -order reduced density matrices. In practice, though, this very promising possibility faces the tremendous theoretical problem of N-representability, which has been solved for the former, but, until now, voids any hope of theoretically determining the latter. However, it has been shown that single determinant reduced density matrices of any order may be recovered from coherent X-ray diffraction data, if one provides a proper Quantum Mechanical description of the Crystallography experiment. A deeper investigation of this method is the purpose of this work, where we, first, further study the calculation of X-ray reduced density matrices N-representable by a single Slater determinant. In this context, we independently derive necessary and sufficient conditions for the uniqueness of the method. We then show how to account for electron correlation in this model. For the first time, indeed, we derive highly accurate, yet practical, density matrices approximately N-representable by correlated-determinant wavefunctions. The interest of such a result lies in the Quantum Mechanical validity of these density matrices, their property of being entirely obtainable from X-ray coherent diffraction data, their very high accuracy conferred by this known property of the N-representing wavefunction, as well as their definition as explicit functionals of the density. All of these properties are finally used in both a theoretical and a numerical application: in the former, we show that these density matrices may be used in the context of Density Functional Theory to highly accurately determine the unknown HK functional, associated with the theorem of Hohenberg and Kohn. The latter is provided by the calculation of helium correlation energy, where we test approximating the second-order density function by the leading term of its McLaurin's series expansion.

Fast Nonlinear Generalized Inversion of Gravity Data with Application to the Three-Dimensional Crustal Density Structure of Sichuan Basin, Southwest China

NASA Astrophysics Data System (ADS)

Wang, Jun; Meng, Xiaohong; Li, Fang

2017-11-01

Generalized inversion is one of the important steps in the quantitative interpretation of gravity data. With appropriate algorithm and parameters, it gives a view of the subsurface which characterizes different geological bodies. However, generalized inversion of gravity data is time consuming due to the large amount of data points and model cells adopted. Incorporating of various prior information as constraints deteriorates the above situation. In the work discussed in this paper, a method for fast nonlinear generalized inversion of gravity data is proposed. The fast multipole method is employed for forward modelling. The inversion objective function is established with weighted data misfit function along with model objective function. The total objective function is solved by a dataspace algorithm. Moreover, depth weighing factor is used to improve depth resolution of the result, and bound constraint is incorporated by a transfer function to limit the model parameters in a reliable range. The matrix inversion is accomplished by a preconditioned conjugate gradient method. With the above algorithm, equivalent density vectors can be obtained, and interpolation is performed to get the finally density model on the fine mesh in the model domain. Testing on synthetic gravity data demonstrated that the proposed method is faster than conventional generalized inversion algorithm to produce an acceptable solution for gravity inversion problem. The new developed inversion method was also applied for inversion of the gravity data collected over Sichuan basin, southwest China. The established density structure in this study helps understanding the crustal structure of Sichuan basin and provides reference for further oil and gas exploration in this area.

Objective Molecular Dynamics with Self-consistent Charge Density Functional Tight-Binding (SCC-DFTB) Method

NASA Astrophysics Data System (ADS)

Dumitrica, Traian; Hourahine, Ben; Aradi, Balint; Frauenheim, Thomas

We discus the coupling of the objective boundary conditions into the SCC density functional-based tight binding code DFTB+. The implementation is enabled by a generalization to the helical case of the classical Ewald method, specifically by Ewald-like formulas that do not rely on a unit cell with translational symmetry. The robustness of the method in addressing complex hetero-nuclear nano- and bio-fibrous systems is demonstrated with illustrative simulations on a helical boron nitride nanotube, a screw dislocated zinc oxide nanowire, and an ideal double-strand DNA. Work supported by NSF CMMI 1332228.

Digital simulation of two-dimensional random fields with arbitrary power spectra and non-Gaussian probability distribution functions.

PubMed

Yura, Harold T; Hanson, Steen G

2012-04-01

Methods for simulation of two-dimensional signals with arbitrary power spectral densities and signal amplitude probability density functions are disclosed. The method relies on initially transforming a white noise sample set of random Gaussian distributed numbers into a corresponding set with the desired spectral distribution, after which this colored Gaussian probability distribution is transformed via an inverse transform into the desired probability distribution. In most cases the method provides satisfactory results and can thus be considered an engineering approach. Several illustrative examples with relevance for optics are given.

Bivariate sub-Gaussian model for stock index returns

NASA Astrophysics Data System (ADS)

Jabłońska-Sabuka, Matylda; Teuerle, Marek; Wyłomańska, Agnieszka

2017-11-01

Financial time series are commonly modeled with methods assuming data normality. However, the real distribution can be nontrivial, also not having an explicitly formulated probability density function. In this work we introduce novel parameter estimation and high-powered distribution testing methods which do not rely on closed form densities, but use the characteristic functions for comparison. The approach applied to a pair of stock index returns demonstrates that such a bivariate vector can be a sample coming from a bivariate sub-Gaussian distribution. The methods presented here can be applied to any nontrivially distributed financial data, among others.

Study on transport properties of silicene monolayer under external field using NEGF method

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

Syaputra, Marhamni, E-mail: marhamni@students.itb.ac.id; Wella, Sasfan Arman; Wungu, Triati Dewi Kencana

2015-09-30

We investigate the current-voltage (I-V) characteristics of a pristine monolayer silicene using non-equilibrium Green function (NEGF) method combining with density functional theory (DFT). This method succeeded in showing the relationship of I and V on silicene corresponding to the electronic characteristics such as density of states. The external field perpendicular to the silicene monolayer affects in increasing of the current. Under 0.2 eV external field, the current reaches the maximum peak at Vb = 0.3 eV with the increase is about 60% from what it is in zero external field.

Periodic subsystem density-functional theory

NASA Astrophysics Data System (ADS)

Genova, Alessandro; Ceresoli, Davide; Pavanello, Michele

2014-11-01

By partitioning the electron density into subsystem contributions, the Frozen Density Embedding (FDE) formulation of subsystem Density Functional Theory (DFT) has recently emerged as a powerful tool for reducing the computational scaling of Kohn-Sham DFT. To date, however, FDE has been employed to molecular systems only. Periodic systems, such as metals, semiconductors, and other crystalline solids have been outside the applicability of FDE, mostly because of the lack of a periodic FDE implementation. To fill this gap, in this work we aim at extending FDE to treat subsystems of molecular and periodic character. This goal is achieved by a dual approach. On one side, the development of a theoretical framework for periodic subsystem DFT. On the other, the realization of the method into a parallel computer code. We find that periodic FDE is capable of reproducing total electron densities and (to a lesser extent) also interaction energies of molecular systems weakly interacting with metallic surfaces. In the pilot calculations considered, we find that FDE fails in those cases where there is appreciable density overlap between the subsystems. Conversely, we find FDE to be in semiquantitative agreement with Kohn-Sham DFT when the inter-subsystem density overlap is low. We also conclude that to make FDE a suitable method for describing molecular adsorption at surfaces, kinetic energy density functionals that go beyond the GGA level must be employed.

Periodic subsystem density-functional theory.

PubMed

Genova, Alessandro; Ceresoli, Davide; Pavanello, Michele

2014-11-07

By partitioning the electron density into subsystem contributions, the Frozen Density Embedding (FDE) formulation of subsystem Density Functional Theory (DFT) has recently emerged as a powerful tool for reducing the computational scaling of Kohn-Sham DFT. To date, however, FDE has been employed to molecular systems only. Periodic systems, such as metals, semiconductors, and other crystalline solids have been outside the applicability of FDE, mostly because of the lack of a periodic FDE implementation. To fill this gap, in this work we aim at extending FDE to treat subsystems of molecular and periodic character. This goal is achieved by a dual approach. On one side, the development of a theoretical framework for periodic subsystem DFT. On the other, the realization of the method into a parallel computer code. We find that periodic FDE is capable of reproducing total electron densities and (to a lesser extent) also interaction energies of molecular systems weakly interacting with metallic surfaces. In the pilot calculations considered, we find that FDE fails in those cases where there is appreciable density overlap between the subsystems. Conversely, we find FDE to be in semiquantitative agreement with Kohn-Sham DFT when the inter-subsystem density overlap is low. We also conclude that to make FDE a suitable method for describing molecular adsorption at surfaces, kinetic energy density functionals that go beyond the GGA level must be employed.

Periodic subsystem density-functional theory

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

Genova, Alessandro; Pavanello, Michele, E-mail: m.pavanello@rutgers.edu; Ceresoli, Davide

2014-11-07

By partitioning the electron density into subsystem contributions, the Frozen Density Embedding (FDE) formulation of subsystem Density Functional Theory (DFT) has recently emerged as a powerful tool for reducing the computational scaling of Kohn–Sham DFT. To date, however, FDE has been employed to molecular systems only. Periodic systems, such as metals, semiconductors, and other crystalline solids have been outside the applicability of FDE, mostly because of the lack of a periodic FDE implementation. To fill this gap, in this work we aim at extending FDE to treat subsystems of molecular and periodic character. This goal is achieved by a dualmore » approach. On one side, the development of a theoretical framework for periodic subsystem DFT. On the other, the realization of the method into a parallel computer code. We find that periodic FDE is capable of reproducing total electron densities and (to a lesser extent) also interaction energies of molecular systems weakly interacting with metallic surfaces. In the pilot calculations considered, we find that FDE fails in those cases where there is appreciable density overlap between the subsystems. Conversely, we find FDE to be in semiquantitative agreement with Kohn–Sham DFT when the inter-subsystem density overlap is low. We also conclude that to make FDE a suitable method for describing molecular adsorption at surfaces, kinetic energy density functionals that go beyond the GGA level must be employed.« less

Multicomponent Density Functional Theory: Impact of Nuclear Quantum Effects on Proton Affinities and Geometries.

PubMed

Brorsen, Kurt R; Yang, Yang; Hammes-Schiffer, Sharon

2017-08-03

Nuclear quantum effects such as zero point energy play a critical role in computational chemistry and often are included as energetic corrections following geometry optimizations. The nuclear-electronic orbital (NEO) multicomponent density functional theory (DFT) method treats select nuclei, typically protons, quantum mechanically on the same level as the electrons. Electron-proton correlation is highly significant, and inadequate treatments lead to highly overlocalized nuclear densities. A recently developed electron-proton correlation functional, epc17, has been shown to provide accurate nuclear densities for molecular systems. Herein, the NEO-DFT/epc17 method is used to compute the proton affinities for a set of molecules and to examine the role of nuclear quantum effects on the equilibrium geometry of FHF - . The agreement of the computed results with experimental and benchmark values demonstrates the promise of this approach for including nuclear quantum effects in calculations of proton affinities, pK a 's, optimized geometries, and reaction paths.

Extracting physical quantities from BES data

NASA Astrophysics Data System (ADS)

Fox, Michael; Field, Anthony; Schekochihin, Alexander; van Wyk, Ferdinand; MAST Team

2015-11-01

We propose a method to extract the underlying physical properties of turbulence from measurements, thereby facilitating quantitative comparisons between theory and experiment. Beam Emission Spectroscopy (BES) diagnostics record fluctuating intensity time series, which are related to the density field in the plasma through Point-Spread Functions (PSFs). Assuming a suitable form for the correlation function of the underlying turbulence, analytical expressions are derived that relate the correlation parameters of the intensity field: the radial and poloidal correlation lengths and wavenumbers, the correlation time and the fluctuation amplitude, to the equivalent correlation properties of the density field. In many cases, the modification caused by the PSFs is substantial enough to change conclusions about physics. Our method is tested by applying PSFs to the ``real'' density field, generated by non-linear gyrokinetic simulations of MAST, to create synthetic turbulence data, from which the method successfully recovers the correlation function of the ``real'' density field. This method is applied to BES data from MAST to determine the scaling of the 2D structure of the ion-scale turbulence with equilibrium parameters, including the ExB flow shear. Work funded by the Euratom research and training programme 2014-2018 under grant agreement No 633053 and from the RCUK Energy Programme [grant number EP/I501045].

Protein Structure Classification and Loop Modeling Using Multiple Ramachandran Distributions.

PubMed

Najibi, Seyed Morteza; Maadooliat, Mehdi; Zhou, Lan; Huang, Jianhua Z; Gao, Xin

2017-01-01

Recently, the study of protein structures using angular representations has attracted much attention among structural biologists. The main challenge is how to efficiently model the continuous conformational space of the protein structures based on the differences and similarities between different Ramachandran plots. Despite the presence of statistical methods for modeling angular data of proteins, there is still a substantial need for more sophisticated and faster statistical tools to model the large-scale circular datasets. To address this need, we have developed a nonparametric method for collective estimation of multiple bivariate density functions for a collection of populations of protein backbone angles. The proposed method takes into account the circular nature of the angular data using trigonometric spline which is more efficient compared to existing methods. This collective density estimation approach is widely applicable when there is a need to estimate multiple density functions from different populations with common features. Moreover, the coefficients of adaptive basis expansion for the fitted densities provide a low-dimensional representation that is useful for visualization, clustering, and classification of the densities. The proposed method provides a novel and unique perspective to two important and challenging problems in protein structure research: structure-based protein classification and angular-sampling-based protein loop structure prediction.

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.

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.

Experimental and DFT studies on the vibrational spectra of 1H-indene-2-boronic acid

NASA Astrophysics Data System (ADS)

Alver, Özgur; Kaya, Mehmet Fatih

2014-11-01

Stable conformers and geometrical molecular structures of 1H-indene-2-boronic acid (I-2B(OH)2) were studied experimentally and theoretically using FT-IR and FT-Raman spectroscopic methods. FT-IR and FT-Raman spectra were recorded in the region of 4000-400 cm-1, and 3700-400 cm-1, respectively. The optimized geometric structures were searched by Becke-3-Lee-Yang-Parr (B3LYP) hybrid density functional theory method with 6-31++G(d,p) basis set. Vibrational wavenumbers of I-2B(OH)2 were calculated using B3LYP density functional methods including 6-31++G(d,p) basis set. Experimental and theoretical results show that density functional B3LYP method gives satisfactory results for predicting vibrational wavenumbers except OH stretching modes which is probably due to increasing unharmonicity in the high wave number region and possible intra and inter molecular interaction at OH edges. To support the assigned vibrational wavenumbers, the potential energy distribution (PED) values were also calculated using VEDA 4 (Vibrational Energy Distribution Analysis) program.

Regression-assisted deconvolution.

PubMed

McIntyre, Julie; Stefanski, Leonard A

2011-06-30

We present a semi-parametric deconvolution estimator for the density function of a random variable biX that is measured with error, a common challenge in many epidemiological studies. Traditional deconvolution estimators rely only on assumptions about the distribution of X and the error in its measurement, and ignore information available in auxiliary variables. Our method assumes the availability of a covariate vector statistically related to X by a mean-variance function regression model, where regression errors are normally distributed and independent of the measurement errors. Simulations suggest that the estimator achieves a much lower integrated squared error than the observed-data kernel density estimator when models are correctly specified and the assumption of normal regression errors is met. We illustrate the method using anthropometric measurements of newborns to estimate the density function of newborn length. Copyright © 2011 John Wiley & Sons, Ltd.

Discovering charge density functionals and structure-property relationships with PROPhet: A general framework for coupling machine learning and first-principles methods

DOE PAGES

Kolb, Brian; Lentz, Levi C.; Kolpak, Alexie M.

2017-04-26

Modern ab initio methods have rapidly increased our understanding of solid state materials properties, chemical reactions, and the quantum interactions between atoms. However, poor scaling often renders direct ab initio calculations intractable for large or complex systems. There are two obvious avenues through which to remedy this problem: (i) develop new, less expensive methods to calculate system properties, or (ii) make existing methods faster. This paper describes an open source framework designed to pursue both of these avenues. PROPhet (short for PROPerty Prophet) utilizes machine learning techniques to find complex, non-linear mappings between sets of material or system properties. Themore » result is a single code capable of learning analytical potentials, non-linear density functionals, and other structure-property or property-property relationships. These capabilities enable highly accurate mesoscopic simulations, facilitate computation of expensive properties, and enable the development of predictive models for systematic materials design and optimization. Here, this work explores the coupling of machine learning to ab initio methods through means both familiar (e.g., the creation of various potentials and energy functionals) and less familiar (e.g., the creation of density functionals for arbitrary properties), serving both to demonstrate PROPhet’s ability to create exciting post-processing analysis tools and to open the door to improving ab initio methods themselves with these powerful machine learning techniques.« less

Discovering charge density functionals and structure-property relationships with PROPhet: A general framework for coupling machine learning and first-principles methods

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

Kolb, Brian; Lentz, Levi C.; Kolpak, Alexie M.

Modern ab initio methods have rapidly increased our understanding of solid state materials properties, chemical reactions, and the quantum interactions between atoms. However, poor scaling often renders direct ab initio calculations intractable for large or complex systems. There are two obvious avenues through which to remedy this problem: (i) develop new, less expensive methods to calculate system properties, or (ii) make existing methods faster. This paper describes an open source framework designed to pursue both of these avenues. PROPhet (short for PROPerty Prophet) utilizes machine learning techniques to find complex, non-linear mappings between sets of material or system properties. Themore » result is a single code capable of learning analytical potentials, non-linear density functionals, and other structure-property or property-property relationships. These capabilities enable highly accurate mesoscopic simulations, facilitate computation of expensive properties, and enable the development of predictive models for systematic materials design and optimization. Here, this work explores the coupling of machine learning to ab initio methods through means both familiar (e.g., the creation of various potentials and energy functionals) and less familiar (e.g., the creation of density functionals for arbitrary properties), serving both to demonstrate PROPhet’s ability to create exciting post-processing analysis tools and to open the door to improving ab initio methods themselves with these powerful machine learning techniques.« less

Level Density in the Complex Scaling Method

NASA Astrophysics Data System (ADS)

Suzuki, R.; Myo, T.; Katō, K.

2005-06-01

It is shown that the continuum level density (CLD) at unbound energies can be calculated with the complex scaling method (CSM), in which the energy spectra of bound states, resonances and continuum states are obtained in terms of L(2) basis functions. In this method, the extended completeness relation is applied to the calculation of the Green functions, and the continuum-state part is approximately expressed in terms of discretized complex scaled continuum solutions. The obtained result is compared with the CLD calculated exactly from the scattering phase shift. The discretization in the CSM is shown to give a very good description of continuum states. We discuss how the scattering phase shifts can inversely be calculated from the discretized CLD using a basis function technique in the CSM.

Communication: Density functional theory overcomes the failure of predicting intermolecular interaction energies

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

Podeszwa, Rafal; Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716; Szalewicz, Krzysztof

2012-04-28

Density-functional theory (DFT) revolutionized the ability of computational quantum mechanics to describe properties of matter and is by far the most often used method. However, all the standard variants of DFT fail to predict intermolecular interaction energies. In recent years, a number of ways to go around this problem has been proposed. We show that some of these approaches can reproduce interaction energies with median errors of only about 5% in the complete range of intermolecular configurations. Such errors are comparable to typical uncertainties of wave-function-based methods in practical applications. Thus, these DFT methods are expected to find broad applicationsmore » in modelling of condensed phases and of biomolecules.« less

High density event-related potential data acquisition in cognitive neuroscience.

PubMed

Slotnick, Scott D

2010-04-16

Functional magnetic resonance imaging (fMRI) is currently the standard method of evaluating brain function in the field of Cognitive Neuroscience, in part because fMRI data acquisition and analysis techniques are readily available. Because fMRI has excellent spatial resolution but poor temporal resolution, this method can only be used to identify the spatial location of brain activity associated with a given cognitive process (and reveals virtually nothing about the time course of brain activity). By contrast, event-related potential (ERP) recording, a method that is used much less frequently than fMRI, has excellent temporal resolution and thus can track rapid temporal modulations in neural activity. Unfortunately, ERPs are under utilized in Cognitive Neuroscience because data acquisition techniques are not readily available and low density ERP recording has poor spatial resolution. In an effort to foster the increased use of ERPs in Cognitive Neuroscience, the present article details key techniques involved in high density ERP data acquisition. Critically, high density ERPs offer the promise of excellent temporal resolution and good spatial resolution (or excellent spatial resolution if coupled with fMRI), which is necessary to capture the spatial-temporal dynamics of human brain function.

Density functional theory and an experimentally-designed energy functional of electron density.

PubMed

Miranda, David A; Bueno, Paulo R

2016-09-21

We herein demonstrate that capacitance spectroscopy (CS) experimentally allows access to the energy associated with the quantum mechanical ground state of many-electron systems. Priorly, electrochemical capacitance, C [small mu, Greek, macron] [ρ], was previously understood from conceptual and computational density functional theory (DFT) calculations. Thus, we herein propose a quantum mechanical experiment-based variational method for electron charging processes based on an experimentally-designed functional of the ground state electron density. In this methodology, the electron state density, ρ, and an energy functional of the electron density, E [small mu, Greek, macron] [ρ], can be obtained from CS data. CS allows the derivative of the electrochemical potential with respect to the electron density, (δ[small mu, Greek, macron][ρ]/δρ), to be obtained as a unique functional of the energetically minimised system, i.e., β/C [small mu, Greek, macron] [ρ], where β is a constant (associated with the size of the system) and C [small mu, Greek, macron] [ρ] is an experimentally observable quantity. Thus the ground state energy (at a given fixed external potential) can be obtained simply as E [small mu, Greek, macron] [ρ], from the experimental measurement of C [small mu, Greek, macron] [ρ]. An experimental data-set was interpreted to demonstrate the potential of this quantum mechanical experiment-based variational principle.

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

Theoretical Study of Sodium Effect on the Gasification of Carbonaceous Materials with Carbon Dioxide.

PubMed

Calderón, Lucas A; Garza, Jorge; Espinal, Juan F

2015-12-24

The effect of sodium on the thermodynamics and kinetics of carbon gasification with carbon dioxide was studied by using quantum chemistry methods. Specifically, in the density functional context, two exchange-correlation functionals were used: B3LYP and M06. Some results obtained by these exchange-correlation functionals were contrasted with those obtained by the CCSD(T) method. It was found that density functional theory gives similar conclusions with respect to the coupled-cluster method. As one important conclusion we can mention that the thermodynamics of carbon monoxide desorption is not favored by the sodium presence. However, the presence of this metal induces: (a) an easier formation of one semiquinone group, (b) the dissociation of carbon dioxide, and (c) an increment on the CO desorption rate for one of the proposed pathways.

Symmetry properties of the electron density and following from it limits on the KS-DFT applications

NASA Astrophysics Data System (ADS)

Kaplan, Ilya G.

2018-03-01

At present, the Density Functional Theory (DFT) approach elaborated by Kohn with co-authors more than 50 years ago became the most widely used method for study molecules and solids. Using modern computation facilities, it can be applied to systems with million atoms. In the atmosphere of such great popularity, it is particularly important to know the limits of the applicability of DFT methods. In this report, I will discuss two cases when the conventional DFT approaches, using only electron density ρ and its gradients, cannot be applied (I will not consider the Ψ-versions of DFT). The first case is quite evident. In the degenerated states, the electron density may not be defined, since electronic and nuclear motions cannot be separated, the vibronic interaction mixed them. The second case is related to the spin of the state. As it was rigorously proved by group theoretical methods at the theorem level, the electron density does not depend on the total spin S of the arbitrary N-electron state. It means that the Kohn-Sham equations have the same form for states with different S. The critical survey of elaborated DFT procedures, taking into account spin, shows that they modified only exchange functionals, the correlation functionals do not correspond to the spin of the state. The point is that the conception of spin cannot be defined in the framework of the electron density formalism, which corresponds to the one-particle reduced density matrix. This is the main reason of the problems arising in the study by DFT of magnetic properties of the transition metals. The possible way of resolving these problems can be found in the two-particle reduced density matrix formulation of DFT.

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

Orbital-free bond breaking via machine learning

NASA Astrophysics Data System (ADS)

Snyder, John C.; Rupp, Matthias; Hansen, Katja; Blooston, Leo; Müller, Klaus-Robert; Burke, Kieron

2013-12-01

Using a one-dimensional model, we explore the ability of machine learning to approximate the non-interacting kinetic energy density functional of diatomics. This nonlinear interpolation between Kohn-Sham reference calculations can (i) accurately dissociate a diatomic, (ii) be systematically improved with increased reference data and (iii) generate accurate self-consistent densities via a projection method that avoids directions with no data. With relatively few densities, the error due to the interpolation is smaller than typical errors in standard exchange-correlation functionals.

A new wavelet transform to sparsely represent cortical current densities for EEG/MEG inverse problems.

PubMed

Liao, Ke; Zhu, Min; Ding, Lei

2013-08-01

The present study investigated the use of transform sparseness of cortical current density on human brain surface to improve electroencephalography/magnetoencephalography (EEG/MEG) inverse solutions. Transform sparseness was assessed by evaluating compressibility of cortical current densities in transform domains. To do that, a structure compression method from computer graphics was first adopted to compress cortical surface structure, either regular or irregular, into hierarchical multi-resolution meshes. Then, a new face-based wavelet method based on generated multi-resolution meshes was proposed to compress current density functions defined on cortical surfaces. Twelve cortical surface models were built by three EEG/MEG softwares and their structural compressibility was evaluated and compared by the proposed method. Monte Carlo simulations were implemented to evaluate the performance of the proposed wavelet method in compressing various cortical current density distributions as compared to other two available vertex-based wavelet methods. The present results indicate that the face-based wavelet method can achieve higher transform sparseness than vertex-based wavelet methods. Furthermore, basis functions from the face-based wavelet method have lower coherence against typical EEG and MEG measurement systems than vertex-based wavelet methods. Both high transform sparseness and low coherent measurements suggest that the proposed face-based wavelet method can improve the performance of L1-norm regularized EEG/MEG inverse solutions, which was further demonstrated in simulations and experimental setups using MEG data. Thus, this new transform on complicated cortical structure is promising to significantly advance EEG/MEG inverse source imaging technologies. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

A Scalable Implementation of Van der Waals Density Functionals

NASA Astrophysics Data System (ADS)

Wu, Jun; Gygi, Francois

2010-03-01

Recently developed Van der Waals density functionals[1] offer the promise to account for weak intermolecular interactions that are not described accurately by local exchange-correlation density functionals. In spite of recent progress [2], the computational cost of such calculations remains high. We present a scalable parallel implementation of the functional proposed by Dion et al.[1]. The method is implemented in the Qbox first-principles simulation code (http://eslab.ucdavis.edu/software/qbox). Application to large molecular systems will be presented. [4pt] [1] M. Dion et al. Phys. Rev. Lett. 92, 246401 (2004).[0pt] [2] G. Roman-Perez and J. M. Soler, Phys. Rev. Lett. 103, 096102 (2009).

An evaluation of random analysis methods for the determination of panel damping

NASA Technical Reports Server (NTRS)

Bhat, W. V.; Wilby, J. F.

1972-01-01

An analysis is made of steady-state and non-steady-state methods for the measurement of panel damping. Particular emphasis is placed on the use of random process techniques in conjunction with digital data reduction methods. The steady-state methods considered use the response power spectral density, response autocorrelation, excitation-response crosspower spectral density, or single-sided Fourier transform (SSFT) of the response autocorrelation function. Non-steady-state methods are associated mainly with the use of rapid frequency sweep excitation. Problems associated with the practical application of each method are evaluated with specific reference to the case of a panel exposed to a turbulent airflow, and two methods, the power spectral density and the single-sided Fourier transform methods, are selected as being the most suitable. These two methods are demonstrated experimentally, and it is shown that the power spectral density method is satisfactory under most conditions, provided that appropriate corrections are applied to account for filter bandwidth and background noise errors. Thus, the response power spectral density method is recommended for the measurement of the damping of panels exposed to a moving airflow.

Bone density and functional results after femoral revision with a cementless press-fit stem.

PubMed

Canovas, F; Roche, O; Girard, J; Bonnomet, F; Goldschild, M; Le Béguec, P

2015-05-01

The influence of radiographic bone density changes in the area surrounding a total hip arthroplasty (THA) revision with a cementless press-fit stem is unknown, notably in terms of functional results. We have therefore conducted a study aiming to (1) propose a radiographic method to assess bone density, (2) measure the functional effects of reduced bone density, and (3) determine the factors contributing to these modifications. A reduction in radiographic bone density has a negative influence on the functional result after revision using a cementless press-fit stem. We retrospectively assessed 150 THA revisions at a mean follow-up of 6.3 ± 3.2 years (range, 2-15 years). The clinical assessment was based on the Harris Hip Score. Bone density modifications were measured radiographically and the method was evaluated. The change in bone density was classified into two groups: (1) bone density not reduced or < 2 Gruen zones (118 cases [79%]); (2) bone density reduced ≥ 2 zones (32 cases [21%]). The variables showing a potential influence were the Cortical Index (CI), the type of primary stability with the press-fit system, and the femoral implant length. Inter- and intraobserver reliability of radiographic bone density measurement was evaluated as moderate or good (Kappa, 0.58; 0.60 and 0.67, respectively). For the Harris Hip Score at follow-up, there was a borderline statistical relation between stages 1 and 2: for the 118 stage 1 patients, this score was 83.62 ± 11.54 (range, 27-99) versus 78.34 ± 15.98 (range, 62-91) for stage 2 patients (P = 0.09). A CI ≤ 0.44 showed mediocre bone quality contributing to decreased bone density (P < 0.02). On the other hand, there was no statistically significant relation with the type of primary fixation (P = 0.34) or the length of the implant (P = 0.23). A cementless revision femoral stem can induce a reduction in bone density with possible functional effects. The negative role played by bone scarcity on the functional score is confirmed, and even though the difference is not statistically significant, we suggest using a short stem when this is possible. Copyright © 2015 Elsevier Masson SAS. All rights reserved.

Analytic second derivative of the energy for density-functional tight-binding combined with the fragment molecular orbital method

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

Nakata, Hiroya, E-mail: hiroya.nakata.gt@kyocera.jp; Nishimoto, Yoshio; Fedorov, Dmitri G.

2016-07-28

The analytic second derivative of the energy is developed for the fragment molecular orbital (FMO) method combined with density-functional tight-binding (DFTB), enabling simulations of infrared and Raman spectra of large molecular systems. The accuracy of the method is established in comparison to full DFTB without fragmentation for a set of representative systems. The performance of the FMO-DFTB Hessian is discussed for molecular systems containing up to 10 041 atoms. The method is applied to the study of the binding of α-cyclodextrin to polyethylene glycol, and the calculated IR spectrum of an epoxy amine oligomer reproduces experiment reasonably well.

Classical density functional theory and the phase-field crystal method using a rational function to describe the two-body direct correlation function.

PubMed

Pisutha-Arnond, N; Chan, V W L; Iyer, M; Gavini, V; Thornton, K

2013-01-01

We introduce a new approach to represent a two-body direct correlation function (DCF) in order to alleviate the computational demand of classical density functional theory (CDFT) and enhance the predictive capability of the phase-field crystal (PFC) method. The approach utilizes a rational function fit (RFF) to approximate the two-body DCF in Fourier space. We use the RFF to show that short-wavelength contributions of the two-body DCF play an important role in determining the thermodynamic properties of materials. We further show that using the RFF to empirically parametrize the two-body DCF allows us to obtain the thermodynamic properties of solids and liquids that agree with the results of CDFT simulations with the full two-body DCF without incurring significant computational costs. In addition, the RFF can also be used to improve the representation of the two-body DCF in the PFC method. Last, the RFF allows for a real-space reformulation of the CDFT and PFC method, which enables descriptions of nonperiodic systems and the use of nonuniform and adaptive grids.

Reporting Recommended Patch Density from Vehicle Panel Vibration Convergence Studies using both DAF and TBL Fits of the Spatial Correlation Function

NASA Technical Reports Server (NTRS)

Smith, Andrew M.; Davis, Robert Ben; LaVerde, Bruce T.; Jones, Douglas C.; Band, Jonathon L.

2012-01-01

Using the patch method to represent the continuous spatial correlation function of a phased pressure field over a structural surface is an approximation. The approximation approaches the continuous function as patches become smaller. Plotting comparisons of the approximation vs the continuous function may provide insight revealing: (1) For what patch size/density should the approximation be very good? (2) What the approximation looks like when it begins to break down? (3) What the approximation looks like when the patch size is grossly too large. Following these observations with a convergence study using one FEM may allow us to see the importance of patch density. We may develop insights that help us to predict sufficient patch density to provide adequate convergence for the intended purpose frequency range of interest

A reformulation of the coupled perturbed self-consistent field equations entirely within a local atomic orbital density matrix-based scheme

NASA Astrophysics Data System (ADS)

Ochsenfeld, Christian; Head-Gordon, Martin

1997-05-01

To exploit the exponential decay found in numerical studies for the density matrix and its derivative with respect to nuclear displacements, we reformulate the coupled perturbed self-consistent field (CPSCF) equations and a quadratically convergent SCF (QCSCF) method for Hartree-Fock and density functional theory within a local density matrix-based scheme. Our D-CPSCF (density matrix-based CPSCF) and D-QCSCF schemes open the way for exploiting sparsity and to achieve asymptotically linear scaling of computational complexity with molecular size ( M), in case of D-CPSCF for all O( M) derivative densities. Furthermore, these methods are even for small molecules strongly competitive to conventional algorithms.

Method of altering the effective bulk density of solid material and the resulting product

DOEpatents

Kool, Lawrence B.; Nolen, Robert L.; Solomon, David E.

1983-01-01

A method of adjustably tailoring the effective bulk density of a solid material in which a mixture comprising the solid material, a film-forming polymer and a volatile solvent are sprayed into a drying chamber such that the solvent evaporates and the polymer dries into hollow shells having the solid material captured within the shell walls. Shell density may be varied as a function of solid/polymer concentration, droplet size and drying temperature.

Measuring the Autocorrelation Function of Nanoscale Three-Dimensional Density Distribution in Individual Cells Using Scanning Transmission Electron Microscopy, Atomic Force Microscopy, and a New Deconvolution Algorithm.

PubMed

Li, Yue; Zhang, Di; Capoglu, Ilker; Hujsak, Karl A; Damania, Dhwanil; Cherkezyan, Lusik; Roth, Eric; Bleher, Reiner; Wu, Jinsong S; Subramanian, Hariharan; Dravid, Vinayak P; Backman, Vadim

2017-06-01

Essentially all biological processes are highly dependent on the nanoscale architecture of the cellular components where these processes take place. Statistical measures, such as the autocorrelation function (ACF) of the three-dimensional (3D) mass-density distribution, are widely used to characterize cellular nanostructure. However, conventional methods of reconstruction of the deterministic 3D mass-density distribution, from which these statistical measures can be calculated, have been inadequate for thick biological structures, such as whole cells, due to the conflict between the need for nanoscale resolution and its inverse relationship with thickness after conventional tomographic reconstruction. To tackle the problem, we have developed a robust method to calculate the ACF of the 3D mass-density distribution without tomography. Assuming the biological mass distribution is isotropic, our method allows for accurate statistical characterization of the 3D mass-density distribution by ACF with two data sets: a single projection image by scanning transmission electron microscopy and a thickness map by atomic force microscopy. Here we present validation of the ACF reconstruction algorithm, as well as its application to calculate the statistics of the 3D distribution of mass-density in a region containing the nucleus of an entire mammalian cell. This method may provide important insights into architectural changes that accompany cellular processes.

Measuring the Autocorrelation Function of Nanoscale Three-Dimensional Density Distribution in Individual Cells Using Scanning Transmission Electron Microscopy, Atomic Force Microscopy, and a New Deconvolution Algorithm

PubMed Central

Li, Yue; Zhang, Di; Capoglu, Ilker; Hujsak, Karl A.; Damania, Dhwanil; Cherkezyan, Lusik; Roth, Eric; Bleher, Reiner; Wu, Jinsong S.; Subramanian, Hariharan; Dravid, Vinayak P.; Backman, Vadim

2018-01-01

Essentially all biological processes are highly dependent on the nanoscale architecture of the cellular components where these processes take place. Statistical measures, such as the autocorrelation function (ACF) of the three-dimensional (3D) mass–density distribution, are widely used to characterize cellular nanostructure. However, conventional methods of reconstruction of the deterministic 3D mass–density distribution, from which these statistical measures can be calculated, have been inadequate for thick biological structures, such as whole cells, due to the conflict between the need for nanoscale resolution and its inverse relationship with thickness after conventional tomographic reconstruction. To tackle the problem, we have developed a robust method to calculate the ACF of the 3D mass–density distribution without tomography. Assuming the biological mass distribution is isotropic, our method allows for accurate statistical characterization of the 3D mass–density distribution by ACF with two data sets: a single projection image by scanning transmission electron microscopy and a thickness map by atomic force microscopy. Here we present validation of the ACF reconstruction algorithm, as well as its application to calculate the statistics of the 3D distribution of mass–density in a region containing the nucleus of an entire mammalian cell. This method may provide important insights into architectural changes that accompany cellular processes. PMID:28416035

An Efficient Acoustic Density Estimation Method with Human Detectors Applied to Gibbons in Cambodia.

PubMed

Kidney, Darren; Rawson, Benjamin M; Borchers, David L; Stevenson, Ben C; Marques, Tiago A; Thomas, Len

2016-01-01

Some animal species are hard to see but easy to hear. Standard visual methods for estimating population density for such species are often ineffective or inefficient, but methods based on passive acoustics show more promise. We develop spatially explicit capture-recapture (SECR) methods for territorial vocalising species, in which humans act as an acoustic detector array. We use SECR and estimated bearing data from a single-occasion acoustic survey of a gibbon population in northeastern Cambodia to estimate the density of calling groups. The properties of the estimator are assessed using a simulation study, in which a variety of survey designs are also investigated. We then present a new form of the SECR likelihood for multi-occasion data which accounts for the stochastic availability of animals. In the context of gibbon surveys this allows model-based estimation of the proportion of groups that produce territorial vocalisations on a given day, thereby enabling the density of groups, instead of the density of calling groups, to be estimated. We illustrate the performance of this new estimator by simulation. We show that it is possible to estimate density reliably from human acoustic detections of visually cryptic species using SECR methods. For gibbon surveys we also show that incorporating observers' estimates of bearings to detected groups substantially improves estimator performance. Using the new form of the SECR likelihood we demonstrate that estimates of availability, in addition to population density and detection function parameters, can be obtained from multi-occasion data, and that the detection function parameters are not confounded with the availability parameter. This acoustic SECR method provides a means of obtaining reliable density estimates for territorial vocalising species. It is also efficient in terms of data requirements since since it only requires routine survey data. We anticipate that the low-tech field requirements will make this method an attractive option in many situations where populations can be surveyed acoustically by humans.

Inferring probabilistic stellar rotation periods using Gaussian processes

NASA Astrophysics Data System (ADS)

Angus, Ruth; Morton, Timothy; Aigrain, Suzanne; Foreman-Mackey, Daniel; Rajpaul, Vinesh

2018-02-01

Variability in the light curves of spotted, rotating stars is often non-sinusoidal and quasi-periodic - spots move on the stellar surface and have finite lifetimes, causing stellar flux variations to slowly shift in phase. A strictly periodic sinusoid therefore cannot accurately model a rotationally modulated stellar light curve. Physical models of stellar surfaces have many drawbacks preventing effective inference, such as highly degenerate or high-dimensional parameter spaces. In this work, we test an appropriate effective model: a Gaussian Process with a quasi-periodic covariance kernel function. This highly flexible model allows sampling of the posterior probability density function of the periodic parameter, marginalizing over the other kernel hyperparameters using a Markov Chain Monte Carlo approach. To test the effectiveness of this method, we infer rotation periods from 333 simulated stellar light curves, demonstrating that the Gaussian process method produces periods that are more accurate than both a sine-fitting periodogram and an autocorrelation function method. We also demonstrate that it works well on real data, by inferring rotation periods for 275 Kepler stars with previously measured periods. We provide a table of rotation periods for these and many more, altogether 1102 Kepler objects of interest, and their posterior probability density function samples. Because this method delivers posterior probability density functions, it will enable hierarchical studies involving stellar rotation, particularly those involving population modelling, such as inferring stellar ages, obliquities in exoplanet systems, or characterizing star-planet interactions. The code used to implement this method is available online.

Recent progress in density functional theory

NASA Astrophysics Data System (ADS)

Truhlar, Donald

2014-03-01

Ongoing work involves several areas of density functional theory: new methods for computing electronic excitation energies, including a new way to remove spin contamination in the spin-flip Tamm-Dancoff approximation and a configuration-interaction-corrected Tamm-Dancoff Approximation for treating conical intersections; new ways to treat open-shell states, including a reinterpreted broken-symmetry method and multi-configuration Kohn-Sham theory; a new exchange-correlation functional; new tests of density functional theory against databases for electronic transition energies and molecules and solids containing metal atoms; and applications. A selection of results will be presented. I am grateful to the following collaborators for contributions to the ongoing work: Boris Averkiev, Rebecca Carlson, Laura Fernandez, Laura Gagliardi, Chad Hoyer, Francesc Illas, Miho Isegawa, Shaohong Li, Giovanni Li Manni, Sijie Luo, Dongxia Ma, Remi Maurice, Rubén Means-Pañeda, Roberto Peverati, Nora Planas, Prasenjit Seal, Pragya Verma, Bo Wang, Xuefei Xu, Ke R. Yang, Haoyu Yu, Wenjing Zhang, and Jingjing Zheng. Supported in part by the AFOSR and U.S. DOE.

A Wigner Monte Carlo approach to density functional theory

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

Sellier, J.M., E-mail: jeanmichel.sellier@gmail.com; Dimov, I.

2014-08-01

In order to simulate quantum N-body systems, stationary and time-dependent density functional theories rely on the capacity of calculating the single-electron wave-functions of a system from which one obtains the total electron density (Kohn–Sham systems). In this paper, we introduce the use of the Wigner Monte Carlo method in ab-initio calculations. This approach allows time-dependent simulations of chemical systems in the presence of reflective and absorbing boundary conditions. It also enables an intuitive comprehension of chemical systems in terms of the Wigner formalism based on the concept of phase-space. Finally, being based on a Monte Carlo method, it scales verymore » well on parallel machines paving the way towards the time-dependent simulation of very complex molecules. A validation is performed by studying the electron distribution of three different systems, a Lithium atom, a Boron atom and a hydrogenic molecule. For the sake of simplicity, we start from initial conditions not too far from equilibrium and show that the systems reach a stationary regime, as expected (despite no restriction is imposed in the choice of the initial conditions). We also show a good agreement with the standard density functional theory for the hydrogenic molecule. These results demonstrate that the combination of the Wigner Monte Carlo method and Kohn–Sham systems provides a reliable computational tool which could, eventually, be applied to more sophisticated problems.« less

Calculation of exchange coupling constants in triply-bridged dinuclear Cu(II) compounds based on spin-flip constricted variational density functional theory.

PubMed

Seidu, Issaka; Zhekova, Hristina R; Seth, Michael; Ziegler, Tom

2012-03-08

The performance of the second-order spin-flip constricted variational density functional theory (SF-CV(2)-DFT) for the calculation of the exchange coupling constant (J) is assessed by application to a series of triply bridged Cu(II) dinuclear complexes. A comparison of the J values based on SF-CV(2)-DFT with those obtained by the broken symmetry (BS) DFT method and experiment is provided. It is demonstrated that our methodology constitutes a viable alternative to the BS-DFT method. The strong dependence of the calculated exchange coupling constants on the applied functionals is demonstrated. Both SF-CV(2)-DFT and BS-DFT affords the best agreement with experiment for hybrid functionals.

Extending density functional embedding theory for covalently bonded systems.

PubMed

Yu, Kuang; Carter, Emily A

2017-12-19

Quantum embedding theory aims to provide an efficient solution to obtain accurate electronic energies for systems too large for full-scale, high-level quantum calculations. It adopts a hierarchical approach that divides the total system into a small embedded region and a larger environment, using different levels of theory to describe each part. Previously, we developed a density-based quantum embedding theory called density functional embedding theory (DFET), which achieved considerable success in metals and semiconductors. In this work, we extend DFET into a density-matrix-based nonlocal form, enabling DFET to study the stronger quantum couplings between covalently bonded subsystems. We name this theory density-matrix functional embedding theory (DMFET), and we demonstrate its performance in several test examples that resemble various real applications in both chemistry and biochemistry. DMFET gives excellent results in all cases tested thus far, including predicting isomerization energies, proton transfer energies, and highest occupied molecular orbital-lowest unoccupied molecular orbital gaps for local chromophores. Here, we show that DMFET systematically improves the quality of the results compared with the widely used state-of-the-art methods, such as the simple capped cluster model or the widely used ONIOM method.

Peripheral transverse densities of the baryon octet from chiral effective field theory and dispersion analysis

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

Alarcón, J. M.; Hiller Blin, A. N.; Vicente Vacas, M. J.

2017-05-08

The baryon electromagnetic form factors are expressed in terms of two-dimensional densities describing the distribution of charge and magnetization in transverse space at fixed light-front time. In this paper, we calculate the transverse densities of the spin-1/2 flavor-octet baryons at peripheral distances b=O(Mmore » $$-1\\atop{π}$$) using methods of relativistic chiral effective field theory (χ EFT) and dispersion analysis. The densities are represented as dispersive integrals over the imaginary parts of the form factors in the timelike region (spectral functions). The isovector spectral functions on the two-pion cut t > 4 M$$2\\atop{π}$$ are calculated using relativistic χEFT including octet and decuplet baryons. The χEFT calculations are extended into the ρ meson mass region using an N/D method that incorporates the pion electromagnetic form factor data. The isoscalar spectral functions are modeled by vector meson poles. We compute the peripheral charge and magnetization densities in the octet baryon states, estimate the uncertainties, and determine the quark flavor decomposition. Finally, the approach can be extended to baryon form factors of other operators and the moments of generalized parton distributions.« less

NMR shieldings from density functional perturbation theory: GIPAW versus all-electron calculations

NASA Astrophysics Data System (ADS)

de Wijs, G. A.; Laskowski, R.; Blaha, P.; Havenith, R. W. A.; Kresse, G.; Marsman, M.

2017-02-01

We present a benchmark of the density functional linear response calculation of NMR shieldings within the gauge-including projector-augmented-wave method against all-electron augmented-plane-wave+local-orbital and uncontracted Gaussian basis set results for NMR shieldings in molecular and solid state systems. In general, excellent agreement between the aforementioned methods is obtained. Scalar relativistic effects are shown to be quite large for nuclei in molecules in the deshielded limit. The small component makes up a substantial part of the relativistic corrections.

NMR shieldings from density functional perturbation theory: GIPAW versus all-electron calculations.

PubMed

de Wijs, G A; Laskowski, R; Blaha, P; Havenith, R W A; Kresse, G; Marsman, M

2017-02-14

We present a benchmark of the density functional linear response calculation of NMR shieldings within the gauge-including projector-augmented-wave method against all-electron augmented-plane-wave+local-orbital and uncontracted Gaussian basis set results for NMR shieldings in molecular and solid state systems. In general, excellent agreement between the aforementioned methods is obtained. Scalar relativistic effects are shown to be quite large for nuclei in molecules in the deshielded limit. The small component makes up a substantial part of the relativistic corrections.

Statistics of some atmospheric turbulence records relevant to aircraft response calculations

NASA Technical Reports Server (NTRS)

Mark, W. D.; Fischer, R. W.

1981-01-01

Methods for characterizing atmospheric turbulence are described. The methods illustrated include maximum likelihood estimation of the integral scale and intensity of records obeying the von Karman transverse power spectral form, constrained least-squares estimation of the parameters of a parametric representation of autocorrelation functions, estimation of the power spectra density of the instantaneous variance of a record with temporally fluctuating variance, and estimation of the probability density functions of various turbulence components. Descriptions of the computer programs used in the computations are given, and a full listing of these programs is included.

How Well Can Modern Density Functionals Predict Internuclear Distances at Transition States?

PubMed

Xu, Xuefei; Alecu, I M; Truhlar, Donald G

2011-06-14

We introduce a new database called TSG48 containing 48 transition state geometrical data (in particular, internuclear distances in transition state structures) for 16 main group reactions. The 16 reactions are the 12 reactions in the previously published DBH24 database (which includes hydrogen transfer reactions, heavy-atom transfer reactions, nucleophilic substitution reactions, and association reactions plus one unimolecular isomerization) plus four H-transfer reactions in which a hydrogen atom is abstracted by the methyl or hydroperoxyl radical from the two different positions in methanol. The data in TSG48 include data for four reactions that have previously been treated at a very high level in the literature. These data are used to test and validate methods that are affordable for the entire test suite, and the most accurate of these methods is found to be the multilevel BMC-CCSD method. The data that constitute the TSG48 database are therefore taken to consist of these very high level calculations for the four reactions where they are available and BMC-CCSD calculations for the other 12 reactions. The TSG48 database is used to assess the performance of the eight Minnesota density functionals from the M05-M08 families and 26 other high-performance and popular density functionals for locating transition state geometries. For comparison, the MP2 and QCISD wave function methods have also been tested for transition state geometries. The MC3BB and MC3MPW doubly hybrid functionals and the M08-HX and M06-2X hybrid meta-GGAs are found to have the best performance of all of the density functionals tested. M08-HX is the most highly recommended functional due to the excellent performance for all five subsets of TSG48, as well as having a lower cost when compared to doubly hybrid functionals. The mean absolute errors in transition state internuclear distances associated with breaking and forming bonds as calculated by the B2PLYP, MP2, and B3LYP methods are respectively about 2, 3, and 5 times larger than those calculated by MC3BB and M08-HX.

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.

Self-Consistent Optimization of Excited States within Density-Functional Tight-Binding.

PubMed

Kowalczyk, Tim; Le, Khoa; Irle, Stephan

2016-01-12

We present an implementation of energies and gradients for the ΔDFTB method, an analogue of Δ-self-consistent-field density functional theory (ΔSCF) within density-functional tight-binding, for the lowest singlet excited state of closed-shell molecules. Benchmarks of ΔDFTB excitation energies, optimized geometries, Stokes shifts, and vibrational frequencies reveal that ΔDFTB provides a qualitatively correct description of changes in molecular geometries and vibrational frequencies due to excited-state relaxation. The accuracy of ΔDFTB Stokes shifts is comparable to that of ΔSCF-DFT, and ΔDFTB performs similarly to ΔSCF with the PBE functional for vertical excitation energies of larger chromophores where the need for efficient excited-state methods is most urgent. We provide some justification for the use of an excited-state reference density in the DFTB expansion of the electronic energy and demonstrate that ΔDFTB preserves many of the properties of its parent ΔSCF approach. This implementation fills an important gap in the extended framework of DFTB, where access to excited states has been limited to the time-dependent linear-response approach, and affords access to rapid exploration of a valuable class of excited-state potential energy surfaces.

Orthogonality of embedded wave functions for different states in frozen-density embedding theory

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

Zech, Alexander; Wesolowski, Tomasz A.; Aquilante, Francesco

2015-10-28

Other than lowest-energy stationary embedded wave functions obtained in Frozen-Density Embedding Theory (FDET) [T. A. Wesolowski, Phys. Rev. A 77, 012504 (2008)] can be associated with electronic excited states but they can be mutually non-orthogonal. Although this does not violate any physical principles — embedded wave functions are only auxiliary objects used to obtain stationary densities — working with orthogonal functions has many practical advantages. In the present work, we show numerically that excitation energies obtained using conventional FDET calculations (allowing for non-orthogonality) can be obtained using embedded wave functions which are strictly orthogonal. The used method preserves the mathematicalmore » structure of FDET and self-consistency between energy, embedded wave function, and the embedding potential (they are connected through the Euler-Lagrange equations). The orthogonality is built-in through the linearization in the embedded density of the relevant components of the total energy functional. Moreover, we show formally that the differences between the expectation values of the embedded Hamiltonian are equal to the excitation energies, which is the exact result within linearized FDET. Linearized FDET is shown to be a robust approximation for a large class of reference densities.« less

An improved numerical method for the kernel density functional estimation of disperse flow

NASA Astrophysics Data System (ADS)

Smith, Timothy; Ranjan, Reetesh; Pantano, Carlos

2014-11-01

We present an improved numerical method to solve the transport equation for the one-point particle density function (pdf), which can be used to model disperse flows. The transport equation, a hyperbolic partial differential equation (PDE) with a source term, is derived from the Lagrangian equations for a dilute particle system by treating position and velocity as state-space variables. The method approximates the pdf by a discrete mixture of kernel density functions (KDFs) with space and time varying parameters and performs a global Rayleigh-Ritz like least-square minimization on the state-space of velocity. Such an approximation leads to a hyperbolic system of PDEs for the KDF parameters that cannot be written completely in conservation form. This system is solved using a numerical method that is path-consistent, according to the theory of non-conservative hyperbolic equations. The resulting formulation is a Roe-like update that utilizes the local eigensystem information of the linearized system of PDEs. We will present the formulation of the base method, its higher-order extension and further regularization to demonstrate that the method can predict statistics of disperse flows in an accurate, consistent and efficient manner. This project was funded by NSF Project NSF-DMS 1318161.

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

Local density approximation in site-occupation embedding theory

NASA Astrophysics Data System (ADS)

Senjean, Bruno; Tsuchiizu, Masahisa; Robert, Vincent; Fromager, Emmanuel

2017-01-01

Site-occupation embedding theory (SOET) is a density functional theory (DFT)-based method which aims at modelling strongly correlated electrons. It is in principle exact and applicable to model and quantum chemical Hamiltonians. The theory is presented here for the Hubbard Hamiltonian. In contrast to conventional DFT approaches, the site (or orbital) occupations are deduced in SOET from a partially interacting system consisting of one (or more) impurity site(s) and non-interacting bath sites. The correlation energy of the bath is then treated implicitly by means of a site-occupation functional. In this work, we propose a simple impurity-occupation functional approximation based on the two-level (2L) Hubbard model which is referred to as two-level impurity local density approximation (2L-ILDA). Results obtained on a prototypical uniform eight-site Hubbard ring are promising. The extension of the method to larger systems and more sophisticated model Hamiltonians is currently in progress.

Structure determination and characterization of two rare-earth molybdenum borate compounds: LnMoBO(6) (Ln = La, Ce).

PubMed

Zhao, Dan; Cheng, Wen-Dan; Zhang, Hao; Hang, Shu-Ping; Fang, Ming

2008-07-28

The structural, optical, and electronic properties of two rare-earth molybdenum borate compounds, LnMoBO(6) (Ln = La, Ce), have been investigated by means of single-crystal X-ray diffraction, elemental analyses, and spectral measurements, as well as calculations of energy band structures, density of states, and optical response functions by the density functional method. The title compounds, which crystallize in monoclinic space group P2(1)/c, possess a similar network of interconnected [Ce(2)(MoO(4))(2)](2+) chains and [BO(2)](-) wavy chains. Novel 1D molybdenum oxide chains are contained in their three-dimensional (3D) networks. The calculated results of crystal energy band structure by the density functional theory (DFT) method show that the solid-state compound LaMoBO(6) is a semiconductor with indirect band gaps.

The exact solution of the monoenergetic transport equation for critical cylinders

NASA Technical Reports Server (NTRS)

Westfall, R. M.; Metcalf, D. R.

1972-01-01

An analytic solution for the critical, monoenergetic, bare, infinite cylinder is presented. The solution is obtained by modifying a previous development based on a neutron density transform and Case's singular eigenfunction method. Numerical results for critical radii and the neutron density as a function of position are included and compared with the results of other methods.

Generalized-active-space pair-density functional theory: an efficient method to study large, strongly correlated, conjugated systems

DOE PAGES

Ghosh, Soumen; Cramer, Christopher J.; Truhlar, Donald G.; ...

2017-01-19

Predicting ground- and excited-state properties of open-shell organic molecules by electronic structure theory can be challenging because an accurate treatment has to correctly describe both static and dynamic electron correlation. Strongly correlated systems, i.e., systems with near-degeneracy correlation effects, are particularly troublesome. Multiconfigurational wave function methods based on an active space are adequate in principle, but it is impractical to capture most of the dynamic correlation in these methods for systems characterized by many active electrons. Here, we recently developed a new method called multiconfiguration pair-density functional theory (MC-PDFT), that combines the advantages of wave function theory and density functionalmore » theory to provide a more practical treatment of strongly correlated systems. Here we present calculations of the singlet–triplet gaps in oligoacenes ranging from naphthalene to dodecacene. Calculations were performed for unprecedently large orbitally optimized active spaces of 50 electrons in 50 orbitals, and we test a range of active spaces and active space partitions, including four kinds of frontier orbital partitions. We show that MC-PDFT can predict the singlet–triplet splittings for oligoacenes consistent with the best available and much more expensive methods, and indeed MC-PDFT may constitute the benchmark against which those other models should be compared, given the absence of experimental data.« less

Generalized-active-space pair-density functional theory: an efficient method to study large, strongly correlated, conjugated systems

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

Ghosh, Soumen; Cramer, Christopher J.; Truhlar, Donald G.

Predicting ground- and excited-state properties of open-shell organic molecules by electronic structure theory can be challenging because an accurate treatment has to correctly describe both static and dynamic electron correlation. Strongly correlated systems, i.e., systems with near-degeneracy correlation effects, are particularly troublesome. Multiconfigurational wave function methods based on an active space are adequate in principle, but it is impractical to capture most of the dynamic correlation in these methods for systems characterized by many active electrons. Here, we recently developed a new method called multiconfiguration pair-density functional theory (MC-PDFT), that combines the advantages of wave function theory and density functionalmore » theory to provide a more practical treatment of strongly correlated systems. Here we present calculations of the singlet–triplet gaps in oligoacenes ranging from naphthalene to dodecacene. Calculations were performed for unprecedently large orbitally optimized active spaces of 50 electrons in 50 orbitals, and we test a range of active spaces and active space partitions, including four kinds of frontier orbital partitions. We show that MC-PDFT can predict the singlet–triplet splittings for oligoacenes consistent with the best available and much more expensive methods, and indeed MC-PDFT may constitute the benchmark against which those other models should be compared, given the absence of experimental data.« less

Multiconfiguration pair-density functional theory for doublet excitation energies and excited state geometries: the excited states of CN.

PubMed

Bao, Jie J; Gagliardi, Laura; Truhlar, Donald G

2017-11-15

Multiconfiguration pair-density functional theory (MC-PDFT) is a post multiconfiguration self-consistent field (MCSCF) method with similar performance to complete active space second-order perturbation theory (CASPT2) but with greater computational efficiency. Cyano radical (CN) is a molecule whose spectrum is well established from experiments and whose excitation energies have been used as a testing ground for theoretical methods to treat excited states of open-shell systems, which are harder and much less studied than excitation energies of closed-shell singlets. In the present work, we studied the adiabatic excitation energies of CN with MC-PDFT. Then we compared this multireference (MR) method to some single-reference (SR) methods, including time-dependent density functional theory (TDDFT) and completely renormalized equation-of-motion coupled-cluster theory with singles, doubles and noniterative triples [CR-EOM-CCSD(T)]; we also compared to some other MR methods, including configuration interaction singles and doubles (MR-CISD) and multistate CASPT2 (MS-CASPT2). Through a comparison between SR and MR methods, we achieved a better appreciation of the need to use MR methods to accurately describe higher excited states, and we found that among the MR methods, MC-PDFT stands out for its accuracy for the first four states out of the five doublet states studied this paper; this shows its efficiency for calculating doublet excited states.

Stochastic chaos induced by diffusion processes with identical spectral density but different probability density functions.

PubMed

Lei, Youming; Zheng, Fan

2016-12-01

Stochastic chaos induced by diffusion processes, with identical spectral density but different probability density functions (PDFs), is investigated in selected lightly damped Hamiltonian systems. The threshold amplitude of diffusion processes for the onset of chaos is derived by using the stochastic Melnikov method together with a mean-square criterion. Two quasi-Hamiltonian systems, namely, a damped single pendulum and damped Duffing oscillator perturbed by stochastic excitations, are used as illustrative examples. Four different cases of stochastic processes are taking as the driving excitations. It is shown that in such two systems the spectral density of diffusion processes completely determines the threshold amplitude for chaos, regardless of the shape of their PDFs, Gaussian or otherwise. Furthermore, the mean top Lyapunov exponent is employed to verify analytical results. The results obtained by numerical simulations are in accordance with the analytical results. This demonstrates that the stochastic Melnikov method is effective in predicting the onset of chaos in the quasi-Hamiltonian systems.

Development of multicomponent hybrid density functional theory with polarizable continuum model for the analysis of nuclear quantum effect and solvent effect on NMR chemical shift.

PubMed

Kanematsu, Yusuke; Tachikawa, Masanori

2014-04-28

We have developed the multicomponent hybrid density functional theory [MC_(HF+DFT)] method with polarizable continuum model (PCM) for the analysis of molecular properties including both nuclear quantum effect and solvent effect. The chemical shifts and H/D isotope shifts of the picolinic acid N-oxide (PANO) molecule in chloroform and acetonitrile solvents are applied by B3LYP electron exchange-correlation functional for our MC_(HF+DFT) method with PCM (MC_B3LYP/PCM). Our MC_B3LYP/PCM results for PANO are in reasonable agreement with the corresponding experimental chemical shifts and isotope shifts. We further investigated the applicability of our method for acetylacetone in several solvents.

RADC Multi-Dimensional Signal-Processing Research Program.

DTIC Science & Technology

1980-09-30

Formulation 7 3.2.2 Methods of Accelerating Convergence 8 3.2.3 Application to Image Deblurring 8 3.2.4 Extensions 11 3.3 Convergence of Iterative Signal... noise -driven linear filters, permit development of the joint probability density function oz " kelihood function for the image. With an expression...spatial linear filter driven by white noise (see Fig. i). If the probability density function for the white noise is known, Fig. t. Model for image

The harmonic frequencies of benzene

NASA Astrophysics Data System (ADS)

Handy, Nicholas C.; Maslen, Paul E.; Amos, Roger D.; Andrews, Jamie S.; Murray, Christopher W.; Laming, Gregory J.

1992-09-01

We report calculations for the harmonic frequencies of C 6H 6 and C 6D 6. Our most sophisticated quantum chemistry values are obtained with the MP2 method and a TZ2P+f basis set (288 basis functions), which are the largest such calculations reported on benzene to date. Using the SCF density, we also calculate the frequencies using the exchange and correlation expressions of density functional theory. We compare our calculated harmonic frequencies with those deduced from experiment by Goodman, Ozkabak and Thakur. The density functional frequencies appear to be more reliable predictions than the MP2 frequencies and they are obtained at significantly less cost.

Unveiling the nature of post-linear response Z-vector method for time-dependent density functional theory.

PubMed

Pastore, Mariachiara; Assfeld, Xavier; Mosconi, Edoardo; Monari, Antonio; Etienne, Thibaud

2017-07-14

We report a theoretical study on the analysis of the relaxed one-particle difference density matrix characterizing the passage from the ground to the excited state of a molecular system, as obtained from time-dependent density functional theory. In particular, this work aims at using the physics contained in the so-called Z-vector, which differentiates between unrelaxed and relaxed difference density matrices to analyze excited states' nature. For this purpose, we introduce novel quantum-mechanical quantities, based on the detachment/attachment methodology, for analysing the Z-vector transformation for different molecules and density functional theory functionals. A derivation pathway of these novel descriptors is reported, involving a numerical integration to be performed in the Euclidean space on the density functions. This topological analysis is then applied to two sets of chromophores, and the correlation between the level of theory and the behavior of our descriptors is properly rationalized. In particular, the effect of range-separation on the relaxation amplitude is discussed. The relaxation term is finally shown to be system-specific (for a given level of theory) and independent of the number of electrons (i.e., the relaxation amplitude is not simply the result of a collective phenomenon).

High density diffusion-free nanowell arrays.

PubMed

Takulapalli, Bharath R; Qiu, Ji; Magee, D Mitchell; Kahn, Peter; Brunner, Al; Barker, Kristi; Means, Steven; Miersch, Shane; Bian, Xiaofang; Mendoza, Alex; Festa, Fernanda; Syal, Karan; Park, Jin G; LaBaer, Joshua; Wiktor, Peter

2012-08-03

Proteomics aspires to elucidate the functions of all proteins. Protein microarrays provide an important step by enabling high-throughput studies of displayed proteins. However, many functional assays of proteins include untethered intermediates or products, which could frustrate the use of planar arrays at very high densities because of diffusion to neighboring features. The nucleic acid programmable protein array (NAPPA) is a robust in situ synthesis method for producing functional proteins just-in-time, which includes steps with diffusible intermediates. We determined that diffusion of expressed proteins led to cross-binding at neighboring spots at very high densities with reduced interspot spacing. To address this limitation, we have developed an innovative platform using photolithographically etched discrete silicon nanowells and used NAPPA as a test case. This arrested protein diffusion and cross-binding. We present confined high density protein expression and display, as well as functional protein-protein interactions, in 8000 nanowell arrays. This is the highest density of individual proteins in nanovessels demonstrated on a single slide. We further present proof of principle results on ultrahigh density protein arrays capable of up to 24000 nanowells on a single slide.

First-principle study of structural, electronic and magnetic properties of (FeC)n (n = 1-8) and (FeC)8TM (TM = V, Cr, Mn and Co) clusters.

PubMed

Li, Cheng-Gang; Zhang, Jie; Zhang, Wu-Qin; Tang, Ya-Nan; Ren, Bao-Zeng; Hu, Yan-Fei

2017-12-13

The structural, electronic and magnetic properties of the (FeC) n (n = 1-8) clusters are studied using the unbiased CALYPSO structure search method and density functional theory. A combination of the PBE functional and 6-311 + G* basis set is used for determining global minima on potential energy surfaces of (FeC) n clusters. Relatively stabilities are analyzed via computing their binding energies, second order difference and HOMO-LUMO gaps. In addition, the origin of magnetic properties, spin density and density of states are discussed in detail, respectively. At last, based on the same computational method, the structures, magnetic properties and density of states are systemically investigated for the 3d (V, Cr, Mn and Co) atom doped (FeC) 8 cluster.

Low-memory iterative density fitting.

PubMed

Grajciar, Lukáš

2015-07-30

A new low-memory modification of the density fitting approximation based on a combination of a continuous fast multipole method (CFMM) and a preconditioned conjugate gradient solver is presented. Iterative conjugate gradient solver uses preconditioners formed from blocks of the Coulomb metric matrix that decrease the number of iterations needed for convergence by up to one order of magnitude. The matrix-vector products needed within the iterative algorithm are calculated using CFMM, which evaluates them with the linear scaling memory requirements only. Compared with the standard density fitting implementation, up to 15-fold reduction of the memory requirements is achieved for the most efficient preconditioner at a cost of only 25% increase in computational time. The potential of the method is demonstrated by performing density functional theory calculations for zeolite fragment with 2592 atoms and 121,248 auxiliary basis functions on a single 12-core CPU workstation. © 2015 Wiley Periodicals, Inc.

Efficient algorithm for multiconfiguration pair-density functional theory with application to the heterolytic dissociation energy of ferrocene

NASA Astrophysics Data System (ADS)

Sand, Andrew M.; Truhlar, Donald G.; Gagliardi, Laura

2017-01-01

The recently developed multiconfiguration pair-density functional theory (MC-PDFT) combines multiconfiguration wave function theory with a density functional that depends on the on-top pair density of an electronic system. In an MC-PDFT calculation, there are two steps: a conventional multiconfiguration self-consistent-field (MCSCF) calculation and a post-MCSCF evaluation of the energy with an on-top density functional. In this work, we present the details of the MC-PDFT algorithm that avoids steeply scaling steps that are present in other post-self-consistent-field multireference calculations of dynamic correlation energy. We demonstrate the favorable scaling by considering systems of H2 molecules with active spaces of several different sizes. We then apply the MC-PDFT method to calculate the heterolytic dissociation enthalpy of ferrocene. We find that MC-PDFT yields results that are at least as accurate as complete active space second-order perturbation theory and are more stable with respect to basis set, but at a fraction of the cost in both time and memory.

Efficient algorithm for multiconfiguration pair-density functional theory with application to the heterolytic dissociation energy of ferrocene.

PubMed

Sand, Andrew M; Truhlar, Donald G; Gagliardi, Laura

2017-01-21

The recently developed multiconfiguration pair-density functional theory (MC-PDFT) combines multiconfiguration wave function theory with a density functional that depends on the on-top pair density of an electronic system. In an MC-PDFT calculation, there are two steps: a conventional multiconfiguration self-consistent-field (MCSCF) calculation and a post-MCSCF evaluation of the energy with an on-top density functional. In this work, we present the details of the MC-PDFT algorithm that avoids steeply scaling steps that are present in other post-self-consistent-field multireference calculations of dynamic correlation energy. We demonstrate the favorable scaling by considering systems of H 2 molecules with active spaces of several different sizes. We then apply the MC-PDFT method to calculate the heterolytic dissociation enthalpy of ferrocene. We find that MC-PDFT yields results that are at least as accurate as complete active space second-order perturbation theory and are more stable with respect to basis set, but at a fraction of the cost in both time and memory.

Excited State Studies of Polyacenes Using the All-Order Constricted Variational Density Functional Theory with Orbital Relaxation.

PubMed

Senn, Florian; Krykunov, Mykhaylo

2015-10-22

For the polyacenes series from naphthalene to hexacene, we present the vertical singlet excitation energies 1 (1)La and 1 (1)Lb, as well as the first triplet excitation energies obtained by the all-order constricted variational density functional theory with orbital relaxation (R-CV(∞)-DFT). R-CV(∞)-DFT is a further development of variational density functional theory (CV(∞)-DFT), which has already been successfully applied for the calculation of the vertical singlet excitation energies (1)La and (1)Lb for polyacenes,15 and we show that one obtains consistent excitation energies using the local density approximation as a functional for singlet as well as for triplet excitations when going beyond the linear response theory. Furthermore, we apply self-consistent field density functional theory (ΔSCF-DFT) and compare the obtained excitation energies for the first triplet excitations T1, where, due to the character of the transition, ΔSCF-DFT and R-CV(∞)-DFT become numerically equivalent, and for the singlet excitations 1 (1)La and 1 (1)Lb, where the two methods differ.

Cetacean population density estimation from single fixed sensors using passive acoustics.

PubMed

Küsel, Elizabeth T; Mellinger, David K; Thomas, Len; Marques, Tiago A; Moretti, David; Ward, Jessica

2011-06-01

Passive acoustic methods are increasingly being used to estimate animal population density. Most density estimation methods are based on estimates of the probability of detecting calls as functions of distance. Typically these are obtained using receivers capable of localizing calls or from studies of tagged animals. However, both approaches are expensive to implement. The approach described here uses a MonteCarlo model to estimate the probability of detecting calls from single sensors. The passive sonar equation is used to predict signal-to-noise ratios (SNRs) of received clicks, which are then combined with a detector characterization that predicts probability of detection as a function of SNR. Input distributions for source level, beam pattern, and whale depth are obtained from the literature. Acoustic propagation modeling is used to estimate transmission loss. Other inputs for density estimation are call rate, obtained from the literature, and false positive rate, obtained from manual analysis of a data sample. The method is applied to estimate density of Blainville's beaked whales over a 6-day period around a single hydrophone located in the Tongue of the Ocean, Bahamas. Results are consistent with those from previous analyses, which use additional tag data. © 2011 Acoustical Society of America

Multi-scale and Multi-physics Numerical Methods for Modeling Transport in Mesoscopic Systems

DTIC Science & Technology

2014-10-13

function and wide band Fast multipole methods for Hankel waves. (2) a new linear scaling discontinuous Galerkin density functional theory, which provide a...inflow boundary condition for Wigner quantum transport equations. Also, a book titled "Computational Methods for Electromagnetic Phenomena...equationsin layered media with FMM for Bessel functions , Science China Mathematics, (12 2013): 2561. doi: TOTAL: 6 Number of Papers published in peer

An efficient method for quantum transport simulations in the time domain

NASA Astrophysics Data System (ADS)

Wang, Y.; Yam, C.-Y.; Frauenheim, Th.; Chen, G. H.; Niehaus, T. A.

2011-11-01

An approximate method based on adiabatic time dependent density functional theory (TDDFT) is presented, that allows for the description of the electron dynamics in nanoscale junctions under arbitrary time dependent external potentials. The density matrix of the device region is propagated according to the Liouville-von Neumann equation. The semi-infinite leads give rise to dissipative terms in the equation of motion which are calculated from first principles in the wide band limit. In contrast to earlier ab initio implementations of this formalism, the Hamiltonian is here approximated in the spirit of the density functional based tight-binding (DFTB) method. Results are presented for two prototypical molecular devices and compared to full TDDFT calculations. The temporal profile of the current traces is qualitatively well captured by the DFTB scheme. Steady state currents show considerable variations, both in comparison of approximate and full TDDFT, but also among TDDFT calculations with different basis sets.

A simple model to predict the biodiesel blend density as simultaneous function of blend percent and temperature.

PubMed

Gaonkar, Narayan; Vaidya, R G

2016-05-01

A simple method to estimate the density of biodiesel blend as simultaneous function of temperature and volume percent of biodiesel is proposed. Employing the Kay's mixing rule, we developed a model and investigated theoretically the density of different vegetable oil biodiesel blends as a simultaneous function of temperature and volume percent of biodiesel. Key advantage of the proposed model is that it requires only a single set of density values of components of biodiesel blends at any two different temperatures. We notice that the density of blend linearly decreases with increase in temperature and increases with increase in volume percent of the biodiesel. The lower values of standard estimate of error (SEE = 0.0003-0.0022) and absolute average deviation (AAD = 0.03-0.15 %) obtained using the proposed model indicate the predictive capability. The predicted values found good agreement with the recent available experimental data.

Electronic structure calculations of PbS quantum rods and tubes

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

Pimachev, Artem; Dahnovsky, Yuri, E-mail: yurid@uwyo.edu

2014-01-28

We study absorption spectra, optical and HOMO-LUMO gaps, and the density of states for PbS quantum rods (QRs) and tubes (QTs). We find some similarities and also differences in QR and QT properties. For both QRs and QTs, the optical and HOMO-LUMO gaps reach the plateaus for small lengths. We find that tubes are as stable as rods. The optical spectra exhibit a peak that can be due to the electron-hole interaction or be a prototype of an S{sub e}–S{sub h} transition in the effective mass approximation. We also calculate the density of states by the density functional theory (DFT)more » and time-dependent density functional theory (TDDFT) methods. The TDDFT density of states function is shifted towards the red side by 0.5 eV indicating the strong e-h interaction.« less

Transitioning NWChem to the Next Generation of Manycore Machines

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

Bylaska, Eric J.; Apra, Edoardo; Kowalski, Karol

The NorthWest Chemistry (NWChem) modeling software is a popular molecular chemistry simulation software that was designed from the start to work on massively parallel processing supercomputers[6, 28, 49]. It contains an umbrella of modules that today includes Self Consistent Field (SCF), second order Mller-Plesset perturbation theory (MP2), Coupled Cluster, multi-conguration selfconsistent eld (MCSCF), selected conguration interaction (CI), tensor contraction engine (TCE) many body methods, density functional theory (DFT), time-dependent density functional theory (TDDFT), real time time-dependent density functional theory, pseudopotential plane-wave density functional theory (PSPW), band structure (BAND), ab initio molecular dynamics, Car-Parrinello molecular dynamics, classical molecular dynamics (MD), QM/MM,more » AIMD/MM, GIAO NMR, COSMO, COSMO-SMD, and RISM solvation models, free energy simulations, reaction path optimization, parallel in time, among other capabilities[ 22]. Moreover new capabilities continue to be added with each new release.« less

Communication: Density functional theory model for multi-reference systems based on the exact-exchange hole normalization

NASA Astrophysics Data System (ADS)

Laqua, Henryk; Kussmann, Jörg; Ochsenfeld, Christian

2018-03-01

The correct description of multi-reference electronic ground states within Kohn-Sham density functional theory (DFT) requires an ensemble-state representation, employing fractionally occupied orbitals. However, the use of fractional orbital occupation leads to non-normalized exact-exchange holes, resulting in large fractional-spin errors for conventional approximative density functionals. In this communication, we present a simple approach to directly include the exact-exchange-hole normalization into DFT. Compared to conventional functionals, our model strongly improves the description for multi-reference systems, while preserving the accuracy in the single-reference case. We analyze the performance of our proposed method at the example of spin-averaged atoms and spin-restricted bond dissociation energy surfaces.

Gentlest ascent dynamics for calculating first excited state and exploring energy landscape of Kohn-Sham density functionals.

PubMed

Li, Chen; Lu, Jianfeng; Yang, Weitao

2015-12-14

We develop the gentlest ascent dynamics for Kohn-Sham density functional theory to search for the index-1 saddle points on the energy landscape of the Kohn-Sham density functionals. These stationary solutions correspond to excited states in the ground state functionals. As shown by various examples, the first excited states of many chemical systems are given by these index-1 saddle points. Our novel approach provides an alternative, more robust way to obtain these excited states, compared with the widely used ΔSCF approach. The method can be easily generalized to target higher index saddle points. Our results also reveal the physical interest and relevance of studying the Kohn-Sham energy landscape.

Probability density function learning by unsupervised neurons.

PubMed

Fiori, S

2001-10-01

In a recent work, we introduced the concept of pseudo-polynomial adaptive activation function neuron (FAN) and presented an unsupervised information-theoretic learning theory for such structure. The learning model is based on entropy optimization and provides a way of learning probability distributions from incomplete data. The aim of the present paper is to illustrate some theoretical features of the FAN neuron, to extend its learning theory to asymmetrical density function approximation, and to provide an analytical and numerical comparison with other known density function estimation methods, with special emphasis to the universal approximation ability. The paper also provides a survey of PDF learning from incomplete data, as well as results of several experiments performed on real-world problems and signals.

Communication: Density functional theory model for multi-reference systems based on the exact-exchange hole normalization.

PubMed

Laqua, Henryk; Kussmann, Jörg; Ochsenfeld, Christian

2018-03-28

The correct description of multi-reference electronic ground states within Kohn-Sham density functional theory (DFT) requires an ensemble-state representation, employing fractionally occupied orbitals. However, the use of fractional orbital occupation leads to non-normalized exact-exchange holes, resulting in large fractional-spin errors for conventional approximative density functionals. In this communication, we present a simple approach to directly include the exact-exchange-hole normalization into DFT. Compared to conventional functionals, our model strongly improves the description for multi-reference systems, while preserving the accuracy in the single-reference case. We analyze the performance of our proposed method at the example of spin-averaged atoms and spin-restricted bond dissociation energy surfaces.

A simple method for finding explicit analytic transition densities of diffusion processes with general diploid selection.

PubMed

Song, Yun S; Steinrücken, Matthias

2012-03-01

The transition density function of the Wright-Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright-Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation-selection balance.

A Simple Method for Finding Explicit Analytic Transition Densities of Diffusion Processes with General Diploid Selection

PubMed Central

Song, Yun S.; Steinrücken, Matthias

2012-01-01

The transition density function of the Wright–Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright–Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation–selection balance. PMID:22209899

Uncertainty quantification of voice signal production mechanical model and experimental updating

NASA Astrophysics Data System (ADS)

Cataldo, E.; Soize, C.; Sampaio, R.

2013-11-01

The aim of this paper is to analyze the uncertainty quantification in a voice production mechanical model and update the probability density function corresponding to the tension parameter using the Bayes method and experimental data. Three parameters are considered uncertain in the voice production mechanical model used: the tension parameter, the neutral glottal area and the subglottal pressure. The tension parameter of the vocal folds is mainly responsible for the changing of the fundamental frequency of a voice signal, generated by a mechanical/mathematical model for producing voiced sounds. The three uncertain parameters are modeled by random variables. The probability density function related to the tension parameter is considered uniform and the probability density functions related to the neutral glottal area and the subglottal pressure are constructed using the Maximum Entropy Principle. The output of the stochastic computational model is the random voice signal and the Monte Carlo method is used to solve the stochastic equations allowing realizations of the random voice signals to be generated. For each realization of the random voice signal, the corresponding realization of the random fundamental frequency is calculated and the prior pdf of this random fundamental frequency is then estimated. Experimental data are available for the fundamental frequency and the posterior probability density function of the random tension parameter is then estimated using the Bayes method. In addition, an application is performed considering a case with a pathology in the vocal folds. The strategy developed here is important mainly due to two things. The first one is related to the possibility of updating the probability density function of a parameter, the tension parameter of the vocal folds, which cannot be measured direct and the second one is related to the construction of the likelihood function. In general, it is predefined using the known pdf. Here, it is constructed in a new and different manner, using the own system considered.

C library for topological study of the electronic charge density.

PubMed

Vega, David; Aray, Yosslen; Rodríguez, Jesús

2012-12-05

The topological study of the electronic charge density is useful to obtain information about the kinds of bonds (ionic or covalent) and the atom charges on a molecule or crystal. For this study, it is necessary to calculate, at every space point, the electronic density and its electronic density derivatives values up to second order. In this work, a grid-based method for these calculations is described. The library, implemented for three dimensions, is based on a multidimensional Lagrange interpolation in a regular grid; by differentiating the resulting polynomial, the gradient vector, the Hessian matrix and the Laplacian formulas were obtained for every space point. More complex functions such as the Newton-Raphson method (to find the critical points, where the gradient is null) and the Cash-Karp Runge-Kutta method (used to make the gradient paths) were programmed. As in some crystals, the unit cell has angles different from 90°, the described library includes linear transformations to correct the gradient and Hessian when the grid is distorted (inclined). Functions were also developed to handle grid containing files (grd from DMol® program, CUBE from Gaussian® program and CHGCAR from VASP® program). Each one of these files contains the data for a molecular or crystal electronic property (such as charge density, spin density, electrostatic potential, and others) in a three-dimensional (3D) grid. The library can be adapted to make the topological study in any regular 3D grid by modifying the code of these functions. Copyright © 2012 Wiley Periodicals, Inc.

On the way to a microscopic derivation of covariant density functionals in nuclei

NASA Astrophysics Data System (ADS)

Ring, Peter

2018-02-01

Several methods are discussed to derive covariant density functionals from the microscopic input of bare nuclear forces. In a first step there are semi-microscopic functionals, which are fitted to ab-initio calculations of nuclear matter and depend in addition on very few phenomenological parameters. They are able to describe nuclear properties with the same precision as fully phenomenological functionals. In a second step we present first relativistic Brueckner-Hartree-Fock calculations in finite nuclei in order to study properties of such functionals, which cannot be obtained from nuclear matter calculations.

Fast inversion of gravity data using the symmetric successive over-relaxation (SSOR) preconditioned conjugate gradient algorithm

NASA Astrophysics Data System (ADS)

Meng, Zhaohai; Li, Fengting; Xu, Xuechun; Huang, Danian; Zhang, Dailei

2017-02-01

The subsurface three-dimensional (3D) model of density distribution is obtained by solving an under-determined linear equation that is established by gravity data. Here, we describe a new fast gravity inversion method to recover a 3D density model from gravity data. The subsurface will be divided into a large number of rectangular blocks, each with an unknown constant density. The gravity inversion method introduces a stabiliser model norm with a depth weighting function to produce smooth models. The depth weighting function is combined with the model norm to counteract the skin effect of the gravity potential field. As the numbers of density model parameters is NZ (the number of layers in the vertical subsurface domain) times greater than the observed gravity data parameters, the inverse density parameter is larger than the observed gravity data parameters. Solving the full set of gravity inversion equations is very time-consuming, and applying a new algorithm to estimate gravity inversion can significantly reduce the number of iterations and the computational time. In this paper, a new symmetric successive over-relaxation (SSOR) iterative conjugate gradient (CG) method is shown to be an appropriate algorithm to solve this Tikhonov cost function (gravity inversion equation). The new, faster method is applied on Gaussian noise-contaminated synthetic data to demonstrate its suitability for 3D gravity inversion. To demonstrate the performance of the new algorithm on actual gravity data, we provide a case study that includes ground-based measurement of residual Bouguer gravity anomalies over the Humble salt dome near Houston, Gulf Coast Basin, off the shore of Louisiana. A 3D distribution of salt rock concentration is used to evaluate the inversion results recovered by the new SSOR iterative method. In the test model, the density values in the constructed model coincide with the known location and depth of the salt dome.

Analytic second derivative of the energy for density functional theory based on the three-body fragment molecular orbital method

NASA Astrophysics Data System (ADS)

Nakata, Hiroya; Fedorov, Dmitri G.; Zahariev, Federico; Schmidt, Michael W.; Kitaura, Kazuo; Gordon, Mark S.; Nakamura, Shinichiro

2015-03-01

Analytic second derivatives of the energy with respect to nuclear coordinates have been developed for spin restricted density functional theory (DFT) based on the fragment molecular orbital method (FMO). The derivations were carried out for the three-body expansion (FMO3), and the two-body expressions can be obtained by neglecting the three-body corrections. Also, the restricted Hartree-Fock (RHF) Hessian for FMO3 can be obtained by neglecting the density-functional related terms. In both the FMO-RHF and FMO-DFT Hessians, certain terms with small magnitudes are neglected for computational efficiency. The accuracy of the FMO-DFT Hessian in terms of the Gibbs free energy is evaluated for a set of polypeptides and water clusters and found to be within 1 kcal/mol of the corresponding full (non-fragmented) ab initio calculation. The FMO-DFT method is also applied to transition states in SN2 reactions and for the computation of the IR and Raman spectra of a small Trp-cage protein (PDB: 1L2Y). Some computational timing analysis is also presented.

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.

Electron correlation and the self-interaction error of density functional theory

NASA Astrophysics Data System (ADS)

Polo, Victor; Kraka, Elfi; Cremer, Dieter

The self-interaction error (SIE) of commonly used DFT functionals has been systematically investigated by comparing the electron density distribution ρ( r ) generated by self-interaction corrected DFT (SIC-DFT) with a series of reference densities obtained by DFT or wavefunction theory (WFT) methods that cover typical electron correlation effects. Although the SIE of GGA functionals is considerably smaller than that of LDA functionals, it has significant consequences for the coverage of electron correlation effects at the DFT level of theory. The exchange SIE mimics long range (non-dynamic) pair correlation effects, and is responsible for the fact that the electron density of DFT exchange-only calculations resembles often that of MP4, MP2 or even CCSD(T) calculations. Changes in the electron density caused by SICDFT exchange are comparable with those that are associated with HF exchange. Correlation functionals contract the density towards the bond and the valence region, thus taking negative charge out of the van der Waals region where these effects are exaggerated by the influence of the SIE of the correlation functional. Hence, SIC-DFT leads in total to a relatively strong redistribution of negative charge from van der Waals, non-bonding, and valence regions of heavy atoms to the bond regions. These changes, although much stronger, resemble those obtained when comparing the densities of hybrid functionals such as B3LYP with the corresponding GGA functional BLYP. Hence, the balanced mixing of local and non-local exchange and correlation effects as it is achieved by hybrid functionals mimics SIC-DFT and can be considered as an economic way to include some SIC into standard DFT. However, the investigation shows also that the SIC-DFT description of molecules is unreliable because the standard functionals used were optimized for DFT including the SIE.

A method to deconvolve stellar rotational velocities II. The probability distribution function via Tikhonov regularization

NASA Astrophysics Data System (ADS)

Christen, Alejandra; Escarate, Pedro; Curé, Michel; Rial, Diego F.; Cassetti, Julia

2016-10-01

Aims: Knowing the distribution of stellar rotational velocities is essential for understanding stellar evolution. Because we measure the projected rotational speed v sin I, we need to solve an ill-posed problem given by a Fredholm integral of the first kind to recover the "true" rotational velocity distribution. Methods: After discretization of the Fredholm integral we apply the Tikhonov regularization method to obtain directly the probability distribution function for stellar rotational velocities. We propose a simple and straightforward procedure to determine the Tikhonov parameter. We applied Monte Carlo simulations to prove that the Tikhonov method is a consistent estimator and asymptotically unbiased. Results: This method is applied to a sample of cluster stars. We obtain confidence intervals using a bootstrap method. Our results are in close agreement with those obtained using the Lucy method for recovering the probability density distribution of rotational velocities. Furthermore, Lucy estimation lies inside our confidence interval. Conclusions: Tikhonov regularization is a highly robust method that deconvolves the rotational velocity probability density function from a sample of v sin I data directly without the need for any convergence criteria.

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.

Laser modification of graphene oxide layers

NASA Astrophysics Data System (ADS)

Malinský, Petr; Macková, Anna; Cutroneo, Mariapompea; Siegel, Jakub; Bohačová, Marie; Klímova, Kateřina; Švorčík, Václav; Sofer, Zdenĕk

2018-01-01

The effect of linearly polarized laser irradiation with various energy densities was successfully used for reduction of graphene oxide (GO). The ion beam analytical methods (RBS, ERDA) were used to follow the elemental composition which is expected as the consequence of GO reduction. The chemical composition analysis was accompanied by structural study showing changed functionalities in the irradiated GO foils using spectroscopy techniques including XPS, FTIR and Raman spectroscopy. The AFM was employed to identify the surface morphology and electric properties evolution were subsequently studied using standard two point method measurement. The used analytical methods report on reduction of irradiated graphene oxide on the surface and the decrease of surface resistivity as a growing function of the laser beam energy density.

Fast semi-analytical method for precise prediction of ion energy distribution functions and sheath electric field in multi-frequency capacitively coupled plasmas

NASA Astrophysics Data System (ADS)

Chen, Wencong; Zhang, Xi; Diao, Dongfeng

2018-05-01

We propose a fast semi-analytical method to predict ion energy distribution functions and sheath electric field in multi-frequency capacitively coupled plasmas, which are difficult to measure in commercial plasma reactors. In the intermediate frequency regime, the ion density within the sheath is strongly modulated by the low-frequency sheath electric field, making the time-independent ion density assumption employed in conventional models invalid. Our results are in a good agreement with experimental measurements and computer simulations. The application of this method will facilitate the understanding of ion–material interaction mechanisms and development of new-generation plasma etching devices.

A unified framework for constructing, tuning and assessing photometric redshift density estimates in a selection bias setting

NASA Astrophysics Data System (ADS)

Freeman, P. E.; Izbicki, R.; Lee, A. B.

2017-07-01

Photometric redshift estimation is an indispensable tool of precision cosmology. One problem that plagues the use of this tool in the era of large-scale sky surveys is that the bright galaxies that are selected for spectroscopic observation do not have properties that match those of (far more numerous) dimmer galaxies; thus, ill-designed empirical methods that produce accurate and precise redshift estimates for the former generally will not produce good estimates for the latter. In this paper, we provide a principled framework for generating conditional density estimates (I.e. photometric redshift PDFs) that takes into account selection bias and the covariate shift that this bias induces. We base our approach on the assumption that the probability that astronomers label a galaxy (I.e. determine its spectroscopic redshift) depends only on its measured (photometric and perhaps other) properties x and not on its true redshift. With this assumption, we can explicitly write down risk functions that allow us to both tune and compare methods for estimating importance weights (I.e. the ratio of densities of unlabelled and labelled galaxies for different values of x) and conditional densities. We also provide a method for combining multiple conditional density estimates for the same galaxy into a single estimate with better properties. We apply our risk functions to an analysis of ≈106 galaxies, mostly observed by Sloan Digital Sky Survey, and demonstrate through multiple diagnostic tests that our method achieves good conditional density estimates for the unlabelled galaxies.

A method for the estimation of the significance of cross-correlations in unevenly sampled red-noise time series

NASA Astrophysics Data System (ADS)

Max-Moerbeck, W.; Richards, J. L.; Hovatta, T.; Pavlidou, V.; Pearson, T. J.; Readhead, A. C. S.

2014-11-01

We present a practical implementation of a Monte Carlo method to estimate the significance of cross-correlations in unevenly sampled time series of data, whose statistical properties are modelled with a simple power-law power spectral density. This implementation builds on published methods; we introduce a number of improvements in the normalization of the cross-correlation function estimate and a bootstrap method for estimating the significance of the cross-correlations. A closely related matter is the estimation of a model for the light curves, which is critical for the significance estimates. We present a graphical and quantitative demonstration that uses simulations to show how common it is to get high cross-correlations for unrelated light curves with steep power spectral densities. This demonstration highlights the dangers of interpreting them as signs of a physical connection. We show that by using interpolation and the Hanning sampling window function we are able to reduce the effects of red-noise leakage and to recover steep simple power-law power spectral densities. We also introduce the use of a Neyman construction for the estimation of the errors in the power-law index of the power spectral density. This method provides a consistent way to estimate the significance of cross-correlations in unevenly sampled time series of data.

A principled dimension-reduction method for the population density approach to modeling networks of neurons with synaptic dynamics.

PubMed

Ly, Cheng

2013-10-01

The population density approach to neural network modeling has been utilized in a variety of contexts. The idea is to group many similar noisy neurons into populations and track the probability density function for each population that encompasses the proportion of neurons with a particular state rather than simulating individual neurons (i.e., Monte Carlo). It is commonly used for both analytic insight and as a time-saving computational tool. The main shortcoming of this method is that when realistic attributes are incorporated in the underlying neuron model, the dimension of the probability density function increases, leading to intractable equations or, at best, computationally intensive simulations. Thus, developing principled dimension-reduction methods is essential for the robustness of these powerful methods. As a more pragmatic tool, it would be of great value for the larger theoretical neuroscience community. For exposition of this method, we consider a single uncoupled population of leaky integrate-and-fire neurons receiving external excitatory synaptic input only. We present a dimension-reduction method that reduces a two-dimensional partial differential-integral equation to a computationally efficient one-dimensional system and gives qualitatively accurate results in both the steady-state and nonequilibrium regimes. The method, termed modified mean-field method, is based entirely on the governing equations and not on any auxiliary variables or parameters, and it does not require fine-tuning. The principles of the modified mean-field method have potential applicability to more realistic (i.e., higher-dimensional) neural networks.

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.

Downlink Probability Density Functions for EOS-McMurdo Sound

NASA Technical Reports Server (NTRS)

Christopher, P.; Jackson, A. H.

1996-01-01

The visibility times and communication link dynamics for the Earth Observations Satellite (EOS)-McMurdo Sound direct downlinks have been studied. The 16 day EOS periodicity may be shown with the Goddard Trajectory Determination System (GTDS) and the entire 16 day period should be simulated for representative link statistics. We desire many attributes of the downlink, however, and a faster orbital determination method is desirable. We use the method of osculating elements for speed and accuracy in simulating the EOS orbit. The accuracy of the method of osculating elements is demonstrated by closely reproducing the observed 16 day Landsat periodicity. An autocorrelation function method is used to show the correlation spike at 16 days. The entire 16 day record of passes over McMurdo Sound is then used to generate statistics for innage time, outage time, elevation angle, antenna angle rates, and propagation loss. The levation angle probability density function is compared with 1967 analytic approximation which has been used for medium to high altitude satellites. One practical result of this comparison is seen to be the rare occurrence of zenith passes. The new result is functionally different than the earlier result, with a heavy emphasis on low elevation angles. EOS is one of a large class of sun synchronous satellites which may be downlinked to McMurdo Sound. We examine delay statistics for an entire group of sun synchronous satellites ranging from 400 km to 1000 km altitude. Outage probability density function results are presented three dimensionally.

Predictive equation of state method for heavy materials based on the Dirac equation and density functional theory

NASA Astrophysics Data System (ADS)

Wills, John M.; Mattsson, Ann E.

2012-02-01

Density functional theory (DFT) provides a formally predictive base for equation of state properties. Available approximations to the exchange/correlation functional provide accurate predictions for many materials in the periodic table. For heavy materials however, DFT calculations, using available functionals, fail to provide quantitative predictions, and often fail to be even qualitative. This deficiency is due both to the lack of the appropriate confinement physics in the exchange/correlation functional and to approximations used to evaluate the underlying equations. In order to assess and develop accurate functionals, it is essential to eliminate all other sources of error. In this talk we describe an efficient first-principles electronic structure method based on the Dirac equation and compare the results obtained with this method with other methods generally used. Implications for high-pressure equation of state of relativistic materials are demonstrated in application to Ce and the light actinides. Sandia National Laboratories is a multi-program laboratory managed andoperated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Continuation of probability density functions using a generalized Lyapunov approach

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

Baars, S., E-mail: s.baars@rug.nl; Viebahn, J.P., E-mail: viebahn@cwi.nl; Mulder, T.E., E-mail: t.e.mulder@uu.nl

Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining probability density functions of systems of stochastic partial differential equations near fixed points, under a small noise approximation. Key innovation is the efficient solution of a generalized Lyapunov equation using an iterative method involving low-rank approximations. We apply and illustrate the capabilities of the method using a problem in physical oceanography, i.e. the occurrence of multiple steady states of the Atlantic Ocean circulation.

Theoretical studies of electronically excited states

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

Besley, Nicholas A.

2014-10-06

Time-dependent density functional theory is the most widely used quantum chemical method for studying molecules in electronically excited states. However, excited states can also be computed within Kohn-Sham density functional theory by exploiting methods that converge the self-consistent field equations to give excited state solutions. The usefulness of single reference self-consistent field based approaches for studying excited states is demonstrated by considering the calculation of several types of spectroscopy including the infrared spectroscopy of molecules in an electronically excited state, the rovibrational spectrum of the NO-Ar complex, core electron binding energies and the emission spectroscopy of BODIPY in water.

Gaussian polarizable-ion tight binding.

PubMed

Boleininger, Max; Guilbert, Anne Ay; Horsfield, Andrew P

2016-10-14

To interpret ultrafast dynamics experiments on large molecules, computer simulation is required due to the complex response to the laser field. We present a method capable of efficiently computing the static electronic response of large systems to external electric fields. This is achieved by extending the density-functional tight binding method to include larger basis sets and by multipole expansion of the charge density into electrostatically interacting Gaussian distributions. Polarizabilities for a range of hydrocarbon molecules are computed for a multipole expansion up to quadrupole order, giving excellent agreement with experimental values, with average errors similar to those from density functional theory, but at a small fraction of the cost. We apply the model in conjunction with the polarizable-point-dipoles model to estimate the internal fields in amorphous poly(3-hexylthiophene-2,5-diyl).

Gaussian polarizable-ion tight binding

NASA Astrophysics Data System (ADS)

Boleininger, Max; Guilbert, Anne AY; Horsfield, Andrew P.

2016-10-01

To interpret ultrafast dynamics experiments on large molecules, computer simulation is required due to the complex response to the laser field. We present a method capable of efficiently computing the static electronic response of large systems to external electric fields. This is achieved by extending the density-functional tight binding method to include larger basis sets and by multipole expansion of the charge density into electrostatically interacting Gaussian distributions. Polarizabilities for a range of hydrocarbon molecules are computed for a multipole expansion up to quadrupole order, giving excellent agreement with experimental values, with average errors similar to those from density functional theory, but at a small fraction of the cost. We apply the model in conjunction with the polarizable-point-dipoles model to estimate the internal fields in amorphous poly(3-hexylthiophene-2,5-diyl).

Calibration and evaluation of a nuclear density and moisture measuring apparatus.

DOT National Transportation Integrated Search

1963-11-01

The research objectives of this project were to investigate a new : method of in-place determination of soils densities and moisture levels : employing a nuclear physics principle of the gamma radiation function as : the measurement technique, with s...

Statistics of Smoothed Cosmic Fields in Perturbation Theory. I. Formulation and Useful Formulae in Second-Order Perturbation Theory

NASA Astrophysics Data System (ADS)

Matsubara, Takahiko

2003-02-01

We formulate a general method for perturbative evaluations of statistics of smoothed cosmic fields and provide useful formulae for application of the perturbation theory to various statistics. This formalism is an extensive generalization of the method used by Matsubara, who derived a weakly nonlinear formula of the genus statistic in a three-dimensional density field. After describing the general method, we apply the formalism to a series of statistics, including genus statistics, level-crossing statistics, Minkowski functionals, and a density extrema statistic, regardless of the dimensions in which each statistic is defined. The relation between the Minkowski functionals and other geometrical statistics is clarified. These statistics can be applied to several cosmic fields, including three-dimensional density field, three-dimensional velocity field, two-dimensional projected density field, and so forth. The results are detailed for second-order theory of the formalism. The effect of the bias is discussed. The statistics of smoothed cosmic fields as functions of rescaled threshold by volume fraction are discussed in the framework of second-order perturbation theory. In CDM-like models, their functional deviations from linear predictions plotted against the rescaled threshold are generally much smaller than that plotted against the direct threshold. There is still a slight meatball shift against rescaled threshold, which is characterized by asymmetry in depths of troughs in the genus curve. A theory-motivated asymmetry factor in the genus curve is proposed.

PAREMD: A parallel program for the evaluation of momentum space properties of atoms and molecules

NASA Astrophysics Data System (ADS)

Meena, Deep Raj; Gadre, Shridhar R.; Balanarayan, P.

2018-03-01

The present work describes a code for evaluating the electron momentum density (EMD), its moments and the associated Shannon information entropy for a multi-electron molecular system. The code works specifically for electronic wave functions obtained from traditional electronic structure packages such as GAMESS and GAUSSIAN. For the momentum space orbitals, the general expression for Gaussian basis sets in position space is analytically Fourier transformed to momentum space Gaussian basis functions. The molecular orbital coefficients of the wave function are taken as an input from the output file of the electronic structure calculation. The analytic expressions of EMD are evaluated over a fine grid and the accuracy of the code is verified by a normalization check and a numerical kinetic energy evaluation which is compared with the analytic kinetic energy given by the electronic structure package. Apart from electron momentum density, electron density in position space has also been integrated into this package. The program is written in C++ and is executed through a Shell script. It is also tuned for multicore machines with shared memory through OpenMP. The program has been tested for a variety of molecules and correlated methods such as CISD, Møller-Plesset second order (MP2) theory and density functional methods. For correlated methods, the PAREMD program uses natural spin orbitals as an input. The program has been benchmarked for a variety of Gaussian basis sets for different molecules showing a linear speedup on a parallel architecture.

Calculation of nuclear spin-spin coupling constants using frozen density embedding

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

Götz, Andreas W., E-mail: agoetz@sdsc.edu; Autschbach, Jochen; Visscher, Lucas, E-mail: visscher@chem.vu.nl

2014-03-14

We present a method for a subsystem-based calculation of indirect nuclear spin-spin coupling tensors within the framework of current-spin-density-functional theory. Our approach is based on the frozen-density embedding scheme within density-functional theory and extends a previously reported subsystem-based approach for the calculation of nuclear magnetic resonance shielding tensors to magnetic fields which couple not only to orbital but also spin degrees of freedom. This leads to a formulation in which the electron density, the induced paramagnetic current, and the induced spin-magnetization density are calculated separately for the individual subsystems. This is particularly useful for the inclusion of environmental effects inmore » the calculation of nuclear spin-spin coupling constants. Neglecting the induced paramagnetic current and spin-magnetization density in the environment due to the magnetic moments of the coupled nuclei leads to a very efficient method in which the computationally expensive response calculation has to be performed only for the subsystem of interest. We show that this approach leads to very good results for the calculation of solvent-induced shifts of nuclear spin-spin coupling constants in hydrogen-bonded systems. Also for systems with stronger interactions, frozen-density embedding performs remarkably well, given the approximate nature of currently available functionals for the non-additive kinetic energy. As an example we show results for methylmercury halides which exhibit an exceptionally large shift of the one-bond coupling constants between {sup 199}Hg and {sup 13}C upon coordination of dimethylsulfoxide solvent molecules.« less

Quest for a universal density functional: the accuracy of density functionals across a broad spectrum of databases in chemistry and physics.

PubMed

Peverati, Roberto; Truhlar, Donald G

2014-03-13

Kohn-Sham density functional theory is in principle an exact formulation of quantum mechanical electronic structure theory, but in practice we have to rely on approximate exchange-correlation (xc) functionals. The objective of our work has been to design an xc functional with broad accuracy across as wide an expanse of chemistry and physics as possible, leading--as a long-range goal--to a functional with good accuracy for all problems, i.e. a universal functional. To guide our path towards that goal and to measure our progress, we have developed-building on earlier work of our group-a set of databases of reference data for a variety of energetic and structural properties in chemistry and physics. These databases include energies of molecular processes, such as atomization, complexation, proton addition and ionization; they also include molecular geometries and solid-state lattice constants, chemical reaction barrier heights, and cohesive energies and band gaps of solids. For this paper, we gather many of these databases into four comprehensive databases, two with 384 energetic data for chemistry and solid-state physics and another two with 68 structural data for chemistry and solid-state physics, and we test two wave function methods and 77 density functionals (12 Minnesota meta functionals and 65 others) in a consistent way across this same broad set of data. We especially highlight the Minnesota density functionals, but the results have broader implications in that one may see the successes and failures of many kinds of density functionals when they are all applied to the same data. Therefore, the results provide a status report on the quest for a universal functional.

First-row diatomics: Calculation of the geometry and energetics using self-consistent gradient-functional approximations

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

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

1992-02-15

A fully self-consistent series of nonlocal (gradient) density-functional calculations has been carried out using the augmented-Gaussian-orbital method to determine the magnitude of gradient corrections to the potential-energy curves of the first-row diatomics, Li{sub 2} through F{sub 2}. Both the Langreth-Mehl-Hu and the Perdew-Wang gradient-density functionals were used in calculations of the binding energy, bond length, and vibrational frequency for each dimer. Comparison with results obtained in the local-spin-density approximation (LSDA) using the Vosko-Wilk-Nusair functional, and with experiment, reveals that bond lengths and vibrational frequencies are rather insensitive to details of the gradient functionals, including self-consistency effects, but the gradient correctionsmore » reduce the overbinding commonly observed in the LSDA calculations of first-row diatomics (with the exception of Li{sub 2}, the gradient-functional binding-energy error is only 50--12 % of the LSDA error). The improved binding energies result from a large differential energy lowering, which occurs in open-shell atoms relative to the diatomics. The stabilization of the atom arises from the use of nonspherical charge and spin densities in the gradient-functional calculations. This stabilization is negligibly small in LSDA calculations performed with nonspherical densities.« less

Scalable Methods for Electronic Excitations and Optical Responses of Nanostructures: Mathematics to Algorithms to Observables

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

Carter, Emily A

2013-02-02

Kohn-Sham density functional theory (DFT) is a powerful, well-established tool for the study of condensed phase electronic structure. However, there are still a number of situations where its applicability is limited. The basic theme of our research is the development of first principles electronic structure approaches for condensed matter that goes beyond what can currently be done with standard implementations ofKohn-Sham DFT. Our efforts to this end have focused on two classes or' methods. The first addresses the well-lmown inability of DFT to handle strong, many-body electron correlation effects. Our approach is a DFT -based embedding theory, to treat localizedmore » features (e.g. impurity, adsorbate, vacancy, etc.) embedded in a periodic, metallic crystal. A description for the embedded region is provided by explicitly correlated, ab initio wave function methods. DFT, as a fo1n1ally ground state theory, does not give a good description of excited states; an additional feature of our approach is the ability to obtain excitations localized in this region. We apply our method to a first-principles study of the adsorption of a single magnetic Co ada tom on non-magnetic Cu( 111 ), a known Kondo system whose behavior is governed by strong electron correlation. The second class of methods that we are developing is an orbital-free density functional theory (OFDFT), which addresses the speed limitations ofKohn-Sham DFT. OFDFT is a powerful, O(N) scaling method for electronic structure calculations. Unlike Kohn-Sham DFT, OFDFT goes back to the original Hohenberg-Kohn idea of directly optimizing an energy functional which is an explicit functional of the density, without invoking an orbital description. This eliminates the need to manipulate orbitals, which leads to O(N{sup 3}) scaling in the Kahn-Sham approach. The speed of OFDFT allows direct electronic structure calculations on large systems on the order of thousands to tens of thousands of atoms, an expensive feat within Kohn-Sham. Due to our incomplete knowledge of the exact, universal energy density functional, this speedup comes at the cost of some accuracy with respect to Kohn-Sham methods. However, OFDFT has been shown to be remarkably accurate with respect to Kohn-Sham when used in the study of nearly-free-electron-like metals, e.g., AI, for which good density functionals have been derived. Examples of past applications of OFDFT include the prediction of properties of bulk crystals, surfaces, vacancies, vacancy clusters, nanoclusters, and dislocations, as well as OFDFT -based multiscale simulations of nanoindentation in AI and Al-Mg alloys.« less

Validation of electronic structure methods for isomerization reactions of large organic molecules.

PubMed

Luo, Sijie; Zhao, Yan; Truhlar, Donald G

2011-08-14

In this work the ISOL24 database of isomerization energies of large organic molecules presented by Huenerbein et al. [Phys. Chem. Chem. Phys., 2010, 12, 6940] is updated, resulting in the new benchmark database called ISOL24/11, and this database is used to test 50 electronic model chemistries. To accomplish the update, the very expensive and highly accurate CCSD(T)-F12a/aug-cc-pVDZ method is first exploited to investigate a six-reaction subset of the 24 reactions, and by comparison of various methods with the benchmark, MCQCISD-MPW is confirmed to be of high accuracy. The final ISOL24/11 database is composed of six reaction energies calculated by CCSD(T)-F12a/aug-cc-pVDZ and 18 calculated by MCQCISD-MPW. We then tested 40 single-component density functionals (both local and hybrid), eight doubly hybrid functionals, and two other methods against ISOL24/11. It is found that the SCS-MP3/CBS method, which is used as benchmark for the original ISOL24, has an MUE of 1.68 kcal mol(-1), which is close to or larger than some of the best tested DFT methods. Using the new benchmark, we find ωB97X-D and MC3MPWB to be the best single-component and doubly hybrid functionals respectively, with PBE0-D3 and MC3MPW performing almost as well. The best single-component density functionals without molecular mechanics dispersion-like terms are M08-SO, M08-HX, M05-2X, and M06-2X. The best single-component density functionals without Hartree-Fock exchange are M06-L-D3 when MM terms are included and M06-L when they are not.

Performance of the DFTB method in comparison to DFT and semiempirical methods for geometries and energies of C20-C86fullerene isomers

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

Zheng, Guishan; Irle, Stephan; Morokuma, Keiji

2005-07-20

The research described in this product was performed in part in the Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the Department of Energy's Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory. The performance of both non-iterative (NCC) and self-consistent charge (SCC) versions of the density functional tight binding (DFTB) method, as well as AM1 and PM3 methods, has been compared with the B3LYP method, a hybrid density functional theory (DFT) method, for equilibrium geometries and relative energies of various isomers of C20–C86 fullerenes. Both NCC- and SCCDFTB methods compare very favorablymore » with B3LYP both in geometries and isomer relative energies, while AM1 and PM3 do noticeably worse.« less

Computational studies of molecular charge transfer complexes of heterocyclic 4-methylepyridine-2-azomethine-p-benzene derivatives with picric acid and m-dinitrobenzene.

PubMed

Al-Harbi, L M; El-Mossalamy, E H; Obaid, A Y; Al-Jedaani, A H

2014-01-01

Charge transfer complexes of substituted aryl Schiff bases as donors with picric acid and m-dinitrobenzene as acceptors were investigated by using computational analysis calculated by Configuration Interaction Singles Hartree-Fock (CIS-HF) at standard 6-31G∗ basis set and Time-Dependent Density-Functional Theory (TD-DFT) levels of theory at standard 6-31G∗∗ basis set, infrared spectra, visible and nuclear magnetic resonance spectra are investigated. The optimized geometries and vibrational frequencies were evaluated. The energy and oscillator strength were calculated by Configuration Interaction Singles Hartree-Fock method (CIS-HF) and the Time-Dependent Density-Functional Theory (TD-DFT) results. Electronic properties, such as HOMO and LUMO energies and band gaps of CTCs set, were studied by the Time-Dependent density functional theory with Becke-Lee-Young-Parr (B3LYP) composite exchange correlation functional and by Configuration Interaction Singles Hartree-Fock method (CIS-HF). The ionization potential Ip and electron affinity EA were calculated by PM3, HF and DFT methods. The columbic force was calculated theoretically by using (CIS-HF and TD-DFT) methods. This study confirms that the theoretical calculation of vibrational frequencies for (aryl Schiff bases--(m-dinitrobenzene and picric acid)) complexes are quite useful for the vibrational assignment and for predicting new vibrational frequencies. Copyright © 2013 Elsevier B.V. All rights reserved.

Benchmarking Density Functional Theory Based Methods To Model NiOOH Material Properties: Hubbard and van der Waals Corrections vs Hybrid Functionals.

PubMed

Zaffran, Jeremie; Caspary Toroker, Maytal

2016-08-09

NiOOH has recently been used to catalyze water oxidation by way of electrochemical water splitting. Few experimental data are available to rationalize the successful catalytic capability of NiOOH. Thus, theory has a distinctive role for studying its properties. However, the unique layered structure of NiOOH is associated with the presence of essential dispersion forces within the lattice. Hence, the choice of an appropriate exchange-correlation functional within Density Functional Theory (DFT) is not straightforward. In this work, we will show that standard DFT is sufficient to evaluate the geometry, but DFT+U and hybrid functionals are required to calculate the oxidation states. Notably, the benefit of DFT with van der Waals correction is marginal. Furthermore, only hybrid functionals succeed in opening a bandgap, and such methods are necessary to study NiOOH electronic structure. In this work, we expect to give guidelines to theoreticians dealing with this material and to present a rational approach in the choice of the DFT method of calculation.

On-line prognosis of fatigue crack propagation based on Gaussian weight-mixture proposal particle filter.

PubMed

Chen, Jian; Yuan, Shenfang; Qiu, Lei; Wang, Hui; Yang, Weibo

2018-01-01

Accurate on-line prognosis of fatigue crack propagation is of great meaning for prognostics and health management (PHM) technologies to ensure structural integrity, which is a challenging task because of uncertainties which arise from sources such as intrinsic material properties, loading, and environmental factors. The particle filter algorithm has been proved to be a powerful tool to deal with prognostic problems those are affected by uncertainties. However, most studies adopted the basic particle filter algorithm, which uses the transition probability density function as the importance density and may suffer from serious particle degeneracy problem. This paper proposes an on-line fatigue crack propagation prognosis method based on a novel Gaussian weight-mixture proposal particle filter and the active guided wave based on-line crack monitoring. Based on the on-line crack measurement, the mixture of the measurement probability density function and the transition probability density function is proposed to be the importance density. In addition, an on-line dynamic update procedure is proposed to adjust the parameter of the state equation. The proposed method is verified on the fatigue test of attachment lugs which are a kind of important joint components in aircraft structures. Copyright © 2017 Elsevier B.V. All rights reserved.

Density Functional Theory Calculations of the Dissociation of H[2] on (100) 2H-MoS[2] Surfaces: A Key Step in the Hydroprocessing of Crude Oil

ERIC Educational Resources Information Center

Todorova, Teodora; Alexiev, Valentin; Weber, Thomas

2006-01-01

Hydrogen activation on the (100) surface of MoS[2] structures was investigated by means of density functional theory calculations. Linear and quadratic synchronous transit methods with a conjugate gradient refinement of the saddle point were used to localize transition states. The calculations include heterolytic and homolytic dissociation of…

A Study of Terrain Reductions, Density Anomalies and Geophysical Inversion Methods in Gravity Field Modelling

DTIC Science & Technology

1984-04-01

5.15) where a is a positive constant and 11 IIH the Hilbert space norm associated with the chosen covariance function K. The constant a is arbitrary...Density Anomalies 14 5. Unknown Densities - Geophysical Inversion 16 6. Density Modelling Using Rectangular Prisms 24 6.1 Space Domain 24 6.2 Frequency...theory: to calculate the gravity potential and its derivatives in space due to 6 • given density distributions. When the prime interest is in "external

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

Size-dependent error of the density functional theory ionization potential in vacuum and solution

DOE PAGES

Sosa Vazquez, Xochitl A.; Isborn, Christine M.

2015-12-22

Density functional theory is often the method of choice for modeling the energetics of large molecules and including explicit solvation effects. It is preferable to use a method that treats systems of different sizes and with different amounts of explicit solvent on equal footing. However, recent work suggests that approximate density functional theory has a size-dependent error in the computation of the ionization potential. We here investigate the lack of size-intensivity of the ionization potential computed with approximate density functionals in vacuum and solution. We show that local and semi-local approximations to exchange do not yield a constant ionization potentialmore » for an increasing number of identical isolated molecules in vacuum. Instead, as the number of molecules increases, the total energy required to ionize the system decreases. Rather surprisingly, we find that this is still the case in solution, whether using a polarizable continuum model or with explicit solvent that breaks the degeneracy of each solute, and we find that explicit solvent in the calculation can exacerbate the size-dependent delocalization error. We demonstrate that increasing the amount of exact exchange changes the character of the polarization of the solvent molecules; for small amounts of exact exchange the solvent molecules contribute a fraction of their electron density to the ionized electron, but for larger amounts of exact exchange they properly polarize in response to the cationic solute. As a result, in vacuum and explicit solvent, the ionization potential can be made size-intensive by optimally tuning a long-range corrected hybrid functional.« less

Size-dependent error of the density functional theory ionization potential in vacuum and solution

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

Sosa Vazquez, Xochitl A.; Isborn, Christine M., E-mail: cisborn@ucmerced.edu

2015-12-28

Density functional theory is often the method of choice for modeling the energetics of large molecules and including explicit solvation effects. It is preferable to use a method that treats systems of different sizes and with different amounts of explicit solvent on equal footing. However, recent work suggests that approximate density functional theory has a size-dependent error in the computation of the ionization potential. We here investigate the lack of size-intensivity of the ionization potential computed with approximate density functionals in vacuum and solution. We show that local and semi-local approximations to exchange do not yield a constant ionization potentialmore » for an increasing number of identical isolated molecules in vacuum. Instead, as the number of molecules increases, the total energy required to ionize the system decreases. Rather surprisingly, we find that this is still the case in solution, whether using a polarizable continuum model or with explicit solvent that breaks the degeneracy of each solute, and we find that explicit solvent in the calculation can exacerbate the size-dependent delocalization error. We demonstrate that increasing the amount of exact exchange changes the character of the polarization of the solvent molecules; for small amounts of exact exchange the solvent molecules contribute a fraction of their electron density to the ionized electron, but for larger amounts of exact exchange they properly polarize in response to the cationic solute. In vacuum and explicit solvent, the ionization potential can be made size-intensive by optimally tuning a long-range corrected hybrid functional.« less

Prediction of three sigma maximum dispersed density for aerospace applications

NASA Technical Reports Server (NTRS)

Charles, Terri L.; Nitschke, Michael D.

1993-01-01

Free molecular heating (FMH) is caused by the transfer of energy during collisions between the upper atmosphere molecules and a space vehicle. The dispersed free molecular heating on a surface is an important constraint for space vehicle thermal analyses since it can be a significant source of heating. To reduce FMH to a spacecraft, the parking orbit is often designed to a higher altitude at the expense of payload capability. Dispersed FMH is a function of both space vehicle velocity and atmospheric density, however, the space vehicle velocity variations are insignificant when compared to the atmospheric density variations. The density of the upper atmosphere molecules is a function of altitude, but also varies with other environmental factors, such as solar activity, geomagnetic activity, location, and time. A method has been developed to predict three sigma maximum dispersed density for up to 15 years into the future. This method uses a state-of-the-art atmospheric density code, MSIS 86, along with 50 years of solar data, NASA and NOAA solar activity predictions for the next 15 years, and an Aerospace Corporation correlation to account for density code inaccuracies to generate dispersed maximum density ratios denoted as 'K-factors'. The calculated K-factors can be used on a mission unique basis to calculate dispersed density, and hence dispersed free molecular heating rates. These more accurate K-factors can allow lower parking orbit altitudes, resulting in increased payload capability.

Assessment of Methods to Consolidate Iodine-Loaded Silver-Functionalized Silica Aerogel

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

Matyas, Josef; Engler, Robert K.

2013-09-01

The U.S. Department of Energy is currently investigating alternative sorbents for the removal and immobilization of radioiodine from the gas streams in a nuclear fuel reprocessing plant. One of these new sorbents, Ag0-functionalized silica aerogels, shows great promise as a potential replacement for Ag-bearing mordenites because of its high selectivity and sorption capacity for iodine. Moreover, a feasible consolidation of iodine-loaded Ag0-functionalized silica aerogels to a durable SiO2-based waste form makes this aerogel an attractive choice for sequestering radioiodine. This report provides a preliminary assessment of the methods that can be used to consolidate iodine-loaded Ag0-functionalized silica aerogels into amore » final waste form. In particular, it focuses on experimental investigation of densification of as prepared Ag0-functionalized silica aerogels powders, with or without organic moiety and with or without sintering additive (colloidal silica), with three commercially available techniques: 1) hot uniaxial pressing (HUP), 2) hot isostatic pressing (HIP), and 3) spark plasma sintering (SPS). The densified products were evaluated with helium gas pycnometer for apparent density, with the Archimedes method for apparent density and open porosity, and with high-resolution scanning electron microscopy and energy dispersive spectroscopy (SEM-EDS) for the extent of densification and distribution of individual elements. The preliminary investigation of HUP, HIP, and SPS showed that these sintering methods can effectively consolidate powders of Ag0-functionalized silica aerogel into products of near-theoretical density. Also, removal of organic moiety and adding 5.6 mass% of colloidal silica to Ag0-functionalized silica aerogel powders before processing provided denser products. Furthermore, the ram travel data for SPS indicated that rapid consolidation of powders can be performed at temperatures below 950°C.« less

A systematic way for the cost reduction of density fitting methods

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

Kállay, Mihály, E-mail: kallay@mail.bme.hu

2014-12-28

We present a simple approach for the reduction of the size of auxiliary basis sets used in methods exploiting the density fitting (resolution of identity) approximation for electron repulsion integrals. Starting out of the singular value decomposition of three-center two-electron integrals, new auxiliary functions are constructed as linear combinations of the original fitting functions. The new functions, which we term natural auxiliary functions (NAFs), are analogous to the natural orbitals widely used for the cost reduction of correlation methods. The use of the NAF basis enables the systematic truncation of the fitting basis, and thereby potentially the reduction of themore » computational expenses of the methods, though the scaling with the system size is not altered. The performance of the new approach has been tested for several quantum chemical methods. It is demonstrated that the most pronounced gain in computational efficiency can be expected for iterative models which scale quadratically with the size of the fitting basis set, such as the direct random phase approximation. The approach also has the promise of accelerating local correlation methods, for which the processing of three-center Coulomb integrals is a bottleneck.« less

Uncertain Photometric Redshifts with Deep Learning Methods

NASA Astrophysics Data System (ADS)

D'Isanto, A.

2017-06-01

The need for accurate photometric redshifts estimation is a topic that has fundamental importance in Astronomy, due to the necessity of efficiently obtaining redshift information without the need of spectroscopic analysis. We propose a method for determining accurate multi-modal photo-z probability density functions (PDFs) using Mixture Density Networks (MDN) and Deep Convolutional Networks (DCN). A comparison with a Random Forest (RF) is performed.

Serial Scanning and Registration of High Resolution Quantitative Computed Tomography Volume Scans for the Determination of Local Bone Density Changes

NASA Technical Reports Server (NTRS)

Whalen, Robert T.; Napel, Sandy; Yan, Chye H.

1996-01-01

Progress in development of the methods required to study bone remodeling as a function of time is reported. The following topics are presented: 'A New Methodology for Registration Accuracy Evaluation', 'Registration of Serial Skeletal Images for Accurately Measuring Changes in Bone Density', and 'Precise and Accurate Gold Standard for Multimodality and Serial Registration Method Evaluations.'

Calculation of the exchange coupling constants of copper binuclear systems based on spin-flip constricted variational density functional theory.

PubMed

Zhekova, Hristina R; Seth, Michael; Ziegler, Tom

2011-11-14

We have recently developed a methodology for the calculation of exchange coupling constants J in weakly interacting polynuclear metal clusters. The method is based on unrestricted and restricted second order spin-flip constricted variational density functional theory (SF-CV(2)-DFT) and is here applied to eight binuclear copper systems. Comparison of the SF-CV(2)-DFT results with experiment and with results obtained from other DFT and wave function based methods has been made. Restricted SF-CV(2)-DFT with the BH&HLYP functional yields consistently J values in excellent agreement with experiment. The results acquired from this scheme are comparable in quality to those obtained by accurate multi-reference wave function methodologies such as difference dedicated configuration interaction and the complete active space with second-order perturbation theory. © 2011 American Institute of Physics

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.

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.

High Density Diffusion-Free Nanowell Arrays

PubMed Central

Takulapalli, Bharath R; Qiu, Ji; Magee, D. Mitchell; Kahn, Peter; Brunner, Al; Barker, Kristi; Means, Steven; Miersch, Shane; Bian, Xiaofang; Mendoza, Alex; Festa, Fernanda; Syal, Karan; Park, Jin; LaBaer, Joshua; Wiktor, Peter

2012-01-01

Proteomics aspires to elucidate the functions of all proteins. Protein microarrays provide an important step by enabling high-throughput studies of displayed proteins. However, many functional assays of proteins include untethered intermediates or products, which could frustrate the use of planar arrays at very high densities because of diffusion to neighboring features. The nucleic acid programmable protein array (NAPPA), is a robust, in situ synthesis method for producing functional proteins just-in-time, which includes steps with diffusible intermediates. We determined that diffusion of expressed proteins led to cross-binding at neighboring spots at very high densities with reduced inter-spot spacing. To address this limitation, we have developed an innovative platform using photolithographically-etched discrete silicon nanowells and used NAPPA as a test case. This arrested protein diffusion and cross-binding. We present confined high density protein expression and display, as well as functional protein-protein interactions, in 8,000 nanowell arrays. This is the highest density of individual proteins in nano-vessels demonstrated on a single slide. We further present proof of principle results on ultra-high density protein arrays capable of up to 24,000 nanowells on a single slide. PMID:22742968

Low cost estimation of the contribution of post-CCSD excitations to the total atomization energy using density functional theory calculations

NASA Astrophysics Data System (ADS)

Sánchez, H. R.; Pis Diez, R.

2016-04-01

Based on the Aλ diagnostic for multireference effects recently proposed [U.R. Fogueri, S. Kozuch, A. Karton, J.M. Martin, Theor. Chem. Acc. 132 (2013) 1], a simple method for improving total atomization energies and reaction energies calculated at the CCSD level of theory is proposed. The method requires a CCSD calculation and two additional density functional theory calculations for the molecule. Two sets containing 139 and 51 molecules are used as training and validation sets, respectively, for total atomization energies. An appreciable decrease in the mean absolute error from 7-10 kcal mol-1 for CCSD to about 2 kcal mol-1 for the present method is observed. The present method provides atomization energies and reaction energies that compare favorably with relatively recent scaled CCSD methods.

Enhanced NMR Discrimination of Pharmaceutically Relevant Molecular Crystal Forms through Fragment-Based Ab Initio Chemical Shift Predictions.

PubMed

Hartman, Joshua D; Day, Graeme M; Beran, Gregory J O

2016-11-02

Chemical shift prediction plays an important role in the determination or validation of crystal structures with solid-state nuclear magnetic resonance (NMR) spectroscopy. One of the fundamental theoretical challenges lies in discriminating variations in chemical shifts resulting from different crystallographic environments. Fragment-based electronic structure methods provide an alternative to the widely used plane wave gauge-including projector augmented wave (GIPAW) density functional technique for chemical shift prediction. Fragment methods allow hybrid density functionals to be employed routinely in chemical shift prediction, and we have recently demonstrated appreciable improvements in the accuracy of the predicted shifts when using the hybrid PBE0 functional instead of generalized gradient approximation (GGA) functionals like PBE. Here, we investigate the solid-state 13 C and 15 N NMR spectra for multiple crystal forms of acetaminophen, phenobarbital, and testosterone. We demonstrate that the use of the hybrid density functional instead of a GGA provides both higher accuracy in the chemical shifts and increased discrimination among the different crystallographic environments. Finally, these results also provide compelling evidence for the transferability of the linear regression parameters mapping predicted chemical shieldings to chemical shifts that were derived in an earlier study.

Enhanced NMR Discrimination of Pharmaceutically Relevant Molecular Crystal Forms through Fragment-Based Ab Initio Chemical Shift Predictions

PubMed Central

2016-01-01

Chemical shift prediction plays an important role in the determination or validation of crystal structures with solid-state nuclear magnetic resonance (NMR) spectroscopy. One of the fundamental theoretical challenges lies in discriminating variations in chemical shifts resulting from different crystallographic environments. Fragment-based electronic structure methods provide an alternative to the widely used plane wave gauge-including projector augmented wave (GIPAW) density functional technique for chemical shift prediction. Fragment methods allow hybrid density functionals to be employed routinely in chemical shift prediction, and we have recently demonstrated appreciable improvements in the accuracy of the predicted shifts when using the hybrid PBE0 functional instead of generalized gradient approximation (GGA) functionals like PBE. Here, we investigate the solid-state 13C and 15N NMR spectra for multiple crystal forms of acetaminophen, phenobarbital, and testosterone. We demonstrate that the use of the hybrid density functional instead of a GGA provides both higher accuracy in the chemical shifts and increased discrimination among the different crystallographic environments. Finally, these results also provide compelling evidence for the transferability of the linear regression parameters mapping predicted chemical shieldings to chemical shifts that were derived in an earlier study. PMID:27829821

Density, Electrical Conductivity and Viscosity of Hg(0.8)Cd(0.2)Te Melt

NASA Technical Reports Server (NTRS)

Li, C.; Scripa, R. N.; Ban, H.; Su, C.-H.; Lehoczky, S. L.

2004-01-01

The density, viscosity, and electrical conductivity of Hg(0.8)Cd(0.2)Te melt were measured as a function of temperature. A pycnometric method was used to measure the melt density in the temperature range of 1072 to 1122 K. The viscosity and electrical conductivity were determined using a transient torque method from 1068 to 1132 K. The density result from this study is within 0.3% of the published data. However, the current viscosity result is approximately 30% lower than the existing data. The electrical conductivity of Hg(0.8)Cd(0.2)Te melt as a function of temperature, which is not available in the literature, is also determined. The analysis of the temperature dependent electrical conductivity and the relationship between the kinematic viscosity and density indicated that the structure of the melt appeared to be homogeneous when the temperature was above 1090 K. A structural transition occurred in the Hg(0.8)Cd(0.2)Te melt as the temperature was decreased to below 1090 K

Density, Electrical Conductivity and Viscosity of Hg(sub 0.8)Cd(sub 0.2)Te Melt

NASA Technical Reports Server (NTRS)

Li, C.; Scripa, R. N.; Ban, H.; Lin, B.; Su, C.-H.; Lehoczky, S. L.

2004-01-01

The density, viscosity, and electrical conductivity of Hg(sub 0.8)Cd(sub 0.2)Te melt were measures as a function of temperature. A pycnometric method was used to measure the melt density in the temperature range of 1072 to 1122 K. The viscosity and electrical conductivity were determined using a transient torque method from 1068 to 1132 K. The density result from this study is within 0.3% of the published data. However, the current viscosity result is approximately 30% lower than the existing data. The electrical conductivity of Hg(sub 0.8)Cd(sub 0.2)Te melt as a function of temperature, which is not available in the literature, is also determined. The analysis of the temperature dependent electrical conductivity and the relationship between the kinematic viscosity and density indicated that the structure of the melt appeared to be homogeneous when the temperature was above 1090 K. A structural transition occurred in the Hg(sub 0.8)Cd(sub 0.2)Te melt as the temperature was decreased to below 1090 K.

Linear-scaling method for calculating nuclear magnetic resonance chemical shifts using gauge-including atomic orbitals within Hartree-Fock and density-functional theory.

PubMed

Kussmann, Jörg; Ochsenfeld, Christian

2007-08-07

Details of a new density matrix-based formulation for calculating nuclear magnetic resonance chemical shifts at both Hartree-Fock and density functional theory levels are presented. For systems with a nonvanishing highest occupied molecular orbital-lowest unoccupied molecular orbital gap, the method allows us to reduce the asymptotic scaling order of the computational effort from cubic to linear, so that molecular systems with 1000 and more atoms can be tackled with today's computers. The key feature is a reformulation of the coupled-perturbed self-consistent field (CPSCF) theory in terms of the one-particle density matrix (D-CPSCF), which avoids entirely the use of canonical MOs. By means of a direct solution for the required perturbed density matrices and the adaptation of linear-scaling integral contraction schemes, the overall scaling of the computational effort is reduced to linear. A particular focus of our formulation is to ensure numerical stability when sparse-algebra routines are used to obtain an overall linear-scaling behavior.

Transitioning NWChem to the Next Generation of Manycore Machines

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

Bylaska, Eric J.; Apra, E; Kowalski, Karol

The NorthWest chemistry (NWChem) modeling software is a popular molecular chemistry simulation software that was designed from the start to work on massively parallel processing supercomputers [1-3]. It contains an umbrella of modules that today includes self-consistent eld (SCF), second order Møller-Plesset perturbation theory (MP2), coupled cluster (CC), multiconguration self-consistent eld (MCSCF), selected conguration interaction (CI), tensor contraction engine (TCE) many body methods, density functional theory (DFT), time-dependent density functional theory (TDDFT), real-time time-dependent density functional theory, pseudopotential plane-wave density functional theory (PSPW), band structure (BAND), ab initio molecular dynamics (AIMD), Car-Parrinello molecular dynamics (MD), classical MD, hybrid quantum mechanicsmore » molecular mechanics (QM/MM), hybrid ab initio molecular dynamics molecular mechanics (AIMD/MM), gauge independent atomic orbital nuclear magnetic resonance (GIAO NMR), conductor like screening solvation model (COSMO), conductor-like screening solvation model based on density (COSMO-SMD), and reference interaction site model (RISM) solvation models, free energy simulations, reaction path optimization, parallel in time, among other capabilities [4]. Moreover, new capabilities continue to be added with each new release.« less

Modeling L2,3-Edge X-ray Absorption Spectroscopy with Real-Time Exact Two-Component Relativistic Time-Dependent Density Functional Theory.

PubMed

Kasper, Joseph M; Lestrange, Patrick J; Stetina, Torin F; Li, Xiaosong

2018-04-10

X-ray absorption spectroscopy is a powerful technique to probe local electronic and nuclear structure. There has been extensive theoretical work modeling K-edge spectra from first principles. However, modeling L-edge spectra directly with density functional theory poses a unique challenge requiring further study. Spin-orbit coupling must be included in the model, and a noncollinear density functional theory is required. Using the real-time exact two-component method, we are able to variationally include one-electron spin-orbit coupling terms when calculating the absorption spectrum. The abilities of different basis sets and density functionals to model spectra for both closed- and open-shell systems are investigated using SiCl 4 and three transition metal complexes, TiCl 4 , CrO 2 Cl 2 , and [FeCl 6 ] 3- . Although we are working in the real-time framework, individual molecular orbital transitions can still be recovered by projecting the density onto the ground state molecular orbital space and separating contributions to the time evolving dipole moment.

Multivariate Density Estimation and Remote Sensing

NASA Technical Reports Server (NTRS)

Scott, D. W.

1983-01-01

Current efforts to develop methods and computer algorithms to effectively represent multivariate data commonly encountered in remote sensing applications are described. While this may involve scatter diagrams, multivariate representations of nonparametric probability density estimates are emphasized. The density function provides a useful graphical tool for looking at data and a useful theoretical tool for classification. This approach is called a thunderstorm data analysis.

Fluids density functional theory and initializing molecular dynamics simulations of block copolymers

NASA Astrophysics Data System (ADS)

Brown, Jonathan R.; Seo, Youngmi; Maula, Tiara Ann D.; Hall, Lisa M.

2016-03-01

Classical, fluids density functional theory (fDFT), which can predict the equilibrium density profiles of polymeric systems, and coarse-grained molecular dynamics (MD) simulations, which are often used to show both structure and dynamics of soft materials, can be implemented using very similar bead-based polymer models. We aim to use fDFT and MD in tandem to examine the same system from these two points of view and take advantage of the different features of each methodology. Additionally, the density profiles resulting from fDFT calculations can be used to initialize the MD simulations in a close to equilibrated structure, speeding up the simulations. Here, we show how this method can be applied to study microphase separated states of both typical diblock and tapered diblock copolymers in which there is a region with a gradient in composition placed between the pure blocks. Both methods, applied at constant pressure, predict a decrease in total density as segregation strength or the length of the tapered region is increased. The predictions for the density profiles from fDFT and MD are similar across materials with a wide range of interfacial widths.

Structure and Electronic Properties of Neutral and Negatively Charged RhBn Clusters (n = 3-10): A Density Functional Theory Study.

PubMed

Li, Peifang; Mei, Tingting; Lv, Linxia; Lu, Cheng; Wang, Weihua; Bao, Gang; Gutsev, Gennady L

2017-08-31

The geometrical structure and electronic properties of the neutral RhB n and singly negatively charged RhB n - clusters are obtained in the range of 3 ≤ n ≤ 10 using the unbiased CALYPSO structure search method and density functional theory (DFT). A combination of the PBE0 functional and the def2-TZVP basis set is used for determining global minima on potential energy surfaces of the Rh-doped B n clusters. The photoelectron spectra of the anions are simulated using the time-dependent density functional theory (TD-DFT) method. Good agreement between our simulated and experimentally obtained photoelectron spectra for RhB 9 - provides support to the validity of our theoretical method. The relative stabilities of the ground-state RhB n and RhB n - clusters are estimated using the calculated binding energies, second-order total energy differences, and HOMO-LUMO gaps. It is found that RhB 7 and RhB 8 - are the most stable species in the neutral and anionic series, respectively. The chemical bonding analysis reveals that the RhB 8 - cluster possesses two sets of delocalized σ and π bonds. In both cases, the Hückel 4N + 2 rule is fulfilled and this cluster possesses both σ and π aromaticities.

Statistical tests for whether a given set of independent, identically distributed draws comes from a specified probability density.

PubMed

Tygert, Mark

2010-09-21

We discuss several tests for determining whether a given set of independent and identically distributed (i.i.d.) draws does not come from a specified probability density function. The most commonly used are Kolmogorov-Smirnov tests, particularly Kuiper's variant, which focus on discrepancies between the cumulative distribution function for the specified probability density and the empirical cumulative distribution function for the given set of i.i.d. draws. Unfortunately, variations in the probability density function often get smoothed over in the cumulative distribution function, making it difficult to detect discrepancies in regions where the probability density is small in comparison with its values in surrounding regions. We discuss tests without this deficiency, complementing the classical methods. The tests of the present paper are based on the plain fact that it is unlikely to draw a random number whose probability is small, provided that the draw is taken from the same distribution used in calculating the probability (thus, if we draw a random number whose probability is small, then we can be confident that we did not draw the number from the same distribution used in calculating the probability).

Level densities and γ-ray strength functions in Sn isotopes

NASA Astrophysics Data System (ADS)

Toft, H. K.; Larsen, A. C.; Agvaanluvsan, U.; Bürger, A.; Guttormsen, M.; Mitchell, G. E.; Nyhus, H. T.; Schiller, A.; Siem, S.; Syed, N. U. H.; Voinov, A.

2010-06-01

The nuclear level densities of Sn118,119 and the γ-ray strength functions of Sn116,118,119 below the neutron separation energy are extracted with the Oslo method using the (He3,αγ) and (He3,He3'γ) reactions. The level-density function of Sn119 displays steplike structures. The microcanonical entropies are deduced from the level densities, and the single neutron entropy of Sn119 is determined to be 1.7 ± 0.2 kB. Results from a combinatorial model support the interpretation that some of the low-energy steps in the level density function are caused by neutron pair breaking. An enhancement in all the γ-ray strength functions of Sn116-119, compared to standard models for radiative strength, is observed for the γ-ray energy region of ≃4-11 MeV. These small resonances all have a centroid energy of 8.0(1) MeV and an integrated strength corresponding to 1.7(9)% of the classical Thomas-Reiche-Kuhn sum rule. The Sn resonances may be due to electric dipole neutron skin oscillations or to an enhancement of the giant magnetic dipole resonance.

Polymorphism and thermodynamic ground state of silver fulminate studied from van der Waals density functional calculations

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

Yedukondalu, N.; Vaitheeswaran, G., E-mail: gvsp@uohyd.ernet.in

2014-06-14

Silver fulminate (AgCNO) is a primary explosive, which exists in two polymorphic phases, namely, orthorhombic (Cmcm) and trigonal (R3{sup ¯}) forms at ambient conditions. In the present study, we have investigated the effect of pressure and temperature on relative phase stability of the polymorphs using planewave pseudopotential approaches based on Density Functional Theory (DFT). van der Waals interactions play a significant role in predicting the phase stability and they can be effectively captured by semi-empirical dispersion correction methods in contrast to standard DFT functionals. Based on our total energy calculations using DFT-D2 method, the Cmcm structure is found to bemore » the preferred thermodynamic equilibrium phase under studied pressure and temperature range. Hitherto Cmcm and R3{sup ¯} phases denoted as α- and β-forms of AgCNO, respectively. Also a pressure induced polymorphic phase transition is seen using DFT functionals and the same was not observed with DFT-D2 method. The equation of state and compressibility of both polymorphic phases were investigated. Electronic structure and optical properties were calculated using full potential linearized augmented plane wave method within the Tran-Blaha modified Becke-Johnson potential. The calculated electronic structure shows that α, β phases are indirect bandgap insulators with a bandgap values of 3.51 and 4.43 eV, respectively. The nature of chemical bonding is analyzed through the charge density plots and partial density of states. Optical anisotropy, electric-dipole transitions, and photo sensitivity to light of the polymorphs are analyzed from the calculated optical spectra. Overall, the present study provides an early indication to experimentalists to avoid the formation of unstable β-form of AgCNO.« less

Density-functional theory simulation of large quantum dots

NASA Astrophysics Data System (ADS)

Jiang, Hong; Baranger, Harold U.; Yang, Weitao

2003-10-01

Kohn-Sham spin-density functional theory provides an efficient and accurate model to study electron-electron interaction effects in quantum dots, but its application to large systems is a challenge. Here an efficient method for the simulation of quantum dots using density-function theory is developed; it includes the particle-in-the-box representation of the Kohn-Sham orbitals, an efficient conjugate-gradient method to directly minimize the total energy, a Fourier convolution approach for the calculation of the Hartree potential, and a simplified multigrid technique to accelerate the convergence. We test the methodology in a two-dimensional model system and show that numerical studies of large quantum dots with several hundred electrons become computationally affordable. In the noninteracting limit, the classical dynamics of the system we study can be continuously varied from integrable to fully chaotic. The qualitative difference in the noninteracting classical dynamics has an effect on the quantum properties of the interacting system: integrable classical dynamics leads to higher-spin states and a broader distribution of spacing between Coulomb blockade peaks.

Adaptive frozen orbital treatment for the fragment molecular orbital method combined with density-functional tight-binding

NASA Astrophysics Data System (ADS)

Nishimoto, Yoshio; Fedorov, Dmitri G.

2018-02-01

The exactly analytic gradient is derived and implemented for the fragment molecular orbital (FMO) method combined with density-functional tight-binding (DFTB) using adaptive frozen orbitals. The response contributions which arise from freezing detached molecular orbitals on the border between fragments are computed by solving Z-vector equations. The accuracy of the energy, its gradient, and optimized structures is verified on a set of representative inorganic materials and polypeptides. FMO-DFTB is applied to optimize the structure of a silicon nano-wire, and the results are compared to those of density functional theory and experiment. FMO accelerates the DFTB calculation of a boron nitride nano-ring with 7872 atoms by a factor of 406. Molecular dynamics simulations using FMO-DFTB applied to a 10.7 μm chain of boron nitride nano-rings, consisting of about 1.2 × 106 atoms, reveal the rippling and twisting of nano-rings at room temperature.

Kohn-Sham potentials from electron densities using a matrix representation within finite atomic orbital basis sets

NASA Astrophysics Data System (ADS)

Zhang, Xing; Carter, Emily A.

2018-01-01

We revisit the static response function-based Kohn-Sham (KS) inversion procedure for determining the KS effective potential that corresponds to a given target electron density within finite atomic orbital basis sets. Instead of expanding the potential in an auxiliary basis set, we directly update the potential in its matrix representation. Through numerical examples, we show that the reconstructed density rapidly converges to the target density. Preliminary results are presented to illustrate the possibility of obtaining a local potential in real space from the optimized potential in its matrix representation. We have further applied this matrix-based KS inversion approach to density functional embedding theory. A proof-of-concept study of a solvated proton transfer reaction demonstrates the method's promise.

Density functional study of molecular interactions in secondary structures of proteins.

PubMed

Takano, Yu; Kusaka, Ayumi; Nakamura, Haruki

2016-01-01

Proteins play diverse and vital roles in biology, which are dominated by their three-dimensional structures. The three-dimensional structure of a protein determines its functions and chemical properties. Protein secondary structures, including α-helices and β-sheets, are key components of the protein architecture. Molecular interactions, in particular hydrogen bonds, play significant roles in the formation of protein secondary structures. Precise and quantitative estimations of these interactions are required to understand the principles underlying the formation of three-dimensional protein structures. In the present study, we have investigated the molecular interactions in α-helices and β-sheets, using ab initio wave function-based methods, the Hartree-Fock method (HF) and the second-order Møller-Plesset perturbation theory (MP2), density functional theory, and molecular mechanics. The characteristic interactions essential for forming the secondary structures are discussed quantitatively.

Mott Transition in GdMnO3: an Ab Initio Study

NASA Astrophysics Data System (ADS)

Ferreira, W. S.; Moreira, E.; Frazão, N. F.

2018-04-01

Orthorhombic GdMnO3 is studied using density functional theory considering the pseudo-potential plane-wave method within local-spin-density approximation, LSDA. The electronic band structure and density of states, for several hydrostatic pressures, are studied. The Mott transition was observed at 60 GPa. Calculated lattice parameters are close to the experimental measurements, and some indirect band gaps (S→Γ) were obtained within the LSDA level of calculation, between the occupied O-2 p and unoccupied Gd-4 f states. The variation of the gap reduces with increasing pressure, being well fitted to a quadratic function.

Energy density functional on a microscopic basis

NASA Astrophysics Data System (ADS)

Baldo, M.; Robledo, L.; Schuck, P.; Viñas, X.

2010-06-01

In recent years impressive progress has been made in the development of highly accurate energy density functionals, which allow us to treat medium-heavy nuclei. In this approach one tries to describe not only the ground state but also the first relevant excited states. In general, higher accuracy requires a larger set of parameters, which must be carefully chosen to avoid redundancy. Following this line of development, it is unavoidable that the connection of the functional with the bare nucleon-nucleon interaction becomes more and more elusive. In principle, the construction of a density functional from a density matrix expansion based on the effective nucleon-nucleon interaction is possible, and indeed the approach has been followed by few authors. However, to what extent a density functional based on such a microscopic approach can reach the accuracy of the fully phenomenological ones remains an open question. A related question is to establish which part of a functional can be actually derived by a microscopic approach and which part, in contrast, must be left as purely phenomenological. In this paper we discuss the main problems that are encountered when the microscopic approach is followed. To this purpose we will use the method we have recently introduced to illustrate the different aspects of these problems. In particular we will discuss the possible connection of the density functional with the nuclear matter equation of state and the distinct features of finite-size effect typical of nuclei.

Orthogonal polynomial projectors for the Projector Augmented Wave (PAW) formalism.

NASA Astrophysics Data System (ADS)

Holzwarth, N. A. W.; Matthews, G. E.; Tackett, A. R.; Dunning, R. B.

1998-03-01

The PAW method for density functional electronic structure calculations developed by Blöchl(Phys. Rev. B 50), 17953 (1994) and also used by our group(Phys. Rev. B 55), 2005 (1997) has numerical advantages of a pseudopotential technique while retaining the physics of an all-electron formalism. We describe a new method for generating the necessary set of atom-centered projector and basis functions, based on choosing the projector functions from a set of orthogonal polynomials multiplied by a localizing weight factor. Numerical benefits of the new scheme result from having direct control of the shape of the projector functions and from the use of a simple repulsive local potential term to eliminate ``ghost state" problems, which can haunt calculations of this kind. We demonstrate the method by calculating the cohesive energies of CaF2 and Mo and the density of states of CaMoO4 which shows detailed agreement with LAPW results over a 66 eV range of energy including upper core, valence, and conduction band states.

Coupling of ab initio density functional theory and molecular dynamics for the multiscale modeling of carbon nanotubes

NASA Astrophysics Data System (ADS)

Ng, T. Y.; Yeak, S. H.; Liew, K. M.

2008-02-01

A multiscale technique is developed that couples empirical molecular dynamics (MD) and ab initio density functional theory (DFT). An overlap handshaking region between the empirical MD and ab initio DFT regions is formulated and the interaction forces between the carbon atoms are calculated based on the second-generation reactive empirical bond order potential, the long-range Lennard-Jones potential as well as the quantum-mechanical DFT derived forces. A density of point algorithm is also developed to track all interatomic distances in the system, and to activate and establish the DFT and handshaking regions. Through parallel computing, this multiscale method is used here to study the dynamic behavior of single-walled carbon nanotubes (SWCNTs) under asymmetrical axial compression. The detection of sideways buckling due to the asymmetrical axial compression is reported and discussed. It is noted from this study on SWCNTs that the MD results may be stiffer compared to those with electron density considerations, i.e. first-principle ab initio methods.

Theoretical prediction of nuclear magnetic shieldings and indirect spin-spin coupling constants in 1,1-, cis-, and trans-1,2-difluoroethylenes

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

Nozirov, Farhod, E-mail: teobaldk@gmail.com, E-mail: farhod.nozirov@gmail.com; Stachów, Michał, E-mail: michal.stachow@gmail.com; Kupka, Teobald, E-mail: teobaldk@gmail.com, E-mail: farhod.nozirov@gmail.com

2014-04-14

A theoretical prediction of nuclear magnetic shieldings and indirect spin-spin coupling constants in 1,1-, cis- and trans-1,2-difluoroethylenes is reported. The results obtained using density functional theory (DFT) combined with large basis sets and gauge-independent atomic orbital calculations were critically compared with experiment and conventional, higher level correlated electronic structure methods. Accurate structural, vibrational, and NMR parameters of difluoroethylenes were obtained using several density functionals combined with dedicated basis sets. B3LYP/6-311++G(3df,2pd) optimized structures of difluoroethylenes closely reproduced experimental geometries and earlier reported benchmark coupled cluster results, while BLYP/6-311++G(3df,2pd) produced accurate harmonic vibrational frequencies. The most accurate vibrations were obtained using B3LYP/6-311++G(3df,2pd)more » with correction for anharmonicity. Becke half and half (BHandH) density functional predicted more accurate {sup 19}F isotropic shieldings and van Voorhis and Scuseria's τ-dependent gradient-corrected correlation functional yielded better carbon shieldings than B3LYP. A surprisingly good performance of Hartree-Fock (HF) method in predicting nuclear shieldings in these molecules was observed. Inclusion of zero-point vibrational correction markedly improved agreement with experiment for nuclear shieldings calculated by HF, MP2, CCSD, and CCSD(T) methods but worsened the DFT results. The threefold improvement in accuracy when predicting {sup 2}J(FF) in 1,1-difluoroethylene for BHandH density functional compared to B3LYP was observed (the deviations from experiment were −46 vs. −115 Hz)« less

First-passage problems: A probabilistic dynamic analysis for degraded structures

NASA Technical Reports Server (NTRS)

Shiao, Michael C.; Chamis, Christos C.

1990-01-01

Structures subjected to random excitations with uncertain system parameters degraded by surrounding environments (a random time history) are studied. Methods are developed to determine the statistics of dynamic responses, such as the time-varying mean, the standard deviation, the autocorrelation functions, and the joint probability density function of any response and its derivative. Moreover, the first-passage problems with deterministic and stationary/evolutionary random barriers are evaluated. The time-varying (joint) mean crossing rate and the probability density function of the first-passage time for various random barriers are derived.

An unscaled quantum mechanical harmonic force field for p-benzoquinone

NASA Astrophysics Data System (ADS)

Nonella, Marco; Tavan, Paul

1995-10-01

Structure and harmonic vibrational frequencies of p-benzoquinone have been calculated using quantum chemical ab initio and density functional methods. Our calculations show that a satisfactory description of fundamentals and normal mode compositions is achieved upon consideration of correlation effects by means of Møller-Plesset perturbation expansion (MP2) or by density functional theory (DFT). Furthermore, for correct prediction of CO bondlength and force constant, basis sets augmented by polarization functions are required. Applying such basis sets, MP2 and DFT calculations both give results which are generally in reasonable agreement with experimental data. The quantitatively better agreement, however, is achieved with the computationally less demanding DFT method. This method particularly allows very precise prediction of the experimentally important absorptions in the frequency region between 1500 and 1800 cm -1 and of the isotopic shifts of these vibrations due to 13C or 18O substitution.

Dielectric function and plasmons in graphene: A self-consistent-field calculation within a Markovian master equation formalism

DOE PAGES

Karimi, F.; Davoody, A. H.; Knezevic, I.

2016-05-12

We introduce a method for calculating the dielectric function of nanostructures with an arbitrary band dispersion and Bloch wave functions. The linear response of a dissipative electronic system to an external electromagnetic field is calculated by a self-consistent-field approach within a Markovian master equation formalism (SCF-MMEF) coupled with full-wave electromagnetic equations. The SCF-MMEF accurately accounts for several concurrent scattering mechanisms. The method captures interband electron-hole-pair generation, as well as the interband and intraband electron scattering with phonons and impurities. We employ the SCF-MMEF to calculate the dielectric function, complex conductivity, and loss function for supported graphene. From the loss-function maximum,more » we obtain plasmon dispersion and propagation length for different substrate types [nonpolar diamondlike carbon (DLC) and polar SiO 2 and hBN], impurity densities, carrier densities, and temperatures. Plasmons on the two polar substrates are suppressed below the highest surface phonon energy, while the spectrum is broad on the nonpolar DLC. Plasmon propagation lengths are comparable on polar and nonpolar substrates and are on the order of tens of nanometers, considerably shorter than previously reported. As a result, they improve with fewer impurities, at lower temperatures, and at higher carrier densities.« less

Characterizing the potential energy surface of the water dimer with DFT: failures of some popular functionals for hydrogen bonding.

PubMed

Anderson, Julie A; Tschumper, Gregory S

2006-06-08

Ten stationary points on the water dimer potential energy surface have been examined with ten density functional methods (X3LYP, B3LYP, B971, B98, MPWLYP, PBE1PBE, PBE, MPW1K, B3P86, and BHandHLYP). Geometry optimizations and vibrational frequency calculations were carried out with the TZ2P(f,d)+dif basis set. All ten of the density functionals correctly describe the relative energies of the ten stationary points. However, correctly describing the curvature of the potential energy surface is far more difficult. Only one functional (BHandHLYP) reproduces the number of imaginary frequencies from CCSD(T) calculations. The other nine density functionals fail to correctly characterize the nature of at least one of the ten (H(2)O)(2) stationary points studied here.

EFFECTS OF LASER RADIATION ON MATTER: Distribution function of microinclusions in polymethylmethacrylate and its evolution under the influence of a series of laser pulses

NASA Astrophysics Data System (ADS)

Glauberman, G. Ya; Savanin, S. Yu; Shkunov, V. V.; Shumov, D. E.

1990-08-01

A new method is proposed for the derivation of the distribution function of the experimentally determined breakdown thresholds of absorbing microinclusions in a transparent insulator. Expressions are obtained for describing the evolution of this function in the course of irradiation of the insulator with laser pulses of constant energy density. The method is applied to calculate the distribution function of microinclusions in polymethylmethacrylate and the evolution of this function.

Radial basis function network learns ceramic processing and predicts related strength and density

NASA Technical Reports Server (NTRS)

Cios, Krzysztof J.; Baaklini, George Y.; Vary, Alex; Tjia, Robert E.

1993-01-01

Radial basis function (RBF) neural networks were trained using the data from 273 Si3N4 modulus of rupture (MOR) bars which were tested at room temperature and 135 MOR bars which were tested at 1370 C. Milling time, sintering time, and sintering gas pressure were the processing parameters used as the input features. Flexural strength and density were the outputs by which the RBF networks were assessed. The 'nodes-at-data-points' method was used to set the hidden layer centers and output layer training used the gradient descent method. The RBF network predicted strength with an average error of less than 12 percent and density with an average error of less than 2 percent. Further, the RBF network demonstrated a potential for optimizing and accelerating the development and processing of ceramic materials.

Ionic and electronic transport properties in dense plasmas by orbital-free density functional theory

DOE PAGES

Sjostrom, Travis; Daligault, Jérôme

2015-12-09

We validate the application of our recent orbital-free density functional theory (DFT) approach, [Phys. Rev. Lett. 113, 155006 (2014)], for the calculation of ionic and electronic transport properties of dense plasmas. To this end, we calculate the self-diffusion coefficient, the viscosity coefficient, the electrical and thermal conductivities, and the reflectivity coefficient of hydrogen and aluminum plasmas. Very good agreement is found with orbital-based Kohn-Sham DFT calculations at lower temperatures. Because the computational costs of the method do not increase with temperature, we can produce results at much higher temperatures than is accessible by the Kohn-Sham method. Our results for warmmore » dense aluminum at solid density are inconsistent with the recent experimental results reported by Sperling et al. [Phys. Rev. Lett. 115, 115001 (2015)].« less

Obtaining macroscopic quantities for the contact line problem from Density Functional Theory using asymptotic methods

NASA Astrophysics Data System (ADS)

Sibley, David; Nold, Andreas; Kalliadasis, Serafim

2015-11-01

Density Functional Theory (DFT), a statistical mechanics of fluids approach, captures microscopic details of the fluid density structure in the vicinity of contact lines, as seen in computations in our recent study. Contact lines describe the location where interfaces between two fluids meet solid substrates, and have stimulated a wealth of research due to both their ubiquity in nature and technological applications and also due to their rich multiscale behaviour. Whilst progress can be made computationally to capture the microscopic to mesoscopic structure from DFT, complete analytical results to fully bridge to the macroscale are lacking. In this work, we describe our efforts to bring asymptotic methods to DFT to obtain results for contact angles and other macroscopic quantities in various parameter regimes. We acknowledge financial support from European Research Council via Advanced Grant No. 247031.

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.

Cryogenic terahertz spectrum of (+)-methamphetamine hydrochloride and assignment using solid-state density functional theory.

PubMed

Hakey, Patrick M; Allis, Damian G; Ouellette, Wayne; Korter, Timothy M

2009-04-30

The cryogenic terahertz spectrum of (+)-methamphetamine hydrochloride from 10.0 to 100.0 cm(-1) is presented, as is the complete structural analysis and vibrational assignment of the compound using solid-state density functional theory. This cryogenic investigation reveals multiple spectral features that were not previously reported in room-temperature terahertz studies of the title compound. Modeling of the compound employed eight density functionals utilizing both solid-state and isolated-molecule methods. The results clearly indicate the necessity of solid-state simulations for the accurate assignment of solid-state THz spectra. Assignment of the observed spectral features to specific atomic motions is based on the BP density functional, which provided the best-fit solid-state simulation of the experimental spectrum. The seven experimental spectral features are the result of thirteen infrared-active vibrational modes predicted at a BP/DNP level of theory with more than 90% of the total spectral intensity associated with external crystal vibrations.

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

Towards the blackbox computation of magnetic exchange coupling parameters in polynuclear transition-metal complexes: theory, implementation, and application.

PubMed

Phillips, Jordan J; Peralta, Juan E

2013-05-07

We present a method for calculating magnetic coupling parameters from a single spin-configuration via analytic derivatives of the electronic energy with respect to the local spin direction. This method does not introduce new approximations beyond those found in the Heisenberg-Dirac Hamiltonian and a standard Kohn-Sham Density Functional Theory calculation, and in the limit of an ideal Heisenberg system it reproduces the coupling as determined from spin-projected energy-differences. Our method employs a generalized perturbative approach to constrained density functional theory, where exact expressions for the energy to second order in the constraints are obtained by analytic derivatives from coupled-perturbed theory. When the relative angle between magnetization vectors of metal atoms enters as a constraint, this allows us to calculate all the magnetic exchange couplings of a system from derivatives with respect to local spin directions from the high-spin configuration. Because of the favorable computational scaling of our method with respect to the number of spin-centers, as compared to the broken-symmetry energy-differences approach, this opens the possibility for the blackbox exploration of magnetic properties in large polynuclear transition-metal complexes. In this work we outline the motivation, theory, and implementation of this method, and present results for several model systems and transition-metal complexes with a variety of density functional approximations and Hartree-Fock.

Diffusion quantum Monte Carlo and density functional calculations of the structural stability of bilayer arsenene

NASA Astrophysics Data System (ADS)

Kadioglu, Yelda; Santana, Juan A.; Özaydin, H. Duygu; Ersan, Fatih; Aktürk, O. Üzengi; Aktürk, Ethem; Reboredo, Fernando A.

2018-06-01

We have studied the structural stability of monolayer and bilayer arsenene (As) in the buckled (b) and washboard (w) phases with diffusion quantum Monte Carlo (DMC) and density functional theory (DFT) calculations. DMC yields cohesive energies of 2.826(2) eV/atom for monolayer b-As and 2.792(3) eV/atom for w-As. In the case of bilayer As, DMC and DFT predict that AA-stacking is the more stable form of b-As, while AB is the most stable form of w-As. The DMC layer-layer binding energies for b-As-AA and w-As-AB are 30(1) and 53(1) meV/atom, respectively. The interlayer separations were estimated with DMC at 3.521(1) Å for b-As-AA and 3.145(1) Å for w-As-AB. A comparison of DMC and DFT results shows that the van der Waals density functional method yields energetic properties of arsenene close to DMC, while the DFT + D3 method closely reproduced the geometric properties from DMC. The electronic properties of monolayer and bilayer arsenene were explored with various DFT methods. The bandgap values vary significantly with the DFT method, but the results are generally qualitatively consistent. We expect the present work to be useful for future experiments attempting to prepare multilayer arsenene and for further development of DFT methods for weakly bonded systems.

Simulation Of Wave Function And Probability Density Of Modified Poschl Teller Potential Derived Using Supersymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

Angraini, Lily Maysari; Suparmi, Variani, Viska Inda

2010-12-01

SUSY quantum mechanics can be applied to solve Schrodinger equation for high dimensional system that can be reduced into one dimensional system and represented in lowering and raising operators. Lowering and raising operators can be obtained using relationship between original Hamiltonian equation and the (super) potential equation. In this paper SUSY quantum mechanics is used as a method to obtain the wave function and the energy level of the Modified Poschl Teller potential. The graph of wave function equation and probability density is simulated by using Delphi 7.0 programming language. Finally, the expectation value of quantum mechanics operator could be calculated analytically using integral form or probability density graph resulted by the programming.

Theory of time-resolved photoelectron imaging. Comparison of a density functional with a time-dependent density functional approach

NASA Astrophysics Data System (ADS)

Suzuki, Yoshi-ichi; Seideman, Tamar; Stener, Mauro

2004-01-01

Time-resolved photoelectron differential cross sections are computed within a quantum dynamical theory that combines a formally exact solution of the nuclear dynamics with density functional theory (DFT)-based approximations of the electronic dynamics. Various observables of time-resolved photoelectron imaging techniques are computed at the Kohn-Sham and at the time-dependent DFT levels. Comparison of the results serves to assess the reliability of the former method and hence its usefulness as an economic approach for time-domain photoelectron cross section calculations, that is applicable to complex polyatomic systems. Analysis of the matrix elements that contain the electronic dynamics provides insight into a previously unexplored aspect of femtosecond-resolved photoelectron imaging.

Assessment of the Density Functional Tight Binding Method for Protic Ionic Liquids

PubMed Central

2015-01-01

Density functional tight binding (DFTB), which is ∼100–1000 times faster than full density functional theory (DFT), has been used to simulate the structure and properties of protic ionic liquid (IL) ions, clusters of ions and the bulk liquid. Proton affinities for a wide range of IL cations and anions determined using DFTB generally reproduce G3B3 values to within 5–10 kcal/mol. The structures and thermodynamic stabilities of n-alkyl ammonium nitrate clusters (up to 450 quantum chemical atoms) predicted with DFTB are in excellent agreement with those determined using DFT. The IL bulk structure simulated using DFTB with periodic boundary conditions is in excellent agreement with published neutron diffraction data. PMID:25328497

An atomic orbital based real-time time-dependent density functional theory for computing electronic circular dichroism band spectra

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

Goings, Joshua J.; Li, Xiaosong, E-mail: xsli@uw.edu

2016-06-21

One of the challenges of interpreting electronic circular dichroism (ECD) band spectra is that different states may have different rotatory strength signs, determined by their absolute configuration. If the states are closely spaced and opposite in sign, observed transitions may be washed out by nearby states, unlike absorption spectra where transitions are always positive additive. To accurately compute ECD bands, it is necessary to compute a large number of excited states, which may be prohibitively costly if one uses the linear-response time-dependent density functional theory (TDDFT) framework. Here we implement a real-time, atomic-orbital based TDDFT method for computing the entiremore » ECD spectrum simultaneously. The method is advantageous for large systems with a high density of states. In contrast to previous implementations based on real-space grids, the method is variational, independent of nuclear orientation, and does not rely on pseudopotential approximations, making it suitable for computation of chiroptical properties well into the X-ray regime.« less

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.

Effect of Non-speckle Echo Signals on Tissue Characteristics for Liver Fibrosis using Probability Density Function of Ultrasonic B-mode image

NASA Astrophysics Data System (ADS)

Mori, Shohei; Hirata, Shinnosuke; Yamaguchi, Tadashi; Hachiya, Hiroyuki

To develop a quantitative diagnostic method for liver fibrosis using an ultrasound B-mode image, a probability imaging method of tissue characteristics based on a multi-Rayleigh model, which expresses a probability density function of echo signals from liver fibrosis, has been proposed. In this paper, an effect of non-speckle echo signals on tissue characteristics estimated from the multi-Rayleigh model was evaluated. Non-speckle signals were determined and removed using the modeling error of the multi-Rayleigh model. The correct tissue characteristics of fibrotic tissue could be estimated with the removal of non-speckle signals.

Analytic second derivative of the energy for density functional theory based on the three-body fragment molecular orbital method

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

Nakata, Hiroya, E-mail: nakata.h.ab@m.titech.ac.jp; RIKEN, Research Cluster for Innovation, Nakamura Lab, 2-1 Hirosawa, Wako, Saitama 351-0198; Japan Society for the Promotion of Science, Kojimachi Business Center Building, 5-3-1 Kojimachi, Chiyoda-ku, Tokyo 102-0083

2015-03-28

Analytic second derivatives of the energy with respect to nuclear coordinates have been developed for spin restricted density functional theory (DFT) based on the fragment molecular orbital method (FMO). The derivations were carried out for the three-body expansion (FMO3), and the two-body expressions can be obtained by neglecting the three-body corrections. Also, the restricted Hartree-Fock (RHF) Hessian for FMO3 can be obtained by neglecting the density-functional related terms. In both the FMO-RHF and FMO-DFT Hessians, certain terms with small magnitudes are neglected for computational efficiency. The accuracy of the FMO-DFT Hessian in terms of the Gibbs free energy is evaluatedmore » for a set of polypeptides and water clusters and found to be within 1 kcal/mol of the corresponding full (non-fragmented) ab initio calculation. The FMO-DFT method is also applied to transition states in S{sub N}2 reactions and for the computation of the IR and Raman spectra of a small Trp-cage protein (PDB: 1L2Y). Some computational timing analysis is also presented.« less

Ultra-fast computation of electronic spectra for large systems by tight-binding based simplified Tamm-Dancoff approximation (sTDA-xTB)

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

Grimme, Stefan, E-mail: grimme@thch.uni-bonn.de; Bannwarth, Christoph

2016-08-07

The computational bottleneck of the extremely fast simplified Tamm-Dancoff approximated (sTDA) time-dependent density functional theory procedure [S. Grimme, J. Chem. Phys. 138, 244104 (2013)] for the computation of electronic spectra for large systems is the determination of the ground state Kohn-Sham orbitals and eigenvalues. This limits such treatments to single structures with a few hundred atoms and hence, e.g., sampling along molecular dynamics trajectories for flexible systems or the calculation of chromophore aggregates is often not possible. The aim of this work is to solve this problem by a specifically designed semi-empirical tight binding (TB) procedure similar to the wellmore » established self-consistent-charge density functional TB scheme. The new special purpose method provides orbitals and orbital energies of hybrid density functional character for a subsequent and basically unmodified sTDA procedure. Compared to many previous semi-empirical excited state methods, an advantage of the ansatz is that a general eigenvalue problem in a non-orthogonal, extended atomic orbital basis is solved and therefore correct occupied/virtual orbital energy splittings as well as Rydberg levels are obtained. A key idea for the success of the new model is that the determination of atomic charges (describing an effective electron-electron interaction) and the one-particle spectrum is decoupled and treated by two differently parametrized Hamiltonians/basis sets. The three-diagonalization-step composite procedure can routinely compute broad range electronic spectra (0-8 eV) within minutes of computation time for systems composed of 500-1000 atoms with an accuracy typical of standard time-dependent density functional theory (0.3-0.5 eV average error). An easily extendable parametrization based on coupled-cluster and density functional computed reference data for the elements H–Zn including transition metals is described. The accuracy of the method termed sTDA-xTB is first benchmarked for vertical excitation energies of open- and closed-shell systems in comparison to other semi-empirical methods and applied to exemplary problems in electronic spectroscopy. As side products of the development, a robust and efficient valence electron TB method for the accurate determination of atomic charges as well as a more accurate calculation scheme of dipole rotatory strengths within the Tamm-Dancoff approximation is proposed.« less

Subsystem real-time time dependent density functional theory.

PubMed

Krishtal, Alisa; Ceresoli, Davide; Pavanello, Michele

2015-04-21

We present the extension of Frozen Density Embedding (FDE) formulation of subsystem Density Functional Theory (DFT) to real-time Time Dependent Density Functional Theory (rt-TDDFT). FDE is a DFT-in-DFT embedding method that allows to partition a larger Kohn-Sham system into a set of smaller, coupled Kohn-Sham systems. Additional to the computational advantage, FDE provides physical insight into the properties of embedded systems and the coupling interactions between them. The extension to rt-TDDFT is done straightforwardly by evolving the Kohn-Sham subsystems in time simultaneously, while updating the embedding potential between the systems at every time step. Two main applications are presented: the explicit excitation energy transfer in real time between subsystems is demonstrated for the case of the Na4 cluster and the effect of the embedding on optical spectra of coupled chromophores. In particular, the importance of including the full dynamic response in the embedding potential is demonstrated.

A Density Functional Study of Atomic Hydrogen and Oxygen Chemisorptions on the (0001) Surface of Double Hexagonal Close Packed Americium

NASA Astrophysics Data System (ADS)

Dholabhai, Pratik; Atta-Fynn, Raymond; Ray, Asok

2008-03-01

Ab initio total energy calculations within the framework of density functional theory have been performed for atomic hydrogen and oxygen chemisorptions on the (0001) surface of double hexagonal packed americium using a full-potential all-electron linearized augmented plane wave plus local orbitals (FLAPW+lo) method. The three-fold hollow hcp site was found to be the most stable site for H adsorption, while the two-fold bridge adsorption site was found to be the most stable site for O adsorption. Chemisorption energies and adsorption geometries for different adsorption sites will be discussed. The change in work functions, magnetic moments, partial charges inside muffin-tins, difference charge density distributions and density of states for the bare Am slab and the Am slab after adsorption of the adatom will be discussed. The implications of chemisorption on Am 5f electron localization-delocalization will also be discussed.

Screened exchange hybrid density functional for accurate and efficient structures and interaction energies.

PubMed

Brandenburg, Jan Gerit; Caldeweyher, Eike; Grimme, Stefan

2016-06-21

We extend the recently introduced PBEh-3c global hybrid density functional [S. Grimme et al., J. Chem. Phys., 2015, 143, 054107] by a screened Fock exchange variant based on the Henderson-Janesko-Scuseria exchange hole model. While the excellent performance of the global hybrid is maintained for small covalently bound molecules, its performance for computed condensed phase mass densities is further improved. Most importantly, a speed up of 30 to 50% can be achieved and especially for small orbital energy gap cases, the method is numerically much more robust. The latter point is important for many applications, e.g., for metal-organic frameworks, organic semiconductors, or protein structures. This enables an accurate density functional based electronic structure calculation of a full DNA helix structure on a single core desktop computer which is presented as an example in addition to comprehensive benchmark results.

Excited State Charge Transfer reaction with dual emission from 5-(4-dimethylamino-phenyl)-penta-2,4-dienenitrile: Spectral measurement and theoretical density functional theory calculation

NASA Astrophysics Data System (ADS)

Jana, Sankar; Dalapati, Sasanka; Ghosh, Shalini; Kar, Samiran; Guchhait, Nikhil

2011-07-01

The excited state intramolecular charge transfer process in donor-chromophore-acceptor system 5-(4-dimethylamino-phenyl)-penta-2,4-dienenitrile (DMAPPDN) has been investigated by steady state absorption and emission spectroscopy in combination with Density Functional Theory (DFT) calculations. This flexible donor acceptor molecule DMAPPDN shows dual fluorescence corresponding to emission from locally excited and charge transfer state in polar solvent. Large solvatochromic emission shift, effect of variation of pH and HOMO-LUMO molecular orbital pictures support excited state intramolecular charge transfer process. The experimental findings have been correlated with the calculated structure and potential energy surfaces based on the Twisted Intramolecular Charge Transfer (TICT) model obtained at DFT level using B3LYP functional and 6-31+G( d, p) basis set. The theoretical potential energy surfaces for the excited states have been generated in vacuo and acetonitrile solvent using Time Dependent Density Functional Theory (TDDFT) and Time Dependent Density Functional Theory Polarized Continuum Model (TDDFT-PCM) method, respectively. All the theoretical results show well agreement with the experimental observations.

Functional Data Analysis in NTCP Modeling: A New Method to Explore the Radiation Dose-Volume Effects

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

Benadjaoud, Mohamed Amine, E-mail: mohamedamine.benadjaoud@gustaveroussy.fr; Université Paris sud, Le Kremlin-Bicêtre; Institut Gustave Roussy, Villejuif

2014-11-01

Purpose/Objective(s): To describe a novel method to explore radiation dose-volume effects. Functional data analysis is used to investigate the information contained in differential dose-volume histograms. The method is applied to the normal tissue complication probability modeling of rectal bleeding (RB) for patients irradiated in the prostatic bed by 3-dimensional conformal radiation therapy. Methods and Materials: Kernel density estimation was used to estimate the individual probability density functions from each of the 141 rectum differential dose-volume histograms. Functional principal component analysis was performed on the estimated probability density functions to explore the variation modes in the dose distribution. The functional principalmore » components were then tested for association with RB using logistic regression adapted to functional covariates (FLR). For comparison, 3 other normal tissue complication probability models were considered: the Lyman-Kutcher-Burman model, logistic model based on standard dosimetric parameters (LM), and logistic model based on multivariate principal component analysis (PCA). Results: The incidence rate of grade ≥2 RB was 14%. V{sub 65Gy} was the most predictive factor for the LM (P=.058). The best fit for the Lyman-Kutcher-Burman model was obtained with n=0.12, m = 0.17, and TD50 = 72.6 Gy. In PCA and FLR, the components that describe the interdependence between the relative volumes exposed at intermediate and high doses were the most correlated to the complication. The FLR parameter function leads to a better understanding of the volume effect by including the treatment specificity in the delivered mechanistic information. For RB grade ≥2, patients with advanced age are significantly at risk (odds ratio, 1.123; 95% confidence interval, 1.03-1.22), and the fits of the LM, PCA, and functional principal component analysis models are significantly improved by including this clinical factor. Conclusion: Functional data analysis provides an attractive method for flexibly estimating the dose-volume effect for normal tissues in external radiation therapy.« less

Spectral densities for Frenkel exciton dynamics in molecular crystals: A TD-DFTB approach

NASA Astrophysics Data System (ADS)

Plötz, Per-Arno; Megow, Jörg; Niehaus, Thomas; Kühn, Oliver

2017-02-01

Effects of thermal fluctuations on the electronic excitation energies and intermonomeric Coulomb couplings are investigated for a perylene-tetracarboxylic-diimide crystal. To this end, time dependent density functional theory based tight binding (TD-DFTB) in the linear response formulation is used in combination with electronic ground state classical molecular dynamics. As a result, a parametrized Frenkel exciton Hamiltonian is obtained, with the effect of exciton-vibrational coupling being described by spectral densities. Employing dynamically defined normal modes, these spectral densities are analyzed in great detail, thus providing insight into the effect of specific intramolecular motions on excitation energies and Coulomb couplings. This distinguishes the present method from approaches using fixed transition densities. The efficiency by which intramolecular contributions to the spectral density can be calculated is a clear advantage of this method as compared with standard TD-DFT.

Many-Body Theory of Pyrochlore Iridates and Related Materials

NASA Astrophysics Data System (ADS)

Wang, Runzhi

In this thesis we focus on two problems. First we propose a numerical method for generating optimized Wannier functions with desired properties. Second we perform the state of the art density functional plus dynamical mean-field calculations in pyrochlore iridates, to investigate the physics induced by the cooperation of spin-orbit coupling and electron correlation. We begin with the introduction for maximally localized Wannier functions and other related extensions. Then we describe the current research in the field of spin-orbit coupling and its interplay with correlation effects, followed by a brief introduction of the `hot' materials of iridates. Before the end of the introduction, we discuss the numerical methods employed in our work, including the density functional theory; dynamical mean-field theory and its combination with the exact diagonalization impurity solver. Then we propose our approach for constructing an optimized set of Wannier functions, which is a generalization of the functionality of the classic maximal localization method put forward by Marzari and Vanderbilt. Our work is motivated by the requirement of the effective description of the local subspace of the Hamiltonian by the beyond density functional theory methods. In extensions of density functional theory such as dynamical mean-field theory, one may want highly accurate description of particular local orbitals, including correct centers and symmetries; while the basis for the remaining degrees of freedom is unimportant. Therefore, we develop the selectively localized Wannier function approach which allows for a greater localization in the selected subset of Wannier functions and at the same time allows us to fix the centers and ensure the point symmetries. Applications in real materials are presented to demonstrate the power of our approach. Next we move to the investigation of pyrochlore iridates, focussing on the metal-insulator transition and material dependence in these compounds. We perform combined density functional plus dynamical mean-field calculations in Lu2Ir2O7, Y2Ir2O 7, Eu2Ir2O7, with spin-orbit coupling included and both single-site and cluster approximations appiled. A broad range of Weyl metal is predicted as the intervening phase in the metal-insulator transition. By comparing to experiments, we find that the single-site approximation fails to predict the gap values and substantial difference between the Y and Eu-compound, demonstrating the inadequacy of this approximation and indicating the key role played by the intersite effects. Finally, we provide a more accurate description of the vicinity of the metal-insulator and topological transitions implied by density functional plus cluster dynamical mean-field calculations of pyrochlore iridates. We find definitive evidence of the Weyl semimetal phase, the electronic structure of which can be approximately described as ``Weyl rings" with an extremely flat dispersion of one of the Weyl bands. This Weyl semimetal phase is further investigated by the k • p analysis fitting to the numerical results. We find that this unusual structure leads to interesting behavior in the optical conductivity including a Hall effect in the interband component, and to an enhanced susceptibility.

Wood density-moisture profiles in old-growth Douglas-fir and western hemlock.

Treesearch

W.Y. Pong; Dale R. Waddell; Lambert Michael B.

1986-01-01

Accurate estimation of the weight of each load of logs is necessary for safe and efficient aerial logging operations. The prediction of green density (lb/ft3) as a function of height is a critical element in the accurate estimation of tree bole and log weights. Two sampling methods, disk and increment core (Bergstrom xylodensimeter), were used to measure the density-...

Lower grey matter density and functional connectivity in the anterior insula in smokers compared to never-smokers

PubMed Central

Stoeckel, Luke E.; Chai, Xiaoqian J.; Zhang, Jiahe; Whitfield-Gabrieli, Susan; Evins, A. Eden

2015-01-01

Rationale While nicotine addiction is characterized by both structural and functional abnormalities in brain networks involved in salience and cognitive control, few studies have integrated these data to understand how these abnormalities may support addiction. Objectives (1) To evaluate grey matter density and functional connectivity of the anterior insula in cigarette smokers and never-smokers and (2) characterize how differences in these measures related to smoking behavior. Methods We compared structural MRI (grey matter density via voxel-based morphometry) and seed-based functional connectivity MRI data in 16 minimally deprived smokers and 16 matched never-smokers. Results Compared to controls, smokers had lower grey matter density in left anterior insula extending into inferior frontal and temporal cortex. Grey matter density in this region was inversely correlated with cigarettes smoked per day. Smokers exhibited negative functional connectivity (anti-correlation) between the anterior insula and regions involved in cognitive control (left lateral prefrontal cortex) and semantic processing / emotion regulation (lateral temporal cortex), whereas controls exhibited positive connectivity between these regions. Conclusions There were differences in the anterior insula, a central region in the brain’s salience network, when comparing both volumetric and functional connectivity data between cigarette smokers and never smokers. Volumetric data, but not the functional connectivity data, was also associated with an aspect of smoking behavior (daily cigarettes smoked). PMID:25990865

First Principles Study of Chemically Functionalized Graphene

NASA Astrophysics Data System (ADS)

Jha, Sanjiv; Vasiliev, Igor

2015-03-01

The electronic, structural and vibrational properties of carbon nanomaterials can be affected by chemical functionalization. We applied ab initio computational methods based on density functional theory to study the covalent functionalization of graphene with benzyne, carboxyl groups and tetracyanoethylene oxide (TCNEO). Our calculations were carried out using the SIESTA and Quantum-ESPRESSO electronic structure codes combined with the local density and generalized gradient approximations for the exchange correlation functional and norm-conserving Troullier-Martins pseudopotentials. The simulated Raman and infrared spectra of graphene functionalized with carboxyl groups and TCNEO were consistent with the available experimental results. The computed vibrational spectra of graphene functionalized with carboxyl groups showed that the presence of point defects near the functionalization site affects the Raman and infrared spectroscopic signatures of functionalized graphene. Supported by NSF CHE-1112388.

Bayesian nonparametric regression with varying residual density

PubMed Central

Pati, Debdeep; Dunson, David B.

2013-01-01

We consider the problem of robust Bayesian inference on the mean regression function allowing the residual density to change flexibly with predictors. The proposed class of models is based on a Gaussian process prior for the mean regression function and mixtures of Gaussians for the collection of residual densities indexed by predictors. Initially considering the homoscedastic case, we propose priors for the residual density based on probit stick-breaking (PSB) scale mixtures and symmetrized PSB (sPSB) location-scale mixtures. Both priors restrict the residual density to be symmetric about zero, with the sPSB prior more flexible in allowing multimodal densities. We provide sufficient conditions to ensure strong posterior consistency in estimating the regression function under the sPSB prior, generalizing existing theory focused on parametric residual distributions. The PSB and sPSB priors are generalized to allow residual densities to change nonparametrically with predictors through incorporating Gaussian processes in the stick-breaking components. This leads to a robust Bayesian regression procedure that automatically down-weights outliers and influential observations in a locally-adaptive manner. Posterior computation relies on an efficient data augmentation exact block Gibbs sampler. The methods are illustrated using simulated and real data applications. PMID:24465053

Thermal density functional theory, ensemble density functional theory, and potential functional theory for warm dense matter

NASA Astrophysics Data System (ADS)

Pribram-Jones, Aurora

Warm dense matter (WDM) is a high energy phase between solids and plasmas, with characteristics of both. It is present in the centers of giant planets, within the earth's core, and on the path to ignition of inertial confinement fusion. The high temperatures and pressures of warm dense matter lead to complications in its simulation, as both classical and quantum effects must be included. One of the most successful simulation methods is density functional theory-molecular dynamics (DFT-MD). Despite great success in a diverse array of applications, DFT-MD remains computationally expensive and it neglects the explicit temperature dependence of electron-electron interactions known to exist within exact DFT. Finite-temperature density functional theory (FT DFT) is an extension of the wildly successful ground-state DFT formalism via thermal ensembles, broadening its quantum mechanical treatment of electrons to include systems at non-zero temperatures. Exact mathematical conditions have been used to predict the behavior of approximations in limiting conditions and to connect FT DFT to the ground-state theory. An introduction to FT DFT is given within the context of ensemble DFT and the larger field of DFT is discussed for context. Ensemble DFT is used to describe ensembles of ground-state and excited systems. Exact conditions in ensemble DFT and the performance of approximations depend on ensemble weights. Using an inversion method, exact Kohn-Sham ensemble potentials are found and compared to approximations. The symmetry eigenstate Hartree-exchange approximation is in good agreement with exact calculations because of its inclusion of an ensemble derivative discontinuity. Since ensemble weights in FT DFT are temperature-dependent Fermi weights, this insight may help develop approximations well-suited to both ground-state and FT DFT. A novel, highly efficient approach to free energy calculations, finite-temperature potential functional theory, is derived, which has the potential to transform the simulation of warm dense matter. As a semiclassical method, it connects the normally disparate regimes of cold condensed matter physics and hot plasma physics. This orbital-free approach captures the smooth classical density envelope and quantum density oscillations that are both crucial to accurate modeling of materials where temperature and pressure effects are influential.

Stochastic density functional theory at finite temperatures

NASA Astrophysics Data System (ADS)

Cytter, Yael; Rabani, Eran; Neuhauser, Daniel; Baer, Roi

2018-03-01

Simulations in the warm dense matter regime using finite temperature Kohn-Sham density functional theory (FT-KS-DFT), while frequently used, are computationally expensive due to the partial occupation of a very large number of high-energy KS eigenstates which are obtained from subspace diagonalization. We have developed a stochastic method for applying FT-KS-DFT, that overcomes the bottleneck of calculating the occupied KS orbitals by directly obtaining the density from the KS Hamiltonian. The proposed algorithm scales as O (" close=")N3T3)">N T-1 and is compared with the high-temperature limit scaling O Multiconfigurational short-range density-functional theory for open-shell systems

NASA Astrophysics Data System (ADS)

Hedegârd, Erik Donovan; Toulouse, Julien; Jensen, Hans Jørgen Aagaard

2018-06-01

Many chemical systems cannot be described by quantum chemistry methods based on a single-reference wave function. Accurate predictions of energetic and spectroscopic properties require a delicate balance between describing the most important configurations (static correlation) and obtaining dynamical correlation efficiently. The former is most naturally done through a multiconfigurational (MC) wave function, whereas the latter can be done by, e.g., perturbation theory. We have employed a different strategy, namely, a hybrid between multiconfigurational wave functions and density-functional theory (DFT) based on range separation. The method is denoted by MC short-range DFT (MC-srDFT) and is more efficient than perturbative approaches as it capitalizes on the efficient treatment of the (short-range) dynamical correlation by DFT approximations. In turn, the method also improves DFT with standard approximations through the ability of multiconfigurational wave functions to recover large parts of the static correlation. Until now, our implementation was restricted to closed-shell systems, and to lift this restriction, we present here the generalization of MC-srDFT to open-shell cases. The additional terms required to treat open-shell systems are derived and implemented in the DALTON program. This new method for open-shell systems is illustrated on dioxygen and [Fe(H2O)6]3+.

Constrained variation in Jastrow method at high density

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

Owen, J.C.; Bishop, R.F.; Irvine, J.M.

1976-11-01

A method is derived for constraining the correlation function in a Jastrow variational calculation which permits the truncation of the cluster expansion after two-body terms, and which permits exact minimization of the two-body cluster by functional variation. This method is compared with one previously proposed by Pandharipande and is found to be superior both theoretically and practically. The method is tested both on liquid /sup 3/He, by using the Lennard--Jones potential, and on the model system of neutrons treated as Boltzmann particles (''homework'' problem). Good agreement is found both with experiment and with other calculations involving the explicit evaluation ofmore » higher-order terms in the cluster expansion. The method is then applied to a more realistic model of a neutron gas up to a density of 4 neutrons per F/sup 3/, and is found to give ground-state energies considerably lower than those of Pandharipande. (AIP)« less

Computer-based quantitative computed tomography image analysis in idiopathic pulmonary fibrosis: A mini review.

PubMed

Ohkubo, Hirotsugu; Nakagawa, Hiroaki; Niimi, Akio

2018-01-01

Idiopathic pulmonary fibrosis (IPF) is the most common type of progressive idiopathic interstitial pneumonia in adults. Many computer-based image analysis methods of chest computed tomography (CT) used in patients with IPF include the mean CT value of the whole lungs, density histogram analysis, density mask technique, and texture classification methods. Most of these methods offer good assessment of pulmonary functions, disease progression, and mortality. Each method has merits that can be used in clinical practice. One of the texture classification methods is reported to be superior to visual CT scoring by radiologist for correlation with pulmonary function and prediction of mortality. In this mini review, we summarize the current literature on computer-based CT image analysis of IPF and discuss its limitations and several future directions. Copyright © 2017 The Japanese Respiratory Society. Published by Elsevier B.V. All rights reserved.

Final Technical Report for DE-SC0001878 [Theory and Simulation of Defects in Oxide Materials

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

Chelikowsky, James R.

2014-04-14

We explored a wide variety of oxide materials and related problems, including materials at the nanoscale and generic problems associated with oxide materials such as the development of more efficient computational tools to examine these materials. We developed and implemented methods to understand the optical and structural properties of oxides. For ground state properties, our work is predominantly based on pseudopotentials and density functional theory (DFT), including new functionals and going beyond the local density approximation (LDA): LDA+U. To study excited state properties (quasiparticle and optical excitations), we use time dependent density functional theory, the GW approach, and GW plusmore » Bethe-Salpeter equation (GW-BSE) methods based on a many-body Green function approaches. Our work focused on the structural, electronic, optical and magnetic properties of defects (such as oxygen vacancies) in hafnium oxide, titanium oxide (both bulk and clusters) and related materials. We calculated the quasiparticle defect states and charge transition levels of oxygen vacancies in monoclinic hafnia. we presented a milestone G0W0 study of two of the crystalline phases of dye-sensitized TiO{sub 2} clusters. We employed hybrid density functional theory to examine the electronic structure of sexithiophene/ZnO interfaces. To identify the possible effect of epitaxial strain on stabilization of the ferromagnetic state of LaCoO{sub 3} (LCO), we compare the total energy of the magnetic and nonmagnetic states of the strained theoretical bulk structure.« less

Bonding and Microstructural Stability in Ni55Ti45 Studied by Experimental and Theoretical Methods

NASA Technical Reports Server (NTRS)

Stott, Amanda C.; Brauer, Jonathan I.; Garg, Anita; Pepper, Stephen V.; Abel, Phillip B.; DellaCorte, Christopher; Noebe, Ronald D.; Glennon, Glenn; Bylaska, Eric; Dixon, David A.

2010-01-01

Spiral orbit tribometry friction tests performed on Ni-rich Ni55Ti45 titanium ball bearings indicate that this alloy is a promising candidate for future aerospace bearing applications. Microstructural characterization of the bearing specimens was performed using transmission electron microscopy and energy dispersive spectroscopy, with NiTi, Ni4Ti3, Ni3Ti, and Ni2Ti4Ox phases identified within the microstructure of the alloy. Density functional theory was applied to predict the electronic structure of the NixTiy phases, including the band structure and site projected density of states. Ultraviolet photoemission spectroscopy was used to verify the density of states results from the density functional theory calculations, with good agreement observed between experiment and theory.

Accurately predicting the structure, density, and hydrostatic compression of crystalline β-1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane based on its wave-function-based potential

NASA Astrophysics Data System (ADS)

Song, H.-J.; Huang, F.

2011-09-01

A wave-function-based intermolecular potential of the β phase 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (HMX) molecule has been constructed from first principles using the Williams-Stone-Misquitta method and the symmetry-adapted perturbation theory. Using the potential and its derivatives, we have accurately predicted not only the structure and lattice energy of the crystalline β-HMX at 0 K, but also its densities at temperatures of 0-403 K within an accuracy of 1% of density. The calculated densities at pressures within 0-6 GPa excellently agree with the results from the experiments on hydrostatic compression.

Time-dependent density functional theory (TD-DFT) coupled with reference interaction site model self-consistent field explicitly including spatial electron density distribution (RISM-SCF-SEDD)

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

Yokogawa, D., E-mail: d.yokogawa@chem.nagoya-u.ac.jp; Institute of Transformative Bio-Molecules

2016-09-07

Theoretical approach to design bright bio-imaging molecules is one of the most progressing ones. However, because of the system size and computational accuracy, the number of theoretical studies is limited to our knowledge. To overcome the difficulties, we developed a new method based on reference interaction site model self-consistent field explicitly including spatial electron density distribution and time-dependent density functional theory. We applied it to the calculation of indole and 5-cyanoindole at ground and excited states in gas and solution phases. The changes in the optimized geometries were clearly explained with resonance structures and the Stokes shift was correctly reproduced.

Electronic structure and electron momentum densities of Ag2CrO4

NASA Astrophysics Data System (ADS)

Meena, Seema Kumari; Ahuja, B. L.

2018-05-01

We present the first-ever experimental electron momentum density of Ag2CrO4 using 661.65 keV γ-rays from 20 Ci 137Cs source. To validate our experimental data, we have also deduced theoretical Compton profiles, energy bands and density of states using linear combination of atomic orbitals (LCAO) method in the framework of density functional theory. It is seen that the DFT-LDA gives a better agreement with experimental data than free atom model. The energy bands and density of states are also discussed.

Novel density functional methodology for the computation of accurate electronic and thermodynamic properties of molecular systems and improved long-range behavior

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

Kafafi, S.A.

1998-12-10

A novel general purpose density functional methodology for the computation of accurate electronic and thermodynamic properties of molecules and improved long-range behavior is reported. Assuming the separability of the exchange (E{sub x}) and correlation (E{sub c}) contributions to the total exchange-correlation energy functional (E{sub xc}), the E{sub x} term consists of a hybrid mixture of 37.5% Hartree-Fock exchange and the appropriate local spin density exchange using the adiabatic connection formula. He demonstrated that E{sub x} and its corresponding potential V{sub x} [=dE{sub x}/d{rho}(r)] have the proper asymptotic limits at r = 0 and r {r_arrow} {infinity}, E{sub c} consists ofmore » the Vosko, Wilk, and Nusair formula for the free-electron gas correlation energy and a generalized gradient approximation term with one adjustable parameter. V{sub c} [=dE{sub c}/d{rho}(r)] was shown to obey the r {r_arrow} {infinity} limit of the corresponding potential derived from exact atomic exchange-correlation computations; namely, V{sub c} is proportional to r{sup {minus}4}. Most importantly, he demonstrated that, at r values where dispersion forces are operating, V{sub c} is proportional to 1/r{sup n} (n = 4, 6, 8, {hor_ellipsis}). The reported method was denoted by K2-BVWN because it used two adjustable parameters in its formulation. The K2-BVWN scheme scales as N{sup 3}, where N is the number of basis functions, compared to {approximately}N{sup 7} for Gaussian-2 (G2) ab initio theory and related methods, {approximately}N{sup 5} for Barone`s mPW1,3PW, and {approximately}N{sup 4} for Becke`s three-parameter density functional approaches. The G2 data set complemented by the reported molecular systems investigated in this work was recommended as a critical test for evaluating novel ab initio and density functional methodologies. The K2-BVWN method has been implemented in the Gaussian series of programs.« less

Space-Pseudo-Time Method: Application to the One-Dimensional Coulomb Potential and Density Funtional Theory

NASA Astrophysics Data System (ADS)

Weatherford, Charles; Gebremedhin, Daniel

2016-03-01

A new and efficient way of evolving a solution to an ordinary differential equation is presented. A finite element method is used where we expand in a convenient local basis set of functions that enforce both function and first derivative continuity across the boundaries of each element. We also implement an adaptive step size choice for each element that is based on a Taylor series expansion. The method is applied to solve for the eigenpairs of the one-dimensional soft-coulomb potential and the hard-coulomb limit is studied. The method is then used to calculate a numerical solution of the Kohn-Sham differential equation within the local density approximation is presented and is applied to the helium atom. Supported by the National Nuclear Security Agency, the Nuclear Regulatory Commission, and the Defense Threat Reduction Agency.

A third-generation density-functional-theory-based method for calculating canonical molecular orbitals of large molecules.

PubMed

Hirano, Toshiyuki; Sato, Fumitoshi

2014-07-28

We used grid-free modified Cholesky decomposition (CD) to develop a density-functional-theory (DFT)-based method for calculating the canonical molecular orbitals (CMOs) of large molecules. Our method can be used to calculate standard CMOs, analytically compute exchange-correlation terms, and maximise the capacity of next-generation supercomputers. Cholesky vectors were first analytically downscaled using low-rank pivoted CD and CD with adaptive metric (CDAM). The obtained Cholesky vectors were distributed and stored on each computer node in a parallel computer, and the Coulomb, Fock exchange, and pure exchange-correlation terms were calculated by multiplying the Cholesky vectors without evaluating molecular integrals in self-consistent field iterations. Our method enables DFT and massively distributed memory parallel computers to be used in order to very efficiently calculate the CMOs of large molecules.

Inhomogeneous hard homonuclear molecules

NASA Astrophysics Data System (ADS)

Quintana, Jacqueline

A review is given of some features of theories for inhomogeneous fluids of nonspherical molecules that take as input the direct correlation function of the corresponding homogeneous system. Two different methods are described for defining the structure of hard homonuclear molecules close to a hard planar wall. A spherical harmonics expanison (SHE) within the integral equation (IE) method is presented and, for comparison, a version of density functional theory for orientable hard bodies. In both cases the Pynn-Lado model is employed and a comparison is made with Monte Carlo data. The results indicate that for hard molecules the IE approach does not always capture the effects of orientation due to the characteristics of the SHE for the step function. This disadvantage is particularly true in the case of the orientationally averaged density profile.

Proton affinity of diastereoisomers of modified prolines using the kinetic method and density functional theory calculations: role of the cis/trans substituent on the endo/exo ring conformation.

PubMed

Mezzache, S; Pepe, C; Karoyan, P; Fournier, F; Tabet, J-C

2005-01-01

The proton affinity (PA) of cis/trans-3-prolinoleucines and cis/trans-3-prolinoglutamic acids have been studied by the kinetic method and density functional theory (DFT) calculations. Several conformations of the neutral and the protonated modified prolines, in particular the endo and exo ring conformations, were analyzed with respect to their contribution to the PA values. When the substituent is an alkyl, both the diastereoisomers have the same PA value. However, the PA values for the diastereoisomers are different when the substituted chain contains functional groups (e.g. a carboxyl group). This variation in PA values could be attributed to the existence of intramolecular hydrogen bonds. Copyright (c) 2005 John Wiley & Sons, Ltd.

Microhartree precision in density functional theory calculations

NASA Astrophysics Data System (ADS)

Gulans, Andris; Kozhevnikov, Anton; Draxl, Claudia

2018-04-01

To address ultimate precision in density functional theory calculations we employ the full-potential linearized augmented plane-wave + local-orbital (LAPW + lo) method and justify its usage as a benchmark method. LAPW + lo and two completely unrelated numerical approaches, the multiresolution analysis (MRA) and the linear combination of atomic orbitals, yield total energies of atoms with mean deviations of 0.9 and 0.2 μ Ha , respectively. Spectacular agreement with the MRA is reached also for total and atomization energies of the G2-1 set consisting of 55 molecules. With the example of α iron we demonstrate the capability of LAPW + lo to reach μ Ha /atom precision also for periodic systems, which allows also for the distinction between the numerical precision and the accuracy of a given functional.

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.

Multiresolution quantum chemistry in multiwavelet bases: excited states from time-dependent Hartree–Fock and density functional theory via linear response

DOE PAGES

Yanai, Takeshi; Fann, George I.; Beylkin, Gregory; ...

2015-02-25

Using the fully numerical method for time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) with the Tamm–Dancoff (TD) approximation we use a multiresolution analysis (MRA) approach to present our findings. From a reformulation with effective use of the density matrix operator, we obtain a general form of the HF/DFT linear response equation in the first quantization formalism. It can be readily rewritten as an integral equation with the bound-state Helmholtz (BSH) kernel for the Green's function. The MRA implementation of the resultant equation permits excited state calculations without virtual orbitals. Moreover, the integral equation is efficiently and adaptively solved using amore » numerical multiresolution solver with multiwavelet bases. Our implementation of the TD-HF/DFT methods is applied for calculating the excitation energies of H 2, Be, N 2, H 2O, and C 2H 4 molecules. The numerical errors of the calculated excitation energies converge in proportion to the residuals of the equation in the molecular orbitals and response functions. The energies of the excited states at a variety of length scales ranging from short-range valence excitations to long-range Rydberg-type ones are consistently accurate. It is shown that the multiresolution calculations yield the correct exponential asymptotic tails for the response functions, whereas those computed with Gaussian basis functions are too diffuse or decay too rapidly. Finally, we introduce a simple asymptotic correction to the local spin-density approximation (LSDA) so that in the TDDFT calculations, the excited states are correctly bound.« less

Using the Opposition Effect in Remotely Sensed Data to Assist in the Retrieval of Bulk Density

NASA Astrophysics Data System (ADS)

Ambeau, Brittany L.

Bulk density is an important geophysical property that impacts the mobility of military vehicles and personnel. Accurate retrieval of bulk density from remotely sensed data is, therefore, needed to estimate the mobility on "off-road" terrain. For a particulate surface, the functional form of the opposition effect can provide valuable information about composition and structure. In this research, we examine the relationship between bulk density and angular width of the opposition effect for a controlled set of laboratory experiments. Given a sample with a known bulk density, we collect reflectance measurements on a spherical grid for various illumination and view geometries -- increasing the amount of reflectance measurements collected at small phase angles near the opposition direction. Bulk densities are varied using a custom-made pluviation device, samples are measured using the Goniometer of the Rochester Institute of Technology-Two (GRIT-T), and observations are fit to the Hapke model using a grid-search method. The method that is selected allows for the direct estimation of five parameters: the single-scattering albedo, the amplitude of the opposition effect, the angular width of the opposition effect, and the two parameters that describe the single-particle phase function. As a test of the Hapke model, the retrieved bulk densities are compared to the known bulk densities. Results show that with an increase in the availability of multi-angular reflectance measurements, the prospects for retrieving the spatial distribution of bulk density from satellite and airborne sensors are imminent.

Estimation of the characteristic parameters of the multilayered film model using the patterson differential function

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

Astaf'ev, S. B., E-mail: webmaster@ns.crys.ras.ru; Shchedrin, B. M.; Yanusova, L. G.

The possibility of estimating the layered film structural parameters by constructing the autocorrelation function P{sub F}(z) (referred to as the Patterson differential function) for the derivative d{rho}/dz of electron density along the normal to the sample surface has been considered. An analytical expression P{sub F}(z) is presented for a multilayered film within the box model of the electron density profile. The possibilities of selecting structural information about layered films by analyzing the features of this function are demonstrated by model and real examples, in particular, by applying the method of shifted systems of peaks for the function P{sub F}(z).

Wigner distribution function and entropy of the damped harmonic oscillator within the theory of the open quantum systems

NASA Technical Reports Server (NTRS)

Isar, Aurelian

1995-01-01

The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.

Nuclear magnetic resonance spin-spin coupling constants from coupled perturbed density functional theory

NASA Astrophysics Data System (ADS)

Sychrovský, Vladimír; Gräfenstein, Jürgen; Cremer, Dieter

2000-09-01

For the first time, a complete implementation of coupled perturbed density functional theory (CPDFT) for the calculation of NMR spin-spin coupling constants (SSCCs) with pure and hybrid DFT is presented. By applying this method to several hydrides, hydrocarbons, and molecules with multiple bonds, the performance of DFT for the calculation of SSCCs is analyzed in dependence of the XC functional used. The importance of electron correlation effects is demonstrated and it is shown that the hybrid functional B3LYP leads to the best accuracy of calculated SSCCs. Also, CPDFT is compared with sum-over-states (SOS) DFT where it turns out that the former method is superior to the latter because it explicitly considers the dependence of the Kohn-Sham operator on the perturbed orbitals in DFT when calculating SSCCs. The four different coupling mechanisms contributing to the SSCC are discussed in connection with the electronic structure of the molecule.

Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

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

None, None

Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. Our paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper also studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases we studied indicate that themore » Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.« less

Local structure analysis on (La,Ba)(Ga,Mg)O3-δ by the pair distribution function method using a neutron source and density functional theory calculations

NASA Astrophysics Data System (ADS)

Kitamura, Naoto; Vogel, Sven C.; Idemoto, Yasushi

2013-06-01

In this work, we focused on La0.95Ba0.05Ga0.8Mg0.2O3-δ with the perovskite structure, and investigated the local structure around the oxygen vacancy by pair distribution function (PDF) method and density functional theory (DFT) calculation. By comparing the G(r) simulated based on the DFT calculation and the experimentally-observed G(r), it was suggested that the oxygen vacancy was trapped by Ba2+ at the La3+ site at least at room temperature. Such a defect association may be one of the reasons why the La0.95Ba0.05Ga0.8Mg0.2O3-δ showed lower oxide-ion conductivity than (La,Sr)(Ga,Mg)O3-δ which was widely-used as an electrolyte of the solid oxide fuel cell.

Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

DOE PAGES

None, None

2016-11-21

Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. Our paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper also studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases we studied indicate that themore » Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.« less

Fast Time-Dependent Density Functional Theory Calculations of the X-ray Absorption Spectroscopy of Large Systems.

PubMed

Besley, Nicholas A

2016-10-11

The computational cost of calculations of K-edge X-ray absorption spectra using time-dependent density functional (TDDFT) within the Tamm-Dancoff approximation is significantly reduced through the introduction of a severe integral screening procedure that includes only integrals that involve the core s basis function of the absorbing atom(s) coupled with a reduced quality numerical quadrature for integrals associated with the exchange and correlation functionals. The memory required for the calculations is reduced through construction of the TDDFT matrix within the absorbing core orbitals excitation space and exploiting further truncation of the virtual orbital space. The resulting method, denoted fTDDFTs, leads to much faster calculations and makes the study of large systems tractable. The capability of the method is demonstrated through calculations of the X-ray absorption spectra at the carbon K-edge of chlorophyll a, C 60 and C 70 .

Continuum Level Density of a Coupled-Channel System in the Complex Scaling Method

NASA Astrophysics Data System (ADS)

Suzuki, R.; Kruppa, A. T.; Giraud, B. G.; Katō, K.

2008-06-01

We study the continuum level density (CLD) in the formalism of the complex scaling method (CSM) for coupled-channel systems. We apply the formalism to the ^{4}He = [^{3}H + p] + [^3{He} + n] coupled-channel cluster model where there are resonances at low energy. Numerical calculations of the CLD in the CSM with a finite number of L^{2} basis functions are consistent with the exact result calculated from the S-matrix by solving coupled-channel equations. We also study channel densities. In this framework, the extended completeness relation (ECR) plays an important role.

A theoretical study for electronic and transport properties of covalent functionalized MoS2 monolayer

NASA Astrophysics Data System (ADS)

Gao, Lijuan; Yang, Zhao-Di; Zhang, Guiling

2017-06-01

The geometries, electronic and electron transport properties of a series of functionalized MoS2 monolayers were investigated using density-functional theory (DFT) and the non-equilibrium Green's function (NEGF) methods. n-Propyl, n-trisilicyl, phenyl, p-nitrophenyl and p-methoxyphenyl are chosen as electron-donating groups. The results show covalent functionalization with electron-donating groups could make a transformation from typical semiconducting to metallic properties for appearance of midgap level across the Fermi level (Ef). The calculations of transport properties for two-probe devices indicate that conductivities of functionalized systems are obviously enhanced relative to pristine MoS2 monolayer. Grafted groups contribute to the major transport path and play an important role in enhancing conductivity. The NDR effect is found. The influence of grafted density is also studied. Larger grafted density leads to wider bandwidth of midgap level, larger current response of I-V curves and larger current difference between peak and valley.

A Semi-Analytical Method for the PDFs of A Ship Rolling in Random Oblique Waves

NASA Astrophysics Data System (ADS)

Liu, Li-qin; Liu, Ya-liu; Xu, Wan-hai; Li, Yan; Tang, You-gang

2018-03-01

The PDFs (probability density functions) and probability of a ship rolling under the random parametric and forced excitations were studied by a semi-analytical method. The rolling motion equation of the ship in random oblique waves was established. The righting arm obtained by the numerical simulation was approximately fitted by an analytical function. The irregular waves were decomposed into two Gauss stationary random processes, and the CARMA (2, 1) model was used to fit the spectral density function of parametric and forced excitations. The stochastic energy envelope averaging method was used to solve the PDFs and the probability. The validity of the semi-analytical method was verified by the Monte Carlo method. The C11 ship was taken as an example, and the influences of the system parameters on the PDFs and probability were analyzed. The results show that the probability of ship rolling is affected by the characteristic wave height, wave length, and the heading angle. In order to provide proper advice for the ship's manoeuvring, the parametric excitations should be considered appropriately when the ship navigates in the oblique seas.

Generalized non-equilibrium vertex correction method in coherent medium theory for quantum transport simulation of disordered nanoelectronics

NASA Astrophysics Data System (ADS)

Yan, Jiawei; Ke, Youqi

In realistic nanoelectronics, disordered impurities/defects are inevitable and play important roles in electron transport. However, due to the lack of effective quantum transport method, the important effects of disorders remain poorly understood. Here, we report a generalized non-equilibrium vertex correction (NVC) method with coherent potential approximation to treat the disorder effects in quantum transport simulation. With this generalized NVC method, any averaged product of two single-particle Green's functions can be obtained by solving a set of simple linear equations. As a result, the averaged non-equilibrium density matrix and various important transport properties, including averaged current, disordered induced current fluctuation and the averaged shot noise, can all be efficiently computed in a unified scheme. Moreover, a generalized form of conditionally averaged non-equilibrium Green's function is derived to incorporate with density functional theory to enable first-principles simulation. We prove the non-equilibrium coherent potential equals the non-equilibrium vertex correction. Our approach provides a unified, efficient and self-consistent method for simulating non-equilibrium quantum transport through disorder nanoelectronics. Shanghaitech start-up fund.

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

Improving the efficiency of configurational-bias Monte Carlo: A density-guided method for generating bending angle trials for linear and branched molecules

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

Sepehri, Aliasghar; Loeffler, Troy D.; Chen, Bin, E-mail: binchen@lsu.edu

2014-08-21

A new method has been developed to generate bending angle trials to improve the acceptance rate and the speed of configurational-bias Monte Carlo. Whereas traditionally the trial geometries are generated from a uniform distribution, in this method we attempt to use the exact probability density function so that each geometry generated is likely to be accepted. In actual practice, due to the complexity of this probability density function, a numerical representation of this distribution function would be required. This numerical table can be generated a priori from the distribution function. This method has been tested on a united-atom model ofmore » alkanes including propane, 2-methylpropane, and 2,2-dimethylpropane, that are good representatives of both linear and branched molecules. It has been shown from these test cases that reasonable approximations can be made especially for the highly branched molecules to reduce drastically the dimensionality and correspondingly the amount of the tabulated data that is needed to be stored. Despite these approximations, the dependencies between the various geometrical variables can be still well considered, as evident from a nearly perfect acceptance rate achieved. For all cases, the bending angles were shown to be sampled correctly by this method with an acceptance rate of at least 96% for 2,2-dimethylpropane to more than 99% for propane. Since only one trial is required to be generated for each bending angle (instead of thousands of trials required by the conventional algorithm), this method can dramatically reduce the simulation time. The profiling results of our Monte Carlo simulation code show that trial generation, which used to be the most time consuming process, is no longer the time dominating component of the simulation.« less

Universal analytical scattering form factor for shell-, core-shell, or homogeneous particles with continuously variable density profile shape.

PubMed

Foster, Tobias

2011-09-01

A novel analytical and continuous density distribution function with a widely variable shape is reported and used to derive an analytical scattering form factor that allows us to universally describe the scattering from particles with the radial density profile of homogeneous spheres, shells, or core-shell particles. Composed by the sum of two Fermi-Dirac distribution functions, the shape of the density profile can be altered continuously from step-like via Gaussian-like or parabolic to asymptotically hyperbolic by varying a single "shape parameter", d. Using this density profile, the scattering form factor can be calculated numerically. An analytical form factor can be derived using an approximate expression for the original Fermi-Dirac distribution function. This approximation is accurate for sufficiently small rescaled shape parameters, d/R (R being the particle radius), up to values of d/R ≈ 0.1, and thus captures step-like, Gaussian-like, and parabolic as well as asymptotically hyperbolic profile shapes. It is expected that this form factor is particularly useful in a model-dependent analysis of small-angle scattering data since the applied continuous and analytical function for the particle density profile can be compared directly with the density profile extracted from the data by model-free approaches like the generalized inverse Fourier transform method. © 2011 American Chemical Society

Generalization of the van der Pauw Method: Analyzing Longitudinal Magnetoresistance Asymmetry to Quantify Doping Gradients

NASA Astrophysics Data System (ADS)

Grayson, M.; Zhou, Wang; Yoo, Heun-Mo; Prabhu-Gaunkar, S.; Tiemann, L.; Reichl, C.; Wegscheider, W.

A longitudinal magnetoresistance asymmetry (LMA) between a positive and negative magnetic field is known to occur in both the extreme quantum limit and the classical Drude limit in samples with a nonuniform doping density. By analyzing the current stream function in van der Pauw measurement geometry, it is shown that the electron density gradient can be quantitatively deduced from this LMA in the Drude regime. Results agree with gradients interpolated from local densities calibrated across an entire wafer, establishing a generalization of the van der Pauw method to quantify density gradients. Results will be shown of various semoconductor systems where this method is applied, from bulk doped semiconductors, to exfoliated 2D materials. McCormick Catalyst Award from Northwestern University, EECS Bridge Funding, and AFOSR FA9550-15-1-0247.

Nonlinear electronic excitations in crystalline solids using meta-generalized gradient approximation and hybrid functional in time-dependent density functional theory

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

Sato, Shunsuke A.; Taniguchi, Yasutaka; Department of Medical and General Sciences, Nihon Institute of Medical Science, 1276 Shimogawara, Moroyama-Machi, Iruma-Gun, Saitama 350-0435

2015-12-14

We develop methods to calculate electron dynamics in crystalline solids in real-time time-dependent density functional theory employing exchange-correlation potentials which reproduce band gap energies of dielectrics; a meta-generalized gradient approximation was proposed by Tran and Blaha [Phys. Rev. Lett. 102, 226401 (2009)] (TBm-BJ) and a hybrid functional was proposed by Heyd, Scuseria, and Ernzerhof [J. Chem. Phys. 118, 8207 (2003)] (HSE). In time evolution calculations employing the TB-mBJ potential, we have found it necessary to adopt the predictor-corrector step for a stable time evolution. We have developed a method to evaluate electronic excitation energy without referring to the energy functionalmore » which is unknown for the TB-mBJ potential. For the HSE functional, we have developed a method for the operation of the Fock-like term in Fourier space to facilitate efficient use of massive parallel computers equipped with graphic processing units. We compare electronic excitations in silicon and germanium induced by femtosecond laser pulses using the TB-mBJ, HSE, and a simple local density approximation (LDA). At low laser intensities, electronic excitations are found to be sensitive to the band gap energy: they are close to each other using TB-mBJ and HSE and are much smaller in LDA. At high laser intensities close to the damage threshold, electronic excitation energies do not differ much among the three cases.« less

Estimation of effective x-ray tissue attenuation differences for volumetric breast density measurement

NASA Astrophysics Data System (ADS)

Chen, Biao; Ruth, Chris; Jing, Zhenxue; Ren, Baorui; Smith, Andrew; Kshirsagar, Ashwini

2014-03-01

Breast density has been identified to be a risk factor of developing breast cancer and an indicator of lesion diagnostic obstruction due to masking effect. Volumetric density measurement evaluates fibro-glandular volume, breast volume, and breast volume density measures that have potential advantages over area density measurement in risk assessment. One class of volume density computing methods is based on the finding of the relative fibro-glandular tissue attenuation with regards to the reference fat tissue, and the estimation of the effective x-ray tissue attenuation differences between the fibro-glandular and fat tissue is key to volumetric breast density computing. We have modeled the effective attenuation difference as a function of actual x-ray skin entrance spectrum, breast thickness, fibro-glandular tissue thickness distribution, and detector efficiency. Compared to other approaches, our method has threefold advantages: (1) avoids the system calibration-based creation of effective attenuation differences which may introduce tedious calibrations for each imaging system and may not reflect the spectrum change and scatter induced overestimation or underestimation of breast density; (2) obtains the system specific separate and differential attenuation values of fibroglandular and fat for each mammographic image; and (3) further reduces the impact of breast thickness accuracy to volumetric breast density. A quantitative breast volume phantom with a set of equivalent fibro-glandular thicknesses has been used to evaluate the volume breast density measurement with the proposed method. The experimental results have shown that the method has significantly improved the accuracy of estimating breast density.

Brownian systems with spatially inhomogeneous activity

NASA Astrophysics Data System (ADS)

Sharma, A.; Brader, J. M.

2017-09-01

We generalize the Green-Kubo approach, previously applied to bulk systems of spherically symmetric active particles [J. Chem. Phys. 145, 161101 (2016), 10.1063/1.4966153], to include spatially inhomogeneous activity. The method is applied to predict the spatial dependence of the average orientation per particle and the density. The average orientation is given by an integral over the self part of the Van Hove function and a simple Gaussian approximation to this quantity yields an accurate analytical expression. Taking this analytical result as input to a dynamic density functional theory approximates the spatial dependence of the density in good agreement with simulation data. All theoretical predictions are validated using Brownian dynamics simulations.

IPS analysis on relationship among velocity, density and temperature of the solar wind

NASA Astrophysics Data System (ADS)

Hayashi, K.; Tokumaru, M.; Fujiki, K.

2015-12-01

The IPS(Interplanetary Scintillation)-MHD(magnetohydrodynamics) tomography is a method we have developed to determine three-dimensional MHD solution of the solar wind that best matches the line-of-sight IPS solar-wind speed data (Hayashi et al., 2003). The tomographic approach is an iteration method in which IPS observations are simulated in MHD steady-state solution, then differences between the simulated observation and the actual IPS observation is reduced by modifying solar-wind boundary map at 50 solar radii. This forward model needs to assume solar wind density and temperature as function of speed. We use empirical functions, N(V) and T(V), derived from Helios in-situ measurement data within 0.5 AU in 1970s. For recent years, especially after 2006, these functions yield higher densities and lower temperatures than in-situ measurements indicate. To characterize the differences between the simulated and actual solar wind plasma, we tune parameters in the functions so that agreements with in-situ data (near the Earth and at Ulysses) will be optimized. This optimization approach can help better simulations of the solar corona and heliosphere, and will help our understandings on roles of magnetic field in solar wind heating and acceleration.

Including screening in van der Waals corrected density functional theory calculations: the case of atoms and small molecules physisorbed on graphene.

PubMed

Silvestrelli, Pier Luigi; Ambrosetti, Alberto

2014-03-28

The Density Functional Theory (DFT)/van der Waals-Quantum Harmonic Oscillator-Wannier function (vdW-QHO-WF) method, recently developed to include the vdW interactions in approximated DFT by combining the quantum harmonic oscillator model with the maximally localized Wannier function technique, is applied to the cases of atoms and small molecules (X=Ar, CO, H2, H2O) weakly interacting with benzene and with the ideal planar graphene surface. Comparison is also presented with the results obtained by other DFT vdW-corrected schemes, including PBE+D, vdW-DF, vdW-DF2, rVV10, and by the simpler Local Density Approximation (LDA) and semilocal generalized gradient approximation approaches. While for the X-benzene systems all the considered vdW-corrected schemes perform reasonably well, it turns out that an accurate description of the X-graphene interaction requires a proper treatment of many-body contributions and of short-range screening effects, as demonstrated by adopting an improved version of the DFT/vdW-QHO-WF method. We also comment on the widespread attitude of relying on LDA to get a rough description of weakly interacting systems.

Hybrid functional studies of stability and diffusion of hydrogen in Mg-doped GaN

NASA Astrophysics Data System (ADS)

Park, Ji-Sang; Chang, K. J.

2012-02-01

Nitride semiconductors are known to suffer from low p-type doping efficiency due to the high activation energy of Mg acceptors and the compensation of hole carriers. To enhance hole carrier concentration, the hydrogen co-doping method is widely used, in which hydrogen is intentionally doped with Mg dopants and removed by subsequent thermal annealing. In this work, we perform first-principles density functional calculations to study the stability and diffusion of hydrogen in Mg-doped GaN. For the exchange-correlation potential, we employ both the generalized gradient approximation (GGA) proposed by Perdew, Burke, and Ernzerhof and the hybrid density functional of Heyd, Scuseria, and Ernzerhof. We examine the diffusion pathways and dissociation barriers of H from the Mg-H complex using the nudged elastic band and dimer methods. We compare the results of the GGA and hybrid density functional calculations for the stability of various H interstitial configurations and the migration barriers for H diffusion. Finally, using the calculated migration barriers as inputs, we perform kinetic Monte Carlo simulations for the dissociation of the Mg-H complex and find that the Mg acceptors are activated by thermal annealing up to 700-800 ^oC, in good agreement with experiments.

Globally optimal superconducting magnets part I: minimum stored energy (MSE) current density map.

PubMed

Tieng, Quang M; Vegh, Viktor; Brereton, Ian M

2009-01-01

An optimal current density map is crucial in magnet design to provide the initial values within search spaces in an optimization process for determining the final coil arrangement of the magnet. A strategy for obtaining globally optimal current density maps for the purpose of designing magnets with coaxial cylindrical coils in which the stored energy is minimized within a constrained domain is outlined. The current density maps obtained utilising the proposed method suggests that peak current densities occur around the perimeter of the magnet domain, where the adjacent peaks have alternating current directions for the most compact designs. As the dimensions of the domain are increased, the current density maps yield traditional magnet designs of positive current alone. These unique current density maps are obtained by minimizing the stored magnetic energy cost function and therefore suggest magnet coil designs of minimal system energy. Current density maps are provided for a number of different domain arrangements to illustrate the flexibility of the method and the quality of the achievable designs.

DGDFT: A massively parallel method for large scale density functional theory calculations.

PubMed

Hu, Wei; Lin, Lin; Yang, Chao

2015-09-28

We describe a massively parallel implementation of the recently developed discontinuous Galerkin density functional theory (DGDFT) method, for efficient large-scale Kohn-Sham DFT based electronic structure calculations. The DGDFT method uses adaptive local basis (ALB) functions generated on-the-fly during the self-consistent field iteration to represent the solution to the Kohn-Sham equations. The use of the ALB set provides a systematic way to improve the accuracy of the approximation. By using the pole expansion and selected inversion technique to compute electron density, energy, and atomic forces, we can make the computational complexity of DGDFT scale at most quadratically with respect to the number of electrons for both insulating and metallic systems. We show that for the two-dimensional (2D) phosphorene systems studied here, using 37 basis functions per atom allows us to reach an accuracy level of 1.3 × 10(-4) Hartree/atom in terms of the error of energy and 6.2 × 10(-4) Hartree/bohr in terms of the error of atomic force, respectively. DGDFT can achieve 80% parallel efficiency on 128,000 high performance computing cores when it is used to study the electronic structure of 2D phosphorene systems with 3500-14 000 atoms. This high parallel efficiency results from a two-level parallelization scheme that we will describe in detail.

Excitons in Potassium Bromide: A Study using Embedded Time-dependent Density Functional Theory and Equation-of-Motion Coupled Cluster Methods

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

Govind, Niranjan; Sushko, Petr V.; Hess, Wayne P.

2009-03-05

We present a study of the electronic excitations in insulating materials using an embedded- cluster method. The excited states of the embedded cluster are studied systematically using time-dependent density functional theory (TDDFT) and high-level equation-of-motion coupled cluster (EOMCC) methods. In particular, we have used EOMCC models with singles and doubles (EOMCCSD) and two approaches which account for the e®ect of triply excited con¯gurations in non-iterative and iterative fashions. We present calculations of the lowest surface excitations of the well-studied potassium bromide (KBr) system and compare our results with experiment. The bulk-surface exciton shift is also calculated at the TDDFT levelmore » and compared with experiment.« less

Prediction of thermal cycling induced matrix cracking

NASA Technical Reports Server (NTRS)

Mcmanus, Hugh L.

1992-01-01

Thermal fatigue has been observed to cause matrix cracking in laminated composite materials. A method is presented to predict transverse matrix cracks in composite laminates subjected to cyclic thermal load. Shear lag stress approximations and a simple energy-based fracture criteria are used to predict crack densities as a function of temperature. Prediction of crack densities as a function of thermal cycling is accomplished by assuming that fatigue degrades the material's inherent resistance to cracking. The method is implemented as a computer program. A simple experiment provides data on progressive cracking of a laminate with decreasing temperature. Existing data on thermal fatigue is also used. Correlations of the analytical predictions to the data are very good. A parametric study using the analytical method is presented which provides insight into material behavior under cyclical thermal loads.

Methode de calcul a N-corps basee sur la G0W0: Etude du couplage electron-phonon dans le C60 et developpement d'une approche acceleree pour materiaux organiques

NASA Astrophysics Data System (ADS)

Laflamme Janssen, Jonathan

This thesis studies the limitations of density functional theory. These limits are explored in the context of a traditional implementation using a plane waves basis set. First, we investigate the limit of the size of the systems that can be treated. Cutting edge methods that assess these limitations are then used to simulate nanoscale systems. More specifically, the grafting of bromophenyl molecules on the sidewall of carbon nanotubes is studied with these methods, as a better understanding of this procedure could have substantial impact on the electronic industry. Second, the limitations of the precision of density functional theory are explored. We begin with a quantitative study of the uncertainty of this method for the case of electron-phonon coupling calculations and find it to be substantially higher than what is widely presumed in the literature. The uncertainty on electronphonon coupling calculations is then explored within the G0W0 method, which is found to be a substantially more precise alternative. However, this method has the drawback of being severely limitated in the size of systems that can be computed. In the following, theoretical solutions to overcome these limitations are developed and presented. The increased performance and precision of the resulting implementation opens new possibilities for the study and design of materials, such as superconductors, polymers for organic photovoltaics and semiconductors. Keywords: Condensed matter physics, ab initio calculations, density functional theory, nanotechnology, carbon nanotubes, many-body perturbation theory, G0W0 method..

Reconstructing the Initial Density Field of the Local Universe: Methods and Tests with Mock Catalogs

NASA Astrophysics Data System (ADS)

Wang, Huiyuan; Mo, H. J.; Yang, Xiaohu; van den Bosch, Frank C.

2013-07-01

Our research objective in this paper is to reconstruct an initial linear density field, which follows the multivariate Gaussian distribution with variances given by the linear power spectrum of the current cold dark matter model and evolves through gravitational instabilities to the present-day density field in the local universe. For this purpose, we develop a Hamiltonian Markov Chain Monte Carlo method to obtain the linear density field from a posterior probability function that consists of two components: a prior of a Gaussian density field with a given linear spectrum and a likelihood term that is given by the current density field. The present-day density field can be reconstructed from galaxy groups using the method developed in Wang et al. Using a realistic mock Sloan Digital Sky Survey DR7, obtained by populating dark matter halos in the Millennium simulation (MS) with galaxies, we show that our method can effectively and accurately recover both the amplitudes and phases of the initial, linear density field. To examine the accuracy of our method, we use N-body simulations to evolve these reconstructed initial conditions to the present day. The resimulated density field thus obtained accurately matches the original density field of the MS in the density range 0.3 \\lesssim \\rho /\\bar{\\rho } \\lesssim 20 without any significant bias. In particular, the Fourier phases of the resimulated density fields are tightly correlated with those of the original simulation down to a scale corresponding to a wavenumber of ~1 h Mpc-1, much smaller than the translinear scale, which corresponds to a wavenumber of ~0.15 h Mpc-1.

Validation and application of auxiliary density perturbation theory and non-iterative approximation to coupled-perturbed Kohn-Sham approach for calculation of dipole-quadrupole polarizability

NASA Astrophysics Data System (ADS)

Shedge, Sapana V.; Pal, Sourav; Köster, Andreas M.

2011-07-01

Recently, two non-iterative approaches have been proposed to calculate response properties within density functional theory (DFT). These approaches are auxiliary density perturbation theory (ADPT) and the non-iterative approach to the coupled-perturbed Kohn-Sham (NIA-CPKS) method. Though both methods are non-iterative, they use different techniques to obtain the perturbed Kohn-Sham matrix. In this Letter, for the first time, both of these two independent methods have been used for the calculation of dipole-quadrupole polarizabilities. To validate these methods, three tetrahedral molecules viz., P4,CH4 and adamantane (C10H16) have been used as examples. The comparison with MP2 and CCSD proves the reliability of the methodology.

Standardized Pearson type 3 density function area tables

NASA Technical Reports Server (NTRS)

Cohen, A. C.; Helm, F. R.; Sugg, M.

1971-01-01

Tables constituting extension of similar tables published in 1936 are presented in report form. Single and triple parameter gamma functions are discussed. Report tables should interest persons concerned with development and use of numerical analysis and evaluation methods.

Multiconfiguration Pair-Density Functional Theory Predicts Spin-State Ordering in Iron Complexes with the Same Accuracy as Complete Active Space Second-Order Perturbation Theory at a Significantly Reduced Computational Cost.

PubMed

Wilbraham, Liam; Verma, Pragya; Truhlar, Donald G; Gagliardi, Laura; Ciofini, Ilaria

2017-05-04

The spin-state orderings in nine Fe(II) and Fe(III) complexes with ligands of diverse ligand-field strength were investigated with multiconfiguration pair-density functional theory (MC-PDFT). The performance of this method was compared to that of complete active space second-order perturbation theory (CASPT2) and Kohn-Sham density functional theory. We also investigated the dependence of CASPT2 and MC-PDFT results on the size of the active-space. MC-PDFT reproduces the CASPT2 spin-state ordering, the dependence on the ligand field strength, and the dependence on active space at a computational cost that is significantly reduced as compared to CASPT2.

Study of high-performance canonical molecular orbitals calculation for proteins

NASA Astrophysics Data System (ADS)

Hirano, Toshiyuki; Sato, Fumitoshi

2017-11-01

The canonical molecular orbital (CMO) calculation can help to understand chemical properties and reactions in proteins. However, it is difficult to perform the CMO calculation of proteins because of its self-consistent field (SCF) convergence problem and expensive computational cost. To certainly obtain the CMO of proteins, we work in research and development of high-performance CMO applications and perform experimental studies. We have proposed the third-generation density-functional calculation method of calculating the SCF, which is more advanced than the FILE and direct method. Our method is based on Cholesky decomposition for two-electron integrals calculation and the modified grid-free method for the pure-XC term evaluation. By using the third-generation density-functional calculation method, the Coulomb, the Fock-exchange, and the pure-XC terms can be given by simple linear algebraic procedure in the SCF loop. Therefore, we can expect to get a good parallel performance in solving the SCF problem by using a well-optimized linear algebra library such as BLAS on the distributed memory parallel computers. The third-generation density-functional calculation method is implemented to our program, ProteinDF. To achieve computing electronic structure of the large molecule, not only overcoming expensive computation cost and also good initial guess for safe SCF convergence are required. In order to prepare a precise initial guess for the macromolecular system, we have developed the quasi-canonical localized orbital (QCLO) method. The QCLO has the characteristics of both localized and canonical orbital in a certain region of the molecule. We have succeeded in the CMO calculations of proteins by using the QCLO method. For simplified and semi-automated calculation of the QCLO method, we have also developed a Python-based program, QCLObot.

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.

Implementation of Two-Component Time-Dependent Density Functional Theory in TURBOMOLE.

PubMed

Kühn, Michael; Weigend, Florian

2013-12-10

We report the efficient implementation of a two-component time-dependent density functional theory proposed by Wang et al. (Wang, F.; Ziegler, T.; van Lenthe, E.; van Gisbergen, S.; Baerends, E. J. J. Chem. Phys. 2005, 122, 204103) that accounts for spin-orbit effects on excitations of closed-shell systems by employing a noncollinear exchange-correlation kernel. In contrast to the aforementioned implementation, our method is based on two-component effective core potentials as well as Gaussian-type basis functions. It is implemented in the TURBOMOLE program suite for functionals of the local density approximation and the generalized gradient approximation. Accuracy is assessed by comparison of two-component vertical excitation energies of heavy atoms and ions (Cd, Hg, Au(+)) and small molecules (I2, TlH) to other two- and four-component approaches. Efficiency is demonstrated by calculating the electronic spectrum of Au20.

Optimized Vertex Method and Hybrid Reliability

NASA Technical Reports Server (NTRS)

Smith, Steven A.; Krishnamurthy, T.; Mason, B. H.

2002-01-01

A method of calculating the fuzzy response of a system is presented. This method, called the Optimized Vertex Method (OVM), is based upon the vertex method but requires considerably fewer function evaluations. The method is demonstrated by calculating the response membership function of strain-energy release rate for a bonded joint with a crack. The possibility of failure of the bonded joint was determined over a range of loads. After completing the possibilistic analysis, the possibilistic (fuzzy) membership functions were transformed to probability density functions and the probability of failure of the bonded joint was calculated. This approach is called a possibility-based hybrid reliability assessment. The possibility and probability of failure are presented and compared to a Monte Carlo Simulation (MCS) of the bonded joint.

Thermal Performance of Cryogenic Multilayer Insulation at Various Layer Spacings

NASA Technical Reports Server (NTRS)

Johnson, Wesley Louis

2010-01-01

Multilayer insulation (MLI) has been shown to be the best performing cryogenic insulation system at high vacuum (less that 10 (exp 3) torr), and is widely used on spaceflight vehicles. Over the past 50 years, many investigations into MLI have yielded a general understanding of the many variables that are associated with MLI. MLI has been shown to be a function of variables such as warm boundary temperature, the number of reflector layers, and the spacer material in between reflectors, the interstitial gas pressure and the interstitial gas. Since the conduction between reflectors increases with the thickness of the spacer material, yet the radiation heat transfer is inversely proportional to the number of layers, it stands to reason that the thermal performance of MLI is a function of the number of layers per thickness, or layer density. Empirical equations that were derived based on some of the early tests showed that the conduction term was proportional to the layer density to a power. This power depended on the material combination and was determined by empirical test data. Many authors have graphically shown such optimal layer density, but none have provided any data at such low densities, or any method of determining this density. Keller, Cunnington, and Glassford showed MLI thermal performance as a function of layer density of high layer densities, but they didn't show a minimal layer density or any data below the supposed optimal layer density. However, it was recently discovered that by manipulating the derived empirical equations and taking a derivative with respect to layer density yields a solution for on optimal layer density. Various manufacturers have begun manufacturing MLI at densities below the optimal density. They began this based on the theory that increasing the distance between layers lowered the conductive heat transfer and they had no limitations on volume. By modifying the circumference of these blankets, the layer density can easily be varied. The simplest method of determining the thermal performance of MLI at cryogenic temperature is by boil-off calorimetry. Several blankets were procured and tested at various layer densities at the Cryogenics Test Laboratory at Kennedy Space Center. The densities that the blankets were tested over covered a wide range of layer densities including the analytical minimum. Several of the blankets were tested at the same insulation thickness while changing the layer density (thus a different number of reflector layers). Optimizing the layer density of multilayer insulation systems for heat transfer would remove a layer density from the complex method of designing such insulation systems. Additional testing was performed at various warm boundary temperatures and pressures. The testing and analysis was performed to simplify the analysis of cryogenic thermal insulation systems. This research was funded by the National Aeronautics and Space Administration's Exploration Technology Development Program's Cryogenic Fluid Management Project

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.

Dynamical density functional theory analysis of the laning instability in sheared soft matter.

PubMed

Scacchi, A; Archer, A J; Brader, J M

2017-12-01

Using dynamical density functional theory (DDFT) methods we investigate the laning instability of a sheared colloidal suspension. The nonequilibrium ordering at the laning transition is driven by nonaffine particle motion arising from interparticle interactions. Starting from a DDFT which incorporates the nonaffine motion, we perform a linear stability analysis that enables identification of the regions of parameter space where lanes form. We illustrate our general approach by applying it to a simple one-component fluid of soft penetrable particles.

Photoionization of Atoms and Ions: Application of Time-Dependent Response Method within the Density Functional Theory.

DTIC Science & Technology

1987-10-13

AD-A±95 686 PHOTOIONIZATION OF ATOMS AND IONS: APPLICATION OF III TIME-DEPENDENT RESPONSE..(U) NAVAL RESEARCH LAB WASHINGTON DC U GUPTA ET AL. 13 OCT...on revere if ncemy and idmntify by block number) FIELD GROUP SUBGROUP Photoionization Density functional Atoms Time dependent 1 S. (Continue on...reverse if necenary and identify by block numnbw) The photoionization cross-section of several atoms (AT, Xe, Rn, Cs) and ions (Ne-like Ar, H-like and Li

Physics of Inference

NASA Astrophysics Data System (ADS)

Toroczkai, Zoltan

Jaynes's maximum entropy method provides a family of principled models that allow the prediction of a system's properties as constrained by empirical data (observables). However, their use is often hindered by the degeneracy problem characterized by spontaneous symmetry breaking, where predictions fail. Here we show that degeneracy appears when the corresponding density of states function is not log-concave, which is typically the consequence of nonlinear relationships between the constraining observables. We illustrate this phenomenon on several examples, including from complex networks, combinatorics and classical spin systems (e.g., Blume-Emery-Griffiths lattice-spin models). Exploiting these nonlinear relationships we then propose a solution to the degeneracy problem for a large class of systems via transformations that render the density of states function log-concave. The effectiveness of the method is demonstrated on real-world network data. Finally, we discuss the implications of these findings on the relationship between the geometrical properties of the density of states function and phase transitions in spin systems. Supported in part by Grant No. FA9550-12-1-0405 from AFOSR/DARPA and by Grant No. HDTRA 1-09-1-0039 from DTRA.

Highly Accurate Calculations of the Phase Diagram of Cold Lithium

NASA Astrophysics Data System (ADS)

Shulenburger, Luke; Baczewski, Andrew

The phase diagram of lithium is particularly complicated, exhibiting many different solid phases under the modest application of pressure. Experimental efforts to identify these phases using diamond anvil cells have been complemented by ab initio theory, primarily using density functional theory (DFT). Due to the multiplicity of crystal structures whose enthalpy is nearly degenerate and the uncertainty introduced by density functional approximations, we apply the highly accurate many-body diffusion Monte Carlo (DMC) method to the study of the solid phases at low temperature. These calculations span many different phases, including several with low symmetry, demonstrating the viability of DMC as a method for calculating phase diagrams for complex solids. Our results can be used as a benchmark to test the accuracy of various density functionals. This can strengthen confidence in DFT based predictions of more complex phenomena such as the anomalous melting behavior predicted for lithium at high pressures. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. DOE's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Integrating multiple fitting regression and Bayes decision for cancer diagnosis with transcriptomic data from tumor-educated blood platelets.

PubMed

Huang, Guangzao; Yuan, Mingshun; Chen, Moliang; Li, Lei; You, Wenjie; Li, Hanjie; Cai, James J; Ji, Guoli

2017-10-07

The application of machine learning in cancer diagnostics has shown great promise and is of importance in clinic settings. Here we consider applying machine learning methods to transcriptomic data derived from tumor-educated platelets (TEPs) from individuals with different types of cancer. We aim to define a reliability measure for diagnostic purposes to increase the potential for facilitating personalized treatments. To this end, we present a novel classification method called MFRB (for Multiple Fitting Regression and Bayes decision), which integrates the process of multiple fitting regression (MFR) with Bayes decision theory. MFR is first used to map multidimensional features of the transcriptomic data into a one-dimensional feature. The probability density function of each class in the mapped space is then adjusted using the Gaussian probability density function. Finally, the Bayes decision theory is used to build a probabilistic classifier with the estimated probability density functions. The output of MFRB can be used to determine which class a sample belongs to, as well as to assign a reliability measure for a given class. The classical support vector machine (SVM) and probabilistic SVM (PSVM) are used to evaluate the performance of the proposed method with simulated and real TEP datasets. Our results indicate that the proposed MFRB method achieves the best performance compared to SVM and PSVM, mainly due to its strong generalization ability for limited, imbalanced, and noisy data.

New methods for estimating parameters of weibull functions to characterize future diameter distributions in forest stands

Treesearch

Quang V. Cao; Shanna M. McCarty

2006-01-01

Diameter distributions in a forest stand have been successfully characterized by use of the Weibull function. Of special interest are cases where parameters of a Weibull distribution that models a future stand are predicted, either directly or indirectly, from current stand density and dominant height. This study evaluated four methods of predicting the Weibull...

Temperature dependence of the symmetry energy and neutron skins in Ni, Sn, and Pb isotopic chains

NASA Astrophysics Data System (ADS)

Antonov, A. N.; Kadrev, D. N.; Gaidarov, M. K.; Sarriguren, P.; de Guerra, E. Moya

2017-02-01

The temperature dependence of the symmetry energy for isotopic chains of even-even Ni, Sn, and Pb nuclei is investigated in the framework of the local density approximation (LDA). The Skyrme energy density functional with two Skyrme-class effective interactions, SkM* and SLy4, is used in the calculations. The temperature-dependent proton and neutron densities are calculated through the hfbtho code that solves the nuclear Skyrme-Hartree-Fock-Bogoliubov problem by using the cylindrical transformed deformed harmonic-oscillator basis. In addition, two other density distributions of 208Pb, namely the Fermi-type density determined within the extended Thomas-Fermi (TF) method and symmetrized-Fermi local density obtained within the rigorous density functional approach, are used. The kinetic energy densities are calculated either by the hfbtho code or, for a comparison, by the extended TF method up to second order in temperature (with T2 term). Alternative ways to calculate the symmetry energy coefficient within the LDA are proposed. The results for the thermal evolution of the symmetry energy coefficient in the interval T =0 -4 MeV show that its values decrease with temperature. The temperature dependence of the neutron and proton root-mean-square radii and corresponding neutron skin thickness is also investigated, showing that the effect of temperature leads mainly to a substantial increase of the neutron radii and skins, especially in the more neutron-rich nuclei, a feature that may have consequences on astrophysical processes and neutron stars.

Method to fabricate functionalized conical nanopores

DOEpatents

Small, Leo J.; Spoerke, Erik David; Wheeler, David R.

2016-07-12

A pressure-based chemical etch method is used to shape polymer nanopores into cones. By varying the pressure, the pore tip diameter can be controlled, while the pore base diameter is largely unaffected. The method provides an easy, low-cost approach for conically etching high density nanopores.

Electronic structure and normal vibrations of the 1-ethyl-3-methylimidazolium ethyl sulfate ion pair.

PubMed

Dhumal, Nilesh R; Kim, Hyung J; Kiefer, Johannes

2011-04-21

Electronic and structural properties of the ion pair 1-ethyl-3-methylimidazolium ethyl sulfate are studied using density functional methods. Three locally stable conformers of the ion pair complex are considered to analyze molecular interactions between its cation and anion. Manifestations of these interactions in the vibrational spectra are discussed and compared with experimental IR and Raman spectroscopy data. NBO analysis and difference electron density coupled with molecular electron density topography are used to interpret the frequency shifts of the normal vibrations of the ion pair, compared to the free anion and cation. Excitation energies of low-lying singlet excited states of the conformers are also studied. The density functional theory results are found to be in a reasonable agreement with experimental UV/vis absorption spectra.

Analysis of random signal combinations for spacecraft pointing stability

NASA Technical Reports Server (NTRS)

Howell, L.

1983-01-01

Methods for obtaining the probability density function of random signal combustions are discussed. These methods provide a realistic criteria for the design of control systems subjected to external noise with several important applications for aerospace problems.

Quantitative computed tomography of lung parenchyma in patients with emphysema: analysis of higher-density lung regions

NASA Astrophysics Data System (ADS)

Lederman, Dror; Leader, Joseph K.; Zheng, Bin; Sciurba, Frank C.; Tan, Jun; Gur, David

2011-03-01

Quantitative computed tomography (CT) has been widely used to detect and evaluate the presence (or absence) of emphysema applying the density masks at specific thresholds, e.g., -910 or -950 Hounsfield Unit (HU). However, it has also been observed that subjects with similar density-mask based emphysema scores could have varying lung function, possibly indicating differences of disease severity. To assess this possible discrepancy, we investigated whether density distribution of "viable" lung parenchyma regions with pixel values > -910 HU correlates with lung function. A dataset of 38 subjects, who underwent both pulmonary function testing and CT examinations in a COPD SCCOR study, was assembled. After the lung regions depicted on CT images were automatically segmented by a computerized scheme, we systematically divided the lung parenchyma into different density groups (bins) and computed a number of statistical features (i.e., mean, standard deviation (STD), skewness of the pixel value distributions) in these density bins. We then analyzed the correlations between each feature and lung function. The correlation between diffusion lung capacity (DLCO) and STD of pixel values in the bin of -910HU <= PV < -750HU was -0.43, as compared with a correlation of -0.49 obtained between the post-bronchodilator ratio (FEV1/FVC) measured by the forced expiratory volume in 1 second (FEV1) dividing the forced vital capacity (FVC) and the STD of pixel values in the bin of -1024HU <= PV < -910HU. The results showed an association between the distribution of pixel values in "viable" lung parenchyma and lung function, which indicates that similar to the conventional density mask method, the pixel value distribution features in "viable" lung parenchyma areas may also provide clinically useful information to improve assessments of lung disease severity as measured by lung functional tests.

The response analysis of fractional-order stochastic system via generalized cell mapping method.

PubMed

Wang, Liang; Xue, Lili; Sun, Chunyan; Yue, Xiaole; Xu, Wei

2018-01-01

This paper is concerned with the response of a fractional-order stochastic system. The short memory principle is introduced to ensure that the response of the system is a Markov process. The generalized cell mapping method is applied to display the global dynamics of the noise-free system, such as attractors, basins of attraction, basin boundary, saddle, and invariant manifolds. The stochastic generalized cell mapping method is employed to obtain the evolutionary process of probability density functions of the response. The fractional-order ϕ 6 oscillator and the fractional-order smooth and discontinuous oscillator are taken as examples to give the implementations of our strategies. Studies have shown that the evolutionary direction of the probability density function of the fractional-order stochastic system is consistent with the unstable manifold. The effectiveness of the method is confirmed using Monte Carlo results.

Estimation of vegetation cover at subpixel resolution using LANDSAT data

NASA Technical Reports Server (NTRS)

Jasinski, Michael F.; Eagleson, Peter S.

1986-01-01

The present report summarizes the various approaches relevant to estimating canopy cover at subpixel resolution. The approaches are based on physical models of radiative transfer in non-homogeneous canopies and on empirical methods. The effects of vegetation shadows and topography are examined. Simple versions of the model are tested, using the Taos, New Mexico Study Area database. Emphasis has been placed on using relatively simple models requiring only one or two bands. Although most methods require some degree of ground truth, a two-band method is investigated whereby the percent cover can be estimated without ground truth by examining the limits of the data space. Future work is proposed which will incorporate additional surface parameters into the canopy cover algorithm, such as topography, leaf area, or shadows. The method involves deriving a probability density function for the percent canopy cover based on the joint probability density function of the observed radiances.

Probability and Cumulative Density Function Methods for the Stochastic Advection-Reaction Equation

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

Barajas-Solano, David A.; Tartakovsky, Alexandre M.

We present a cumulative density function (CDF) method for the probabilistic analysis of $d$-dimensional advection-dominated reactive transport in heterogeneous media. We employ a probabilistic approach in which epistemic uncertainty on the spatial heterogeneity of Darcy-scale transport coefficients is modeled in terms of random fields with given correlation structures. Our proposed CDF method employs a modified Large-Eddy-Diffusivity (LED) approach to close and localize the nonlocal equations governing the one-point PDF and CDF of the concentration field, resulting in a $(d + 1)$ dimensional PDE. Compared to the classsical LED localization, the proposed modified LED localization explicitly accounts for the mean-field advectivemore » dynamics over the phase space of the PDF and CDF. To illustrate the accuracy of the proposed closure, we apply our CDF method to one-dimensional single-species reactive transport with uncertain, heterogeneous advection velocities and reaction rates modeled as random fields.« less

Probabilistic density function method for nonlinear dynamical systems driven by colored noise

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

Barajas-Solano, David A.; Tartakovsky, Alexandre M.

2016-05-01

We present a probability density function (PDF) method for a system of nonlinear stochastic ordinary differential equations driven by colored noise. The method provides an integro-differential equation for the temporal evolution of the joint PDF of the system's state, which we close by means of a modified Large-Eddy-Diffusivity-type closure. Additionally, we introduce the generalized local linearization (LL) approximation for deriving a computable PDF equation in the form of the second-order partial differential equation (PDE). We demonstrate the proposed closure and localization accurately describe the dynamics of the PDF in phase space for systems driven by noise with arbitrary auto-correlation time.more » We apply the proposed PDF method to the analysis of a set of Kramers equations driven by exponentially auto-correlated Gaussian colored noise to study the dynamics and stability of a power grid.« less

A Well-Tempered Hybrid Method for Solving Challenging Time-Dependent Density Functional Theory (TDDFT) Systems.

PubMed

Kasper, Joseph M; Williams-Young, David B; Vecharynski, Eugene; Yang, Chao; Li, Xiaosong

2018-04-10

The time-dependent Hartree-Fock (TDHF) and time-dependent density functional theory (TDDFT) equations allow one to probe electronic resonances of a system quickly and inexpensively. However, the iterative solution of the eigenvalue problem can be challenging or impossible to converge, using standard methods such as the Davidson algorithm for spectrally dense regions in the interior of the spectrum, as are common in X-ray absorption spectroscopy (XAS). More robust solvers, such as the generalized preconditioned locally harmonic residual (GPLHR) method, can alleviate this problem, but at the expense of higher average computational cost. A hybrid method is proposed which adapts to the problem in order to maximize computational performance while providing the superior convergence of GPLHR. In addition, a modification to the GPLHR algorithm is proposed to adaptively choose the shift parameter to enforce a convergence of states above a predefined energy threshold.

Dynamic kinetic energy potential for orbital-free density functional theory.

PubMed

Neuhauser, Daniel; Pistinner, Shlomo; Coomar, Arunima; Zhang, Xu; Lu, Gang

2011-04-14

A dynamic kinetic energy potential (DKEP) is developed for time-dependent orbital-free (TDOF) density function theory applications. This potential is constructed to affect only the dynamical (ω ≠ 0) response of an orbital-free electronic system. It aims at making the orbital-free simulation respond in the same way as that of a noninteracting homogenous electron gas (HEG), as required by a correct kinetic energy, therefore enabling extension of the success of orbital-free density functional theory in the static case (e.g., for embedding and description of processes in bulk materials) to dynamic processes. The potential is constructed by expansions of terms, each of which necessitates only simple time evolution (concurrent with the TDOF evolution) and a spatial convolution at each time-step. With 14 such terms a good fit is obtained to the response of the HEG at a large range of frequencies, wavevectors, and densities. The method is demonstrated for simple jellium spheres, approximating Na(9)(+) and Na(65)(+) clusters. It is applicable both to small and large (even ultralarge) excitations and the results converge (i.e., do not blow up) as a function of time. An extension to iterative frequency-resolved extraction is briefly outlined, as well as possibly numerically simpler expansions. The approach could also be extended to fit, instead of the HEG susceptibility, either an experimental susceptibility or a theoretically derived one for a non-HEG system. The DKEP potential should be a powerful tool for embedding a dynamical system described by a more accurate method (such as time-dependent density functional theory, TDDFT) in a large background described by TDOF with a DKEP potential. The type of expansions used and envisioned should be useful for other approaches, such as memory functionals in TDDFT. Finally, an appendix details the formal connection between TDOF and TDDFT.

Ensemble Kalman filtering in presence of inequality constraints

NASA Astrophysics Data System (ADS)

van Leeuwen, P. J.

2009-04-01

Kalman filtering is presence of constraints is an active area of research. Based on the Gaussian assumption for the probability-density functions, it looks hard to bring in extra constraints in the formalism. On the other hand, in geophysical systems we often encounter constraints related to e.g. the underlying physics or chemistry, which are violated by the Gaussian assumption. For instance, concentrations are always non-negative, model layers have non-negative thickness, and sea-ice concentration is between 0 and 1. Several methods to bring inequality constraints into the Kalman-filter formalism have been proposed. One of them is probability density function (pdf) truncation, in which the Gaussian mass from the non-allowed part of the variables is just equally distributed over the pdf where the variables are alolwed, as proposed by Shimada et al. 1998. However, a problem with this method is that the probability that e.g. the sea-ice concentration is zero, is zero! The new method proposed here does not have this drawback. It assumes that the probability-density function is a truncated Gaussian, but the truncated mass is not distributed equally over all allowed values of the variables, but put into a delta distribution at the truncation point. This delta distribution can easily be handled with in Bayes theorem, leading to posterior probability density functions that are also truncated Gaussians with delta distributions at the truncation location. In this way a much better representation of the system is obtained, while still keeping most of the benefits of the Kalman-filter formalism. In the full Kalman filter the formalism is prohibitively expensive in large-scale systems, but efficient implementation is possible in ensemble variants of the kalman filter. Applications to low-dimensional systems and large-scale systems will be discussed.

Double density dynamics: realizing a joint distribution of a physical system and a parameter system

NASA Astrophysics Data System (ADS)

Fukuda, Ikuo; Moritsugu, Kei

2015-11-01

To perform a variety of types of molecular dynamics simulations, we created a deterministic method termed ‘double density dynamics’ (DDD), which realizes an arbitrary distribution for both physical variables and their associated parameters simultaneously. Specifically, we constructed an ordinary differential equation that has an invariant density relating to a joint distribution of the physical system and the parameter system. A generalized density function leads to a physical system that develops under nonequilibrium environment-describing superstatistics. The joint distribution density of the physical system and the parameter system appears as the Radon-Nikodym derivative of a distribution that is created by a scaled long-time average, generated from the flow of the differential equation under an ergodic assumption. The general mathematical framework is fully discussed to address the theoretical possibility of our method, and a numerical example representing a 1D harmonic oscillator is provided to validate the method being applied to the temperature parameters.

The structure and statistics of interstellar turbulence

NASA Astrophysics Data System (ADS)

Kritsuk, A. G.; Ustyugov, S. D.; Norman, M. L.

2017-06-01

We explore the structure and statistics of multiphase, magnetized ISM turbulence in the local Milky Way by means of driven periodic box numerical MHD simulations. Using the higher order-accurate piecewise-parabolic method on a local stencil (PPML), we carry out a small parameter survey varying the mean magnetic field strength and density while fixing the rms velocity to observed values. We quantify numerous characteristics of the transient and steady-state turbulence, including its thermodynamics and phase structure, kinetic and magnetic energy power spectra, structure functions, and distribution functions of density, column density, pressure, and magnetic field strength. The simulations reproduce many observables of the local ISM, including molecular clouds, such as the ratio of turbulent to mean magnetic field at 100 pc scale, the mass and volume fractions of thermally stable Hi, the lognormal distribution of column densities, the mass-weighted distribution of thermal pressure, and the linewidth-size relationship for molecular clouds. Our models predict the shape of magnetic field probability density functions (PDFs), which are strongly non-Gaussian, and the relative alignment of magnetic field and density structures. Finally, our models show how the observed low rates of star formation per free-fall time are controlled by the multiphase thermodynamics and large-scale turbulence.

Density Estimation with Mercer Kernels

NASA Technical Reports Server (NTRS)

Macready, William G.

2003-01-01

We present a new method for density estimation based on Mercer kernels. The density estimate can be understood as the density induced on a data manifold by a mixture of Gaussians fit in a feature space. As is usual, the feature space and data manifold are defined with any suitable positive-definite kernel function. We modify the standard EM algorithm for mixtures of Gaussians to infer the parameters of the density. One benefit of the approach is it's conceptual simplicity, and uniform applicability over many different types of data. Preliminary results are presented for a number of simple problems.

Thermophysical Properties and Structural Transition of Hg(0.8)Cd(0.2)Te Melt

NASA Technical Reports Server (NTRS)

Li, C.; Scripa, R. N.; Ban, H.; Lin, B.; Su, C.; Lehoczky, S. L.

2004-01-01

Thermophysical properties, namely, density, viscosity, and electrical conductivity of Hg(sub o.8)Cd(sub 0.2)Te melt were measured as a function of temperature. A pycnometric method was used to measure the melt density in the temperature range of 1072 to 1122 K. The viscosity and electrical conductivity were simultaneously determined using a transient torque method from 1068 to 1132 K. The density result from this study is within 0.3% of the published data. However, the current viscosity result is approximately 30% lower than the existing data. The electrical conductivity of Hg(sub o.8)Cd(sub 0.2)Te melt as a function of temperature, which is not available in the literature, is also determined. The analysis of the temperature dependent electrical conductivity and the relationship between the kinematic viscosity and density indicated that the structure of the melt appeared to be homogeneous when the temperature was above 1090 K. A structural transition occurred in the Hg(sub 0.8)Cd(0.2)Te melt as the temperature was decreased from 1090 K to the liquidus temperature.

The Equation of State of Triamino-Trinitrobenzene from Density Functional Theory Molecular Dynamics

NASA Astrophysics Data System (ADS)

Wixom, Ryan R.

2017-06-01

The US-uP shock Hugoniot has long been the fundamental relationship used to experimentally define the unreacted equations of state of explosives. These experiments are typically performed on porous or composite samples, providing data that is specific to the density of the samples being tested. However, If the crystalline Hugoniot is known, analytical or numerical methods can be used to transform the US-uP relationship to describe the shock response of the porous material. To obtain an accurate crystalline equation of state for TATB, density functional theory based molecular dynamics were used to map out points on the Hugoniot. Since this method provides the pressure, temperature, density, and internal energy at each point on the Hugoniot, a complete equation of state can be constructed. Isotropic, uniaxial, hydrostatic, and isothermal compression of the simulation cell were used to examine TATB under different thermodynamic conditions. A cusp is observed in the Hugoniot that correlates to loss of aromaticity of the molecule. Results of the calculations will be presented and compared to the available experimental data. Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque NM.

Spin-polarized density-matrix functional theory of the single-impurity Anderson model

NASA Astrophysics Data System (ADS)

Töws, W.; Pastor, G. M.

2012-12-01

Lattice density functional theory (LDFT) is used to investigate spin excitations in the single-impurity Anderson model. In this method, the single-particle density matrix γijσ with respect to the lattice sites replaces the wave function as the basic variable of the many-body problem. A recently developed two-level approximation (TLA) to the interaction-energy functional W[γ] is extended to systems having spin-polarized density distributions and bond orders. This allows us to investigate the effect of external magnetic fields and, in particular, the important singlet-triplet gap ΔE, which determines the Kondo temperature. Applications to finite Anderson rings and square lattices show that the gap ΔE as well as other ground-state and excited-state properties are very accurately reproduced. One concludes that the spin-polarized TLA is reliable in all interaction regimes, from weak to strong correlations, for different hybridization strengths and for all considered impurity valence states. In this way the efficiency of LDFT to account for challenging electron-correlation effects is demonstrated.

Electronic Excitations in Solution: The Interplay between State Specific Approaches and a Time-Dependent Density Functional Theory Description.

PubMed

Guido, Ciro A; Jacquemin, Denis; Adamo, Carlo; Mennucci, Benedetta

2015-12-08

We critically analyze the performances of continuum solvation models when coupled to time-dependent density functional theory (TD-DFT) to predict solvent effects on both absorption and emission energies of chromophores in solution. Different polarization schemes of the polarizable continuum model (PCM), such as linear response (LR) and three different state specific (SS) approaches, are considered and compared. We show the necessity of introducing a SS model in cases where large electron density rearrangements are involved in the excitations, such as charge-transfer transitions in both twisted and quadrupolar compounds, and underline the very delicate interplay between the selected polarization method and the chosen exchange-correlation functional. This interplay originates in the different descriptions of the transition and ground/excited state multipolar moments by the different functionals. As a result, the choice of both the DFT functional and the solvent polarization scheme has to be consistent with the nature of the studied electronic excitation.

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.

Software Toolbox for Low-Frequency Conductivity and Current Density Imaging Using MRI.

PubMed

Sajib, Saurav Z K; Katoch, Nitish; Kim, Hyung Joong; Kwon, Oh In; Woo, Eung Je

2017-11-01

Low-frequency conductivity and current density imaging using MRI includes magnetic resonance electrical impedance tomography (MREIT), diffusion tensor MREIT (DT-MREIT), conductivity tensor imaging (CTI), and magnetic resonance current density imaging (MRCDI). MRCDI and MREIT provide current density and isotropic conductivity images, respectively, using current-injection phase MRI techniques. DT-MREIT produces anisotropic conductivity tensor images by incorporating diffusion weighted MRI into MREIT. These current-injection techniques are finding clinical applications in diagnostic imaging and also in transcranial direct current stimulation (tDCS), deep brain stimulation (DBS), and electroporation where treatment currents can function as imaging currents. To avoid adverse effects of nerve and muscle stimulations due to injected currents, conductivity tensor imaging (CTI) utilizes B1 mapping and multi-b diffusion weighted MRI to produce low-frequency anisotropic conductivity tensor images without injecting current. This paper describes numerical implementations of several key mathematical functions for conductivity and current density image reconstructions in MRCDI, MREIT, DT-MREIT, and CTI. To facilitate experimental studies of clinical applications, we developed a software toolbox for these low-frequency conductivity and current density imaging methods. This MR-based conductivity imaging (MRCI) toolbox includes 11 toolbox functions which can be used in the MATLAB environment. The MRCI toolbox is available at http://iirc.khu.ac.kr/software.html . Its functions were tested by using several experimental datasets, which are provided together with the toolbox. Users of the toolbox can focus on experimental designs and interpretations of reconstructed images instead of developing their own image reconstruction softwares. We expect more toolbox functions to be added from future research outcomes. Low-frequency conductivity and current density imaging using MRI includes magnetic resonance electrical impedance tomography (MREIT), diffusion tensor MREIT (DT-MREIT), conductivity tensor imaging (CTI), and magnetic resonance current density imaging (MRCDI). MRCDI and MREIT provide current density and isotropic conductivity images, respectively, using current-injection phase MRI techniques. DT-MREIT produces anisotropic conductivity tensor images by incorporating diffusion weighted MRI into MREIT. These current-injection techniques are finding clinical applications in diagnostic imaging and also in transcranial direct current stimulation (tDCS), deep brain stimulation (DBS), and electroporation where treatment currents can function as imaging currents. To avoid adverse effects of nerve and muscle stimulations due to injected currents, conductivity tensor imaging (CTI) utilizes B1 mapping and multi-b diffusion weighted MRI to produce low-frequency anisotropic conductivity tensor images without injecting current. This paper describes numerical implementations of several key mathematical functions for conductivity and current density image reconstructions in MRCDI, MREIT, DT-MREIT, and CTI. To facilitate experimental studies of clinical applications, we developed a software toolbox for these low-frequency conductivity and current density imaging methods. This MR-based conductivity imaging (MRCI) toolbox includes 11 toolbox functions which can be used in the MATLAB environment. The MRCI toolbox is available at http://iirc.khu.ac.kr/software.html . Its functions were tested by using several experimental datasets, which are provided together with the toolbox. Users of the toolbox can focus on experimental designs and interpretations of reconstructed images instead of developing their own image reconstruction softwares. We expect more toolbox functions to be added from future research outcomes.

A quadrature based method of moments for nonlinear Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Otten, Dustin L.; Vedula, Prakash

2011-09-01

Fokker-Planck equations which are nonlinear with respect to their probability densities and occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, fermions and bosons can be challenging to solve numerically. To address some underlying challenges, we propose the application of the direct quadrature based method of moments (DQMOM) for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations (NLFPEs). In DQMOM, probability density (or other distribution) functions are represented using a finite collection of Dirac delta functions, characterized by quadrature weights and locations (or abscissas) that are determined based on constraints due to evolution of generalized moments. Three particular examples of nonlinear Fokker-Planck equations considered in this paper include descriptions of: (i) the Shimizu-Yamada model, (ii) the Desai-Zwanzig model (both of which have been developed as models of muscular contraction) and (iii) fermions and bosons. Results based on DQMOM, for the transient and stationary solutions of the nonlinear Fokker-Planck equations, have been found to be in good agreement with other available analytical and numerical approaches. It is also shown that approximate reconstruction of the underlying probability density function from moments obtained from DQMOM can be satisfactorily achieved using a maximum entropy method.

Path integral approach to the Wigner representation of canonical density operators for discrete systems coupled to harmonic baths.

PubMed

Montoya-Castillo, Andrés; Reichman, David R

2017-01-14

We derive a semi-analytical form for the Wigner transform for the canonical density operator of a discrete system coupled to a harmonic bath based on the path integral expansion of the Boltzmann factor. The introduction of this simple and controllable approach allows for the exact rendering of the canonical distribution and permits systematic convergence of static properties with respect to the number of path integral steps. In addition, the expressions derived here provide an exact and facile interface with quasi- and semi-classical dynamical methods, which enables the direct calculation of equilibrium time correlation functions within a wide array of approaches. We demonstrate that the present method represents a practical path for the calculation of thermodynamic data for the spin-boson and related systems. We illustrate the power of the present approach by detailing the improvement of the quality of Ehrenfest theory for the correlation function C zz (t)=Re⟨σ z (0)σ z (t)⟩ for the spin-boson model with systematic convergence to the exact sampling function. Importantly, the numerically exact nature of the scheme presented here and its compatibility with semiclassical methods allows for the systematic testing of commonly used approximations for the Wigner-transformed canonical density.

Conformational analysis, spectroscopic study (FT-IR, FT-Raman, UV, 1H and 13C NMR), molecular orbital energy and NLO properties of 5-iodosalicylic acid

NASA Astrophysics Data System (ADS)

Karaca, Caglar; Atac, Ahmet; Karabacak, Mehmet

2015-02-01

In this study, 5-iodosalicylic acid (5-ISA, C7H5IO3) is structurally characterized by FT-IR, FT-Raman, NMR and UV spectroscopies. There are eight conformers, Cn, n = 1-8 for this molecule therefore the molecular geometry for these eight conformers in the ground state are calculated by using the ab-initio density functional theory (DFT) B3LYP method approach with the aug-cc-pVDZ-PP basis set for iodine and the aug-cc-pVDZ basis set for the other elements. The computational results identified that the most stable conformer of 5-ISA is the C1 form. The vibrational spectra are calculated DFT method invoking the same basis sets and fundamental vibrations are assigned on the basis of the total energy distribution (TED) of the vibrational modes, calculated with scaled quantum mechanics (SQM) method with PQS program. Total density of state (TDOS) and partial density of state (PDOS) and also overlap population density of state (COOP or OPDOS) diagrams analysis for C1 conformer were calculated using the same method. The energy and oscillator strength are calculated by time-dependent density functional theory (TD-DFT) results complement with the experimental findings. Besides, charge transfer occurring in the molecule between HOMO and LUMO energies, frontier energy gap, molecular electrostatic potential (MEP) are calculated and presented. The NMR chemical shifts (1H and 13C) spectra are recorded and calculated using the gauge independent atomic orbital (GIAO) method. Mulliken atomic charges of the title molecule are also calculated, interpreted and compared with salicylic acid. The optimized bond lengths, bond angles and calculated NMR and UV, vibrational wavenumbers showed the best agreement with the experimental results.

Hybrid asymptotic-numerical approach for estimating first-passage-time densities of the two-dimensional narrow capture problem.

PubMed

Lindsay, A E; Spoonmore, R T; Tzou, J C

2016-10-01

A hybrid asymptotic-numerical method is presented for obtaining an asymptotic estimate for the full probability distribution of capture times of a random walker by multiple small traps located inside a bounded two-dimensional domain with a reflecting boundary. As motivation for this study, we calculate the variance in the capture time of a random walker by a single interior trap and determine this quantity to be comparable in magnitude to the mean. This implies that the mean is not necessarily reflective of typical capture times and that the full density must be determined. To solve the underlying diffusion equation, the method of Laplace transforms is used to obtain an elliptic problem of modified Helmholtz type. In the limit of vanishing trap sizes, each trap is represented as a Dirac point source that permits the solution of the transform equation to be represented as a superposition of Helmholtz Green's functions. Using this solution, we construct asymptotic short-time solutions of the first-passage-time density, which captures peaks associated with rapid capture by the absorbing traps. When numerical evaluation of the Helmholtz Green's function is employed followed by numerical inversion of the Laplace transform, the method reproduces the density for larger times. We demonstrate the accuracy of our solution technique with a comparison to statistics obtained from a time-dependent solution of the diffusion equation and discrete particle simulations. In particular, we demonstrate that the method is capable of capturing the multimodal behavior in the capture time density that arises when the traps are strategically arranged. The hybrid method presented can be applied to scenarios involving both arbitrary domains and trap shapes.

Patching the Exchange-Correlation Potential in Density Functional Theory.

PubMed

Huang, Chen

2016-05-10

A method for directly patching exchange-correlation (XC) potentials in materials is derived. The electron density of a system is partitioned into subsystem densities by dividing its Kohn-Sham (KS) potential among the subsystems. Inside each subsystem, its projected KS potential is required to become the total system's KS potential. This requirement, together with the nearsightedness principle of electronic matters, ensures that the electronic structures inside subsystems can be good approximations to the total system's electronic structure. The nearsightedness principle also ensures that subsystem densities could be well localized in their regions, making it possible to use high-level methods to invert the XC potentials for subsystem densities. Two XC patching methods are developed. In the local XC patching method, the total system's XC potential is improved in the cluster region. We show that the coupling between a cluster and its environment is important for achieving a fast convergence of the electronic structure in the cluster region. In the global XC patching method, we discuss how to patch the subsystem XC potentials to construct the XC potential in the total system, aiming to scale up high-level quantum mechanics simulations of materials. Proof-of-principle examples are given.

A proposed simulation method for directed self-assembly of nanographene

NASA Astrophysics Data System (ADS)

Geraets, J. A.; Baldwin, J. P. C.; Twarock, R.; Hancock, Y.

2017-09-01

A methodology for predictive kinetic self-assembly modeling of bottom-up chemical synthesis of nanographene is proposed. The method maintains physical transparency in using a novel array format to efficiently store molecule information and by using array operations to determine reaction possibilities. Within a minimal model approach, the parameter space for the bond activation energies (i.e. molecule functionalization) at fixed reaction temperature and initial molecule concentrations is explored. Directed self-assembly of nanographene from functionalized tetrabenzanthracene and benzene is studied with regions in the activation energy phase-space showing length-to-width ratio tunability. The degree of defects and reaction reproducibility in the simulations is also determined, with the rate of functionalized benzene addition providing additional control of the dimension and quality of the nanographene. Comparison of the reaction energetics to available density functional theory data suggests the synthesis may be experimentally tenable using aryl-halide cross-coupling and noble metal surface-assisted catalysis. With full access to the intermediate reaction network and with dynamic coupling to density functional theory-informed tight-binding simulation, the method is proposed as a computationally efficient means towards detailed simulation-driven design of new nanographene systems.

Computational Investigation of the Geometrical and Electronic Structures of VGen-/0 (n = 1-4) Clusters by Density Functional Theory and Multiconfigurational CASSCF/CASPT2 Method.

PubMed

Tran, Van Tan; Nguyen, Minh Thao; Tran, Quoc Tri

2017-10-12

Density functional theory and the multiconfigurational CASSCF/CASPT2 method have been employed to study the low-lying states of VGe n -/0 (n = 1-4) clusters. For VGe -/0 and VGe 2 -/0 clusters, the relative energies and geometrical structures of the low-lying states are reported at the CASSCF/CASPT2 level. For the VGe 3 -/0 and VGe 4 -/0 clusters, the computational results show that due to the large contribution of the Hartree-Fock exact exchange, the hybrid B3LYP, B3PW91, and PBE0 functionals overestimate the energies of the high-spin states as compared to the pure GGA BP86 and PBE functionals and the CASPT2 method. On the basis of the pure GGA BP86 and PBE functionals and the CASSCF/CASPT2 results, the ground states of anionic and neutral clusters are defined, the relative energies of the excited states are computed, and the electron detachment energies of the anionic clusters are evaluated. The computational results are employed to give new assignments for all features in the photoelectron spectra of VGe 3 - and VGe 4 - clusters.

Theory of Tunneling Spectroscopy in a Mn12 Single-Electron Transistor by Density-Functional Theory Methods

NASA Astrophysics Data System (ADS)

Michalak, Ł.; Canali, C. M.; Pederson, M. R.; Paulsson, M.; Benza, V. G.

2010-01-01

We consider tunneling transport through a Mn12 molecular magnet using spin density functional theory. A tractable methodology for constructing many-body wave functions from Kohn-Sham orbitals allows for the determination of spin-dependent matrix elements for use in transport calculations. The tunneling conductance at finite bias is characterized by peaks representing transitions between spin multiplets, separated by an energy on the order of the magnetic anisotropy. The energy splitting of the spin multiplets and the spatial part of their many-body wave functions, describing the orbital degrees of freedom of the excess charge, strongly affect the electronic transport, and can lead to negative differential conductance.

Fitting of the Thomson scattering density and temperature profiles on the COMPASS tokamak

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

Stefanikova, E.; Division of Fusion Plasma Physics, KTH Royal Institute of Technology, SE-10691 Stockholm; Peterka, M.

2016-11-15

A new technique for fitting the full radial profiles of electron density and temperature obtained by the Thomson scattering diagnostic in H-mode discharges on the COMPASS tokamak is described. The technique combines the conventionally used modified hyperbolic tangent function for the edge transport barrier (pedestal) fitting and a modification of a Gaussian function for fitting the core plasma. Low number of parameters of this combined function and their straightforward interpretability and controllability provide a robust method for obtaining physically reasonable profile fits. Deconvolution with the diagnostic instrument function is applied on the profile fit, taking into account the dependence onmore » the actual magnetic configuration.« less

Theory of tunneling spectroscopy in a Mn12 single-electron transistor by density-functional theory methods.

PubMed

Michalak, Ł; Canali, C M; Pederson, M R; Paulsson, M; Benza, V G

2010-01-08

We consider tunneling transport through a Mn12 molecular magnet using spin density functional theory. A tractable methodology for constructing many-body wave functions from Kohn-Sham orbitals allows for the determination of spin-dependent matrix elements for use in transport calculations. The tunneling conductance at finite bias is characterized by peaks representing transitions between spin multiplets, separated by an energy on the order of the magnetic anisotropy. The energy splitting of the spin multiplets and the spatial part of their many-body wave functions, describing the orbital degrees of freedom of the excess charge, strongly affect the electronic transport, and can lead to negative differential conductance.

Coupled-cluster, Möller Plesset (MP2), Density Fitted Local MP2, and Density Functional Theory Examination of the Energetic and Structural Features of Hydrophobic Solvation: Water and Pentane

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

Ghadar, Yasaman; Clark, Aurora E.

2012-02-02

The interaction potentials between immiscible polar and non-polar solvents are a major driving force behind the formation of liquid:liquid interfaces. In this work, the interaction energy of water–pentane dimer has been determined using coupled-cluster theory with single double (triple) excitations [CCSD(T)], 2nd order Möller Plesset perturbation theory (MP2), density fitted local MP2 (DF-LMP2), as well as density functional theory using a wide variety of density functionals and several different basis sets. The M05-2X exchange correlation functionals exhibit excellent agreement with CCSD(T) and DF-LMP2 after taking into account basis set superposition error. The gas phase water–pentane interaction energy is found tomore » be quite sensitive to the specific pentane isomer (2,2- dimethylpropane vs. n-pentane) and relative orientation of the monomeric constituents. Subsequent solution phase cluster calculations of 2,2-dimethylpropane and n-pentane solvated by water indicate a positive free energy of solvation that is in good agreement with available experimental data. Structural parameters are quite sensitive to the density functional employed and reflect differences in the two-body interaction energy calculated by each method. In contrast, cluster calculations of pentane solvation of H2O solute are found to be inadequate for describing the organic solvent, likely due to limitations associated with the functionals employed (B3LYP, BHandH, and M05-2X).« less

Resonant frequencies of irregularly shaped microstrip antennas using method of moments

NASA Technical Reports Server (NTRS)

Deshpande, Manohar D.; Shively, David G.; Cockrell, C. R.

1993-01-01

This paper describes an application of the method of moments to determine resonant frequencies of irregularly shaped microstrip patches embedded in a grounded dielectric slab. For analysis, the microstrip patch is assumed to be excited by a linearly polarized plane wave that is normal to the patch. The surface-current density that is induced on the patch because of the incident field is expressed in terms of subdomain functions by dividing the patch into identical rectangular subdomains. The amplitudes of the subdomain functions, as a function of frequency, are determined using the electric-field integral equation (EFIE) approach in conjunction with the method of moments. The resonant frequencies of the patch are then obtained by selecting the frequency at which the amplitude of the surface-current density is real. The resonant frequencies of the equilateral triangular and other nonrectangular patches are computed using the present technique, and these frequencies are compared with measurements and other independent calculations.

Fracture analysis of a transversely isotropic high temperature superconductor strip based on real fundamental solutions

NASA Astrophysics Data System (ADS)

Gao, Zhiwen; Zhou, Youhe

2015-04-01

Real fundamental solution for fracture problem of transversely isotropic high temperature superconductor (HTS) strip is obtained. The superconductor E-J constitutive law is characterized by the Bean model where the critical current density is independent of the flux density. Fracture analysis is performed by the methods of singular integral equations which are solved numerically by Gauss-Lobatto-Chybeshev (GSL) collocation method. To guarantee a satisfactory accuracy, the convergence behavior of the kernel function is investigated. Numerical results of fracture parameters are obtained and the effects of the geometric characteristics, applied magnetic field and critical current density on the stress intensity factors (SIF) are discussed.

DNA Nucleotides Detection via capacitance properties of Graphene

NASA Astrophysics Data System (ADS)

Khadempar, Nahid; Berahman, Masoud; Yazdanpanah, Arash

2016-05-01

In the present paper a new method is suggested to detect the DNA nucleotides on a first-principles calculation of the electronic features of DNA bases which chemisorbed to a graphene sheet placed between two gold electrodes in a contact-channel-contact system. The capacitance properties of graphene in the channel are surveyed using non-equilibrium Green's function coupled with the Density Functional Theory. Thus, the capacitance properties of graphene are theoretically investigated in a biological environment, and, using a novel method, the effect of the chemisorbed DNA nucleotides on electrical charges on the surface of graphene is deciphered. Several parameters in this method are also extracted including Electrostatic energy, Induced density, induced electrostatic potential, Electron difference potential and Electron difference density. The qualitative and quantitative differences among these parameters can be used to identify DNA nucleotides. Some of the advantages of this approach include its ease and high accuracy. What distinguishes the current research is that it is the first experiment to investigate the capacitance properties of gaphene changes in the biological environment and the effect of chemisorbed DNA nucleotides on the surface of graphene on the charge.

The PDF method for turbulent combustion

NASA Technical Reports Server (NTRS)

Pope, S. B.

1991-01-01

Probability Density Function (PDF) methods provide a means of calculating the properties of turbulent reacting flows. They have been successfully applied to many turbulent flames, including some with finite rate kinetic effects. Here the methods are reviewed with an emphasis on computational issues and their application to turbulent combustion.

Adjusting the surface areal density of click-reactive azide groups by kinetic control of the azide substitution reaction on bromine-functional SAMs.

PubMed

Zhang, Shuo; Maidenberg, Yanir; Luo, Kai; Koberstein, Jeffrey T

2014-06-03

Azide-alkyne click chemistry has emerged as an important and versatile means for tethering a wide variety of guest molecules to virtually any substrate. In many of these applications, it is important to exercise control over the areal density of surface functional groups to achieve a desired areal density of the tethered guest molecule of interest. We demonstrate herein that the areal density of surface azide groups on flat germanium surfaces and nanoparticle substrates (silica and iron oxide) can be controlled kinetically by appropriately timed quenching of the S(N)2 substitution reaction of bromo-alkane-silane monolayers induced by the addition of sodium azide. The kinetics of the azide substitution reaction on monolayers formed on flat Ge substrates, determined by attenuated total reflection infrared spectroscopy (ATR-IR), are found to be identical to those for monolayers formed on both silica and iron oxide nanoparticles, the latter determined by transmission infrared spectroscopy. To validate the method, the percentages of surface bromine groups converted to azide groups after various reaction times were measured by quenching the S(N)2 reaction followed by analysis with ATR-IR (for Ge) and thermogravimetric analysis (after a subsequent click reaction with an alkyne-terminal polymer) for the nanoparticle substrates. The conversions found after quenching agree well with those expected from the standard kinetic curves. The latter result suggests that the kinetic method for the control of azide group areal density is a versatile means for functionalizing substrates with a prescribed areal density of azide groups for subsequent click reactions, and that the method is universal for any substrate, flat or nanoparticle, that can be modified with bromo-alkane-silane monolayers. Regardless of the surface geometry, we find that the azide substitution reaction is complete within 2-3 h, in sharp contrast to previous reports that indicate times of 48-60 h required for completion of the reaction.

Thermodynamic analysis of energy density in pressure retarded osmosis: The impact of solution volumes and costs

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

Reimund, Kevin K.; McCutcheon, Jeffrey R.; Wilson, Aaron D.

A general method was developed for estimating the volumetric energy efficiency of pressure retarded osmosis via pressure-volume analysis of a membrane process. The resulting model requires only the osmotic pressure, π, and mass fraction, w, of water in the concentrated and dilute feed solutions to estimate the maximum achievable specific energy density, uu, as a function of operating pressure. The model is independent of any membrane or module properties. This method utilizes equilibrium analysis to specify the volumetric mixing fraction of concentrated and dilute solution as a function of operating pressure, and provides results for the total volumetric energy densitymore » of similar order to more complex models for the mixing of seawater and riverwater. Within the framework of this analysis, the total volumetric energy density is maximized, for an idealized case, when the operating pressure is π/(1+√w⁻¹), which is lower than the maximum power density operating pressure, Δπ/2, derived elsewhere, and is a function of the solute osmotic pressure at a given mass fraction. It was also found that a minimum 1.45 kmol of ideal solute is required to produce 1 kWh of energy while a system operating at “maximum power density operating pressure” requires at least 2.9 kmol. Utilizing this methodology, it is possible to examine the effects of volumetric solution cost, operation of a module at various pressure, and operation of a constant pressure module with various feed.« less

Reconstruction of Cell Surface Densities of Ion Pumps, Exchangers, and Channels from mRNA Expression, Conductance Kinetics, Whole-Cell Calcium, and Current-Clamp Voltage Recordings, with an Application to Human Uterine Smooth Muscle Cells

PubMed Central

Atia, Jolene; McCloskey, Conor; Shmygol, Anatoly S.; Rand, David A.; van den Berg, Hugo A.; Blanks, Andrew M.

2016-01-01

Uterine smooth muscle cells remain quiescent throughout most of gestation, only generating spontaneous action potentials immediately prior to, and during, labor. This study presents a method that combines transcriptomics with biophysical recordings to characterise the conductance repertoire of these cells, the ‘conductance repertoire’ being the total complement of ion channels and transporters expressed by an electrically active cell. Transcriptomic analysis provides a set of potential electrogenic entities, of which the conductance repertoire is a subset. Each entity within the conductance repertoire was modeled independently and its gating parameter values were fixed using the available biophysical data. The only remaining free parameters were the surface densities for each entity. We characterise the space of combinations of surface densities (density vectors) consistent with experimentally observed membrane potential and calcium waveforms. This yields insights on the functional redundancy of the system as well as its behavioral versatility. Our approach couples high-throughput transcriptomic data with physiological behaviors in health and disease, and provides a formal method to link genotype to phenotype in excitable systems. We accurately predict current densities and chart functional redundancy. For example, we find that to evoke the observed voltage waveform, the BK channel is functionally redundant whereas hERG is essential. Furthermore, our analysis suggests that activation of calcium-activated chloride conductances by intracellular calcium release is the key factor underlying spontaneous depolarisations. PMID:27105427

Calculated electronic, transport, and related properties of zinc blende boron arsenide (zb-BAs)

NASA Astrophysics Data System (ADS)

Nwigboji, Ifeanyi H.; Malozovsky, Yuriy; Franklin, Lashounda; Bagayoko, Diola

2016-10-01

We present the results from ab-initio, self-consistent density functional theory (DFT) calculations of electronic, transport, and bulk properties of zinc blende boron arsenide. We utilized the local density approximation potential of Ceperley and Alder, as parameterized by Vosko and his group, the linear combination of Gaussian orbitals formalism, and the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF), in carrying out our completely self-consistent calculations. With this method, the results of our calculations have the full, physical content of density functional theory (DFT). Our results include electronic energy bands, densities of states, effective masses, and the bulk modulus. Our calculated, indirect band gap of 1.48 eV, from Γ to a conduction band minimum close to X, for the room temperature lattice constant of 4.777 Å, is in an excellent agreement with the experimental value of 1.46 ± 0.02 eV. We thoroughly explain the reasons for the excellent agreement between our findings and corresponding, experimental ones. This work provides a confirmation of the capability of DFT to describe accurately properties of materials, if the computations adhere strictly to the conditions of validity of DFT, as done by the BZW-EF method.

Combination of Wavefunction and Density Functional Approximations for Describing Electronic Correlation

NASA Astrophysics Data System (ADS)

Garza, Alejandro J.

Perhaps the most important approximations to the electronic structure problem in quantum chemistry are those based on coupled cluster and density functional theories. Coupled cluster theory has been called the ``gold standard'' of quantum chemistry due to the high accuracy that it achieves for weakly correlated systems. Kohn-Sham density functionals based on semilocal approximations are, without a doubt, the most widely used methods in chemistry and material science because of their high accuracy/cost ratio. The root of the success of coupled cluster and density functionals is their ability to efficiently describe the dynamic part of the electron correlation. However, both traditional coupled cluster and density functional approximations may fail catastrophically when substantial static correlation is present. This severely limits the applicability of these methods to a plethora of important chemical and physical problems such as, e.g., the description of bond breaking, transition states, transition metal-, lanthanide- and actinide-containing compounds, and superconductivity. In an attempt to tackle this problem, nonstandard (single-reference) coupled cluster-based techniques that aim to describe static correlation have been recently developed: pair coupled cluster doubles (pCCD) and singlet-paired coupled cluster doubles (CCD0). The ability to describe static correlation in pCCD and CCD0 comes, however, at the expense of important amounts of dynamic correlation so that the high accuracy of standard coupled cluster becomes unattainable. Thus, the reliable and efficient description of static and dynamic correlation in a simultaneous manner remains an open problem for quantum chemistry and many-body theory in general. In this thesis, different ways to combine pCCD and CCD0 with density functionals in order to describe static and dynamic correlation simultaneously (and efficiently) are explored. The combination of wavefunction and density functional methods has a long history in quantum chemistry (practical implementations have appeared in the literature since the 1970s). However, this kind of techniques have not achieved widespread use due to problems such as double counting of correlation and the symmetry dilemma--the fact that wavefunction methods respect the symmetries of Hamiltonian, while modern functionals are designed to work with broken symmetry densities. Here, particular mathematical features of pCCD and CCD0 are exploited to avoid these problems in an efficient manner. The two resulting families of approximations, denoted as pCCD+DFT and CCD0+DFT, are shown to be able to describe static and dynamic correlation in standard benchmark calculations. Furthermore, it is also shown that CCD0+DFT lends itself to combination with correlation from the direct random phase approximation (dRPA). Inclusion of dRPA in the long-range via the technique of range-separation allows for the description of dispersion correlation, the remaining part of the correlation. Thus, when combined with the dRPA, CCD0+DFT can account for all three-types of electron correlation that are necessary to accurately describe molecular systems. Lastly, applications of CCD0+DFT to actinide chemistry are considered in this work. The accuracy of CCD0+DFT for predicting equilibrium geometries and vibrational frequencies of actinide molecules and ions is assessed and compared to that of well-established quantum chemical methods. For this purpose, the f0 actinyl series (UO2 2+, NpO 23+, PuO24+, the isoelectronic NUN, and Thorium (ThO, ThO2+) and Nobelium (NoO, NoO2) oxides are studied. It is shown that the CCD0+DFT description of these species agrees with available experimental data and is comparable with the results given by the highest-level calculations that are possible for such heavy compounds while being, at least, an order of magnitude lower in computational cost.

Correlation functional in screened-exchange density functional theory procedures.

PubMed

Chan, Bun; Kawashima, Yukio; Hirao, Kimihiko

2017-10-15

In the present study, we have explored several prospects for the further development of screened-exchange density functional theory (SX-DFT) procedures. Using the performance of HSE06 as our measure, we find that the use of alternative correlation functionals (as oppose to PBEc in HSE06) also yields adequate results for a diverse set of thermochemical properties. We have further examined the performance of new SX-DFT procedures (termed HSEB-type methods) that comprise the HSEx exchange and a (near-optimal) reparametrized B97c (c OS,0  = c SS,0  = 1, c OS,1  = -1.5, c OS,2  = -0.644, c SS,1  = -0.5, and c SS,2  = 1.10) correlation functionals. The different variants of HSEB all perform comparably to or slightly better than the original HSE-type procedures. These results, together with our fundamental analysis of correlation functionals, point toward various directions for advancing SX-DFT methods. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Communication: Charge-population based dispersion interactions for molecules and materials

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

Stöhr, Martin; Department Chemie, Technische Universität München, Lichtenbergstr. 4, D-85748 Garching; Michelitsch, Georg S.

2016-04-21

We introduce a system-independent method to derive effective atomic C{sub 6} coefficients and polarizabilities in molecules and materials purely from charge population analysis. This enables the use of dispersion-correction schemes in electronic structure calculations without recourse to electron-density partitioning schemes and expands their applicability to semi-empirical methods and tight-binding Hamiltonians. We show that the accuracy of our method is en par with established electron-density partitioning based approaches in describing intermolecular C{sub 6} coefficients as well as dispersion energies of weakly bound molecular dimers, organic crystals, and supramolecular complexes. We showcase the utility of our approach by incorporation of the recentlymore » developed many-body dispersion method [Tkatchenko et al., Phys. Rev. Lett. 108, 236402 (2012)] into the semi-empirical density functional tight-binding method and propose the latter as a viable technique to study hybrid organic-inorganic interfaces.« less

Atomic density functional and diagram of structures in the phase field crystal model

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

Ankudinov, V. E., E-mail: vladimir@ankudinov.org; Galenko, P. K.; Kropotin, N. V.

2016-02-15

The phase field crystal model provides a continual description of the atomic density over the diffusion time of reactions. We consider a homogeneous structure (liquid) and a perfect periodic crystal, which are constructed from the one-mode approximation of the phase field crystal model. A diagram of 2D structures is constructed from the analytic solutions of the model using atomic density functionals. The diagram predicts equilibrium atomic configurations for transitions from the metastable state and includes the domains of existence of homogeneous, triangular, and striped structures corresponding to a liquid, a body-centered cubic crystal, and a longitudinal cross section of cylindricalmore » tubes. The method developed here is employed for constructing the diagram for the homogeneous liquid phase and the body-centered iron lattice. The expression for the free energy is derived analytically from density functional theory. The specific features of approximating the phase field crystal model are compared with the approximations and conclusions of the weak crystallization and 2D melting theories.« less

Chapman Enskog-maximum entropy method on time-dependent neutron transport equation

NASA Astrophysics Data System (ADS)

Abdou, M. A.

2006-09-01

The time-dependent neutron transport equation in semi and infinite medium with linear anisotropic and Rayleigh scattering is proposed. The problem is solved by means of the flux-limited, Chapman Enskog-maximum entropy for obtaining the solution of the time-dependent neutron transport. The solution gives the neutron distribution density function which is used to compute numerically the radiant energy density E(x,t), net flux F(x,t) and reflectivity Rf. The behaviour of the approximate flux-limited maximum entropy neutron density function are compared with those found by other theories. Numerical calculations for the radiant energy, net flux and reflectivity of the proposed medium are calculated at different time and space.

Multiphase aluminum equations of state via density functional theory

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

Sjostrom, Travis; Crockett, Scott; Rudin, Sven

2016-10-03

We have performed density functional theory (DFT) based calculations for aluminum in extreme conditions of both pressure and temperature, up to five times compressed ambient density, and over 1 000 000 K in temperature. In order to cover such a domain, DFT methods including phonon calculations, quantum molecular dynamics, and orbital-free DFT are employed. Our results are then used to construct a SESAME equation of state for the aluminum 1100 alloy, encompassing the fcc, hcp, and bcc solid phases as well as the liquid regime. We also provide extensive comparison with experiment, and based on this we also provide amore » slightly modified equation of state for the aluminum 6061 alloy.« less

Density-based Energy Decomposition Analysis for Intermolecular Interactions with Variationally Determined Intermediate State Energies

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

Wu, Q.; Ayers, P.W.; Zhang, Y.

2009-10-28

The first purely density-based energy decomposition analysis (EDA) for intermolecular binding is developed within the density functional theory. The most important feature of this scheme is to variationally determine the frozen density energy, based on a constrained search formalism and implemented with the Wu-Yang algorithm [Q. Wu and W. Yang, J. Chem. Phys. 118, 2498 (2003) ]. This variational process dispenses with the Heitler-London antisymmetrization of wave functions used in most previous methods and calculates the electrostatic and Pauli repulsion energies together without any distortion of the frozen density, an important fact that enables a clean separation of these twomore » terms from the relaxation (i.e., polarization and charge transfer) terms. The new EDA also employs the constrained density functional theory approach [Q. Wu and T. Van Voorhis, Phys. Rev. A 72, 24502 (2005)] to separate out charge transfer effects. Because the charge transfer energy is based on the density flow in real space, it has a small basis set dependence. Applications of this decomposition to hydrogen bonding in the water dimer and the formamide dimer show that the frozen density energy dominates the binding in these systems, consistent with the noncovalent nature of the interactions. A more detailed examination reveals how the interplay of electrostatics and the Pauli repulsion determines the distance and angular dependence of these hydrogen bonds.« less

The correlation function of galaxy ellipticities produced by gravitational lensing

NASA Technical Reports Server (NTRS)

Miralda-Escude, Jordi

1991-01-01

The correlation of galaxy ellipticities produced by gravitational lensing is calculated as a function of the power spectrum of density fluctuations in the universe by generalizing an analytical method developed by Gunn (1967). The method is applied to a model where identical objects with spherically symmetric density profiles are randomly laid down in space, and to the cold dark matter model. The possibility of detecting this correlation is discussed. Although an ellipticity correlation can also be caused by an intrinsic alignment of the axes of galaxies belonging to a cluster or a supercluster, a method is suggested by which one type of correlation can be distinguished from another. The advantage of this ellipticity correlation is that it is one of the few astronomical observations that can directly probe large-scale mass fluctuations in the universe.

Sensitivity of the Properties of Ruthenium “Blue Dimer” to Method, Basis Set, and Continuum Model

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

Ozkanlar, Abdullah; Clark, Aurora E.

2012-05-23

The ruthenium “blue dimer” [(bpy)2RuIIIOH2]2O4+ is best known as the first well-defined molecular catalyst for water oxidation. It has been subject to numerous computational studies primarily employing density functional theory. However, those studies have been limited in the functionals, basis sets, and continuum models employed. The controversy in the calculated electronic structure and the reaction energetics of this catalyst highlights the necessity of benchmark calculations that explore the role of density functionals, basis sets, and continuum models upon the essential features of blue-dimer reactivity. In this paper, we report Kohn-Sham complete basis set (KS-CBS) limit extrapolations of the electronic structuremore » of “blue dimer” using GGA (BPW91 and BP86), hybrid-GGA (B3LYP), and meta-GGA (M06-L) density functionals. The dependence of solvation free energy corrections on the different cavity types (UFF, UA0, UAHF, UAKS, Bondi, and Pauling) within polarizable and conductor-like polarizable continuum model has also been investigated. The most common basis sets of double-zeta quality are shown to yield results close to the KS-CBS limit; however, large variations are observed in the reaction energetics as a function of density functional and continuum cavity model employed.« less

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.

Multiconfiguration pair-density functional theory investigation of the electronic spectrum of MnO4-

NASA Astrophysics Data System (ADS)

Sharma, Prachi; Truhlar, Donald G.; Gagliardi, Laura

2018-03-01

The electronic spectrum of permanganate ions contains various highly multiconfigurational ligand-to-metal charge transfer states and is notorious for being one of the most challenging systems to be treated by quantum-chemical methods. Here we studied the lowest nine vertical excitation energies using restricted active space second-order perturbation theory (RASPT2) and multiconfiguration pair-density functional theory (MC-PDFT) to test and compare these two theories in computing such a challenging spectrum. The results are compared to literature data, including time-dependent density functional theory, completely renormalized equation-of-motion couple-cluster theory with single and double excitations, symmetry-adapted-cluster configuration interaction, and experimental spectra in the gas phase and solution. Our results show that MC-PDFT accurately predicts the spectrum at a significantly reduced cost as compared to RASPT2.

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

Azadi, Sam, E-mail: s.azadi@ucl.ac.uk; Cohen, R. E.; Department of Earth- and Environmental Sciences, Ludwig Maximilians Universität, Munich 80333

We studied the low-pressure (0–10 GPa) phase diagram of crystalline benzene using quantum Monte Carlo and density functional theory (DFT) methods. We performed diffusion quantum Monte Carlo (DMC) calculations to obtain accurate static phase diagrams as benchmarks for modern van der Waals density functionals. Using density functional perturbation theory, we computed the phonon contributions to the free energies. Our DFT enthalpy-pressure phase diagrams indicate that the Pbca and P2{sub 1}/c structures are the most stable phases within the studied pressure range. The DMC Gibbs free-energy calculations predict that the room temperature Pbca to P2{sub 1}/c phase transition occurs at 2.1(1)more » GPa. This prediction is consistent with available experimental results at room temperature. Our DMC calculations give 50.6 ± 0.5 kJ/mol for crystalline benzene lattice energy.« less

Multiconfiguration pair-density functional theory investigation of the electronic spectrum of MnO4.

PubMed

Sharma, Prachi; Truhlar, Donald G; Gagliardi, Laura

2018-03-28

The electronic spectrum of permanganate ions contains various highly multiconfigurational ligand-to-metal charge transfer states and is notorious for being one of the most challenging systems to be treated by quantum-chemical methods. Here we studied the lowest nine vertical excitation energies using restricted active space second-order perturbation theory (RASPT2) and multiconfiguration pair-density functional theory (MC-PDFT) to test and compare these two theories in computing such a challenging spectrum. The results are compared to literature data, including time-dependent density functional theory, completely renormalized equation-of-motion couple-cluster theory with single and double excitations, symmetry-adapted-cluster configuration interaction, and experimental spectra in the gas phase and solution. Our results show that MC-PDFT accurately predicts the spectrum at a significantly reduced cost as compared to RASPT2.

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections

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

Meek, Garrett A.; Levine, Benjamin G., E-mail: levine@chemistry.msu.edu

2016-05-14

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplingsmore » at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.« less

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections

NASA Astrophysics Data System (ADS)

Meek, Garrett A.; Levine, Benjamin G.

2016-05-01

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections.

PubMed

Meek, Garrett A; Levine, Benjamin G

2016-05-14

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.