Time-Dependent Hartree-Fock Approach to Nuclear Pasta at Finite Temperature

NASA Astrophysics Data System (ADS)

Schuetrumpf, B.; Klatt, M. A.; Iida, K.; Maruhn, J. A.; Mecke, K.; Reinhard, P.-G.

2013-03-01

We present simulations of neutron-rich matter at subnuclear densities, like supernova matter, with the time-dependent Hartree-Fock approximation at temperatures of several MeV. The initial state consists of α particles randomly distributed in space that have a Maxwell-Boltzmann distribution in momentum space. Adding a neutron background initialized with Fermi distributed plane waves the calculations reflect a reasonable approximation of astrophysical matter. This matter evolves into spherical, rod-like, and slab-like shapes and mixtures thereof. The simulations employ a full Skyrme interaction in a periodic three-dimensional grid. By an improved morphological analysis based on Minkowski functionals, all eight pasta shapes can be uniquely identified by the sign of only two valuations, namely the Euler characteristic and the integral mean curvature.

Orbital dependent functionals: An atom projector augmented wave method implementation

NASA Astrophysics Data System (ADS)

Xu, Xiao

This thesis explores the formulation and numerical implementation of orbital dependent exchange-correlation functionals within electronic structure calculations. These orbital-dependent exchange-correlation functionals have recently received renewed attention as a means to improve the physical representation of electron interactions within electronic structure calculations. In particular, electron self-interaction terms can be avoided. In this thesis, an orbital-dependent functional is considered in the context of Hartree-Fock (HF) theory as well as the Optimized Effective Potential (OEP) method and the approximate OEP method developed by Krieger, Li, and Iafrate, known as the KLI approximation. In this thesis, the Fock exchange term is used as a simple well-defined example of an orbital-dependent functional. The Projected Augmented Wave (PAW) method developed by P. E. Blochl has proven to be accurate and efficient for electronic structure calculations for local and semi-local functions because of its accurate evaluation of interaction integrals by controlling multiple moments. We have extended the PAW method to treat orbital-dependent functionals in Hartree-Fock theory and the Optimized Effective Potential method, particularly in the KLI approximation. In the course of study we develop a frozen-core orbital approximation that accurately treats the core electron contributions for above three methods. The main part of the thesis focuses on the treatment of spherical atoms. We have investigated the behavior of PAW-Hartree Fock and PAW-KLI basis, projector, and pseudopotential functions for several elements throughout the periodic table. We have also extended the formalism to the treatment of solids in a plane wave basis and implemented PWPAW-KLI code, which will appear in future publications.

Non-Born-Oppenheimer self-consistent field calculations with cubic scaling

NASA Astrophysics Data System (ADS)

Moncada, Félix; Posada, Edwin; Flores-Moreno, Roberto; Reyes, Andrés

2012-05-01

An efficient nuclear molecular orbital methodology is presented. This approach combines an auxiliary density functional theory for electrons (ADFT) and a localized Hartree product (LHP) representation for the nuclear wave function. A series of test calculations conducted on small molecules exposed that energy and geometry errors introduced by the use of ADFT and LHP approximations are small and comparable to those obtained by the use of electronic ADFT. In addition, sample calculations performed on (HF)n chains disclosed that the combined ADFT/LHP approach scales cubically with system size (n) as opposed to the quartic scaling of Hartree-Fock/LHP or DFT/LHP methods. Even for medium size molecules the improved scaling of the ADFT/LHP approach resulted in speedups of at least 5x with respect to Hartree-Fock/LHP calculations. The ADFT/LHP method opens up the possibility of studying nuclear quantum effects on large size systems that otherwise would be impractical.

Time-dependent Hartree-Fock approach to nuclear ``pasta'' at finite temperature

NASA Astrophysics Data System (ADS)

Schuetrumpf, B.; Klatt, M. A.; Iida, K.; Maruhn, J. A.; Mecke, K.; Reinhard, P.-G.

2013-05-01

We present simulations of neutron-rich matter at subnuclear densities, like supernova matter, with the time-dependent Hartree-Fock approximation at temperatures of several MeV. The initial state consists of α particles randomly distributed in space that have a Maxwell-Boltzmann distribution in momentum space. Adding a neutron background initialized with Fermi distributed plane waves the calculations reflect a reasonable approximation of astrophysical matter. This matter evolves into spherical, rod-like, and slab-like shapes and mixtures thereof. The simulations employ a full Skyrme interaction in a periodic three-dimensional grid. By an improved morphological analysis based on Minkowski functionals, all eight pasta shapes can be uniquely identified by the sign of only two valuations, namely the Euler characteristic and the integral mean curvature. In addition, we propose the variance in the cell density distribution as a measure to distinguish pasta matter from uniform matter.

Compton scattering study of electron momentum distribution in lithium fluoride using 662 keV gamma radiations

NASA Astrophysics Data System (ADS)

Vijayakumar, R.; Shivaramu; Ramamurthy, N.; Ford, M. J.

2008-12-01

Here we report the first ever 137Cs Compton spectroscopy study of lithium fluoride. The spherical average Compton profiles of lithium fluoride are deduced from Compton scattering measurements on poly crystalline sample at gamma ray energy of 662 keV. To compare the experimental data, we have computed the spherical average Compton profiles using self-consistent Hartree-Fock wave functions employed on linear combination of atomic orbital (HF-LCAO) approximation. The directional Compton profiles and their anisotropic effects are also calculated using the same HF-LCAO approximation. The experimental spherical average profiles are found to be in good agreement with the corresponding HF-LCAO calculations and in qualitative agreement with Hartree-Fock free atom values. The present experimental isotropic and calculated directional profiles are also compared with the available experimental isotropic and directional Compton profiles using 59.54 and 159 keV γ-rays.

Approximate spin projection of three-component UHF wavefunctions - The states of the pentachlorocyclopentadienyl cation and the croconate dianion, C5O5/2-/

NASA Technical Reports Server (NTRS)

Phillips, D. H.; Schug, J. C.

1974-01-01

The approximate spin projection method of Amos et al. is extended to handle UHF wave functions having three significant components of differing multiplicity. An expression is given for the energy after single annihilation which differs from that of Amos and Hall. The new expression reproduces the results obtained from a previous exact calculation for which the weights and energies of the components are known. The extended approximate projection method is applied to the pi-electron UHF wave functions for the ground states of the pentachlorocyclopentadienyl cation and the croconate dianion, C5O5(2-). The results indicate a triplet ground state for the former and a singlet ground state for the latter, in agreement with experimental ESR susceptibility measurements for these molecular ions. C5C15(-) cannont be treated by restricted Hartree-Fock theory, due to its open-shell ground state. Incorrect results are obtained for the croconate dianion, if restricted Hartree-Fock theory and singly excited configuration interactions are utilized.

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

Constantin, Lucian A.; Fabiano, Eduardo; Della Sala, Fabio

We introduce a novel non-local ingredient for the construction of exchange density functionals: the reduced Hartree parameter, which is invariant under the uniform scaling of the density and represents the exact exchange enhancement factor for one- and two-electron systems. The reduced Hartree parameter is used together with the conventional meta-generalized gradient approximation (meta-GGA) semilocal ingredients (i.e., the electron density, its gradient, and the kinetic energy density) to construct a new generation exchange functional, termed u-meta-GGA. This u-meta-GGA functional is exact for the exchange of any one- and two-electron systems, is size-consistent and non-empirical, satisfies the uniform density scaling relation, andmore » recovers the modified gradient expansion derived from the semiclassical atom theory. For atoms, ions, jellium spheres, and molecules, it shows a good accuracy, being often better than meta-GGA exchange functionals. Our construction validates the use of the reduced Hartree ingredient in exchange-correlation functional development, opening the way to an additional rung in the Jacob’s ladder classification of non-empirical density functionals.« less

Alternative derivation of an exchange-only density-functional optimized effective potential

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

Joubert, D. P.

2007-10-15

An alternative derivation of the exchange-only density-functional optimized effective potential equation is given. It is shown that the localized Hartree-Fock-common energy denominator Green's function approximation (LHF-CEDA) for the density-functional exchange potential proposed independently by Della Sala and Goerling [J. Chem. Phys. 115, 5718 (2001)] and Gritsenko and Baerends [Phys. Rev. A 64, 42506 (2001)] can be derived as an approximation to the OEP exchange potential in a similar way that the KLI approximation [Phys. Rev. A 45, 5453 (1992)] was derived. An exact expression for the correction term to the LHF-CEDA approximation can thus be found. The correction term canmore » be expressed in terms of the first-order perturbation-theory many-electron wave function shift when the Kohn-Sham Hamiltonian is subjected to a perturbation equal to the difference between the density-functional exchange potential and the Hartree-Fock nonlocal potential, expressed in terms of the Kohn-Sham orbitals. An explicit calculation shows that the density weighted mean of the correction term is zero, confirming that the LHF-CEDA approximation can be interpreted as a mean-field approximation. The corrected LHF-CEDA equation and the optimized effective potential equation are shown to be identical, with information distributed differently between terms in the equations. For a finite system the correction term falls off at least as fast as 1/r{sup 4} for large r.« less

Alternative derivation of an exchange-only density-functional optimized effective potential

NASA Astrophysics Data System (ADS)

Joubert, D. P.

2007-10-01

An alternative derivation of the exchange-only density-functional optimized effective potential equation is given. It is shown that the localized Hartree-Fock common energy denominator Green’s function approximation (LHF-CEDA) for the density-functional exchange potential proposed independently by Della Sala and Görling [J. Chem. Phys. 115, 5718 (2001)] and Gritsenko and Baerends [Phys. Rev. A 64, 42506 (2001)] can be derived as an approximation to the OEP exchange potential in a similar way that the KLI approximation [Phys. Rev. A 45, 5453 (1992)] was derived. An exact expression for the correction term to the LHF-CEDA approximation can thus be found. The correction term can be expressed in terms of the first-order perturbation-theory many-electron wave function shift when the Kohn-Sham Hamiltonian is subjected to a perturbation equal to the difference between the density-functional exchange potential and the Hartree-Fock nonlocal potential, expressed in terms of the Kohn-Sham orbitals. An explicit calculation shows that the density weighted mean of the correction term is zero, confirming that the LHF-CEDA approximation can be interpreted as a mean-field approximation. The corrected LHF-CEDA equation and the optimized effective potential equation are shown to be identical, with information distributed differently between terms in the equations. For a finite system the correction term falls off at least as fast as 1/r4 for large r .

A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. I. General formalism and application to open-shell states.

PubMed

Miranda, R P; Fisher, A J; Stella, L; Horsfield, A P

2011-06-28

The solution of the time-dependent Schrödinger equation for systems of interacting electrons is generally a prohibitive task, for which approximate methods are necessary. Popular approaches, such as the time-dependent Hartree-Fock (TDHF) approximation and time-dependent density functional theory (TDDFT), are essentially single-configurational schemes. TDHF is by construction incapable of fully accounting for the excited character of the electronic states involved in many physical processes of interest; TDDFT, although exact in principle, is limited by the currently available exchange-correlation functionals. On the other hand, multiconfigurational methods, such as the multiconfigurational time-dependent Hartree-Fock (MCTDHF) approach, provide an accurate description of the excited states and can be systematically improved. However, the computational cost becomes prohibitive as the number of degrees of freedom increases, and thus, at present, the MCTDHF method is only practical for few-electron systems. In this work, we propose an alternative approach which effectively establishes a compromise between efficiency and accuracy, by retaining the smallest possible number of configurations that catches the essential features of the electronic wavefunction. Based on a time-dependent variational principle, we derive the MCTDHF working equation for a multiconfigurational expansion with fixed coefficients and specialise to the case of general open-shell states, which are relevant for many physical processes of interest.

An Extension of the Krieger-Li-Iafrate Approximation to the Optimized-Effective-Potential Method

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

Wilson, B.G.

1999-11-11

The Krieger-Li-Iafrate approximation can be expressed as the zeroth order result of an unstable iterative method for solving the integral equation form of the optimized-effective-potential method. By pre-conditioning the iterate a first order correction can be obtained which recovers the bulk of quantal oscillations missing in the zeroth order approximation. A comparison of calculated total energies are given with Krieger-Li-Iafrate, Local Density Functional, and Hyper-Hartree-Fock results for non-relativistic atoms and ions.

On the physical interpretation of the nuclear molecular orbital energy.

PubMed

Charry, Jorge; Pedraza-González, Laura; Reyes, Andrés

2017-06-07

Recently, several groups have extended and implemented molecular orbital (MO) schemes to simultaneously obtain wave functions for electrons and selected nuclei. Many of these schemes employ an extended Hartree-Fock approach as a first step to find approximate electron-nuclear wave functions and energies. Numerous studies conducted with these extended MO methodologies have explored various effects of quantum nuclei on physical and chemical properties. However, to the best of our knowledge no physical interpretation has been assigned to the nuclear molecular orbital energy (NMOE) resulting after solving extended Hartree-Fock equations. This study confirms that the NMOE is directly related to the molecular electrostatic potential at the position of the nucleus.

Big Data Meets Quantum Chemistry Approximations: The Δ-Machine Learning Approach.

PubMed

Ramakrishnan, Raghunathan; Dral, Pavlo O; Rupp, Matthias; von Lilienfeld, O Anatole

2015-05-12

Chemically accurate and comprehensive studies of the virtual space of all possible molecules are severely limited by the computational cost of quantum chemistry. We introduce a composite strategy that adds machine learning corrections to computationally inexpensive approximate legacy quantum methods. After training, highly accurate predictions of enthalpies, free energies, entropies, and electron correlation energies are possible, for significantly larger molecular sets than used for training. For thermochemical properties of up to 16k isomers of C7H10O2 we present numerical evidence that chemical accuracy can be reached. We also predict electron correlation energy in post Hartree-Fock methods, at the computational cost of Hartree-Fock, and we establish a qualitative relationship between molecular entropy and electron correlation. The transferability of our approach is demonstrated, using semiempirical quantum chemistry and machine learning models trained on 1 and 10% of 134k organic molecules, to reproduce enthalpies of all remaining molecules at density functional theory level of accuracy.

DNA-DNA interaction beyond the ground state

NASA Astrophysics Data System (ADS)

Lee, D. J.; Wynveen, A.; Kornyshev, A. A.

2004-11-01

The electrostatic interaction potential between DNA duplexes in solution is a basis for the statistical mechanics of columnar DNA assemblies. It may also play an important role in recombination of homologous genes. We develop a theory of this interaction that includes thermal torsional fluctuations of DNA using field-theoretical methods and Monte Carlo simulations. The theory extends and rationalizes the earlier suggested variational approach which was developed in the context of a ground state theory of interaction of nonhomologous duplexes. It shows that the heuristic variational theory is equivalent to the Hartree self-consistent field approximation. By comparison of the Hartree approximation with an exact solution based on the QM analogy of path integrals, as well as Monte Carlo simulations, we show that this easily analytically-tractable approximation works very well in most cases. Thermal fluctuations do not remove the ability of DNA molecules to attract each other at favorable azimuthal conformations, neither do they wash out the possibility of electrostatic “snap-shot” recognition of homologous sequences, considered earlier on the basis of ground state calculations. At short distances DNA molecules undergo a “torsional alignment transition,” which is first order for nonhomologous DNA and weaker order for homologous sequences.

Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.

PubMed

Khoromskaia, Venera; Khoromskij, Boris N

2015-12-21

We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the tensor-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches.

Optimization of selected molecular orbitals in group basis sets.

PubMed

Ferenczy, György G; Adams, William H

2009-04-07

We derive a local basis equation which may be used to determine the orbitals of a group of electrons in a system when the orbitals of that group are represented by a group basis set, i.e., not the basis set one would normally use but a subset suited to a specific electronic group. The group orbitals determined by the local basis equation minimize the energy of a system when a group basis set is used and the orbitals of other groups are frozen. In contrast, under the constraint of a group basis set, the group orbitals satisfying the Huzinaga equation do not minimize the energy. In a test of the local basis equation on HCl, the group basis set included only 12 of the 21 functions in a basis set one might ordinarily use, but the calculated active orbital energies were within 0.001 hartree of the values obtained by solving the Hartree-Fock-Roothaan (HFR) equation using all 21 basis functions. The total energy found was just 0.003 hartree higher than the HFR value. The errors with the group basis set approximation to the Huzinaga equation were larger by over two orders of magnitude. Similar results were obtained for PCl(3) with the group basis approximation. Retaining more basis functions allows an even higher accuracy as shown by the perfect reproduction of the HFR energy of HCl with 16 out of 21 basis functions in the valence basis set. When the core basis set was also truncated then no additional error was introduced in the calculations performed for HCl with various basis sets. The same calculations with fixed core orbitals taken from isolated heavy atoms added a small error of about 10(-4) hartree. This offers a practical way to calculate wave functions with predetermined fixed core and reduced base valence orbitals at reduced computational costs. The local basis equation can also be used to combine the above approximations with the assignment of local basis sets to groups of localized valence molecular orbitals and to derive a priori localized orbitals. An appropriately chosen localization and basis set assignment allowed a reproduction of the energy of n-hexane with an error of 10(-5) hartree, while the energy difference between its two conformers was reproduced with a similar accuracy for several combinations of localizations and basis set assignments. These calculations include localized orbitals extending to 4-5 heavy atoms and thus they require to solve reduced dimension secular equations. The dimensions are not expected to increase with increasing system size and thus the local basis equation may find use in linear scaling electronic structure calculations.

Heavy baryons in the large N c limit

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

Albertus, C.; Ruiz Arriola, Enrique; Fernando, Ishara P.

It is shown that in the large N c limit heavy baryon masses can be estimated quantitatively in a 1/N c expansion using the Hartree approximation. The results are compared with available lattice calculations for different values of the ratio between the square root of the string tension and the heavy quark mass tension independent of N c. Using a potential adjusted to agree with the one obtained in lattice QCD, a variational analysis of the ground state spin averaged baryon mass is performed using Gaussian Hartree wave functions. Relativistic corrections through the quark kinetic energy are included. Lastly, themore » results provide good estimates for the first sub-leading in 1/N c corrections.« less

Heavy baryons in the large N c limit

DOE PAGES

Albertus, C.; Ruiz Arriola, Enrique; Fernando, Ishara P.; ...

2015-09-16

It is shown that in the large N c limit heavy baryon masses can be estimated quantitatively in a 1/N c expansion using the Hartree approximation. The results are compared with available lattice calculations for different values of the ratio between the square root of the string tension and the heavy quark mass tension independent of N c. Using a potential adjusted to agree with the one obtained in lattice QCD, a variational analysis of the ground state spin averaged baryon mass is performed using Gaussian Hartree wave functions. Relativistic corrections through the quark kinetic energy are included. Lastly, themore » results provide good estimates for the first sub-leading in 1/N c corrections.« less

Connection between the regular approximation and the normalized elimination of the small component in relativistic quantum theory

NASA Astrophysics Data System (ADS)

Filatov, Michael; Cremer, Dieter

2005-02-01

The regular approximation to the normalized elimination of the small component (NESC) in the modified Dirac equation has been developed and presented in matrix form. The matrix form of the infinite-order regular approximation (IORA) expressions, obtained in [Filatov and Cremer, J. Chem. Phys. 118, 6741 (2003)] using the resolution of the identity, is the exact matrix representation and corresponds to the zeroth-order regular approximation to NESC (NESC-ZORA). Because IORA (=NESC-ZORA) is a variationally stable method, it was used as a suitable starting point for the development of the second-order regular approximation to NESC (NESC-SORA). As shown for hydrogenlike ions, NESC-SORA energies are closer to the exact Dirac energies than the energies from the fifth-order Douglas-Kroll approximation, which is much more computationally demanding than NESC-SORA. For the application of IORA (=NESC-ZORA) and NESC-SORA to many-electron systems, the number of the two-electron integrals that need to be evaluated (identical to the number of the two-electron integrals of a full Dirac-Hartree-Fock calculation) was drastically reduced by using the resolution of the identity technique. An approximation was derived, which requires only the two-electron integrals of a nonrelativistic calculation. The accuracy of this approach was demonstrated for heliumlike ions. The total energy based on the approximate integrals deviates from the energy calculated with the exact integrals by less than 5×10-9hartree units. NESC-ZORA and NESC-SORA can easily be implemented in any nonrelativistic quantum chemical program. Their application is comparable in cost with that of nonrelativistic methods. The methods can be run with density functional theory and any wave function method. NESC-SORA has the advantage that it does not imply a picture change.

Many-body Green’s function theory for electron-phonon interactions: Ground state properties of the Holstein dimer

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

Säkkinen, Niko; Leeuwen, Robert van; Peng, Yang

2015-12-21

We study ground-state properties of a two-site, two-electron Holstein model describing two molecules coupled indirectly via electron-phonon interaction by using both exact diagonalization and self-consistent diagrammatic many-body perturbation theory. The Hartree and self-consistent Born approximations used in the present work are studied at different levels of self-consistency. The governing equations are shown to exhibit multiple solutions when the electron-phonon interaction is sufficiently strong, whereas at smaller interactions, only a single solution is found. The additional solutions at larger electron-phonon couplings correspond to symmetry-broken states with inhomogeneous electron densities. A comparison to exact results indicates that this symmetry breaking is stronglymore » correlated with the formation of a bipolaron state in which the two electrons prefer to reside on the same molecule. The results further show that the Hartree and partially self-consistent Born solutions obtained by enforcing symmetry do not compare well with exact energetics, while the fully self-consistent Born approximation improves the qualitative and quantitative agreement with exact results in the same symmetric case. This together with a presented natural occupation number analysis supports the conclusion that the fully self-consistent approximation describes partially the bipolaron crossover. These results contribute to better understanding how these approximations cope with the strong localizing effect of the electron-phonon interaction.« less

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.

Effect of gauge-field interaction on fermion transport in two dimensions: Hartree conductivity correction and dephasing

NASA Astrophysics Data System (ADS)

Ludwig, T.; Gornyi, I. V.; Mirlin, A. D.; Wölfle, P.

2008-06-01

We consider the quantum corrections to the conductivity of fermions interacting via a Chern Simons gauge field and concentrate on the Hartree-type contributions. The first-order Hartree approximation is only valid in the limit of weak coupling λ≪g-1/2 to the gauge field ( g≫1 is the dimensionless conductance) and results in an antilocalizing conductivity correction ˜λ2gln2T . In the case of strong coupling, an infinite summation of higher-order terms is necessary, which includes both the virtual (renormalization of the frequency) and real (dephasing) processes. At intermediate temperatures, T0≪T≪gT0 , where T0˜1/g2τ and τ is the elastic scattering time, the T dependence of the conductivity is determined by the Hartree correction, δσH(T)-δσH(gT0)∝g1/2-(T/T0)1/2[1+ln(gT0/T)1/2] , so that σ(T) increases with lowering T . At low temperatures, T≪T0 , the temperature-dependent part of the Hartree correction assumes a logarithmic form with a coefficient of order unity, δσH∝ln(1/T) . As a result, the negative exchange contribution δσex∝-lngln(1/T) becomes dominant, which yields localization in the limit of T→0 . We further discuss dephasing at strong coupling and show that the dephasing rates are of the order of T , owing to the interplay of inelastic scattering and renormalization. On the other hand, the dephasing length is anomalously short, Lφ≪LT , where LT is the thermal length. For the case of composite fermions with long-range Coulomb interaction, the gauge-field propagator is less singular. The resulting Hartree correction has the usual sign and temperature dependence, δσH∝lngln(1/T) , and for realistic g is overcompensated by the negative exchange contribution due to the gauge-boson and scalar parts of the interaction. In this case, the dephasing length Lφ is of the order of LT for not too low temperatures and exceeds LT for T≲gT0 .

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

PubMed

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

2015-01-13

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

Electron-electron interaction and spin-orbit coupling in InAs/AlSb heterostructures with a two-dimensional electron gas

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

Gavrilenko, V. I.; Krishtopenko, S. S., E-mail: ds_a-teens@mail.ru; Goiran, M.

2011-01-15

The effect of electron-electron interaction on the spectrum of two-dimensional electron states in InAs/AlSb (001) heterostructures with a GaSb cap layer with one filled size-quantization subband. The energy spectrum of two-dimensional electrons is calculated in the Hartree and Hartree-Fock approximations. It is shown that the exchange interaction decreasing the electron energy in subbands increases the energy gap between subbands and the spin-orbit splitting of the spectrum in the entire region of electron concentrations, at which only the lower size-quantization band is filled. The nonlinear dependence of the Rashba splitting constant at the Fermi wave vector on the concentration of two-dimensionalmore » electrons is demonstrated.« less

Photoionization cross sections for atomic chlorine using an open-shell random phase approximation

NASA Technical Reports Server (NTRS)

Starace, A. F.; Armstrong, L., Jr.

1975-01-01

The use of the Random Phase Approximation with Exchange (RPAE) for calculating partial and total photoionization cross sections and photoelectron angular distributions for open shell atoms is examined for atomic chlorine. Whereas the RPAE corrections in argon (Z=18) are large, it is found that those in chlorine (Z=17) are much smaller due to geometric factors. Hartree-Fock calculations with and without core relaxation are also presented. Sizable deviations from the close coupling results of Conneely are also found.

Studies of the electron density in the highest occupied molecular orbitals of PH 3, PF 3 and P(CH 3) 3 by electron momentum spectroscopy and Hartree-Fock, MRSD-CI and DFT calculations

NASA Astrophysics Data System (ADS)

Rolke, J.; Brion, C. E.

1996-06-01

The spherically averaged momentum profiles for the highest occupied molecular orbitals of PF 3 and P(CH 3) 3 have been obtained by electron momentum spectroscopy. The measurements provide a stringent test of basis set effects and the quality of ab-initio methods in the description of these larger molecular systems. As in previous work on the methyl-substituted amines, intuitive arguments fail to predict the correct amount of s- and p-type contributions to the momentum profile while delocalized molecular orbital concepts provide a more adequate description of the HOMOs. The experimental momentum profiles have been compared with theoretical momentum profiles calculated at the level of the target Hartree-Fock approximation with a range of basis sets. New Hartree-Fock calculations are also presented for the HOMO of PH 3 and compared to previously published experimental and theoretical momentum profiles. The experimental momentum profiles have further been compared to calculations at the level of the target Kohn-Sham approximation using density functional theory with the local density approximation and also with gradient corrected (non-local) exchange correlation potentials. In addition, total energies and dipole moments have been calculated for all three molecules by the various theoretical methods and compared to experimental values. Calculated 'density difference maps' show the regions where the HOMO momentum and position electron densities of PF 3 and P(CH 3) 3 change relative to the corresponding HOMO density of PH 3. The results suggest that methyl groups have an electron-attracting effect (relative to H) on the HOMO charge density in trimethyl phosphines. These conclusions are supported by a consideration of dipole moments and the 31P NMR chemical shifts for PH 3, PF 3 and P(CH 3) 3.

Proper and improper zero energy modes in Hartree-Fock theory and their relevance for symmetry breaking and restoration.

PubMed

Cui, Yao; Bulik, Ireneusz W; Jiménez-Hoyos, Carlos A; Henderson, Thomas M; Scuseria, Gustavo E

2013-10-21

We study the spectra of the molecular orbital Hessian (stability matrix) and random-phase approximation (RPA) Hamiltonian of broken-symmetry Hartree-Fock solutions, focusing on zero eigenvalue modes. After all negative eigenvalues are removed from the Hessian by following their eigenvectors downhill, one is left with only positive and zero eigenvalues. Zero modes correspond to orbital rotations with no restoring force. These rotations determine states in the Goldstone manifold, which originates from a spontaneously broken continuous symmetry in the wave function. Zero modes can be classified as improper or proper according to their different mathematical and physical properties. Improper modes arise from symmetry breaking and their restoration always lowers the energy. Proper modes, on the other hand, correspond to degeneracies of the wave function, and their symmetry restoration does not necessarily lower the energy. We discuss how the RPA Hamiltonian distinguishes between proper and improper modes by doubling the number of zero eigenvalues associated with the latter. Proper modes in the Hessian always appear in pairs which do not double in RPA. We present several pedagogical cases exemplifying the above statements. The relevance of these results for projected Hartree-Fock methods is also addressed.

Twist-averaged boundary conditions for nuclear pasta Hartree-Fock calculations

DOE PAGES

Schuetrumpf, B.; Nazarewicz, W.

2015-10-21

Nuclear pasta phases, present in the inner crust of neutron stars, are associated with nucleonic matter at subsaturation densities arranged in regular shapes. Those complex phases, residing in a layer which is approximately 100-m thick, impact many features of neutron stars. Theoretical quantum-mechanical simulations of nuclear pasta are usually carried out in finite three-dimensional boxes assuming periodic boundary conditions. The resulting solutions are affected by spurious finite-size effects. To remove spurious finite-size effects, it is convenient to employ twist-averaged boundary conditions (TABC) used in condensed matter, nuclear matter, and lattice quantum chromodynamics applications. In this work, we study the effectivenessmore » of TABC in the context of pasta phase simulations within nuclear density functional theory. We demonstrated that by applying TABC reliable results can be obtained from calculations performed in relatively small volumes. By studying various contributions to the total energy, we gain insights into pasta phases in mid-density range. Future applications will include the TABC extension of the adaptive multiresolution 3D Hartree-Fock solver and Hartree-Fock-Bogoliubov TABC applications to superfluid pasta phases and complex nucleonic topologies as in fission.« less

Modified Fourth-Order Kinetic Energy Gradient Expansion with Hartree Potential-Dependent Coefficients.

PubMed

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

2017-09-12

Using the semiclassical neutral atom theory, we developed a modified fourth-order kinetic energy (KE) gradient expansion (GE4m) that keeps unchanged all the linear-response terms of the uniform electron gas and gives a significant improvement with respect to the known semilocal functionals for both large atoms and jellium surfaces. On the other hand, GE4m is not accurate for light atoms; thus, we modified the GE4m coefficients making them dependent on a novel ingredient, the reduced Hartree potential, recently introduced in the Journal of Chemical Physics 2016, 145, 084110, in the context of exchange functionals. The resulting KE gradient expansion functional, named uGE4m, belongs to the novel class of u-meta-generalized-gradient-approximations (uMGGA) whose members depend on the conventional ingredients (i.e., the reduced gradient and Laplacian of the density) as well as on the reduced Hartree potential. To test uGE4m, we defined an appropriate benchmark (including total KE and KE differences for atoms, molecules and jellium clusters) for gradient expansion functionals, that is, including only those systems which are mainly described by a slowly varying density regime. While most of the GGA and meta-GGA KE functionals (we tested 18 of them) are accurate for some properties and inaccurate for others, uGE4m shows a consistently good performance for all the properties considered. This represents a qualitative boost in the KE functional development and highlights the importance of the reduced Hartree potential for the construction of next-generation KE functionals.

Quantum soliton in 1D Heisenberg spin chains with Dzyaloshinsky-Moriya and next-nearest-neighbor interactions.

PubMed

Djoufack, Z I; Tala-Tebue, E; Nguenang, J P; Kenfack-Jiotsa, A

2016-10-01

We report in this work, an analytical study of quantum soliton in 1D Heisenberg spin chains with Dzyaloshinsky-Moriya Interaction (DMI) and Next-Nearest-Neighbor Interactions (NNNI). By means of the time-dependent Hartree approximation and the semi-discrete multiple-scale method, the equation of motion for the single-boson wave function is reduced to the nonlinear Schrödinger equation. It comes from this present study that the spectrum of the frequencies increases, its periodicity changes, in the presence of NNNI. The antisymmetric feature of the DMI was probed from the dispersion curve while changing the sign of the parameter controlling it. Five regions were identified in the dispersion spectrum, when the NNNI are taken into account instead of three as in the opposite case. In each of these regions, the quantum model can exhibit quantum stationary localized and stable bright or dark soliton solutions. In each region, we could set up quantum localized n-boson Hartree states as well as the analytical expression of their energy level, respectively. The accuracy of the analytical studies is confirmed by the excellent agreement with the numerical calculations, and it certifies the stability of the stationary quantum localized solitons solutions exhibited in each region. In addition, we found that the intensity of the localization of quantum localized n-boson Hartree states increases when the NNNI are considered. We also realized that the intensity of Hartree n-boson states corresponding to quantum discrete soliton states depend on the wave vector.

Global solutions of restricted open-shell Hartree-Fock theory from semidefinite programming with applications to strongly correlated quantum systems.

PubMed

Veeraraghavan, Srikant; Mazziotti, David A

2014-03-28

We present a density matrix approach for computing global solutions of restricted open-shell Hartree-Fock theory, based on semidefinite programming (SDP), that gives upper and lower bounds on the Hartree-Fock energy of quantum systems. While wave function approaches to Hartree-Fock theory yield an upper bound to the Hartree-Fock energy, we derive a semidefinite relaxation of Hartree-Fock theory that yields a rigorous lower bound on the Hartree-Fock energy. We also develop an upper-bound algorithm in which Hartree-Fock theory is cast as a SDP with a nonconvex constraint on the rank of the matrix variable. Equality of the upper- and lower-bound energies guarantees that the computed solution is the globally optimal solution of Hartree-Fock theory. The work extends a previously presented method for closed-shell systems [S. Veeraraghavan and D. A. Mazziotti, Phys. Rev. A 89, 010502-R (2014)]. For strongly correlated systems the SDP approach provides an alternative to the locally optimized Hartree-Fock energies and densities with a certificate of global optimality. Applications are made to the potential energy curves of C2, CN, Cr2, and NO2.

Hartree-Fock calculation of the differential photoionization cross sections of small Li clusters

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

Galitskiy, S. A.; Artemyev, A. N.; Jänkälä, K.

2015-01-21

Cross sections and angular distribution parameters for the single-photon ionization of all electron orbitals of Li{sub 2−8} are systematically computed in a broad interval of the photoelectron kinetic energies for the energetically most stable geometry of each cluster. Calculations of the partial photoelectron continuum waves in clusters are carried out by the single center method within the Hartree-Fock approximation. We study photoionization cross sections per one electron and analyze in some details general trends in the photoionization of inner and outer shells with respect to the size and geometry of a cluster. The present differential cross sections computed for Li{submore » 2} are in a good agreement with the available theoretical data, whereas those computed for Li{sub 3−8} clusters can be considered as theoretical predictions.« less

Self-consistent Hartree-Fock RPA calculations in 208Pb

NASA Astrophysics Data System (ADS)

Taqi, Ali H.; Ali, Mohammed S.

2018-01-01

The nuclear structure of 208Pb is studied in the framework of the self-consistent random phase approximation (SCRPA). The Hartree-Fock mean field and single particle states are used to implement a completely SCRPA with Skyrme-type interactions. The Hamiltonian is diagonalised within a model space using five Skyrme parameter sets, namely LNS, SkI3, SkO, SkP and SLy4. In view of the huge number of the existing Skyrme-force parameterizations, the question remains which of them provide the best description of data. The approach attempts to accurately describe the structure of the spherical even-even nucleus 208Pb. To illustrate our approach, we compared the binding energy, charge density distribution, excitation energy levels scheme with the available experimental data. Moreover, we calculated isoscalar and isovector monopole, dipole, and quadrupole transition densities and strength functions.

Restoring the Pauli principle in the random phase approximation ground state

NASA Astrophysics Data System (ADS)

Kosov, D. S.

2017-12-01

Random phase approximation ground state contains electronic configurations where two (and more) identical electrons can occupy the same molecular spin-orbital violating the Pauli exclusion principle. This overcounting of electronic configurations happens due to quasiboson approximation in the treatment of electron-hole pair operators. We describe the method to restore the Pauli principle in the RPA wavefunction. The proposed theory is illustrated by the calculations of molecular dipole moments and electronic kinetic energies. The Hartree-Fock based RPA, which is corrected for the Pauli principle, gives the results of comparable accuracy with Møller-Plesset second order perturbation theory and coupled-cluster singles and doubles method.

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

PubMed

Roper, Ian P E; Besley, Nicholas A

2016-03-21

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

Nonequilibrium evolution of scalar fields in FRW cosmologies

NASA Astrophysics Data System (ADS)

Boyanovsky, D.; de Vega, H. J.; Holman, R.

1994-03-01

We derive the effective equations for the out of equilibrium time evolution of the order parameter and the fluctuations of a scalar field theory in spatially flat FRW cosmologies. The calculation is performed both to one loop and in a nonperturbative, self-consistent Hartree approximation. The method consists of evolving an initial functional thermal density matrix in time and is suitable for studying phase transitions out of equilibrium. The renormalization aspects are studied in detail and we find that the counterterms depend on the initial state. We investigate the high temperature expansion and show that it breaks down at long times. We also obtain the time evolution of the initial Boltzmann distribution functions, and argue that to one-loop order or in the Hartree approximation the time evolved state is a ``squeezed'' state. We illustrate the departure from thermal equilibrium by numerically studying the case of a free massive scalar field in de Sitter and radiation-dominated cosmologies. It is found that a suitably defined nonequilibrium entropy per mode increases linearly with comoving time in a de Sitter cosmology, whereas it is not a monotonically increasing function in the radiation-dominated case.

Nuclear Pasta at Finite Temperature with the Time-Dependent Hartree-Fock Approach

NASA Astrophysics Data System (ADS)

Schuetrumpf, B.; Klatt, M. A.; Iida, K.; Maruhn, J. A.; Mecke, K.; Reinhard, P.-G.

2016-01-01

We present simulations of neutron-rich matter at sub-nuclear densities, like supernova matter. With the time-dependent Hartree-Fock approximation we can study the evolution of the system at temperatures of several MeV employing a full Skyrme interaction in a periodic three-dimensional grid [1]. The initial state consists of α particles randomly distributed in space that have a Maxwell-Boltzmann distribution in momentum space. Adding a neutron background initialized with Fermi distributed plane waves the calculations reflect a reasonable approximation of astrophysical matter. The matter evolves into spherical, rod-like, connected rod-like and slab-like shapes. Further we observe gyroid-like structures, discussed e.g. in [2], which are formed spontaneously choosing a certain value of the simulation box length. The ρ-T-map of pasta shapes is basically consistent with the phase diagrams obtained from QMD calculations [3]. By an improved topological analysis based on Minkowski functionals [4], all observed pasta shapes can be uniquely identified by only two valuations, namely the Euler characteristic and the integral mean curvature. In addition we propose the variance in the cell-density distribution as a measure to distinguish pasta matter from uniform matter.

Exchange and Correlation Effects in a Double Barrier Quantum Well

NASA Astrophysics Data System (ADS)

Hasbun, J. E.

2003-03-01

Studies of electronic properties in double barrier resonant tunneling systems usually involve the solution of the BenDaniel-Duke equation (BDK) in the presence of an applied voltage. Electron interactions are included by means of the Hartree term and the wavefunction is self-consistently obtained by coupling the BDK with the Poisson equation. In this work, we go beyond the Hartree approximation by including exchange and correlation effects (v_xc) through the local density functional theory. The analytically parametrized v_xc of Hedin and Lunqvist footnote[1]L. Hedin and B. I. Lundqvist, J. Phys C: Solid. St. Phys. 4, 2064(1971) is employed. While the calculation of v_xc involves extra self-consistency conditions, it is shown that the inclusion of exchange and correlation effects may be important in the electronic characteristics of these devices. For our earlier model footnote[2]J. E. Hasbun, APS Bull. 47, 914(2002) the v_xc potential is comparable to the Hartree electron term at low electric field values, but less so for much higher field. The v_xc employed here ^2 is not appreciably different from the more sophisticated one of Perdew and Zunger footnote[3]J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048(1981). JH wishes to thank Mei-Yin Chou for helpful discussions

Many-body Green’s function theory for electron-phonon interactions: The Kadanoff-Baym approach to spectral properties of the Holstein dimer

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

Säkkinen, Niko; Peng, Yang; Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin-Dahlem

2015-12-21

We present a Kadanoff-Baym formalism to study time-dependent phenomena for systems of interacting electrons and phonons in the framework of many-body perturbation theory. The formalism takes correctly into account effects of the initial preparation of an equilibrium state and allows for an explicit time-dependence of both the electronic and phononic degrees of freedom. The method is applied to investigate the charge neutral and non-neutral excitation spectra of a homogeneous, two-site, two-electron Holstein model. This is an extension of a previous study of the ground state properties in the Hartree (H), partially self-consistent Born (Gd) and fully self-consistent Born (GD) approximationsmore » published in Säkkinen et al. [J. Chem. Phys. 143, 234101 (2015)]. Here, the homogeneous ground state solution is shown to become unstable for a sufficiently strong interaction while a symmetry-broken ground state solution is shown to be stable in the Hartree approximation. Signatures of this instability are observed for the partially self-consistent Born approximation but are not found for the fully self-consistent Born approximation. By understanding the stability properties, we are able to study the linear response regime by calculating the density-density response function by time-propagation. This amounts to a solution of the Bethe-Salpeter equation with a sophisticated kernel. The results indicate that none of the approximations is able to describe the response function during or beyond the bipolaronic crossover for the parameters investigated. Overall, we provide an extensive discussion on when the approximations are valid and how they fail to describe the studied exact properties of the chosen model system.« less

Neutral-atom electron binding energies from relaxed-orbital relativistic Hartree-Fock-Slater calculations for Z between 2 and 106

NASA Technical Reports Server (NTRS)

Huang, K.-N.; Aoyagi, M.; Mark, H.; Chen, M. H.; Crasemann, B.

1976-01-01

Electron binding energies in neutral atoms have been calculated relativistically, with the requirement of complete relaxation. Hartree-Fock-Slater wave functions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first-order correction to the local approximation was thus included. Quantum-electrodynamic corrections were made. For all elements with atomic numbers ranging from 2 to 106, the following quantities are listed: total energies, electron kinetic energies, electron-nucleus potential energies, electron-electron potential energies consisting of electrostatic and Breit interaction (magnetic and retardation) terms, and vacuum polarization energies. Binding energies including relaxation are listed for all electrons in all atoms over the indicated range of atomic numbers. A self-energy correction is included for the 1s, 2s, and 2p(1/2) levels. Results for selected atoms are compared with energies calculated by other methods and with experimental values.

Optimized auxiliary basis sets for density fitted post-Hartree-Fock calculations of lanthanide containing molecules

NASA Astrophysics Data System (ADS)

Chmela, Jiří; Harding, Michael E.

2018-06-01

Optimised auxiliary basis sets for lanthanide atoms (Ce to Lu) for four basis sets of the Karlsruhe error-balanced segmented contracted def2 - series (SVP, TZVP, TZVPP and QZVPP) are reported. These auxiliary basis sets enable the use of the resolution-of-the-identity (RI) approximation in post Hartree-Fock methods - as for example, second-order perturbation theory (MP2) and coupled cluster (CC) theory. The auxiliary basis sets are tested on an enlarged set of about a hundred molecules where the test criterion is the size of the RI error in MP2 calculations. Our tests also show that the same auxiliary basis sets can be used together with different effective core potentials. With these auxiliary basis set calculations of MP2 and CC quality can now be performed efficiently on medium-sized molecules containing lanthanides.

Axial deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator Basis

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

Perez, R. Navarro; Schunck, N.; Lasseri, R.

2017-03-09

HFBTHO is a physics computer code that is used to model the structure of the nucleus. It is an implementation of the nuclear energy Density Functional Theory (DFT), where the energy of the nucleus is obtained by integration over space of some phenomenological energy density, which is itself a functional of the neutron and proton densities. In HFBTHO, the energy density derives either from the zero-range Dkyrme or the finite-range Gogny effective two-body interaction between nucleons. Nuclear superfluidity is treated at the Hartree-Fock-Bogoliubov (HFB) approximation, and axial-symmetry of the nuclear shape is assumed. This version is the 3rd release ofmore » the program; the two previous versions were published in Computer Physics Communications [1,2]. The previous version was released at LLNL under GPL 3 Open Source License and was given release code LLNL-CODE-573953.« less

Two-photon excitation cross section in light and intermediate atoms in frozen-core LS-coupling approximation

NASA Technical Reports Server (NTRS)

Omidvar, K.

1980-01-01

Using the method of explicit summation over the intermediate states two-photon absorption cross sections in light and intermediate atoms based on the simplistic frozen-core approximation and LS coupling have been formulated. Formulas for the cross section in terms of integrals over radial wave functions are given. Two selection rules, one exact and one approximate, valid within the stated approximations are derived. The formulas are applied to two-photon absorptions in nitrogen, oxygen, and chlorine. In evaluating the radial integrals, for low-lying levels, the Hartree-Fock wave functions, and for high-lying levels, hydrogenic wave functions obtained by the quantum-defect method have been used. A relationship between the cross section and the oscillator strengths is derived.

Time-dependent variational approach in terms of squeezed coherent states: Implication to semi-classical approximation

NASA Technical Reports Server (NTRS)

Tsue, Yasuhiko

1994-01-01

A general framework for time-dependent variational approach in terms of squeezed coherent states is constructed with the aim of describing quantal systems by means of classical mechanics including higher order quantal effects with the aid of canonicity conditions developed in the time-dependent Hartree-Fock theory. The Maslov phase occurring in a semi-classical quantization rule is investigated in this framework. In the limit of a semi-classical approximation in this approach, it is definitely shown that the Maslov phase has a geometric nature analogous to the Berry phase. It is also indicated that this squeezed coherent state approach is a possible way to go beyond the usual WKB approximation.

Breit interaction contribution to parity violating potentials in chiral molecules containing light nuclei.

PubMed

Berger, Robert

2008-10-21

The importance of the Breit interaction for an accurate prediction of parity violating energy differences between enantiomers is studied within electroweak quantum chemical frameworks. Besides two-electron orbit-orbit and spin-spin coupling contributions, the Breit interaction gives rise to the spin-other-orbit coupling term of the Breit-Pauli Hamiltonian. The present numerical study demonstrates that neglect of this latter term leads in hydrogen peroxide (H(2)O(2)) to relative deviations in the parity violating potential (V(pv)) by about 10%, whereas further relativistic corrections accounted for within a four-component Dirac-Hartree-Fock-Coulomb (DHFC) framework remain smaller, below 5%. Thus, the main source of discrepancy between previous one-component based (coupled perturbed) Hartree-Fock (HF) and four-component Dirac-Hartree-Fock results for parity violating potentials in H(2)O(2) is the neglect of the Breit contribution in DHFC. In heavier homologs of hydrogen peroxide the relative contribution of the spin-other-orbit coupling term to V(pv) decreases with increasing nuclear charge, whereas other relativistic effects become increasingly important. As shown for the H(2)X(2) (X = O,S,Se,Te,Po) series of molecules and for CHBrClF, to a good approximation these other relativistic influences on V(pv) can be accounted for in one-component based HF calculations with the help of relativistic enhancement factors proposed earlier in the theory of atomic parity violation.

The energy gap in a-Si 1 - xC g: H alloys

NASA Astrophysics Data System (ADS)

Valladares, Ariel A.; Valladares, Alexander; Enrique Sansores, L.; Nelis, Mary Ann Me

1997-02-01

The electronic structure of amorphous tetrahedral clusters of the type a-Si 1 - xC g: H are studied using the pseudopotential SCF Hartree-Fock approximation. The reduced energy gap isgiven by Egr( x) - 1 + 0.84 x for x ⩽ 0.5, whereas experimentally Egr( x) = 1 + 0.96 x. For x ⩾ 0.5 the dip in the gap value reported experimentally is verified.

Tensor force effect on the evolution of single-particle energies in some isotopic chains in the relativistic Hartree-Fock approximation

NASA Astrophysics Data System (ADS)

López-Quelle, M.; Marcos, S.; Niembro, R.; Savushkin, L. N.

2018-03-01

Within a nonlinear relativistic Hartree-Fock approximation combined with the BCS method, we study the effect of the nucleon-nucleon tensor force of the π-exchange potential on the spin- and pseudospin-orbit doublets along the Ca and Sn isotopic chains. We show how the self-consistent tensor force effect modifies the splitting of both kinds of doublets in an interdependent form, leading, quite generally, to opposite effects in the accomplishment of the spin and pseudospin symmetries (the one is restored, the other one deteriorates and vice versa). The ordering of the single-particle energy levels is crucial to this respect. Also, we observe a mutual dependence on the evolution of the shell closure gap Z = 50 and the energy band outside the core, along the Sn chain, as due to the tensor force. In fact, when the shell gap is quenched the outside energy band is enlarged, and vice versa. A reduction of the strength of the pion tensor force with respect to its experimental value from the nucleon-nucleon scattering is needed to get results closer to the experiment. Pairing correlations act to some extent in the opposite direction of the tensor term of the one-pion-exchange force.

Rayleigh scattering of x-ray and γ-ray by 1s and 2s electrons in ions and neutral atoms

NASA Astrophysics Data System (ADS)

Costescu, A.; Karim, K.; Moldovan, M.; Spanulescu, S.; Stoica, C.

2011-02-01

Using the Coulomb-Green function method and considering the nonrelativistic limit for the two-photon S-matrix element, the right nonrelativistic 2s Rayleigh scattering amplitudes are obtained. Our result takes into account all multipoles, retardation and relativistic kinematics contributions, and the old dipole approximation result of Costescu [1] is retrieved as a limit case. The total photoeffect cross-section which is related to the imaginary part of the Rayleigh forward scattering amplitude through the optical theorem is also obtained. Our Coulombian formulae are used in the more realistic case of elastic scattering of photons by bound 1s and 2s electrons in ions and neutral atoms. Screening effects are considered in the independent particle approximation through the Hartree-Fock method. The effective charge Zeff is obtained by fitting the Hartree-Fock charge distribution by a Coulombian one. Good agreement (within 10%) is found when comparing the numerical predictions given by our nonrelativistic formulae with the full relativistic numerical results of Kissel [2] in the case of elastic scattering of photons by 1s and 2s electrons and Scofield [3] in the case of K-shell and 2s subshell photoionization for neutral atoms with 18 <= Z <= 92 and photon energies ω <= αZm.

Wave-function-based approach to quasiparticle bands: Insight into the electronic structure of c-ZnS

NASA Astrophysics Data System (ADS)

Stoyanova, A.; Hozoi, L.; Fulde, P.; Stoll, H.

2011-05-01

Ab initio wave-function-based methods are employed for the study of quasiparticle energy bands of zinc-blende ZnS, with focus on the Zn 3d “semicore” states. The relative energies of these states with respect to the top of the S 3p valence bands appear to be poorly described as compared to experimental values not only within the local density approximation (LDA), but also when many-body corrections within the GW approximation are applied to the LDA or LDA + U mean-field solutions [T. Miyake, P. Zhang, M. L. Cohen, and S. G. Louie, Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.74.245213 74, 245213 (2006)]. In the present study, we show that for the accurate description of the Zn 3d states a correlation treatment based on wave-function methods is needed. Our study rests on a local Hamiltonian approach which rigorously describes the short-range polarization and charge redistribution effects around an extra hole or electron placed into the valence respective conduction bands of semiconductors and insulators. The method also facilitates the computation of electron correlation effects beyond relaxation and polarization. The electron correlation treatment is performed on finite clusters cut off the infinite system. The formalism makes use of localized Wannier functions and embedding potentials derived explicitly from prior periodic Hartree-Fock calculations. The on-site and nearest-neighbor charge relaxation lead to corrections of several eV to the Hartree-Fock band energies and gap. Corrections due to long-range polarization are of the order of 1.0 eV. The dispersion of the Hartree-Fock bands is only slightly affected by electron correlations. We find the Zn 3d “semicore” states to lie ~9.0 eV below the top of the S 3p valence bands, in very good agreement with values from valence-band x-ray photoemission.

Spiral magnetism in the single-band Hubbard model: the Hartree-Fock and slave-boson approaches.

PubMed

Igoshev, P A; Timirgazin, M A; Gilmutdinov, V F; Arzhnikov, A K; Irkhin, V Yu

2015-11-11

The ground-state magnetic phase diagram is investigated within the single-band Hubbard model for square and different cubic lattices. The results of employing the generalized non-correlated mean-field (Hartree-Fock) approximation and generalized slave-boson approach by Kotliar and Ruckenstein with correlation effects included are compared. We take into account commensurate ferromagnetic, antiferromagnetic, and incommensurate (spiral) magnetic phases, as well as phase separation into magnetic phases of different types, which was often lacking in previous investigations. It is found that the spiral states and especially ferromagnetism are generally strongly suppressed up to non-realistically large Hubbard U by the correlation effects if nesting is absent and van Hove singularities are well away from the paramagnetic phase Fermi level. The magnetic phase separation plays an important role in the formation of magnetic states, the corresponding phase regions being especially wide in the vicinity of half-filling. The details of non-collinear and collinear magnetic ordering for different cubic lattices are discussed.

Ab initio effective core potentials including relativistic effects and their application to the electronic structure calculations of heavy atoms and molecules

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

Lee, Y.S.

1977-11-01

The effects of the 4f shell of electrons and the relativity of valence electrons are compared. The effect of 4f shell (lanthanide contraction) is estimated from the numerical Hartree-Fock (HF) calculations of pseudo-atoms corresponding to Hf, Re, Au, Hg, Tl, Pb and Bi without 4f electrons and with atomic numbers reduced by 14. The relativistic effect estimated from the numerical Dirac-Hartree-Fock (DHF) calculations of those atoms is comparable in the magnitude with that of the 4f shell of electrons. Both are larger for 6s than for 5d or 6p electrons. The various relativistic effects on valence electrons are discussed inmore » detail to determine the proper level of the approximation for the valence electron calculations of systems with heavy elements. An effective core potential system has been developed for heavy atoms in which relativistic effects are included in the effective potentials.« less

Modified Hartree-Fock-Bogoliubov theory at finite temperature

NASA Astrophysics Data System (ADS)

Dinh Dang, Nguyen; Arima, Akito

2003-07-01

The modified Hartree-Fock-Bogoliubov (MHFB) theory at finite temperature is derived, which conserves the unitarity relation of the particle-density matrix. This is achieved by constructing a modified-quasiparticle-density matrix, where the fluctuation of the quasiparticle number is microscopically built in. This matrix can be directly obtained from the usual quasiparticle-density matrix by applying the secondary Bogoliubov transformation, which includes the quasiparticle-occupation number. It is shown that, in the limit of constant pairing parameter, the MHFB theory yields the previously obtained modified BCS (MBCS) equations. It is also proved that the modified quasiparticle-random-phase approximation, which is based on the MBCS quasiparticle excitations, conserves the Ikeda sum rule. The numerical calculations of the pairing gap, heat capacity, level density, and level-density parameter within the MBCS theory are carried out for 120Sn. The results show that the superfluid-normal phase transition is completely washed out. The applicability of the MBCS up to a temperature as high as T˜5 MeV is analyzed in detail.

Spin Hartree-Fock approach to studying quantum Heisenberg antiferromagnets in low dimensions

NASA Astrophysics Data System (ADS)

Werth, A.; Kopietz, P.; Tsyplyatyev, O.

2018-05-01

We construct a new mean-field theory for a quantum (spin-1/2) Heisenberg antiferromagnet in one (1D) and two (2D) dimensions using a Hartree-Fock decoupling of the four-point correlation functions. We show that the solution to the self-consistency equations based on two-point correlation functions does not produce any unphysical finite-temperature phase transition, in accord with the Mermin-Wagner theorem, unlike the common approach based on the mean-field equation for the order parameter. The next-neighbor spin-spin correlation functions, calculated within this approach, reproduce closely the strong renormalization by quantum fluctuations obtained via a Bethe ansatz in 1D and a small renormalization of the classical antiferromagnetic state in 2D. The heat capacity approximates with reasonable accuracy the full Bethe ansatz result at all temperatures in 1D. In 2D, we obtain a reduction of the peak height in the heat capacity at a finite temperature that is accessible by high-order 1 /T expansions.

Microscopic optical model potential based on a Dirac Brueckner Hartree Fock approach and the relevant uncertainty analysis

NASA Astrophysics Data System (ADS)

Xu, Ruirui; Ma, Zhongyu; Muether, Herbert; van Dalen, E. N. E.; Liu, Tinjin; Zhang, Yue; Zhang, Zhi; Tian, Yuan

2017-09-01

A relativistic microscopic optical model potential, named CTOM, for nucleon-nucleus scattering is investigated in the framework of Dirac-Brueckner-Hartree-Fock approach. The microscopic feature of CTOM is guaranteed through rigorously adopting the isospin dependent DBHF calculation within the subtracted T matrix scheme. In order to verify its prediction power, a global study n, p+ A scattering are carried out. The predicted scattering observables coincide with experimental data within a good accuracy over a broad range of targets and a large region of energies only with two free items, namely the free-range factor t in the applied improved local density approximation and minor adjustments of the scalar and vector potentials in the low-density region. In addition, to estimate the uncertainty of the theoretical results, the deterministic simple least square approach is preliminarily employed to derive the covariance of predicted angular distributions, which is also briefly contained in this paper.

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

PubMed

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

2018-03-13

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

Density-dependent covariant energy density functionals

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

Lalazissis, G. A.

2012-10-20

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

Accurate and Efficient Approximation to the Optimized Effective Potential for Exchange

NASA Astrophysics Data System (ADS)

Ryabinkin, Ilya G.; Kananenka, Alexei A.; Staroverov, Viktor N.

2013-07-01

We devise an efficient practical method for computing the Kohn-Sham exchange-correlation potential corresponding to a Hartree-Fock electron density. This potential is almost indistinguishable from the exact-exchange optimized effective potential (OEP) and, when used as an approximation to the OEP, is vastly better than all existing models. Using our method one can obtain unambiguous, nearly exact OEPs for any reasonable finite one-electron basis set at the same low cost as the Krieger-Li-Iafrate and Becke-Johnson potentials. For all practical purposes, this solves the long-standing problem of black-box construction of OEPs in exact-exchange calculations.

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

NASA Astrophysics Data System (ADS)

Joubert, D. P.

2012-09-01

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

Highly correlated configuration interaction calculations on water with large orbital bases

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

Almora-Díaz, César X., E-mail: xalmora@fisica.unam.mx

2014-05-14

A priori selected configuration interaction (SCI) with truncation energy error [C. F. Bunge, J. Chem. Phys. 125, 014107 (2006)] and CI by parts [C. F. Bunge and R. Carbó-Dorca, J. Chem. Phys. 125, 014108 (2006)] are used to approximate the total nonrelativistic electronic ground state energy of water at fixed experimental geometry with CI up to sextuple excitations. Correlation-consistent polarized core-valence basis sets (cc-pCVnZ) up to sextuple zeta and augmented correlation-consistent polarized core-valence basis sets (aug-cc-pCVnZ) up to quintuple zeta quality are employed. Truncation energy errors range between less than 1 μhartree, and 100 μhartree for the largest orbital set. Coupledmore » cluster CCSD and CCSD(T) calculations are also obtained for comparison. Our best upper bound, −76.4343 hartree, obtained by SCI with up to sextuple excitations with a cc-pCV6Z basis recovers more than 98.8% of the correlation energy of the system, and it is only about 3 kcal/mol above the “experimental” value. Despite that the present energy upper bounds are far below all previous ones, comparatively large dispersion errors in the determination of the extrapolated energies to the complete basis set do not allow to determine a reliable estimation of the full CI energy with an accuracy better than 0.6 mhartree (0.4 kcal/mol)« less

E4 properties in deformed nuclei and the sdg interacting boson model

NASA Astrophysics Data System (ADS)

Wu, H. C.; Dieperink, A. E. L.; Scholten, O.; Harakeh, M. N.; de Leo, R.; Pignanelli, M.; Morrison, I.

1988-10-01

The hexadecapole transition strength distribution is measured for the deformed nucleus 150Nd using the (p,p') reaction at Ep=30 MeV. The experimental information on B(E4) values in this nucleus and in 156Gd is interpreted in the framework of the sdg interacting boson model. It is found that the main features of the experimental data are fairly well reproduced by a Hartree-Bose method plus Tamm-Dancoff approximation.

Computational Prediction of Kinetic Rate Constants

DTIC Science & Technology

2006-06-09

24 Reactant: P(CH3)F2O (Difluor) Energetics: RHF DZP Frozen Core CCSD: -655.069925 Hartree CCSD(T): -655.090871 Hartree ZPE : 30.59 kcal...655.069925 Hartree CCSD(T): -655.090871 Hartree ZPE : 30.59 kcal/mol Geometry: RHF CCSD(T) Geom. Opt. PC Bond (Å): 1.79575 OP Bond (Å): 1.47117 FP Bond (Å... ZPE : 18.67 kcal/mol Intensity (km/mol)Frequency (cm -1)Symmetry 11.03833324.0968A1 11.03833324.0968A1 0.00003133.6602A1 2.38681429.9058A1

Existence of Hartree-Fock excited states for atoms and molecules

NASA Astrophysics Data System (ADS)

Lewin, Mathieu

2018-04-01

For neutral and positively charged atoms and molecules, we prove the existence of infinitely many Hartree-Fock critical points below the first energy threshold (that is, the lowest energy of the same system with one electron removed). This is the equivalent, in Hartree-Fock theory, of the famous Zhislin-Sigalov theorem which states the existence of infinitely many eigenvalues below the bottom of the essential spectrum of the N-particle linear Schrödinger operator. Our result improves a theorem of Lions in 1987 who already constructed infinitely many Hartree-Fock critical points, but with much higher energy. Our main contribution is the proof that the Hartree-Fock functional satisfies the Palais-Smale property below the first energy threshold. We then use minimax methods in the N-particle space, instead of working in the one-particle space.

Proposed software system for atomic-structure calculation

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

Fischer, C.F.

1981-07-01

Atomic structure calculations are understood well enough that, at a routine level, an atomic structure software package can be developed. At the Atomic Physics Conference in Riga, 1978 L.V. Chernysheva and M.Y. Amusia of Leningrad University, presented a paper on Software for Atomic Calculations. Their system, called ATOM is based on the Hartree-Fock approximation and correlation is included within the framework of RPAE. Energy level calculations, transition probabilities, photo-ionization cross-sections, electron scattering cross-sections are some of the physical properties that can be evaluated by their system. The MCHF method, together with CI techniques and the Breit-Pauli approximation also provides amore » sound theoretical basis for atomic structure calculations.« less

Charge transfer excitations from exact and approximate ensemble Kohn-Sham theory

NASA Astrophysics Data System (ADS)

Gould, Tim; Kronik, Leeor; Pittalis, Stefano

2018-05-01

By studying the lowest excitations of an exactly solvable one-dimensional soft-Coulomb molecular model, we show that components of Kohn-Sham ensembles can be used to describe charge transfer processes. Furthermore, we compute the approximate excitation energies obtained by using the exact ensemble densities in the recently formulated ensemble Hartree-exchange theory [T. Gould and S. Pittalis, Phys. Rev. Lett. 119, 243001 (2017)]. Remarkably, our results show that triplet excitations are accurately reproduced across a dissociation curve in all cases tested, even in systems where ground state energies are poor due to strong static correlations. Singlet excitations exhibit larger deviations from exact results but are still reproduced semi-quantitatively.

Continuous opacity from Ne^-

NASA Astrophysics Data System (ADS)

John, T. L.

1996-04-01

Free-free absorption coefficients of the negative neon ion are calculated by the phase-shift approximation based on multiconfiguration Hartree-Fock continuum wave functions. These wave functions accurately account for electron-neon correlation and polarization, and yield scattering cross-sections in excellent agreement with the latest experimental values. The coefficients are expected to give the best current estimates of Ne^- continuous absorption. We find that Ne^- makes only a small contribution (less than 0.3 per cent) to stellar opacities, including hydrogen-deficient stars with enhanced Ne abundances.

Semiclassical perturbation Stark widths of singly charged argon spectral lines

NASA Astrophysics Data System (ADS)

Hamdi, Rafik; Ben Nessib, Nabil; Sahal-Bréchot, Sylvie; Dimitrijević, Milan S.

2018-03-01

Using a semiclassical perturbation approach with the impact approximation, Stark widths for singly charged argon (Ar II) spectral lines have been calculated. Energy levels and oscillator strengths needed for this calculation have been determined using the Hartree-Fock method with relativistic corrections. Our Stark widths are compared with experimental results for 178 spectral lines. Our results may be of interest not only for laboratory plasma, lasers and technological plasmas but also for white dwarfs and A- and B-type stars.

Tables Of Gaussian-Type Orbital Basis Functions

NASA Technical Reports Server (NTRS)

Partridge, Harry

1992-01-01

NASA technical memorandum contains tables of estimated Hartree-Fock wave functions for atoms lithium through neon and potassium through krypton. Sets contain optimized Gaussian-type orbital exponents and coefficients, and near Hartree-Fock quality. Orbital exponents optimized by minimizing restricted Hartree-Fock energy via scaled Newton-Raphson scheme in which Hessian evaluated numerically by use of analytically determined gradients.

Wavelets in electronic structure calculations

NASA Astrophysics Data System (ADS)

Modisette, Jason Perry

1997-09-01

Ab initio calculations of the electronic structure of bulk materials and large clusters are not possible on today's computers using current techniques. The storage and diagonalization of the Hamiltonian matrix are the limiting factors in both memory and execution time. The scaling of both quantities with problem size can be reduced by using approximate diagonalization or direct minimization of the total energy with respect to the density matrix in conjunction with a localized basis. Wavelet basis members are much more localized than conventional bases such as Gaussians or numerical atomic orbitals. This localization leads to sparse matrices of the operators that arise in SCF multi-electron calculations. We have investigated the construction of the one-electron Hamiltonian, and also the effective one- electron Hamiltonians that appear in density-functional and Hartree-Fock theories. We develop efficient methods for the generation of the kinetic energy and potential matrices, the Hartree and exchange potentials, and the local exchange-correlation potential of the LDA. Test calculations are performed on one-electron problems with a variety of potentials in one and three dimensions.

Low-energy proton induced M X-ray production cross sections for 70Yb, 81Tl and 82Pb

NASA Astrophysics Data System (ADS)

Shehla; Mandal, A.; Kumar, Ajay; Roy Chowdhury, M.; Puri, Sanjiv; Tribedi, L. C.

2018-07-01

The cross sections for production of Mk (k = Mξ, Mαβ, Mγ, Mm1) X-rays of 70Yb, 81Tl and 82Pb induced by 50-250 keV protons have been measured in the present work. The experimental cross sections have been compared with the earlier reported values and those calculated using the ionization cross sections based on the ECPSSR (Perturbed (P) stationary(S) state(S), incident ion energy (E) loss, Coulomb (C) deflection and relativistic (R) correction) model, the X-ray emission rates based on the Dirac-Fock model, the fluorescence and Coster-Kronig yields based on the Dirac-Hartree-Slater (DHS) model. In addition, the present measured proton induced X-ray production cross sections have also been compared with those calculated using the Dirac-Hartree-Slater (DHS) model based ionization cross sections and those based on the Plane wave Born Approximation (PWBA). The measured M X-ray production cross sections are, in general, found to be higher than the ECPSSR and DHS model based values and lower than the PWBA model based cross sections.

Two-component hybrid time-dependent density functional theory within the Tamm-Dancoff approximation.

PubMed

Kühn, Michael; Weigend, Florian

2015-01-21

We report the implementation of a two-component variant of time-dependent density functional theory (TDDFT) for hybrid functionals that accounts for spin-orbit effects within the Tamm-Dancoff approximation (TDA) for closed-shell systems. The influence of the admixture of Hartree-Fock exchange on excitation energies is investigated for several atoms and diatomic molecules by comparison to numbers for pure density functionals obtained previously [M. Kühn and F. Weigend, J. Chem. Theory Comput. 9, 5341 (2013)]. It is further related to changes upon switching to the local density approximation or using the full TDDFT formalism instead of TDA. Efficiency is demonstrated for a comparably large system, Ir(ppy)3 (61 atoms, 1501 basis functions, lowest 10 excited states), which is a prototype molecule for organic light-emitting diodes, due to its "spin-forbidden" triplet-singlet transition.

Axially deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator basis (III) HFBTHO (v3.00): A new version of the program

NASA Astrophysics Data System (ADS)

Perez, R. Navarro; Schunck, N.; Lasseri, R.-D.; Zhang, C.; Sarich, J.

2017-11-01

We describe the new version 3.00 of the code HFBTHO that solves the nuclear Hartree-Fock (HF) or Hartree-Fock-Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the full Gogny force in both particle-hole and particle-particle channels, (ii) the calculation of the nuclear collective inertia at the perturbative cranking approximation, (iii) the calculation of fission fragment charge, mass and deformations based on the determination of the neck, (iv) the regularization of zero-range pairing forces, (v) the calculation of localization functions, (vi) a MPI interface for large-scale mass table calculations. Program Files doi:http://dx.doi.org/10.17632/c5g2f92by3.1 Licensing provisions: GPL v3 Programming language: FORTRAN-95 Journal reference of previous version: M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, and S. Wild, Comput. Phys. Commun. 184 (2013). Does the new version supersede the previous one: Yes Summary of revisions: 1. the Gogny force in both particle-hole and particle-particle channels was implemented; 2. the nuclear collective inertia at the perturbative cranking approximation was implemented; 3. fission fragment charge, mass and deformations were implemented based on the determination of the position of the neck between nascent fragments; 4. the regularization method of zero-range pairing forces was implemented; 5. the localization functions of the HFB solution were implemented; 6. a MPI interface for large-scale mass table calculations was implemented. Nature of problem:HFBTHO is a physics computer code that is used to model the structure of the nucleus. It is an implementation of the energy density functional (EDF) approach to atomic nuclei, where the energy of the nucleus is obtained by integration over space of some phenomenological energy density, which is itself a functional of the neutron and proton intrinsic densities. In the present version of HFBTHO, the energy density derives either from the zero-range Skyrme or the finite-range Gogny effective two-body interaction between nucleons. Nuclear super-fluidity is treated at the Hartree-Fock-Bogolyubov (HFB) approximation. Constraints on the nuclear shape allows probing the potential energy surface of the nucleus as needed e.g., for the description of shape isomers or fission. The implementation of a local scale transformation of the single-particle basis in which the HFB solutions are expanded provide a tool to properly compute the structure of weakly-bound nuclei. Solution method: The program uses the axial Transformed Harmonic Oscillator (THO) single-particle basis to expand quasiparticle wave functions. It iteratively diagonalizes the Hartree-Fock-Bogolyubov Hamiltonian based on generalized Skyrme-like energy densities and zero-range pairing interactions or the finite-range Gogny force until a self-consistent solution is found. A previous version of the program was presented in M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, and S. Wild, Comput. Phys. Commun. 184 (2013) 1592-1604 with much of the formalism presented in the original paper M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz, P. Ring, Comput. Phys. Commun. 167 (2005) 43-63. Additional comments: The user must have access to (i) the LAPACK subroutines DSYEEVR, DSYEVD, DSYTRF and DSYTRI, and their dependencies, which compute eigenvalues and eigenfunctions of real symmetric matrices, (ii) the LAPACK subroutines DGETRI and DGETRF, which invert arbitrary real matrices, and (iii) the BLAS routines DCOPY, DSCAL, DGEMM and DGEMV for double-precision linear algebra (or provide another set of subroutines that can perform such tasks). The BLAS and LAPACK subroutines can be obtained from the Netlib Repository at the University of Tennessee, Knoxville: http://netlib2.cs.utk.edu/.

Efficient exact-exchange time-dependent density-functional theory methods and their relation to time-dependent Hartree-Fock.

PubMed

Hesselmann, Andreas; Görling, Andreas

2011-01-21

A recently introduced time-dependent exact-exchange (TDEXX) method, i.e., a response method based on time-dependent density-functional theory that treats the frequency-dependent exchange kernel exactly, is reformulated. In the reformulated version of the TDEXX method electronic excitation energies can be calculated by solving a linear generalized eigenvalue problem while in the original version of the TDEXX method a laborious frequency iteration is required in the calculation of each excitation energy. The lowest eigenvalues of the new TDEXX eigenvalue equation corresponding to the lowest excitation energies can be efficiently obtained by, e.g., a version of the Davidson algorithm appropriate for generalized eigenvalue problems. Alternatively, with the help of a series expansion of the new TDEXX eigenvalue equation, standard eigensolvers for large regular eigenvalue problems, e.g., the standard Davidson algorithm, can be used to efficiently calculate the lowest excitation energies. With the help of the series expansion as well, the relation between the TDEXX method and time-dependent Hartree-Fock is analyzed. Several ways to take into account correlation in addition to the exact treatment of exchange in the TDEXX method are discussed, e.g., a scaling of the Kohn-Sham eigenvalues, the inclusion of (semi)local approximate correlation potentials, or hybrids of the exact-exchange kernel with kernels within the adiabatic local density approximation. The lowest lying excitations of the molecules ethylene, acetaldehyde, and pyridine are considered as examples.

Development of the Nuclear-Electronic Orbital Approach and Applications to Ionic Liquids and Tunneling Processes

DTIC Science & Technology

2010-02-24

electronic Schrodinger equation . In previous grant cycles, we implemented the NEO approach at the Hartree-Fock (NEO-HF),13 configuration interaction...electronic and nuclear molecular orbitals. The resulting electronic and nuclear Hartree-Fock-Roothaan equations are solved iteratively until self...directly into the standard Hartree- Fock-Roothaan equations , which are solved iteratively to self-consistency. The density matrix representation

Optimized norm-conserving Hartree-Fock pseudopotentials

NASA Astrophysics Data System (ADS)

Walter, Eric J.; Al-Saidi, Wissam A.

2006-03-01

We report soft Hartree-Fock based pseudopotentials obtained using the optimized pseudopotential method. The spurious long range tail due to the non locality of the exchange potential is removed using a self-consistent damping mechanism as employed in exact exchange and recent Hartree-Fock pseudopotentials. The binding energies of several dimers computed using these pseudopotentials within a planewave Hartree-Fock code show good agreement with all-electron results. A. M. Rappe, K. M. Rabe, E. Kaxiras, and J. D. Joannopoulos, Phys. Rev. B 41, 1227 (1990). E. Engel, A. Höck, R. N. Schmid, R. M. Dreizler, and N. Chetty, Phys. Rev. B 64, 125111 (2001). J.R. Trail and R. J. Needs, J. Chem. Phys. 122, 014112 (2005).

Microscopic Modeling of Intersubband Optical Processes in Type II Semiconductor Quantum Wells: Linear Absorption

NASA Technical Reports Server (NTRS)

Li, Jian-Zhong; Kolokolov, Kanstantin I.; Ning, Cun-Zheng

2003-01-01

Linear absorption spectra arising from intersubband transitions in semiconductor quantum well heterostructures are analyzed using quantum kinetic theory by treating correlations to the first order within Hartree-Fock approximation. The resulting intersubband semiconductor Bloch equations take into account extrinsic dephasing contributions, carrier-longitudinal optical phonon interaction and carrier-interface roughness interaction which is considered with Ando s theory. As input for resonance lineshape calculation, a spurious-states-free 8-band kp Hamiltonian is used, in conjunction with the envelop function approximation, to compute self-consistently the energy subband structure of electrons in type II InAs/AlSb single quantum well structures. We demonstrate the interplay of nonparabolicity and many-body effects in the mid-infrared frequency range for such heterostructures.

Electron momentum density and band structure calculations of α- and β-GeTe

NASA Astrophysics Data System (ADS)

Vadkhiya, Laxman; Arora, Gunjan; Rathor, Ashish; Ahuja, B. L.

2011-12-01

We have measured isotropic experimental Compton profile of α-GeTe by employing high energy (662 keV) γ-radiation from a 137Cs isotope. To compare our experiment, we have also computed energy bands, density of states, electron momentum densities and Compton profiles of α- and β-phases of GeTe using the linear combination of atomic orbitals method. The electron momentum density is found to play a major role in understanding the topology of bands in the vicinity of the Fermi level. It is seen that the density functional theory (DFT) with generalised gradient approximation is relatively in better agreement with the experiment than the local density approximation and hybrid Hartree-Fock/DFT.

Probing the 5 f electrons in Am-I by hybrid density functional theory

NASA Astrophysics Data System (ADS)

Atta-Fynn, Raymond; Ray, Asok K.

2009-11-01

The ground states of the actinides and their compounds continue to be matters of considerable controversies. Experimentally, Americium-I (Am-I) is a non-magnetic dhcp metal whereas theoretically an anti-ferromagnetic ground state is predicted. We show that hybrid density functional theory, which admixes a fraction, λ, of exact Hartree-Fock (HF) exchange with approximate DFT exchange, can correctly reproduce the ground state properties of Am. In particular, for λ=0.40, we obtain a non-magnetic ground state with equilibrium atomic volume, bulk modulus, 5 f electron population, and the density of electronic states all in good agreement with experimental data. We argue that the exact HF exchange corrects the overestimation of the approximate DFT exchange interaction.

Total Born approximation cross sections for single electron loss by atoms and ions colliding with atoms

NASA Technical Reports Server (NTRS)

Rule, D. W.

1977-01-01

The first born approximation (FBA) is applied to the calculation of single electron loss cross sections for various ions and atoms containing from one to seven electrons. Screened hydrogenic wave functions were used for the states of the electron ejected from the projectile, and Hartree-Fock elastic and incoherent scattering factors were used to describe the target. The effect of the target atom on the scaling of projectile ionization cross sections with respect to the projectile nuclear charge was explored in the case of hydrogen-like ions. Scaling of the cross section with respect to the target nuclear charge for electron loss by Fe (+25) in collision with neutral atoms ranging from H to Fe is also examined. These results were compared to those of the binary encounter approximation and to the FBA for the case of ionization by completely stripped target ions.

Theoretical study of the density of states and magnetic properties of LaCoO3

NASA Astrophysics Data System (ADS)

Zhuang, Min; Zhang, Weiyi; Hu, Cheng; Ming, Naiben

1998-05-01

The density of states and magnetic properties of low-spin, high-spin, and mixing states of LaCoO3 have been studied within the unrestricted Hartree-Fock approximation. The real-space recursion method is adopted for computing the electronic structure of the disordered system. The paramagnetic high-spin state is dealt with using the usual binary alloy coherent potential approximation (CPA); an extended trinary alloy CPA approximation is developed to describe the mixing state. In agreement with experiments, our results show that the main features of the quasiparticle spectra in the mixing state are not a sensitive function of the high-spin component, but the spectrum does get broadened due to spin scattering. The increasing of the high-spin component also results in a pileup of the density of states at the Fermi energy which indicates an insulator to metal phase transition. Some limitations of the present approach are also discussed.

On the classification of the spectrally stable standing waves of the Hartree problem

NASA Astrophysics Data System (ADS)

Georgiev, Vladimir; Stefanov, Atanas

2018-05-01

We consider the fractional Hartree model, with general power non-linearity and arbitrary spatial dimension. We construct variationally the "normalized" solutions for the corresponding Choquard-Pekar model-in particular a number of key properties, like smoothness and bell-shapedness are established. As a consequence of the construction, we show that these solitons are spectrally stable as solutions to the time-dependent Hartree model. In addition, we analyze the spectral stability of the Moroz-Van Schaftingen solitons of the classical Hartree problem, in any dimensions and power non-linearity. A full classification is obtained, the main conclusion of which is that only and exactly the "normalized" solutions (which exist only in a portion of the range) are spectrally stable.

Polariton biexciton transitions in a ZnSe-based microcavity

NASA Astrophysics Data System (ADS)

Neukirch, U.; Bolton, S. R.; Fromer, N. A.; Sham, L. J.; Chemla, D. S.

2000-06-01

The optical third-order nonlinearity of a ZnSe-based microcavity is investigated by the pump-and-probe method. In the specially designed non-monolithic sample the biexciton binding energy exceeds all damping constants and the normal-mode splitting between exciton and cavity photon. For counter-circular polarized beams the nonlinear response exhibits strong oscillatory structures in the spectral vicinity of the polariton-biexciton transition. Comparison to model calculations shows that in this case the coherent nonlinearity is completely dominated by biexciton-exciton interactions beyond the Hartree-Fock approximation.

Partial Wave Dispersion Relations: Application to Electron-Atom Scattering

NASA Technical Reports Server (NTRS)

Temkin, A.; Drachman, Richard J.

1999-01-01

In this Letter we propose the use of partial wave dispersion relations (DR's) as the way of solving the long-standing problem of correctly incorporating exchange in a valid DR for electron-atom scattering. In particular a method is given for effectively calculating the contribution of the discontinuity and/or poles of the partial wave amplitude which occur in the negative E plane. The method is successfully tested in three cases: (i) the analytically solvable exponential potential, (ii) the Hartree potential, and (iii) the S-wave exchange approximation for electron-hydrogen scattering.

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.

Description of plasmon-like band in silver clusters: the importance of the long-range Hartree-Fock exchange in time-dependent density-functional theory simulations.

PubMed

Rabilloud, Franck

2014-10-14

Absorption spectra of Ag20 and Ag55(q) (q = +1, -3) nanoclusters are investigated in the framework of the time-dependent density functional theory in order to analyse the role of the d electrons in plasmon-like band of silver clusters. The description of the plasmon-like band from calculations using density functionals containing an amount of Hartree-Fock exchange at long range, namely, hybrid and range-separated hybrid (RSH) density functionals, is in good agreement with the classical interpretation of the plasmon-like structure as a collective excitation of valence s-electrons. In contrast, using local or semi-local exchange functionals (generalized gradient approximations (GGAs) or meta-GGAs) leads to a strong overestimation of the role of d electrons in the plasmon-like band. The semi-local asymptotically corrected model potentials also describe the plasmon as mainly associated to d electrons, though calculated spectra are in fairly good agreement with those calculated using the RSH scheme. Our analysis shows that a portion of non-local exchange modifies the description of the plasmon-like band.

Higher order alchemical derivatives from coupled perturbed self-consistent field theory.

PubMed

Lesiuk, Michał; Balawender, Robert; Zachara, Janusz

2012-01-21

We present an analytical approach to treat higher order derivatives of Hartree-Fock (HF) and Kohn-Sham (KS) density functional theory energy in the Born-Oppenheimer approximation with respect to the nuclear charge distribution (so-called alchemical derivatives). Modified coupled perturbed self-consistent field theory is used to calculate molecular systems response to the applied perturbation. Working equations for the second and the third derivatives of HF/KS energy are derived. Similarly, analytical forms of the first and second derivatives of orbital energies are reported. The second derivative of Kohn-Sham energy and up to the third derivative of Hartree-Fock energy with respect to the nuclear charge distribution were calculated. Some issues of practical calculations, in particular the dependence of the basis set and Becke weighting functions on the perturbation, are considered. For selected series of isoelectronic molecules values of available alchemical derivatives were computed and Taylor series expansion was used to predict energies of the "surrounding" molecules. Predicted values of energies are in unexpectedly good agreement with the ones computed using HF/KS methods. Presented method allows one to predict orbital energies with the error less than 1% or even smaller for valence orbitals. © 2012 American Institute of Physics

Spiral magnetic order, non-uniform states and electron correlations in the conducting transition metal systems

NASA Astrophysics Data System (ADS)

Igoshev, P. A.; Timirgazin, M. A.; Arzhnikov, A. K.; Antipin, T. V.; Irkhin, V. Yu.

2017-10-01

The ground-state magnetic phase diagram is calculated within the Hubbard and s-d exchange (Kondo) models for square and simple cubic lattices vs. band filling and interaction parameter. The difference of the results owing to the presence of localized moments in the latter model is discussed. We employ a generalized Hartree-Fock approximation (HFA) to treat commensurate ferromagnetic (FM), antiferromagnetic (AFM), and incommensurate (spiral) magnetic phases. The electron correlations are taken into account within the Hubbard model by using the Kotliar-Ruckenstein slave boson approximation (SBA). The main advantage of this approach is a correct qualitative description of the paramagnetic phase: its energy becomes considerably lower as compared with HFA, and the gain in the energy of magnetic phases is substantially reduced.

A finite-temperature Hartree-Fock code for shell-model Hamiltonians

NASA Astrophysics Data System (ADS)

Bertsch, G. F.; Mehlhaff, J. M.

2016-10-01

The codes HFgradZ.py and HFgradT.py find axially symmetric minima of a Hartree-Fock energy functional for a Hamiltonian supplied in a shell model basis. The functional to be minimized is the Hartree-Fock energy for zero-temperature properties or the Hartree-Fock grand potential for finite-temperature properties (thermal energy, entropy). The minimization may be subjected to additional constraints besides axial symmetry and nucleon numbers. A single-particle operator can be used to constrain the minimization by adding it to the single-particle Hamiltonian with a Lagrange multiplier. One can also constrain its expectation value in the zero-temperature code. Also the orbital filling can be constrained in the zero-temperature code, fixing the number of nucleons having given Kπ quantum numbers. This is particularly useful to resolve near-degeneracies among distinct minima.

Accuracy of electron densities obtained via Koopmans-compliant hybrid functionals

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Axially deformed solution of the Skyrme-Hartree-Fock-Bogoliubov equations using the transformed harmonic oscillator basis (II) HFBTHO v2.00d: A new version of the program

NASA Astrophysics Data System (ADS)

Stoitsov, M. V.; Schunck, N.; Kortelainen, M.; Michel, N.; Nam, H.; Olsen, E.; Sarich, J.; Wild, S.

2013-06-01

We describe the new version 2.00d of the code HFBTHO that solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogoliubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the modified Broyden method for non-linear problems, (ii) optional breaking of reflection symmetry, (iii) calculation of axial multipole moments, (iv) finite temperature formalism for the HFB method, (v) linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations, (vi) blocking of quasi-particles in the Equal Filling Approximation (EFA), (vii) framework for generalized energy density with arbitrary density-dependences, and (viii) shared memory parallelism via OpenMP pragmas. Program summaryProgram title: HFBTHO v2.00d Catalog identifier: ADUI_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUI_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 167228 No. of bytes in distributed program, including test data, etc.: 2672156 Distribution format: tar.gz Programming language: FORTRAN-95. Computer: Intel Pentium-III, Intel Xeon, AMD-Athlon, AMD-Opteron, Cray XT5, Cray XE6. Operating system: UNIX, LINUX, WindowsXP. RAM: 200 Mwords Word size: 8 bits Classification: 17.22. Does the new version supercede the previous version?: Yes Catalog identifier of previous version: ADUI_v1_0 Journal reference of previous version: Comput. Phys. Comm. 167 (2005) 43 Nature of problem: The solution of self-consistent mean-field equations for weakly-bound paired nuclei requires a correct description of the asymptotic properties of nuclear quasi-particle wave functions. In the present implementation, this is achieved by using the single-particle wave functions of the transformed harmonic oscillator, which allows for an accurate description of deformation effects and pairing correlations in nuclei arbitrarily close to the particle drip lines. Solution method: The program uses the axial Transformed Harmonic Oscillator (THO) single- particle basis to expand quasi-particle wave functions. It iteratively diagonalizes the Hartree-Fock-Bogoliubov Hamiltonian based on generalized Skyrme-like energy densities and zero-range pairing interactions until a self-consistent solution is found. A previous version of the program was presented in: M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz, P. Ring, Comput. Phys. Commun. 167 (2005) 43-63. Reasons for new version: Version 2.00d of HFBTHO provides a number of new options such as the optional breaking of reflection symmetry, the calculation of axial multipole moments, the finite temperature formalism for the HFB method, optimized multi-constraint calculations, the treatment of odd-even and odd-odd nuclei in the blocking approximation, and the framework for generalized energy density with arbitrary density-dependences. It is also the first version of HFBTHO to contain threading capabilities. Summary of revisions: The modified Broyden method has been implemented, Optional breaking of reflection symmetry has been implemented, The calculation of all axial multipole moments up to λ=8 has been implemented, The finite temperature formalism for the HFB method has been implemented, The linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations has been implemented, The blocking of quasi-particles in the Equal Filling Approximation (EFA) has been implemented, The framework for generalized energy density functionals with arbitrary density-dependence has been implemented, Shared memory parallelism via OpenMP pragmas has been implemented. Restrictions: Axial- and time-reversal symmetries are assumed. Unusual features: The user must have access to the LAPACK subroutines DSYEVD, DSYTRF and DSYTRI, and their dependences, which compute eigenvalues and eigenfunctions of real symmetric matrices, the LAPACK subroutines DGETRI and DGETRF, which invert arbitrary real matrices, and the BLAS routines DCOPY, DSCAL, DGEMM and DGEMV for double-precision linear algebra (or provide another set of subroutines that can perform such tasks). The BLAS and LAPACK subroutines can be obtained from the Netlib Repository at the University of Tennessee, Knoxville: http://netlib2.cs.utk.edu/. Running time: Highly variable, as it depends on the nucleus, size of the basis, requested accuracy, requested configuration, compiler and libraries, and hardware architecture. An order of magnitude would be a few seconds for ground-state configurations in small bases N≈8-12, to a few minutes in very deformed configuration of a heavy nucleus with a large basis N>20.

Projected Hartree-Fock theory as a polynomial of particle-hole excitations and its combination with variational coupled cluster theory

NASA Astrophysics Data System (ADS)

Qiu, Yiheng; Henderson, Thomas M.; Scuseria, Gustavo E.

2017-05-01

Projected Hartree-Fock theory provides an accurate description of many kinds of strong correlations but does not properly describe weakly correlated systems. Coupled cluster theory, in contrast, does the opposite. It therefore seems natural to combine the two so as to describe both strong and weak correlations with high accuracy in a relatively black-box manner. Combining the two approaches, however, is made more difficult by the fact that the two techniques are formulated very differently. In earlier work, we showed how to write spin-projected Hartree-Fock in a coupled-cluster-like language. Here, we fill in the gaps in that earlier work. Further, we combine projected Hartree-Fock and coupled cluster theory in a variational formulation and show how the combination performs for the description of the Hubbard Hamiltonian and for several small molecular systems.

Generalization of the optimized-effective-potential model to include electron correlation: A variational derivation of the Sham-Schlueter equation for the exact exchange-correlation potential

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

Casida, M.E.

1995-03-01

The now classic optimized-effective-potential (OEP) approach of Sharp and Horton [Phys Rev. 90, 317 (1953)] and Talman and Shadwick [Phys. Rev. A 14, 36 (1976)] seeks the local potential that is variationally optimized to best approximate the Hartree-Fock exchange operator. The resulting OEP can be identified as the exchange potential of Kohn-Sham density-functional theory. The present work generalizes this OEP approach to treat the correlated case, and shows that the Kohn-Sham exchange-correlation potential is the variationally best local approximation to the exchange-correlation self-energy. This provides a variational derivation of the equation for the exact exchange-correlation potential that was derived bymore » Sham and Schlueter using a density condition. Implications for an approximate physical interpretation of the Kohn-Sham orbitals are discussesd. A correlated generalization of the Sharp-Horton--Krieger-Li-Iafrate [Phys Lett. A 146, 256 (1990)] approximation of the exchange potential is introduced in the quasiparticle limit.« less

Relativistic calculation of nuclear magnetic shielding using normalized elimination of the small component

NASA Astrophysics Data System (ADS)

Kudo, K.; Maeda, H.; Kawakubo, T.; Ootani, Y.; Funaki, M.; Fukui, H.

2006-06-01

The normalized elimination of the small component (NESC) theory, recently proposed by Filatov and Cremer [J. Chem. Phys. 122, 064104 (2005)], is extended to include magnetic interactions and applied to the calculation of the nuclear magnetic shielding in HX (X =F,Cl,Br,I) systems. The NESC calculations are performed at the levels of the zeroth-order regular approximation (ZORA) and the second-order regular approximation (SORA). The calculations show that the NESC-ZORA results are very close to the NESC-SORA results, except for the shielding of the I nucleus. Both the NESC-ZORA and NESC-SORA calculations yield very similar results to the previously reported values obtained using the relativistic infinite-order two-component coupled Hartree-Fock method. The difference between NESC-ZORA and NESC-SORA results is significant for the shieldings of iodine.

Zeroth order regular approximation approach to electric dipole moment interactions of the electron.

PubMed

Gaul, Konstantin; Berger, Robert

2017-07-07

A quasi-relativistic two-component approach for an efficient calculation of P,T-odd interactions caused by a permanent electric dipole moment of the electron (eEDM) is presented. The approach uses a (two-component) complex generalized Hartree-Fock and a complex generalized Kohn-Sham scheme within the zeroth order regular approximation. In applications to select heavy-elemental polar diatomic molecular radicals, which are promising candidates for an eEDM experiment, the method is compared to relativistic four-component electron-correlation calculations and confirms values for the effective electric field acting on the unpaired electron for RaF, BaF, YbF, and HgF. The calculations show that purely relativistic effects, involving only the lower component of the Dirac bi-spinor, are well described by treating only the upper component explicitly.

Zeroth order regular approximation approach to electric dipole moment interactions of the electron

NASA Astrophysics Data System (ADS)

Gaul, Konstantin; Berger, Robert

2017-07-01

A quasi-relativistic two-component approach for an efficient calculation of P ,T -odd interactions caused by a permanent electric dipole moment of the electron (eEDM) is presented. The approach uses a (two-component) complex generalized Hartree-Fock and a complex generalized Kohn-Sham scheme within the zeroth order regular approximation. In applications to select heavy-elemental polar diatomic molecular radicals, which are promising candidates for an eEDM experiment, the method is compared to relativistic four-component electron-correlation calculations and confirms values for the effective electric field acting on the unpaired electron for RaF, BaF, YbF, and HgF. The calculations show that purely relativistic effects, involving only the lower component of the Dirac bi-spinor, are well described by treating only the upper component explicitly.

Benchmarking Hydrogen and Carbon NMR Chemical Shifts at HF, DFT, and MP2 Levels.

PubMed

Flaig, Denis; Maurer, Marina; Hanni, Matti; Braunger, Katharina; Kick, Leonhard; Thubauville, Matthias; Ochsenfeld, Christian

2014-02-11

An extensive study of error distributions for calculating hydrogen and carbon NMR chemical shifts at Hartree-Fock (HF), density functional theory (DFT), and Møller-Plesset second-order perturbation theory (MP2) levels is presented. Our investigation employs accurate CCSD(T)/cc-pVQZ calculations for providing reference data for 48 hydrogen and 40 carbon nuclei within an extended set of chemical compounds covering a broad range of the NMR scale with high relevance to chemical applications, especially in organic chemistry. Besides the approximations of HF, a variety of DFT functionals, and conventional MP2, we also present results with respect to a spin component-scaled MP2 (GIAO-SCS-MP2) approach. For each method, the accuracy is analyzed in detail for various basis sets, allowing identification of efficient combinations of method and basis set approximations.

Electronic structure of free and doped actinides: N and Z dependences of energy levels and electronic structure parameters

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

Kulagin, N.

2005-02-15

Theoretical study of electronic structure of antinide ions and its dependence on N and Z are presented in this paper. The main 5f{sup N} and excited 5f{sup N}n'l'{sup N'} configurations of actinides have been studied using Hartree-Fock-Pauli approximation. Results of calculations of radial integrals and the energy of X-ray lines for all 5f ions with electronic state AC{sup +1}-AC{sup +4} show approximate dependence on N and Z. A square of N and cubic of Z are ewalized for the primary electronic parameters of the actinides. Theoretical values of radial integrals for free actinides and for ions in a cluster AC{supmore » +n}:[L]{sub k} are compared, too.« less

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.

Isoscalar and isovector giant resonances in a self-consistent phonon coupling approach

NASA Astrophysics Data System (ADS)

Lyutorovich, N.; Tselyaev, V.; Speth, J.; Krewald, S.; Grümmer, F.; Reinhard, P.-G.

2015-10-01

We present fully self-consistent calculations of isoscalar giant monopole and quadrupole as well as isovector giant dipole resonances in heavy and light nuclei. The description is based on Skyrme energy-density functionals determining the static Hartree-Fock ground state and the excitation spectra within random-phase approximation (RPA) and RPA extended by including the quasiparticle-phonon coupling at the level of the time-blocking approximation (TBA). All matrix elements were derived consistently from the given energy-density functional and calculated without any approximation. As a new feature in these calculations, the single-particle continuum was included thus avoiding the artificial discretization usually implied in RPA and TBA. The step to include phonon coupling in TBA leads to small, but systematic, down shifts of the centroid energies of the giant resonances. These shifts are similar in size for all Skyrme parametrizations investigated here. After all, we demonstrate that one can find Skyrme parametrizations which deliver a good simultaneous reproduction of all three giant resonances within TBA.

Efficient calculation of beyond RPA correlation energies in the dielectric matrix formalism

NASA Astrophysics Data System (ADS)

Beuerle, Matthias; Graf, Daniel; Schurkus, Henry F.; Ochsenfeld, Christian

2018-05-01

We present efficient methods to calculate beyond random phase approximation (RPA) correlation energies for molecular systems with up to 500 atoms. To reduce the computational cost, we employ the resolution-of-the-identity and a double-Laplace transform of the non-interacting polarization propagator in conjunction with an atomic orbital formalism. Further improvements are achieved using integral screening and the introduction of Cholesky decomposed densities. Our methods are applicable to the dielectric matrix formalism of RPA including second-order screened exchange (RPA-SOSEX), the RPA electron-hole time-dependent Hartree-Fock (RPA-eh-TDHF) approximation, and RPA renormalized perturbation theory using an approximate exchange kernel (RPA-AXK). We give an application of our methodology by presenting RPA-SOSEX benchmark results for the L7 test set of large, dispersion dominated molecules, yielding a mean absolute error below 1 kcal/mol. The present work enables calculating beyond RPA correlation energies for significantly larger molecules than possible to date, thereby extending the applicability of these methods to a wider range of chemical systems.

Influence of the Dirac-Hartree-Fock starting potential on the parity-nonconserving electric-dipole-transition amplitudes in cesium and thallium

NASA Technical Reports Server (NTRS)

Perger, W. F.; Das, B. P.

1987-01-01

The parity-nonconserving electric-dipole-transition amplitudes for the 6s1/2-7s1/2 transition in cesium and the 6p1/2-7p1/2 transition in thallium have been calculated by the Dirac-Hartree-Fock method. The effects of using different Dirac-Hartree-Fock atomic core potentials are examined and the transition amplitudes for both the length and velocity gauges are given. It is found that the parity-nonconserving transition amplitudes exhibit a greater dependence on the starting potential for thallium than for cesium.

The any particle molecular orbital grid-based Hartree-Fock (APMO-GBHF) approach

NASA Astrophysics Data System (ADS)

Posada, Edwin; Moncada, Félix; Reyes, Andrés

2018-02-01

The any particle molecular orbital grid-based Hartree-Fock approach (APMO-GBHF) is proposed as an initial step to perform multi-component post-Hartree-Fock, explicitly correlated, and density functional theory methods without basis set errors. The method has been applied to a number of electronic and multi-species molecular systems. Results of these calculations show that the APMO-GBHF total energies are comparable with those obtained at the APMO-HF complete basis set limit. In addition, results reveal a considerable improvement in the description of the nuclear cusps of electronic and non-electronic densities.

Constrained-pairing mean-field theory. IV. Inclusion of corresponding pair constraints and connection to unrestricted Hartree-Fock theory.

PubMed

Tsuchimochi, Takashi; Henderson, Thomas M; Scuseria, Gustavo E; Savin, Andreas

2010-10-07

Our previously developed constrained-pairing mean-field theory (CPMFT) is shown to map onto an unrestricted Hartree-Fock (UHF) type method if one imposes a corresponding pair constraint to the correlation problem that forces occupation numbers to occur in pairs adding to one. In this new version, CPMFT has all the advantages of standard independent particle models (orbitals and orbital energies, to mention a few), yet unlike UHF, it can dissociate polyatomic molecules to the correct ground-state restricted open-shell Hartree-Fock atoms or fragments.

Semiclassical analysis for pseudo-relativistic Hartree equations

NASA Astrophysics Data System (ADS)

Cingolani, Silvia; Secchi, Simone

2015-06-01

In this paper we study the semiclassical limit for the pseudo-relativistic Hartree equation $\\sqrt{-\\varepsilon^2 \\Delta + m^2}u + V u = (I_\\alpha * |u|^{p}) |u|^{p-2}u$ in $\\mathbb{R}^N$ where $m>0$, $2 \\leq p < \\frac{2N}{N-1}$, $V \\colon \\mathbb{R}^N \\to \\mathbb{R}$ is an external scalar potential, $I_\\alpha (x) = \\frac{c_{N,\\alpha}}{|x|^{N-\\alpha}}$ is a convolution kernel, $c_{N,\\alpha}$ is a positive constant and $(N-1)p-N<\\alpha

Spatial and Spin Symmetry Breaking in Semidefinite-Programming-Based Hartree-Fock Theory.

PubMed

Nascimento, Daniel R; DePrince, A Eugene

2018-05-08

The Hartree-Fock problem was recently recast as a semidefinite optimization over the space of rank-constrained two-body reduced-density matrices (RDMs) [ Phys. Rev. A 2014 , 89 , 010502(R) ]. This formulation of the problem transfers the nonconvexity of the Hartree-Fock energy functional to the rank constraint on the two-body RDM. We consider an equivalent optimization over the space of positive semidefinite one-electron RDMs (1-RDMs) that retains the nonconvexity of the Hartree-Fock energy expression. The optimized 1-RDM satisfies ensemble N-representability conditions, and ensemble spin-state conditions may be imposed as well. The spin-state conditions place additional linear and nonlinear constraints on the 1-RDM. We apply this RDM-based approach to several molecular systems and explore its spatial (point group) and spin ( Ŝ 2 and Ŝ 3 ) symmetry breaking properties. When imposing Ŝ 2 and Ŝ 3 symmetry but relaxing point group symmetry, the procedure often locates spatial-symmetry-broken solutions that are difficult to identify using standard algorithms. For example, the RDM-based approach yields a smooth, spatial-symmetry-broken potential energy curve for the well-known Be-H 2 insertion pathway. We also demonstrate numerically that, upon relaxation of Ŝ 2 and Ŝ 3 symmetry constraints, the RDM-based approach is equivalent to real-valued generalized Hartree-Fock theory.

Multi-configuration Dirac-Hartree-Fock (MCDHF) calculations for Ni XXV

NASA Astrophysics Data System (ADS)

Singh, Narendra; Aggarwal, Sunny

2018-03-01

We present accurate 165 fine-structure energy levels related to the configurations 1s22s2, 1s22p2, 1s2nƖn‧l‧ (n = 2, n‧ = 2, 3, 4, 5, Ɩ = s,p Ɩ‧ = s, p, d, f, g) of Ni XXV which may be useful ion for astrophysical and fusion plasma. For the calculations of energy levels and radiative rates, we have used the multiconfiguration Dirac-Hartree-Fock (MCDHF) method employed in GRASP2K code. The calculations are carried out in the active space approximation with the inclusion of the Breit interaction, the finite nuclear size effect, and quantum electrodynamic corrections. The transition wavelengths, transition probabilities, line strengths, and absorption oscillator strengths are reported for electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), magnetic quadrupole (M2) transitions from the ground state. We have compared our calculated results with available theoretical and experimental data and good agreement is achieved. We predict new energy levels, oscillator strengths, line strengths and transition probabilities, where no other experimental or theoretical results are available. The present complete set of results should be of great help in line identification and the interpretation of spectra, as well as in the modelling and diagnostics of astrophysical and fusion plasmas.

Beyond computational difficulties: Survey of the two decades from the elaboration to the extensive application of the Hartree-Fock method

NASA Astrophysics Data System (ADS)

Martinez, Jean-Philippe

2017-11-01

The Hartree-Fock method, one of the first applications of the new quantum mechanics in the frame of the many-body problem, had been elaborated by Rayner Douglas Hartree in 1928 and Vladimir Fock in 1930. Promptly, the challenge of tedious computations was being discussed and it is well known that the application of the method benefited greatly from the development of computers from the mid-to-late 1950s. However, the years from 1930 to 1950 were by no means years of stagnation, as the method was the object of several considerations related to its mathematical formulation, possible extension, and conceptual understanding. Thus, with a focus on the respective attitudes of Hartree and Fock, in particular with respect to the concept of quantum exchange, the present work puts forward some mathematical and conceptual clarifications, which played an important role for a better understanding of the many-body problem in quantum mechanics.

Pasta phases in core-collapse supernova matter

NASA Astrophysics Data System (ADS)

Pais, Helena; Chiacchiera, Silvia; Providência, Constança

2016-04-01

The pasta phase in core-collapse supernova matter (finite temperatures and fixed proton fractions) is studied within relativistic mean field models. Three different calculations are used for comparison, the Thomas-Fermi (TF), the Coexisting Phases (CP) and the Compressible Liquid Drop (CLD) approximations. The effects of including light clusters in nuclear matter and the densities at which the transitions between pasta configurations and to uniform matter occur are also investigated. The free energy and pressure, in the space of particle number densities and temperatures expected to cover the pasta region, are calculated. Finally, a comparison with a finite temperature Skyrme-Hartree-Fock calculation is drawn.

Critical Frequency in Nuclear Chiral Rotation

NASA Astrophysics Data System (ADS)

Olbratowski, P.; Dobaczewski, J.; Dudek, J.; Płóciennik, W.

2004-07-01

Self-consistent solutions for the so-called planar and chiral rotational bands in 132La are obtained for the first time within the Skyrme-Hartree-Fock cranking approach. It is suggested that the chiral rotation cannot exist below a certain critical frequency which under the approximations used is estimated as ℏωcrit≈0.5 0.6 MeV. However, the exact values of ℏωcrit may vary, to an extent, depending on the microscopic model used, in particular, through the pairing correlations and/or calculated equilibrium deformations. The existence of the critical frequency is explained in terms of a simple classical model of two gyroscopes coupled to a triaxial rigid body.

Parity-violating electric-dipole transitions in helium

NASA Technical Reports Server (NTRS)

Hiller, J.; Sucher, J.; Bhatia, A. K.; Feinberg, G.

1980-01-01

The paper examines parity-violating electric-dipole transitions in He in order to gain insight into the reliability of approximate calculations which are carried out for transitions in many-electron atoms. The contributions of the nearest-lying states are computed with a variety of wave functions, including very simple product wave functions, Hartree-Fock functions and Hylleraas-type wave functions with up to 84 parameters. It is found that values of the matrix elements of the parity-violating interaction can differ considerably from the values obtained from the good wave functions, even when these simple wave functions give accurate values for the matrix elements in question

Nonequilibrium itinerant-electron magnetism: A time-dependent mean-field theory

NASA Astrophysics Data System (ADS)

Secchi, A.; Lichtenstein, A. I.; Katsnelson, M. I.

2016-08-01

We study the dynamical magnetic susceptibility of a strongly correlated electronic system in the presence of a time-dependent hopping field, deriving a generalized Bethe-Salpeter equation that is valid also out of equilibrium. Focusing on the single-orbital Hubbard model within the time-dependent Hartree-Fock approximation, we solve the equation in the nonequilibrium adiabatic regime, obtaining a closed expression for the transverse magnetic susceptibility. From this, we provide a rigorous definition of nonequilibrium (time-dependent) magnon frequencies and exchange parameters, expressed in terms of nonequilibrium single-electron Green's functions and self-energies. In the particular case of equilibrium, we recover previously known results.

Nuclear Symmetry Energy and the Breaking of the Isospin Symmetry: How Do They Reconcile with Each Other?

NASA Astrophysics Data System (ADS)

Roca-Maza, X.; Colò, G.; Sagawa, H.

2018-05-01

We analyze and propose a solution to the apparent inconsistency between our current knowledge of the equation of state of asymmetric nuclear matter, the energy of the isobaric analog state (IAS) in a heavy nucleus such as 208Pb, and the isospin symmetry breaking forces in the nuclear medium. This is achieved by performing state-of-the-art Hartree-Fock plus random phase approximation calculations of the IAS that include all isospin symmetry breaking contributions. To this aim, we propose a new effective interaction that is successful in reproducing the IAS excitation energy without compromising other properties of finite nuclei.

Nuclear Symmetry Energy and the Breaking of the Isospin Symmetry: How Do They Reconcile with Each Other?

PubMed

Roca-Maza, X; Colò, G; Sagawa, H

2018-05-18

We analyze and propose a solution to the apparent inconsistency between our current knowledge of the equation of state of asymmetric nuclear matter, the energy of the isobaric analog state (IAS) in a heavy nucleus such as ^{208}Pb, and the isospin symmetry breaking forces in the nuclear medium. This is achieved by performing state-of-the-art Hartree-Fock plus random phase approximation calculations of the IAS that include all isospin symmetry breaking contributions. To this aim, we propose a new effective interaction that is successful in reproducing the IAS excitation energy without compromising other properties of finite nuclei.

Dynamical Correlation In Some Liquid Alkaline Earth Metals Near Melting

NASA Astrophysics Data System (ADS)

Thakore, B. Y.; Suthar, P. H.; Khambholja, S. G.; Gajjar, P. N.; Jani, A. R.

2010-12-01

The study of dynamical variables: velocity autocorrelation function (VACF) and power spectrum of liquid alkaline earth metals (Ca, Sr, and Ba) have been presented based on the static harmonic well approximation. The effective interatomic potential for liquid metals is computed using our well recognized model potential with the exchange correlation functions due to Hartree, Taylor, Ichimaru and Utsumi, Farid et al. and Sarkar et al. It is observed that the VACF computed using Sarkar et al. gives the good agreement with available molecular dynamics simulation (MD) results [Phys Rev. B 62, 14818 (2000)]. The shoulder of the power spectrum depends upon the type of local field correlation function used.

Communication: Biological applications of coupled-cluster frozen-density embedding

NASA Astrophysics Data System (ADS)

Heuser, Johannes; Höfener, Sebastian

2018-04-01

We report the implementation of the Laplace-transform scaled opposite-spin (LT-SOS) resolution-of-the-identity second-order approximate coupled-cluster singles and doubles (RICC2) combined with frozen-density embedding for excitation energies and molecular properties. In the present work, we furthermore employ the Hartree-Fock density for the interaction energy leading to a simplified Lagrangian which is linear in the Lagrangian multipliers. This approximation has the key advantage of a decoupling of the coupled-cluster amplitude and multipliers, leading also to a significant reduction in computation time. Using the new simplified Lagrangian in combination with efficient wavefunction models such as RICC2 or LT-SOS-RICC2 and density-functional theory (DFT) for the environment molecules (CC2-in-DFT) enables the efficient study of biological applications such as the rhodopsin and visual cone pigments using ab initio methods as routine applications.

Beyond the random-phase approximation for the electron correlation energy: the importance of single excitations.

PubMed

Ren, Xinguo; Tkatchenko, Alexandre; Rinke, Patrick; Scheffler, Matthias

2011-04-15

The random-phase approximation (RPA) for the electron correlation energy, combined with the exact-exchange (EX) energy, represents the state-of-the-art exchange-correlation functional within density-functional theory. However, the standard RPA practice--evaluating both the EX and the RPA correlation energies using Kohn-Sham (KS) orbitals from local or semilocal exchange-correlation functionals--leads to a systematic underbinding of molecules and solids. Here we demonstrate that this behavior can be corrected by adding a "single excitation" contribution, so far not included in the standard RPA scheme. A similar improvement can also be achieved by replacing the non-self-consistent EX total energy by the corresponding self-consistent Hartree-Fock total energy, while retaining the RPA correlation energy evaluated using KS orbitals. Both schemes achieve chemical accuracy for a standard benchmark set of noncovalent intermolecular interactions.

Ground-state energies and highest occupied eigenvalues of atoms in exchange-only density-functional theory

NASA Astrophysics Data System (ADS)

Li, Yan; Harbola, Manoj K.; Krieger, J. B.; Sahni, Viraht

1989-11-01

The exchange-correlation potential of the Kohn-Sham density-functional theory has recently been interpreted as the work required to move an electron against the electric field of its Fermi-Coulomb hole charge distribution. In this paper we present self-consistent results for ground-state total energies and highest occupied eigenvalues of closed subshell atoms as obtained by this formalism in the exchange-only approximation. The total energies, which are an upper bound, lie within 50 ppm of Hartree-Fock theory for atoms heavier than Be. The highest occupied eigenvalues, as a consequence of this interpretation, approximate well the experimental ionization potentials. In addition, the self-consistently calculated exchange potentials are very close to those of Talman and co-workers [J. D. Talman and W. F. Shadwick, Phys. Rev. A 14, 36 (1976); K. Aashamar, T. M. Luke, and J. D. Talman, At. Data Nucl. Data Tables 22, 443 (1978)].

Adaptation of the projector-augmented-wave formalism to the treatment of orbital-dependent exchange-correlation functionals

NASA Astrophysics Data System (ADS)

Xu, Xiao; Holzwarth, N. A. W.

2011-10-01

This paper presents the formulation and numerical implementation of a self-consistent treatment of orbital-dependent exchange-correlation functionals within the projector-augmented-wave method of Blöchl [Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.50.17953 50, 17953 (1994)] for electronic structure calculations. The methodology is illustrated with binding energy curves for C in the diamond structure and LiF in the rock salt structure, by comparing results from the Hartree-Fock (HF) formalism and the optimized effective potential formalism in the so-called KLI approximation [Krieger, Li, and Iafrate, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.45.101 45, 101 (1992)] with those of the local density approximation. While the work here uses pure Fock exchange only, the formalism can be extended to treat orbital-dependent functionals more generally.

The positronium and the dipositronium in a Hartree-Fock approximation of quantum electrodynamics

NASA Astrophysics Data System (ADS)

Sok, Jérémy

2016-02-01

The Bogoliubov-Dirac-Fock (BDF) model is a no-photon approximation of quantum electrodynamics. It allows to study relativistic electrons in interaction with the Dirac sea. A state is fully characterized by its one-body density matrix, an infinite rank non-negative projector. We prove the existence of the para-positronium, the bound state of an electron and a positron with antiparallel spins, in the BDF model represented by a critical point of the energy functional in the absence of an external field. We also prove the existence of the dipositronium, a molecule made of two electrons and two positrons that also appears as a critical point. More generally, for any half integer j ∈ 1/2 + Z + , we prove the existence of a critical point of the energy functional made of 2j + 1 electrons and 2j + 1 positrons.

Time-dependent broken-symmetry density functional theory simulation of the optical response of entangled paramagnetic defects: Color centers in lithium fluoride

NASA Astrophysics Data System (ADS)

Janesko, Benjamin G.

2018-02-01

Parameter-free atomistic simulations of entangled solid-state paramagnetic defects may aid in the rational design of devices for quantum information science. This work applies time-dependent density functional theory (TDDFT) embedded-cluster simulations to a prototype entangled-defect system, namely two adjacent singlet-coupled F color centers in lithium fluoride. TDDFT calculations accurately reproduce the experimental visible absorption of both isolated and coupled F centers. The most accurate results are obtained by combining spin symmetry breaking to simulate strong correlation, a large fraction of exact (Hartree-Fock-like) exchange to minimize the defect electrons' self-interaction error, and a standard semilocal approximation for dynamical correlations between the defect electrons and the surrounding ionic lattice. These results motivate application of two-reference correlated ab initio approximations to the M-center, and application of TDDFT in parameter-free simulations of more complex entangled paramagnetic defect architectures.

Non-plane-wave Hartree-Fock states and nuclear homework potentials

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

Gutierrez, G.; Plastino, A.; de Llano, M.

1979-12-01

It is shown that non-plane-wave single-particle Hartree-Fock orbitals giving rise to a ''spin-density-wave-like'' structure give lower energy than plane waves beyond a certain relatively low density in both nuclear and neutron matter with homework pair potentials v/sub 1/ and v/sub 2/.

Few-particle quantum dynamics-comparing nonequilibrium Green functions with the generalized Kadanoff-Baym ansatz to density operator theory

NASA Astrophysics Data System (ADS)

Hermanns, S.; Balzer, K.; Bonitz, M.

2013-03-01

The nonequilibrium description of quantum systems requires, for more than two or three particles, the use of a reduced description to be numerically tractable. Two possible approaches are based on either reduced density matrices or nonequilibrium Green functions (NEGF). Both concepts are formulated in terms of hierarchies of coupled equations—the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy for the reduced density operators and the Martin-Schwinger-hierarchy (MS) for the Green functions, respectively. In both cases, similar approximations are introduced to decouple the hierarchy, yet still many questions regarding the correspondence of both approaches remain open. Here we analyze this correspondence by studying the generalized Kadanoff-Baym ansatz (GKBA) that reduces the NEGF to a single-time theory. Starting from the BBGKY-hierarchy we present the approximations that are necessary to recover the GKBA result both, with Hartree-Fock propagators (HF-GKBA) and propagators in second Born approximation. To test the quality of the HF-GKBA, we study the dynamics of a 4-electron Hubbard nanocluster starting from a strong nonequilibrium initial state and compare to exact results and the Wang-Cassing approximation to the BBGKY hierarchy presented recently by Akbari et al. [1].

Accurate Gaussian basis sets for atomic and molecular calculations obtained from the generator coordinate method with polynomial discretization.

PubMed

Celeste, Ricardo; Maringolo, Milena P; Comar, Moacyr; Viana, Rommel B; Guimarães, Amanda R; Haiduke, Roberto L A; da Silva, Albérico B F

2015-10-01

Accurate Gaussian basis sets for atoms from H to Ba were obtained by means of the generator coordinate Hartree-Fock (GCHF) method based on a polynomial expansion to discretize the Griffin-Wheeler-Hartree-Fock equations (GWHF). The discretization of the GWHF equations in this procedure is based on a mesh of points not equally distributed in contrast with the original GCHF method. The results of atomic Hartree-Fock energies demonstrate the capability of these polynomial expansions in designing compact and accurate basis sets to be used in molecular calculations and the maximum error found when compared to numerical values is only 0.788 mHartree for indium. Some test calculations with the B3LYP exchange-correlation functional for N2, F2, CO, NO, HF, and HCN show that total energies within 1.0 to 2.4 mHartree compared to the cc-pV5Z basis sets are attained with our contracted bases with a much smaller number of polarization functions (2p1d and 2d1f for hydrogen and heavier atoms, respectively). Other molecular calculations performed here are also in very good accordance with experimental and cc-pV5Z results. The most important point to be mentioned here is that our generator coordinate basis sets required only a tiny fraction of the computational time when compared to B3LYP/cc-pV5Z calculations.

A gauge-independent zeroth-order regular approximation to the exact relativistic Hamiltonian—Formulation and applications

NASA Astrophysics Data System (ADS)

Filatov, Michael; Cremer, Dieter

2005-01-01

A simple modification of the zeroth-order regular approximation (ZORA) in relativistic theory is suggested to suppress its erroneous gauge dependence to a high level of approximation. The method, coined gauge-independent ZORA (ZORA-GI), can be easily installed in any existing nonrelativistic quantum chemical package by programming simple one-electron matrix elements for the quasirelativistic Hamiltonian. Results of benchmark calculations obtained with ZORA-GI at the Hartree-Fock (HF) and second-order Møller-Plesset perturbation theory (MP2) level for dihalogens X2 (X=F,Cl,Br,I,At) are in good agreement with the results of four-component relativistic calculations (HF level) and experimental data (MP2 level). ZORA-GI calculations based on MP2 or coupled-cluster theory with single and double perturbations and a perturbative inclusion of triple excitations [CCSD(T)] lead to accurate atomization energies and molecular geometries for the tetroxides of group VIII elements. With ZORA-GI/CCSD(T), an improved estimate for the atomization energy of hassium (Z=108) tetroxide is obtained.

Breakdown of the single-exchange approximation in third-order symmetry-adapted perturbation theory.

PubMed

Lao, Ka Un; Herbert, John M

2012-03-22

We report third-order symmetry-adapted perturbation theory (SAPT) calculations for several dimers whose intermolecular interactions are dominated by induction. We demonstrate that the single-exchange approximation (SEA) employed to derive the third-order exchange-induction correction (E(exch-ind)((30))) fails to quench the attractive nature of the third-order induction (E(ind)((30))), leading to one-dimensional potential curves that become attractive rather than repulsive at short intermolecular separations. A scaling equation for (E(exch-ind)((30))), based on an exact formula for the first-order exchange correction, is introduced to approximate exchange effects beyond the SEA, and qualitatively correct potential energy curves that include third-order induction are thereby obtained. For induction-dominated systems, our results indicate that a "hybrid" SAPT approach, in which a dimer Hartree-Fock calculation is performed in order to obtain a correction for higher-order induction, is necessary not only to obtain quantitative binding energies but also to obtain qualitatively correct potential energy surfaces. These results underscore the need to develop higher-order exchange-induction formulas that go beyond the SEA. © 2012 American Chemical Society

Resolution of identity approximation for the Coulomb term in molecular and periodic systems

NASA Astrophysics Data System (ADS)

Burow, Asbjörn M.; Sierka, Marek; Mohamed, Fawzi

2009-12-01

A new formulation of resolution of identity approximation for the Coulomb term is presented, which uses atom-centered basis and auxiliary basis functions and treats molecular and periodic systems of any dimensionality on an equal footing. It relies on the decomposition of an auxiliary charge density into charged and chargeless components. Applying the Coulomb metric under periodic boundary conditions constrains the explicit form of the charged part. The chargeless component is determined variationally and converged Coulomb lattice sums needed for its determination are obtained using chargeless linear combinations of auxiliary basis functions. The lattice sums are partitioned in near- and far-field portions which are treated through an analytical integration scheme employing two- and three-center electron repulsion integrals and multipole expansions, respectively, operating exclusively in real space. Our preliminary implementation within the TURBOMOLE program package demonstrates consistent accuracy of the method across molecular and periodic systems. Using common auxiliary basis sets the errors of the approximation are small, in average about 20 μhartree per atom, for both molecular and periodic systems.

Formal expressions and corresponding expansions for the exact Kohn-Sham exchange potential

NASA Astrophysics Data System (ADS)

Bulat, Felipe A.; Levy, Mel

2009-11-01

Formal expressions and their corresponding expansions in terms of Kohn-Sham (KS) orbitals are deduced for the exchange potential vx(r) . After an alternative derivation of the basic optimized effective potential integrodifferential equations is given through a Hartree-Fock adiabatic connection perturbation theory, we present an exact infinite expansion for vx(r) that is particularly simple in structure. It contains the very same occupied-virtual quantities that appear in the well-known optimized effective potential integral equation, but in this new expression vx(r) is isolated on one side of the equation. An orbital-energy modified Slater potential is its leading term which gives encouraging numerical results. Along different lines, while the earlier Krieger-Li-Iafrate approximation truncates completely the necessary first-order perturbation orbitals, we observe that the improved localized Hartree-Fock (LHF) potential, or common energy denominator potential (CEDA), or effective local potential (ELP), incorporates the part of each first-order orbital that consists of the occupied KS orbitals. With this in mind, the exact correction to the LHF, CEDA, or ELP potential (they are all equivalent) is deduced and displayed in terms of the virtual portions of the first-order orbitals. We close by observing that the newly derived exact formal expressions and corresponding expansions apply as well for obtaining the correlation potential from an orbital-dependent correlation energy functional.

Half-metallicity and spin-contamination of the electronic ground state of graphene nanoribbons and related systems: An impossible compromise?

NASA Astrophysics Data System (ADS)

Huzak, M.; Deleuze, M. S.; Hajgató, B.

2011-09-01

An analysis using the formalism of crystalline orbitals for extended systems with periodicity in one dimension demonstrates that any antiferromagnetic and half-metallic spin-polarization of the edge states in n-acenes, and more generally in zigzag graphene nanoislands and nanoribbons of finite width, would imply a spin contamination ⟨S2⟩ that increases proportionally to system size, in sharp and clear contradiction with the implications of Lieb's theorem for compensated bipartite lattices and the expected value for a singlet (S = 0) electronic ground state. Verifications on naphthalene, larger n-acenes (n = 3-10) and rectangular nanographene islands of increasing size, as well as a comparison using unrestricted Hartree-Fock theory along with basis sets of improving quality against various many-body treatments demonstrate altogether that antiferromagnetism and half-metallicity in extended graphene nanoribbons will be quenched by an exact treatment of electron correlation, at the confines of non-relativistic many-body quantum mechanics. Indeed, for singlet states, symmetry-breakings in spin-densities are necessarily the outcome of a too approximate treatment of static and dynamic electron correlation in single-determinantal approaches, such as unrestricted Hartree-Fock or Density Functional Theory. In this context, such as the size-extensive spin-contamination to which it relates, half-metallicity is thus nothing else than a methodological artefact.

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.

Effect of Pressure on Some Optical Properties of GaxIn1-xP Semiconductors

NASA Astrophysics Data System (ADS)

Vyas, P.; Gajjar, P.; Jani, A.

2013-06-01

A theoretical procedure is presented for the study of optical properties of ternary alloy GaxIn1-xP. The calculations are based on the pseudopotential formalism in which local potential coupled with the virtual crystal approximation (VCA) is applied to evaluate the effect of pressure on the optical properties like refractive index, electronic polarizability, plasmon energy, dielectric constant and equation of state for gallium concentration x = 0, 0.25, 0.50, 0.75 and 1 of the ternary alloy GaxIn1-xP. To incorporate the screening effect, local field correction functions due to Hartree, Taylor, Ichimaru et al. and Nagy are employed. The refractive index, electronic polarizability and dielectric constant computed for the parent binary compounds GaP and InP are found to be satisfactorily agreeing with the experimental report. It is seen that the refractive index of GaxIn1-xP decreases nonlinearly with the increase in pressure. The results obtained using Hartree's screening functions are not very close to the experimental data as it does not include any exchange and correlation effects. Overall good agreement with the experimental and other theoretical findings confirms the application. The author P. S. Vyas is thankful to UGC, New Delhi, India for providing financial support under minor research project No. F.: 47-651/08(WRO).

Half-metallicity and spin-contamination of the electronic ground state of graphene nanoribbons and related systems: an impossible compromise?

PubMed

Huzak, M; Deleuze, M S; Hajgató, B

2011-09-14

An analysis using the formalism of crystalline orbitals for extended systems with periodicity in one dimension demonstrates that any antiferromagnetic and half-metallic spin-polarization of the edge states in n-acenes, and more generally in zigzag graphene nanoislands and nanoribbons of finite width, would imply a spin contamination S(2) that increases proportionally to system size, in sharp and clear contradiction with the implications of Lieb's theorem for compensated bipartite lattices and the expected value for a singlet (S = 0) electronic ground state. Verifications on naphthalene, larger n-acenes (n = 3-10) and rectangular nanographene islands of increasing size, as well as a comparison using unrestricted Hartree-Fock theory along with basis sets of improving quality against various many-body treatments demonstrate altogether that antiferromagnetism and half-metallicity in extended graphene nanoribbons will be quenched by an exact treatment of electron correlation, at the confines of non-relativistic many-body quantum mechanics. Indeed, for singlet states, symmetry-breakings in spin-densities are necessarily the outcome of a too approximate treatment of static and dynamic electron correlation in single-determinantal approaches, such as unrestricted Hartree-Fock or Density Functional Theory. In this context, such as the size-extensive spin-contamination to which it relates, half-metallicity is thus nothing else than a methodological artefact. © 2011 American Institute of Physics

Stopping power and range calculations in human tissues by using the Hartree-Fock-Roothaan wave functions

NASA Astrophysics Data System (ADS)

Usta, Metin; Tufan, Mustafa Çağatay

2017-11-01

The object of this work is to present the consequences for the stopping power and range values of some human tissues at energies ranging from 1 MeV to 1 GeV and 1-500 MeV, respectively. The considered human tissues are lung, intestine, skin, larynx, breast, bladder, prostate and ovary. In this work, the stopping power is calculated by considering the number of velocity-dependent effective charge and effective mean excitation energies of the target material. We used the Hartree-Fock-Roothaan (HFR) atomic wave function to determine the charge density and the continuous slowing down approximation (CSDA) method for the calculation of the proton range. Electronic stopping power values of tissues results have been compared with the ICRU 44, 46 reports, SRIM, Janni and CasP data over the percent error rate. Range values relate to tissues have compared the range results with the SRIM, FLUKA and Geant4 data. For electronic stopping power results, ICRU, SRIM and Janni's data indicated the best fit with our values at 1-50, 50-250 MeV and 250 MeV-1 GeV, respectively. For range results, the best accordance with the calculated values have been found the SRIM data and the error level is less than 10% in proton therapy. However, greater 30% errors were observed in the 250 MeV and over energies.

Basis set and electron correlation effects on the polarizability and second hyperpolarizability of model open-shell π-conjugated systems

NASA Astrophysics Data System (ADS)

Champagne, Benoı̂t; Botek, Edith; Nakano, Masayoshi; Nitta, Tomoshige; Yamaguchi, Kizashi

2005-03-01

The basis set and electron correlation effects on the static polarizability (α) and second hyperpolarizability (γ) are investigated ab initio for two model open-shell π-conjugated systems, the C5H7 radical and the C6H8 radical cation in their doublet state. Basis set investigations evidence that the linear and nonlinear responses of the radical cation necessitate the use of a less extended basis set than its neutral analog. Indeed, double-zeta-type basis sets supplemented by a set of d polarization functions but no diffuse functions already provide accurate (hyper)polarizabilities for C6H8 whereas diffuse functions are compulsory for C5H7, in particular, p diffuse functions. In addition to the 6-31G*+pd basis set, basis sets resulting from removing not necessary diffuse functions from the augmented correlation consistent polarized valence double zeta basis set have been shown to provide (hyper)polarizability values of similar quality as more extended basis sets such as augmented correlation consistent polarized valence triple zeta and doubly augmented correlation consistent polarized valence double zeta. Using the selected atomic basis sets, the (hyper)polarizabilities of these two model compounds are calculated at different levels of approximation in order to assess the impact of including electron correlation. As a function of the method of calculation antiparallel and parallel variations have been demonstrated for α and γ of the two model compounds, respectively. For the polarizability, the unrestricted Hartree-Fock and unrestricted second-order Møller-Plesset methods bracket the reference value obtained at the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples level whereas the projected unrestricted second-order Møller-Plesset results are in much closer agreement with the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples values than the projected unrestricted Hartree-Fock results. Moreover, the differences between the restricted open-shell Hartree-Fock and restricted open-shell second-order Møller-Plesset methods are small. In what concerns the second hyperpolarizability, the unrestricted Hartree-Fock and unrestricted second-order Møller-Plesset values remain of similar quality while using spin-projected schemes fails for the charged system but performs nicely for the neutral one. The restricted open-shell schemes, and especially the restricted open-shell second-order Møller-Plesset method, provide for both compounds γ values close to the results obtained at the unrestricted coupled cluster level including singles and doubles with a perturbative inclusion of the triples. Thus, to obtain well-converged α and γ values at low-order electron correlation levels, the removal of spin contamination is a necessary but not a sufficient condition. Density-functional theory calculations of α and γ have also been carried out using several exchange-correlation functionals. Those employing hybrid exchange-correlation functionals have been shown to reproduce fairly well the reference coupled cluster polarizability and second hyperpolarizability values. In addition, inclusion of Hartree-Fock exchange is of major importance for determining accurate polarizability whereas for the second hyperpolarizability the gradient corrections are large.

Skyrme-Hartree-Fock calculation on He, Li, and Be isotopes

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

Shen, Y.; Ren, Z.

1996-09-01

The ground-state properties of He, Li, and Be nuclei are investigated by the Skyrme-Hartree-Fock approach with new force parameters SKI4 of Reinhard and Flocard [Nucl. Phys. A {bold 584}, 467 (1995)] plus a density-dependent pairing correlation. Calculations show that the Skyrme-Hartree-Fock model with above force parameters provides a good description on the binding energy and radii of He, Li, and Be isotopes. It also succeeds in reproducing neutron halos in nuclei {sup 6}He, {sup 8}He, {sup 11}Li, and {sup 14}Be. A detailed discussion on numerical results is provided and an explanation for the above success is given. {copyright} {ital 1996more » The American Physical Society.}« less

Calculation of total electron excitation cross-sections and partial electron ionization cross-sections for the elements. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Green, T. J.

1973-01-01

Computer programs were used to calculate the total electron excitation cross-section for atoms and the partial ionization cross-section. The approximations to the scattering amplitude used are as follows: (1) Born, Bethe, and Modified Bethe for non-exchange excitation; (2) Ochkur for exchange excitation; and (3) Coulomb-Born of non-exchange ionization. The amplitudes are related to the differential cross-sections which are integrated to give the total excitation (or partial ionization) cross-section for the collision. The atomic wave functions used are Hartree-Fock-Slater functions for bound states and the coulomb wave function for the continuum. The programs are presented and the results are examined.

One-range addition theorems for derivatives of Slater-type orbitals.

PubMed

Guseinov, Israfil

2004-06-01

Using addition theorems for STOs introduced by the author with the help of complete orthonormal sets of psi(alpha)-ETOs (Guseinov II (2003) J Mol Model 9:190-194), where alpha=1, 0, -1, -2, ..., a large number of one-range addition theorems for first and second derivatives of STOs are established. These addition theorems are especially useful for computation of multicenter-multielectron integrals over STOs that arise in the Hartree-Fock-Roothaan approximation and also in the Hylleraas function method, which play a significant role for the study of electronic structure and electron-nuclei interaction properties of atoms, molecules, and solids. The relationships obtained are valid for arbitrary quantum numbers, screening constants and location of STOs.

Ultrafast Processes in Atoms and Molecules: Integrated treatment of electronic and nuclear motion in ultrashort XUV pulses

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

McCurdy, C. William

This project made use of Multiconfiguration Time-Dependent Hartree-Fock method developed earlier in the McCurdy group in a series of novel applications of the method to ultrafast spectroscopic processes. MCTDHF treats the dynamics of a molecule or atom under the influence of an external field in manner that has all electrons active. That property distinguishes this method from the more popular (and much less computationally demanding) approaches for treating the electron dynamics of atoms and molecules in fields, such as the time-dependent “Configuration Interaction Singles” approximation or approaches that limit the treatment to either one or two-electron models.

Constraints on the {omega}- and {sigma}-meson coupling constants with dibaryons

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

Faessler, A.; Buchmann, A.J.; Krivoruchenko, M.I.

The effect of narrow dibaryon resonances on basic nuclear matter properties and on the structure of neutron stars is investigated in mean-field theory and in relativistic Hartree approximation. The existence of massive neutron stars imposes constraints on the coupling constants of the {omega} and {sigma} mesons with dibaryons. In the allowed region of the parameter space of the coupling constants, a Bose condensate of the light dibaryon candidates d{sub 1}(1920) and d{sup {prime}}(2060) is stable against compression. This proves the stability of the ground state of heterophase nuclear matter with a Bose condensate of light dibaryons. {copyright} {ital 1997} {italmore » The American Physical Society}« less

Double Photoionization of helium atom using Screening Potential Approach

NASA Astrophysics Data System (ADS)

Saha, Haripada

2014-05-01

The triple differential cross section for double Photoionization of helium atom will be investigated using our recently extended MCHF method. It is well known that electron correlation effects in both the initial and the final states are very important. To incorporate these effects we will use the multi-configuration Hartree-Fock method to account for electron correlation in the initial state. The electron correlation in the final state will be taken into account using the angle-dependent screening potential approximation. The triple differential cross section (TDCS) will be calculated for 20 eV photon energy, which has experimental results. Our results will be compared with available experimental and the theoretical observations.

The self-trapping transition in the non-half-filled strongly correlated extended Holstein-Hubbard model in two-dimensions

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

Sankar, I. V., E-mail: ivshankar27@gmail.com; Chatterjee, Ashok, E-mail: ivshankar27@gmail.com

2014-04-24

The two-dimensional extended Holstein-Hubbard model (EHH) has been considered at strong correlation regime in the non-half-filled band case to understand the self-trapping transition of electrons in strongly correlated electron system. We have used the method of optimized canonical transformations to transform an EHH model into an effective extended Hubbard (EEH) model. In the strong on-site correlation limit an EH model can be transformed into a t-J model which is finally solved using Hartree-Fock approximation (HFA). We found that, for non-half-filled band case, the transition is abrupt in the adiabatic region whereas it is continuous in the anti-adiabatic region.

Thermodynamic Properties of Low-Density {}^{132}Xe Gas in the Temperature Range 165-275 K

NASA Astrophysics Data System (ADS)

Akour, Abdulrahman

2018-01-01

The method of static fluctuation approximation was used to calculate selected thermodynamic properties (internal energy, entropy, energy capacity, and pressure) for xenon in a particularly low-temperature range (165-270 K) under different conditions. This integrated microscopic study started from an initial basic assumption as the main input. The basic assumption in this method was to replace the local field operator with its mean value, then numerically solve a closed set of nonlinear equations using an iterative method, considering the Hartree-Fock B2-type dispersion potential as the most appropriate potential for xenon. The results are in very good agreement with those of an ideal gas.

Matter distribution and spin-orbit force in spherical nuclei

NASA Astrophysics Data System (ADS)

Co', G.; Anguiano, M.; De Donno, V.; Lallena, A. M.

2018-03-01

We investigate the possibility that some nuclei show density distributions with a depletion in the center, a semibubble structure, by using a Hartree-Fock plus Bardeen-Cooper-Schrieffer approach. We separately study the proton, neutron, and matter distributions in 37 spherical nuclei mainly in the s -d shell region. We found a relation between the semibubble structure and the energy splitting of spin-orbit partner single particle levels. The presence of semibubble structure reduces this splitting, and we study its consequences on the excitation spectrum of the nuclei under investigation by using a quasiparticle random-phase-approximation approach. The excitation energies of the low-lying 4+ states can be related to the presence of semibubble structure in nuclei.

Semiempirical evaluation of post-Hartree-Fock diagonal-Born-Oppenheimer corrections for organic molecules.

PubMed

Mohallem, José R

2008-04-14

Recent post-Hartree-Fock calculations of the diagonal-Born-Oppenheimer correction empirically show that it behaves quite similar to atomic nuclear mass corrections. An almost constant contribution per electron is identified, which converges with system size for specific series of organic molecules. This feature permits pocket-calculator evaluation of the corrections within thermochemical accuracy (10(-1) mhartree or kcal/mol).

Hartree-Fock study of the Anderson metal-insulator transition in the presence of Coulomb interaction: Two types of mobility edges and their multifractal scaling exponents

NASA Astrophysics Data System (ADS)

Lee, Hyun-Jung; Kim, Ki-Seok

2018-04-01

We investigate the role of Coulomb interaction in the multifractality of Anderson metal-insulator transition, where the Coulomb interaction is treated within the Hartree-Fock approximation, but disorder effects are taken into account exactly. An innovative technical aspect in our simulation is to utilize the Ewald-sum technique, which allows us to introduce the long-range nature of the Coulomb interaction into Hartree-Fock self-consistent equations of order parameters more accurately. This numerical simulation reproduces the Altshuler-Aronov correction in a metallic state and the Efros-Shklovskii pseudogap in an insulating phase, where the density of states ρ (ω ) is evaluated in three dimensions. Approaching the quantum critical point of a metal-insulator transition from either the metallic or insulting phase, we find that the density of states is given by ρ (ω ) ˜|ω| 1 /2 , which determines one critical exponent of the McMillan-Shklovskii scaling theory. Our main result is to evaluate the eigenfunction multifractal scaling exponent αq, given by the Legendre transformation of the fractal dimension τq, which characterizes the scaling behavior of the inverse participation ratio with respect to the system size L . Our multifractal analysis leads us to identify two kinds of mobility edges, one of which occurs near the Fermi energy and the other of which appears at a high energy, where the density of states at the Fermi energy shows the Coulomb-gap feature. We observe that the multifractal exponent at the high-energy mobility edge remains to be almost identical to that of the Anderson localization transition in the absence of Coulomb interactions. On the other hand, we find that the multifractal exponent near the Fermi energy is more enhanced than that at the high-energy mobility edge, suspected to result from interaction effects. However, both the multifractal exponents do not change even if the strength of the Coulomb interaction varies. We also show that the multifractality singular spectrum can be classified into two categories, confirming the appearance of two types of mobility edges.

Implementation of polyatomic MCTDHF capability

NASA Astrophysics Data System (ADS)

Haxton, Daniel; Jones, Jeremiah; Rescigno, Thomas; McCurdy, C. William; Ibrahim, Khaled; Williams, Sam; Vecharynski, Eugene; Rouet, Francois-Henry; Li, Xiaoye; Yang, Chao

2015-05-01

The implementation of the Multiconfiguration Time-Dependent Hartree-Fock method for poly- atomic molecules using a cartesian product grid of sinc basis functions will be discussed. The focus will be on two key components of the method: first, the use of a resolution-of-the-identity approximation; sec- ond, the use of established techniques for triple Toeplitz matrix algebra using fast Fourier transform over distributed memory architectures (MPI 3D FFT). The scaling of two-electron matrix element transformations is converted from O(N4) to O(N log N) by including these components. Here N = n3, with n the number of points on a side. We test the prelim- inary implementation by calculating absorption spectra of small hydro- carbons, using approximately 16-512 points on a side. This work is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under the Early Career program, and by the offices of BES and Advanced Scientific Computing Research, under the SciDAC program.

Solutions of the two-dimensional Hubbard model: Benchmarks and results from a wide range of numerical algorithms

DOE PAGES

LeBlanc, J. P. F.; Antipov, Andrey E.; Becca, Federico; ...

2015-12-14

Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification ofmore » uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Furthermore, cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.« less

Low-density homogeneous symmetric nuclear matter: Disclosing dinucleons in coexisting phases

NASA Astrophysics Data System (ADS)

Arellano, Hugo F.; Delaroche, Jean-Paul

2015-01-01

The effect of in-medium dinucleon bound states on self-consistent single-particle fields in Brueckner, Bethe and Goldstone theory is investigated in symmetric nuclear matter at zero temperature. To this end, dinucleon bound state occurences in the 1 S 0 and 3 SD 1 channels are explicitly accounted for --within the continuous choice for the auxiliary fields-- while imposing self-consistency in Brueckner-Hartree-Fock approximation calculations. Searches are carried out at Fermi momenta in the range fm-1, using the Argonne bare nucleon-nucleon potential without resorting to the effective-mass approximation. As a result, two distinct solutions meeting the self-consistency requirement are found with overlapping domains in the interval 0.130 fm-1 0.285 fm-1, corresponding to mass densities between and g cm-3. Effective masses as high as three times the nucleon mass are found in the coexistence domain. The emergence of superfluidity in relationship with BCS pairing gap solutions is discussed.

Analytic second derivatives of the energy in the fragment molecular orbital method

NASA Astrophysics Data System (ADS)

Nakata, Hiroya; Nagata, Takeshi; Fedorov, Dmitri G.; Yokojima, Satoshi; Kitaura, Kazuo; Nakamura, Shinichiro

2013-04-01

We developed the analytic second derivatives of the energy for the fragment molecular orbital (FMO) method. First we derived the analytic expressions and then introduced some approximations related to the first and second order coupled perturbed Hartree-Fock equations. We developed a parallel program for the FMO Hessian with approximations in GAMESS and used it to calculate infrared (IR) spectra and Gibbs free energies and to locate the transition states in SN2 reactions. The accuracy of the Hessian is demonstrated in comparison to ab initio results for polypeptides and a water cluster. By using the two residues per fragment division, we achieved the accuracy of 3 cm-1 in the reduced mean square deviation of vibrational frequencies from ab initio for all three polyalanine isomers, while the zero point energy had the error not exceeding 0.3 kcal/mol. The role of the secondary structure on IR spectra, zero point energies, and Gibbs free energies is discussed.

Anharmonic Thermal Oscillations of the Electron Momentum Distribution in Lithium Fluoride

NASA Astrophysics Data System (ADS)

Erba, A.; Maul, J.; Itou, M.; Dovesi, R.; Sakurai, Y.

2015-09-01

Anharmonic thermal effects on the electron momentum distribution of a lithium fluoride single crystal are experimentally measured through high-resolution Compton scattering and theoretically modeled with ab initio simulations, beyond the harmonic approximation to the lattice potential, explicitly accounting for thermal expansion. Directional Compton profiles are measured at two different temperatures, 10 and 300 K, with a high momentum space resolution (0.10 a.u. in full width at half maximum), using synchrotron radiation. The effect of temperature on measured directional Compton profiles is clearly revealed by oscillations extending almost up to |p |=4 a .u . , which perfectly match those predicted from quantum-mechanical simulations. The wave-function-based Hartree-Fock method and three classes of the Kohn-Sham density functional theory (local-density, generalized-gradient, and hybrid approximations) are adopted. The lattice thermal expansion, as described with the quasiharmonic approach, is found to entirely account for the effect of temperature on the electron momentum density within the experimental accuracy.

Electron correlation within the relativistic no-pair approximation

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

Almoukhalalati, Adel; Saue, Trond, E-mail: trond.saue@irsamc.ups-tlse.fr; Knecht, Stefan

This paper addresses the definition of correlation energy within 4-component relativistic atomic and molecular calculations. In the nonrelativistic domain the correlation energy is defined as the difference between the exact eigenvalue of the electronic Hamiltonian and the Hartree-Fock energy. In practice, what is reported is the basis set correlation energy, where the “exact” value is provided by a full Configuration Interaction (CI) calculation with some specified one-particle basis. The extension of this definition to the relativistic domain is not straightforward since the corresponding electronic Hamiltonian, the Dirac-Coulomb Hamiltonian, has no bound solutions. Present-day relativistic calculations are carried out within themore » no-pair approximation, where the Dirac-Coulomb Hamiltonian is embedded by projectors eliminating the troublesome negative-energy solutions. Hartree-Fock calculations are carried out with the implicit use of such projectors and only positive-energy orbitals are retained at the correlated level, meaning that the Hartree-Fock projectors are frozen at the correlated level. We argue that the projection operators should be optimized also at the correlated level and that this is possible by full Multiconfigurational Self-Consistent Field (MCSCF) calculations, that is, MCSCF calculations using a no-pair full CI expansion, but including orbital relaxation from the negative-energy orbitals. We show by variational perturbation theory that the MCSCF correlation energy is a pure MP2-like correlation expression, whereas the corresponding CI correlation energy contains an additional relaxation term. We explore numerically our theoretical analysis by carrying out variational and perturbative calculations on the two-electron rare gas atoms with specially tailored basis sets. In particular, we show that the correlation energy obtained by the suggested MCSCF procedure is smaller than the no-pair full CI correlation energy, in accordance with the underlying minmax principle and our theoretical analysis. We also show that the relativistic correlation energy, obtained from no-pair full MCSCF calculations, scales at worst as X{sup −2} with respect to the cardinal number X of our correlation-consistent basis sets optimized for the two-electron atoms. This is better than the X{sup −1} scaling suggested by previous studies, but worse than the X{sup −3} scaling observed in the nonrelativistic domain. The well-known 1/Z- expansion in nonrelativistic atomic theory follows from coordinate scaling. We point out that coordinate scaling for consistency should be accompanied by velocity scaling. In the nonrelativistic domain this comes about automatically, whereas in the relativistic domain an explicit scaling of the speed of light is required. This in turn explains why the relativistic correlation energy to the lowest order is not independent of nuclear charge, in contrast to nonrelativistic theory.« less

Qualitative breakdown of the unrestricted Hartree-Fock energy

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

Mori-Sánchez, Paula, E-mail: paula.mori@uam.es; Cohen, Aron J., E-mail: ajc54@cam.ac.uk

2014-10-28

The stretching of closed-shell molecules is a qualitative problem for restricted Hartree-Fock that is usually circumvented by the use of unrestricted Hartree-Fock (UHF). UHF is well known to break the spin symmetry at the Coulson-Fischer point, leading to a discontinuous derivative in the potential energy surface and incorrect spin density. However, this is generally not considered as a major drawback. In this work, we present a set of two electron molecules which magnify the problem of symmetry breaking and lead to drastically incorrect potential energy surfaces with UHF. These molecules also fail with unrestricted density-functional calculations where a functional suchmore » as B3LYP gives both symmetry breaking and an unphysically low energy due to the delocalization error. The implications for density functional theory are also discussed.« less

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.

Uniform in N global well-posedness of the time-dependent Hartree-Fock-Bogoliubov equations in R^{1+1}

NASA Astrophysics Data System (ADS)

Chong, Jacky Jia Wei

2018-04-01

We prove the global well-posedness of the time-dependent Hartree-Fock-Bogoliubov (TDHFB) equations in R^{1+1} with two-body interaction potential of the form N^{-1}v_N(x) = N^{β -1} v(N^β x) where v≥0 is a sufficiently regular radial function, i.e., v \\in L^1(R)\\cap C^∞ (R) . In particular, using methods of dispersive PDEs similar to the ones used in Grillakis and Machedon (Commun Partial Differ Equ 42:24-67, 2017), we are able to show for any scaling parameter β >0 the TDHFB equations are globally well-posed in some Strichartz-type spaces independent of N, cf. (Bach et al. in The time-dependent Hartree-Fock-Bogoliubov equations for Bosons, 2016. arXiv:1602.05171).

The optimized effective potential and the self-interaction correction in density functional theory: Application to molecules

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

Garza, Jorge; Nichols, Jeffrey A.; Dixon, David A.

2000-05-08

The Krieger, Li, and Iafrate approximation to the optimized effective potential including the self-interaction correction for density functional theory has been implemented in a molecular code, NWChem, that uses Gaussian functions to represent the Kohn and Sham spin-orbitals. The differences between the implementation of the self-interaction correction in codes where planewaves are used with an optimized effective potential are discussed. The importance of the localization of the spin-orbitals to maximize the exchange-correlation of the self-interaction correction is discussed. We carried out exchange-only calculations to compare the results obtained with these approximations, and those obtained with the local spin density approximation,more » the generalized gradient approximation and Hartree-Fock theory. Interesting results for the energy difference (GAP) between the highest occupied molecular orbital, HOMO, and the lowest unoccupied molecular orbital, LUMO, (spin-orbital energies of closed shell atoms and molecules) using the optimized effective potential and the self-interaction correction have been obtained. The effect of the diffuse character of the basis set on the HOMO and LUMO eigenvalues at the various levels is discussed. Total energies obtained with the optimized effective potential and the self-interaction correction show that the exchange energy with these approximations is overestimated and this will be an important topic for future work. (c) 2000 American Institute of Physics.« less

Optical-model potential for electron and positron elastic scattering by atoms

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

Salvat, Francesc

2003-07-01

An optical-model potential for systematic calculations of elastic scattering of electrons and positrons by atoms and positive ions is proposed. The electrostatic interaction is determined from the Dirac-Hartree-Fock self-consistent atomic electron density. In the case of electron projectiles, the exchange interaction is described by means of the local-approximation of Furness and McCarthy. The correlation-polarization potential is obtained by combining the correlation potential derived from the local density approximation with a long-range polarization interaction, which is represented by means of a Buckingham potential with an empirical energy-dependent cutoff parameter. The absorption potential is obtained from the local-density approximation, using the Born-Ochkurmore » approximation and the Lindhard dielectric function to describe the binary collisions with a free-electron gas. The strength of the absorption potential is adjusted by means of an empirical parameter, which has been determined by fitting available absolute elastic differential cross-section data for noble gases and mercury. The Dirac partial-wave analysis with this optical-model potential provides a realistic description of elastic scattering of electrons and positrons with energies in the range from {approx}100 eV up to {approx}5 keV. At higher energies, correlation-polarization and absorption corrections are small and the usual static-exchange approximation is sufficiently accurate for most practical purposes.« less

Positron and electron energy bands in several ionic crystals using restricted Hartree-Fock method

NASA Astrophysics Data System (ADS)

Kunz, A. B.; Waber, J. T.

1981-08-01

Using a restricted Hartree-Fock formalism and suitably localized and symmetrized wave functions, both the positron and electron energy bands were calculated for NaF, MgO and NiO. The lowest positron state at Γ 1 lies above the vacuum level and negative work functions are predicted. Positron annihilation rates were calculated and found to be in good agreement with measured lifetimes.

Near Hartree-Fock quality GTO basis sets for the first- and third-row atoms

NASA Technical Reports Server (NTRS)

Partridge, Harry

1989-01-01

Energy-optimized Gaussian-type-orbital (GTO) basis sets of accuracy approaching that of numerical Hartree-Fock computations are compiled for the elements of the first and third rows of the periodic table. The methods employed in calculating the sets are explained; the applicability of the sets to electronic-structure calculations is discussed; and the results are presented in tables and briefly characterized.

Atomic electron energies including relativistic effects and quantum electrodynamic corrections

NASA Technical Reports Server (NTRS)

Aoyagi, M.; Chen, M. H.; Crasemann, B.; Huang, K. N.; Mark, H.

1977-01-01

Atomic electron energies have been calculated relativistically. Hartree-Fock-Slater wave functions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first order correction to the local approximation was thus included. Quantum-electrodynamic corrections were made. For all orbitals in all atoms with 2 less than or equal to Z less than or equal to 106, the following quantities are listed: total energies, electron kinetic energies, electron-nucleus potential energies, electron-electron potential energies consisting of electrostatic and Breit interaction (magnetic and retardation) terms, and vacuum polarization energies. These results will serve for detailed comparison of calculations based on other approaches. The magnitude of quantum electrodynamic corrections is exhibited quantitatively for each state.

Theory of inhomogeneous quantum systems. III. Variational wave functions for Fermi fluids

NASA Astrophysics Data System (ADS)

Krotscheck, E.

1985-04-01

We develop a general variational theory for inhomogeneous Fermi systems such as the electron gas in a metal surface, the surface of liquid 3He, or simple models of heavy nuclei. The ground-state wave function is expressed in terms of two-body correlations, a one-body attenuation factor, and a model-system Slater determinant. Massive partial summations of cluster expansions are performed by means of Born-Green-Yvon and hypernetted-chain techniques. An optimal single-particle basis is generated by a generalized Hartree-Fock equation in which the two-body correlations screen the bare interparticle interaction. The optimization of the pair correlations leads to a state-averaged random-phase-approximation equation and a strictly microscopic determination of the particle-hole interaction.

Spectra for the reemission of attosecond and shorter electromagnetic pulses by multielectron atoms

NASA Astrophysics Data System (ADS)

Makarov, D. N.; Matveev, V. I.

2017-08-01

Based on the analytical solution of the Schrödinger equation, we have considered the reemission of attosecond and shorter electromagnetic pulses by multielectron atoms in the sudden perturbation approximation. We have developed a technique of calculating the spectra for the reemission of attosecond and shorter electromagnetic pulses by neutral multielectron atoms with nuclear charges from 1 to 92. The results are presented in the form of analytical formulas dependent on several coefficients and screening parameters tabulated for all of the atoms whose electron densities are described by the well-known Dirac-Hartree-Fock-Slater model. As examples we have calculated the spectra for the reemission by lithium, carbon, calcium, and iron atoms for two types of incident pulse: Gaussian and "sombrero."

Two-photon excitation cross-section in light and intermediate atoms

NASA Technical Reports Server (NTRS)

Omidvar, K.

1980-01-01

The method of explicit summation over the intermediate states is used along with LS coupling to derive an expression for two-photon absorption cross section in light and intermediate atoms in terms of integrals over radial wave functions. Two selection rules, one exact and one approximate, are also derived. In evaluating the radial integrals, for low-lying levels, the Hartree-Fock wave functions, and for high-lying levels, hydrogenic wave functions obtained by the quantum defect method are used. A relationship between the cross section and the oscillator strengths is derived. Cross sections due to selected transitions in nitrogen, oxygen, and chlorine are given. The expression for the cross section is useful in calculating the two-photon absorption in light and intermediate atoms.

Compton profiles and electronic properties of TiB{sub 2}

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

Bhatt, Samir, E-mail: sameerbhatt011@gmail.com; Suthar, K. K.; Ahuja, B. L.

In this paper, we report the experimental Compton profile (CP) of TiB{sub 2} using high energy {sup 137}Cs γ-rays Compton spectrometer. To interpret the experimental momentum density, we have calculated the CPs using Hartree-Fock (HF), density functional theory (DFT) and hybridization of DFT and HF within linear combination of atomic orbitals. The theoretical profile with generalized gradient approximation is found to be relatively in better agreement with the experimental profile. A sharp valley in density of states and hence the pseudogap near the Fermi energy is attributed to hybridization of Ti-3d and B-2p states and almost reverse trend of energymore » bands below and above the Fermi energy.« less

Electronic properties of Laves phase ZrFe{sub 2} using Compton spectroscopy

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

Bhatt, Samir, E-mail: sameerbhatto11@gmail.com; Kumar, Kishor; Ahuja, B. L.

First-ever experimental Compton profile of Laves phase ZrFe{sub 2}, using indigenous 20 Ci {sup 137}Cs Compton spectrometer, is presented. To analyze the experimental electron momentum density, we have deduced the theoretical Compton profiles using density functional theory (DFT) and hybridization of DFT and Hartree-Fock scheme within linear combination of atomic orbitals (LCAO) method. The energy bands and density of states are also calculated using LCAO prescription. The theoretical profile based on local density approximation gives a better agreement with the experimental profile than other reported schemes. The present investigations validate the inclusion of correlation potential of Perdew-Zunger in predicting themore » electronic properties of ZrFe{sub 2}.« less

Final Scientific/Technical Report: Breakthrough Design and Implementation of Many-Body Theories for Electron Correlation

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

So Hirata

2012-01-03

This report discusses the following highlights of the project: (1) grid-based Hartree-Fock equation solver; (2) explicitly correlated coupled-cluster and perturbation methods; (3) anharmonic vibrational frequencies and vibrationally averaged NMR and structural parameters of FHF; (4) anharmonic vibrational frequencies and vibrationally averaged structures of hydrocarbon combustion species; (5) anharmonic vibrational analysis of the guanine-cytosine base pair; (6) the nature of the Born-Oppenheimer approximation; (7) Polymers and solids Brillouin-zone downsampling - the modulo MP2 method; (8) explicitly correlated MP2 for extended systems; (9) fast correlated method for molecular crystals - solid formic acid; and (10) fast correlated method for molecular crystals -more » solid hydrogen fluoride.« less

Hybrid and Constrained Resolution-of-Identity Techniques for Coulomb Integrals.

PubMed

Duchemin, Ivan; Li, Jing; Blase, Xavier

2017-03-14

The introduction of auxiliary bases to approximate molecular orbital products has paved the way to significant savings in the evaluation of four-center two-electron Coulomb integrals. We present a generalized dual space strategy that sheds a new light on variants over the standard density and Coulomb-fitting schemes, including the possibility of introducing minimization constraints. We improve in particular the charge- or multipole-preserving strategies introduced respectively by Baerends and Van Alsenoy that we compare to a simple scheme where the Coulomb metric is used for lowest angular momentum auxiliary orbitals only. We explore the merits of these approaches on the basis of extensive Hartree-Fock and MP2 calculations over a standard set of medium size molecules.

Direct mapping between exchange potentials of Hartree-Fock and Kohn-Sham schemes as origin of orbital proximity

NASA Astrophysics Data System (ADS)

Cinal, M.

2010-01-01

It is found that for closed-l-shell atoms, the exact local exchange potential vx(r) calculated in the exchange-only Kohn-Sham (KS) scheme of the density functional theory (DFT) is very well represented within the region of every atomic shell by each of the suitably shifted potentials obtained with the nonlocal Fock exchange operator for the individual Hartree-Fock (HF) orbitals belonging to this shell. This newly revealed property is not related to the well-known steplike shell structure in the response part of vx(r), but it results from specific relations satisfied by the HF orbital exchange potentials. These relations explain the outstanding proximity of the occupied HF and exchange-only KS orbitals as well as the high quality of the Krieger-Li-Iafrate and localized HF (or, equivalently, common-energy-denominator) approximations to the DFT exchange potential vx(r). Another highly accurate representation of vx(r) is given by the continuous piecewise function built of shell-specific exchange potentials, each defined as the weighted average of the shifted orbital exchange potentials corresponding to a given shell. The constant shifts added to the HF orbital exchange potentials, to map them onto vx(r), are nearly equal to the differences between the energies of the corresponding KS and HF orbitals. It is discussed why these differences are positive and grow when the respective orbital energies become lower for inner orbitals.

Structure factors for tunneling ionization rates of molecules: General Hartree-Fock-based integral representation

NASA Astrophysics Data System (ADS)

Madsen, Lars Bojer; Jensen, Frank; Dnestryan, Andrey I.; Tolstikhin, Oleg I.

2017-07-01

In the leading-order approximation of the weak-field asymptotic theory (WFAT), the dependence of the tunneling ionization rate of a molecule in an electric field on its orientation with respect to the field is determined by the structure factor of the ionizing molecular orbital. The WFAT yields an expression for the structure factor in terms of a local property of the orbital in the asymptotic region. However, in general quantum chemistry approaches molecular orbitals are expanded in a Gaussian basis which does not reproduce their asymptotic behavior correctly. This hinders the application of the WFAT to polyatomic molecules, which are attracting increasing interest in strong-field physics. Recently, an integral-equation approach to the WFAT for tunneling ionization of one electron from an arbitrary potential has been developed. The structure factor is expressed in an integral form as a matrix element involving the ionizing orbital. The integral is not sensitive to the asymptotic behavior of the orbital, which resolves the difficulty mentioned above. Here, we extend the integral representation for the structure factor to many-electron systems treated within the Hartree-Fock method and show how it can be implemented on the basis of standard quantum chemistry software packages. We validate the methodology by considering noble-gas atoms and the CO molecule, for which accurate structure factors exist in the literature. We also present benchmark results for CO2 and for NH3 in the pyramidal and planar geometries.

Quantum treatment of protons with the reduced explicitly correlated Hartree-Fock approach

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

Sirjoosingh, Andrew; Pak, Michael V.; Brorsen, Kurt R.

2015-06-07

The nuclear-electronic orbital (NEO) approach treats select nuclei quantum mechanically on the same level as the electrons and includes nonadiabatic effects between the electrons and the quantum nuclei. The practical implementation of this approach is challenging due to the significance of electron-nucleus dynamical correlation. Herein, we present a general extension of the previously developed reduced NEO explicitly correlated Hartree-Fock (RXCHF) approach, in which only select electronic orbitals are explicitly correlated to each quantum nuclear orbital via Gaussian-type geminal functions. Approximations of the electronic exchange between the geminal-coupled electronic orbitals and the other electronic orbitals are also explored. This general approachmore » enables computationally tractable yet accurate calculations on molecular systems with quantum protons. The RXCHF method is applied to the hydrogen cyanide (HCN) and FHF{sup −} systems, where the proton and all electrons are treated quantum mechanically. For the HCN system, only the two electronic orbitals associated with the CH covalent bond are geminal-coupled to the proton orbital. For the FHF{sup −} system, only the four electronic orbitals associated with the two FH covalent bonds are geminal-coupled to the proton orbital. For both systems, the RXCHF method produces qualitatively accurate nuclear densities, in contrast to mean field-based NEO approaches. The development and implementation of the RXCHF method provide the framework to perform calculations on systems such as proton-coupled electron transfer reactions, where electron-proton nonadiabatic effects are important.« less

Effect of exact Coulomb-exchange calculations on band-head spectra of odd-proton nuclei

NASA Astrophysics Data System (ADS)

Koh, Meng-Hock; Nurhafiza, Mohamad Nor

2017-10-01

Previous calculations of band-head energy spectra of odd-mass heavy nuclei in the Hartree-Fock-plus-Bardeen-Cooper-Schrieffer (HF-BCS) framework showed that the agreement with data is better for odd-neutron as compared to odd-proton nuclei. The reason for a poorer agreement with data for the latter have been ascribed to the possible usage of the Slater approximation in calculating the Coulomb-exchange term. In this work, we report the effect of exact Coulomb-exchange calculations on band-head energy spectra of two odd-proton nuclei (namely 237Np and 241Am) as compared to the results obtained using the Slater approximation. We performed self-consistent blocking calculations while taking the breaking of time-reversal symmetry at the mean-field level into account due to the unpaired nucleon. The SkM* and SIII parametrizations of the Skyrme interaction have been employed to approximate the effective nucleon-nucleon interaction while a seniority force is used for the pairing channel. Contrary to what was expected, our preliminary results show no improvement on the band-head spectra as compared to data when the Coulomb-exchange term is calculated exactly.

Exact and approximate many-body dynamics with stochastic one-body density matrix evolution

NASA Astrophysics Data System (ADS)

Lacroix, Denis

2005-06-01

We show that the dynamics of interacting fermions can be exactly replaced by a quantum jump theory in the many-body density matrix space. In this theory, jumps occur between densities formed of pairs of Slater determinants, Dab=|Φa><Φb|, where each state evolves according to the stochastic Schrödinger equation given by O. Juillet and Ph. Chomaz [Phys. Rev. Lett. 88, 142503 (2002)]. A stochastic Liouville-von Neumann equation is derived as well as the associated. Bogolyubov-Born-Green-Kirwood-Yvon hierarchy. Due to the specific form of the many-body density along the path, the presented theory is equivalent to a stochastic theory in one-body density matrix space, in which each density matrix evolves according to its own mean-field augmented by a one-body noise. Guided by the exact reformulation, a stochastic mean-field dynamics valid in the weak coupling approximation is proposed. This theory leads to an approximate treatment of two-body effects similar to the extended time-dependent Hartree-Fock scheme. In this stochastic mean-field dynamics, statistical mixing can be directly considered and jumps occur on a coarse-grained time scale. Accordingly, numerical effort is expected to be significantly reduced for applications.

Roothaan approach in the thermodynamic limit

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

Gutierrez, G.; Plastino, A.

1982-02-01

A systematic method for the solution of the Hartree-Fock equations in the thermodynamic limit is presented. The approach is seen to be a natural extension of the one usually employed in the finite-fermion case, i.e., that developed by Roothaan. The new techniques developed here are applied, as an example, to neutron matter, employing the so-called V/sub 1/ Bethe homework potential. The results obtained are, by far, superior to those that the ordinary plane-wave Hartree-Fock theory yields.

Electron correlation in Hooke's law atom in the high-density limit.

PubMed

Gill, P M W; O'Neill, D P

2005-03-01

Closed-form expressions for the first three terms in the perturbation expansion of the exact energy and Hartree-Fock energy of the lowest singlet and triplet states of the Hooke's law atom are found. These yield elementary formulas for the exact correlation energies (-49.7028 and -5.807 65 mE(h)) of the two states in the high-density limit and lead to a pair of necessary conditions on the exact correlation kernel G(w) in Hartree-Fock-Wigner theory.

Superdeformed bands in neutron-rich sulfur isotopes suggested by cranked Skyrme-Hartree-Fock calculations

NASA Astrophysics Data System (ADS)

Inakura, T.; Mizutori, S.; Yamagami, M.; Matsuyanagi, K.

2003-12-01

On the basis of the cranked Skyrme-Hartree-Fock calculations in the three-dimensional coordinate-mesh representation, we suggest that, in addition to the well-known candidate 32S, the neutron-rich nucleus 36S and the drip-line nuclei, 48S and 50S, are also good candidates for finding superdeformed rotational bands in sulfur isotopes. Calculated density distributions for the superdeformed states in 48S and 50S exhibit superdeformed neutron skins.

Measurement of Kα and Kβ fluorescence cross sections for elements in the range 44<=Z<=68 at 59.5 keV

NASA Astrophysics Data System (ADS)

Budak, G.; Karabulut, A.; Demir, L.; Sahin, Y.

1999-09-01

The Kα and Kβ x-ray fluorescence cross sections have been measured for elements in the range 44<=Z<=68 at an excitation energy of 59.5-keV γ ray from 241Am radioisotope with a Si(Li) detector. A reasonable agreement is found between the present experimental results and the theoretically calculated values based on photoionization cross sections by Scofield using Hartree-Slater and Hartree-Fock central potential theory.

From Hartree Dynamics to the Relativistic Vlasov Equation

NASA Astrophysics Data System (ADS)

Dietler, Elia; Rademacher, Simone; Schlein, Benjamin

2018-02-01

We derive the relativistic Vlasov equation from quantum Hartree dynamics for fermions with relativistic dispersion in the mean-field scaling, which is naturally linked with an effective semiclassic limit. Similar results in the non-relativistic setting have been recently obtained in Benedikter et al. (Arch Rat Mech Anal 221(1): 273-334, 2016). The new challenge that we have to face here, in the relativistic setting, consists in controlling the difference between the quantum kinetic energy and the relativistic transport term appearing in the Vlasov equation.

Quantum chemical approach for positron annihilation spectra of atoms and molecules beyond plane-wave approximation

NASA Astrophysics Data System (ADS)

Ikabata, Yasuhiro; Aiba, Risa; Iwanade, Toru; Nishizawa, Hiroaki; Wang, Feng; Nakai, Hiromi

2018-05-01

We report theoretical calculations of positron-electron annihilation spectra of noble gas atoms and small molecules using the nuclear orbital plus molecular orbital method. Instead of a nuclear wavefunction, the positronic wavefunction is obtained as the solution of the coupled Hartree-Fock or Kohn-Sham equation for a positron and the electrons. The molecular field is included in the positronic Fock operator, which allows an appropriate treatment of the positron-molecule repulsion. The present treatment succeeds in reproducing the Doppler shift, i.e., full width at half maximum (FWHM) of experimentally measured annihilation (γ-ray) spectra for molecules with a mean absolute error less than 10%. The numerical results indicate that the interpretation of the FWHM in terms of a specific molecular orbital is not appropriate.

Composite boson mapping for lattice boson systems.

PubMed

Huerga, Daniel; Dukelsky, Jorge; Scuseria, Gustavo E

2013-07-26

We present a canonical mapping transforming physical boson operators into quadratic products of cluster composite bosons that preserves matrix elements of operators when a physical constraint is enforced. We map the 2D lattice Bose-Hubbard Hamiltonian into 2×2 composite bosons and solve it within a generalized Hartree-Bogoliubov approximation. The resulting Mott insulator-superfluid phase diagram reproduces well quantum Monte Carlo results. The Higgs boson behavior in the superfluid phase along the unit density line is unraveled and in remarkable agreement with experiments. Results for the properties of the ground and excited states are competitive with other state-of-the-art approaches, but at a fraction of their computational cost. The composite boson mapping here introduced can be readily applied to frustrated many-body systems where most methodologies face significant hurdles.

The impact of electron correlations on the energetics and stability of silicon nanoclusters

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

Matsko, N. L.; Baturin, V. S.; Lepeshkin, S. V.

2016-08-21

The first-principles prediction of stable nanocluster structure is often hampered by the existence of many isomer configurations with energies close to the ground state. This fact attaches additional importance to many-electron effects beyond density functional theory (DFT), because their contributions can change a subtle energy order of competitive structures. To analyze this problem, we consider, as an example, the energetics of silicon nanoclusters passivated by hydrogen Si{sub 10}H{sub 2n} (0 ≤ n ≤ 11), where passivation changes the structure from compact to loosely packed and branched. Our calculations performed with DFT, hybrid functionals, and Hartree-Fock methods, as well as bymore » the GW approximation, confirm a considerable sensitivity of isomer energy ordering to many-electron effects.« less

Calculation of (P,T) -odd electric dipole moments for the diamagnetic atoms X129e , Y171b , H199g , R211n , and R225a

NASA Astrophysics Data System (ADS)

Dzuba, V. A.; Flambaum, V. V.; Porsev, S. G.

2009-09-01

Electric dipole moments of diamagnetic atoms of experimental interest are calculated using the relativistic Hartree-Fock and random-phase approximation methods, the many-body perturbation theory, and the configuration-interaction technique. We consider (P,T) -odd interactions, which give rise to atomic electric dipole moment in the second order of the perturbation theory. These include nuclear Schiff moment, (P,T) -odd electron-nucleon interaction, and electron electric dipole moment. Interpretation of an experimental constraint of a permanent electric dipole moment of H199g [W. C. Griffith, M. D. Swallows, T. H. Loftus, M. V. Romalis, B. R. Heckel, and E. N. Fortson, Phys. Rev. Lett. 102, 101601 (2009)] is discussed.

Breaking the theoretical scaling limit for predicting quasiparticle energies: the stochastic GW approach.

PubMed

Neuhauser, Daniel; Gao, Yi; Arntsen, Christopher; Karshenas, Cyrus; Rabani, Eran; Baer, Roi

2014-08-15

We develop a formalism to calculate the quasiparticle energy within the GW many-body perturbation correction to the density functional theory. The occupied and virtual orbitals of the Kohn-Sham Hamiltonian are replaced by stochastic orbitals used to evaluate the Green function G, the polarization potential W, and, thereby, the GW self-energy. The stochastic GW (sGW) formalism relies on novel theoretical concepts such as stochastic time-dependent Hartree propagation, stochastic matrix compression, and spatial or temporal stochastic decoupling techniques. Beyond the theoretical interest, the formalism enables linear scaling GW calculations breaking the theoretical scaling limit for GW as well as circumventing the need for energy cutoff approximations. We illustrate the method for silicon nanocrystals of varying sizes with N_{e}>3000 electrons.

Self-consistent RPA calculations with Skyrme-type interactions: The skyrme_rpa program

NASA Astrophysics Data System (ADS)

Colò, Gianluca; Cao, Ligang; Van Giai, Nguyen; Capelli, Luigi

2013-01-01

Random Phase Approximation (RPA) calculations are nowadays an indispensable tool in nuclear physics studies. We present here a complete version implemented with Skyrme-type interactions, with the spherical symmetry assumption, that can be used in cases where the effects of pairing correlations and of deformation can be ignored. The full self-consistency between the Hartree-Fock mean field and the RPA excitations is enforced, and it is numerically controlled by comparison with energy-weighted sum rules. The main limitations are that charge-exchange excitations and transitions involving spin operators are not included in this version. Program summaryProgram title: skyrme_rpa (v 1.00) Catalogue identifier: AENF_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AENF_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5531 No. of bytes in distributed program, including test data, etc.: 39435 Distribution format: tar.gz Programming language: FORTRAN-90/95; easily downgradable to FORTRAN-77. Computer: PC with Intel Celeron, Intel Pentium, AMD Athlon and Intel Core Duo processors. Operating system: Linux, Windows. RAM: From 4 MBytes to 150 MBytes, depending on the size of the nucleus and of the model space for RPA. Word size: The code is written with a prevalent use of double precision or REAL(8) variables; this assures 15 significant digits. Classification: 17.24. Nature of problem: Systematic observations of excitation properties in finite nuclear systems can lead to improved knowledge of the nuclear matter equation of state as well as a better understanding of the effective interaction in the medium. This is the case of the nuclear giant resonances and low-lying collective excitations, which can be described as small amplitude collective motions in the framework of the Random Phase Approximation (RPA). This work provides a tool where one starts from an assumed form of nuclear effective interaction (the Skyrme forces) and builds the self-consistent Hartree-Fock mean field of a given nucleus, and then the RPA multipole excitations of that nucleus. Solution method: The Hartree-Fock (HF) equations are solved in a radial mesh, using a Numerov algorithm. The solutions are iterated until self-consistency is achieved (in practice, when the energy eigenvalues are stable within a desired accuracy). In the obtained mean field, unoccupied states necessary for the RPA calculations are found. For all single-particle states, box boundary conditions are assumed. To solve the RPA problem for a given value of total angular momentum and parity Jπ a coupled basis is constructed and the RPA matrix is diagonalized (protons and neutrons are treated explicitly, and no approximation related to the use of isospin formalism is introduced). The transition amplitudes and transition strengths associated to given external operators are calculated. The HF densities and RPA transition densities are also evaluated. Restrictions: The main restrictions are related to the assumed spherical symmetry and absence of pairing correlations. Running time: The typical running time depends strongly on the nucleus, on the multipolarity, on the choice of the model space and of course on the computer. It can vary from a few minutes to several hours.

Long-range-corrected Rung 3.5 density functional approximations

NASA Astrophysics Data System (ADS)

Janesko, Benjamin G.; Proynov, Emil; Scalmani, Giovanni; Frisch, Michael J.

2018-03-01

Rung 3.5 functionals are a new class of approximations for density functional theory. They provide a flexible intermediate between exact (Hartree-Fock, HF) exchange and semilocal approximations for exchange. Existing Rung 3.5 functionals inherit semilocal functionals' limitations in atomic cores and density tails. Here we address those limitations using range-separated admixture of HF exchange. We present three new functionals. LRC-ωΠLDA combines long-range HF exchange with short-range Rung 3.5 ΠLDA exchange. SLC-ΠLDA combines short- and long-range HF exchange with middle-range ΠLDA exchange. LRC-ωΠLDA-AC incorporates a combination of HF, semilocal, and Rung 3.5 exchange in the short range, based on an adiabatic connection. We test these in a new Rung 3.5 implementation including up to analytic fourth derivatives. LRC-ωΠLDA and SLC-ΠLDA improve atomization energies and reaction barriers by a factor of 8 compared to the full-range ΠLDA. LRC-ωΠLDA-AC brings further improvement approaching the accuracy of standard long-range corrected schemes LC-ωPBE and SLC-PBE. The new functionals yield highest occupied orbital energies closer to experimental ionization potentials and describe correctly the weak charge-transfer complex of ethylene and dichlorine and the hole-spin distribution created by an Al defect in quartz. This study provides a framework for more flexible range-separated Rung 3.5 approximations.

Theoretical hyperfine structures of 19F i and 17O i

NASA Astrophysics Data System (ADS)

Aourir, Nouria; Nemouchi, Messaoud; Godefroid, Michel; Jönsson, Per

2018-03-01

Multiconfiguration Hartree-Fock (MCHF) and multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations are performed for the 2 p5P2o , 2 p4(3P ) 3 s 4P , 2 p4(3P ) 3 s 2P , and 2 p4(3P ) 3 p 4So states of 19F i to determine their hyperfine constants. Several computing strategies are considered to investigate electron correlation and relativistic effects. High-order correlation contributions are included in MCHF calculations based on single and double multireference expansions. The largest components of the single reference MCHF wave functions are selected to define the multireference (MR) sets. In this scheme, relativistic corrections are evaluated in the Breit-Pauli approximation. A similar strategy is used for the calculation of MCDHF relativistic wave functions and hyperfine parameters. While correlation and relativistic corrections are found to be rather small for the ground state, we highlight large relativistic effects on the hyperfine constant A3 /2 of 2 p4(3P ) 3 p 4So and, to a lesser extent, on A1 /2 of 2 p4(3P ) 3 s 4P . As expected for such a light system, electron correlation effects dominate over relativity in the calculation of the hyperfine interaction of all other levels considered. We also revisit the hyperfine constants of 2 p3(4S ) 3 s S5o and 2 p3(4S ) 3 p 5P in 17O using similar strategies. The results are found to be in excellent agreement with experiment.

The molecular structure and vibrational spectra of N-(2,2-diphenylacetyl)- N'-(naphthalen-1yl)-thiourea by Hartree-Fock and density functional methods

NASA Astrophysics Data System (ADS)

Arslan, Hakan; Mansuroglu, Demet Sezgin; VanDerveer, Don; Binzet, Gun

2009-04-01

N-(2,2-Diphenylacetyl)- N'-(naphthalen-1yl)-thiourea (PANT) has been synthesized and characterized by elemental analysis, IR spectroscopy and 1H NMR spectroscopy. The crystal and molecular structure of the title compound has been determined from single crystal X-ray diffraction data. It crystallizes in the triclinic space group P-1, Z = 2 with a = 10.284(2) Å, b = 10.790(2) Å, c = 11.305(2) Å, α = 64.92(3)°, β = 89.88(3)°, γ = 62.99(3)°, V = 983.7(3) Å 3 and Dcalc = 1.339 Mg/m 3. The molecular structure, vibrational frequencies and infrared intensities of PANT were calculated by the Hartree-Fock and density functional theory methods (BLYP and B3LYP) using the 6-31G* basis set. The calculated geometric parameters were compared to the corresponding X-ray structure of the title compound. We obtained 22 stable conformers for the title compound; however Conformer 1 is approximately 9.53 kcal/mol more stable than Conformer 22. The comparison of the theoretical and experimental geometry of the title compound shows that the X-ray parameters fairly well reproduce the geometry of Conformer 17. The harmonic vibrations computed for this compound by the B3LYP/6-31G* method are in good agreement with the observed IR spectral data. Theoretical vibrational spectra of the title compound were interpreted by means of PEDs using the VEDA 4 program. A general better performance of the investigated methods was calculated by PAVF 1.0 program.

Sharp threshold of blow-up and scattering for the fractional Hartree equation

NASA Astrophysics Data System (ADS)

Guo, Qing; Zhu, Shihui

2018-02-01

We consider the fractional Hartree equation in the L2-supercritical case, and find a sharp threshold of the scattering versus blow-up dichotomy for radial data: If M[u0 ]s -sc/sc E [u0 ] < M[ Q ]s -sc/sc E [ Q ] and M[u0 ]s -sc/sc ‖u0‖ H˙s 2 < M[ Q ]s -sc/sc ‖Q‖ H˙s 2 , then the solution u (t) is globally well-posed and scatters; if M[u0 ]s -sc/sc E [u0 ] < M[ Q ]s -sc/sc E [ Q ] and M[u0 ]s -sc/sc ‖u0‖ H˙s 2 > M[ Q ]s -sc/sc ‖Q‖ H˙s 2 , the solution u (t) blows up in finite time. This condition is sharp in the sense that the solitary wave solution eit Q (x) is global but not scattering, which satisfies the equality in the above conditions. Here, Q is the ground-state solution for the fractional Hartree equation.

Investigation of nuclear structure of 30-44S isotopes using spherical and deformed Skyrme-Hartree-Fock method

NASA Astrophysics Data System (ADS)

Alzubadi, A. A.

2015-06-01

Nuclear many-body system is usually described by a mean-field built upon a nucleon-nucleon effective interaction. In this work, we investigate ground state properties of the sulfur isotopes covering a wide range from the line of stability up to the dripline region (30-44S). For this purpose the Hartree-Fock mean field theory in coordinate space with a Skyrme parameterization SkM* has been utilized. In particular, we calculate the nuclear charge, neutrons, protons, mass densities, the associated radii, neutron skin thickness and binding energy. The charge form factors have been also investigated using SkM*, SkO, SkE, SLy4 and Skxs15 Skyrme parameterizations and the results obtained using the theoretical approach are compared with the available experimental data. To investigate the potential energy surface as a function of the quadrupole deformation for isotopic sulfur chains, Skyrme-Hartree-Fock-Bogoliubov theory has been adopted with SLy4 parameterization.

Analytic model of a multi-electron atom

NASA Astrophysics Data System (ADS)

Skoromnik, O. D.; Feranchuk, I. D.; Leonau, A. U.; Keitel, C. H.

2017-12-01

A fully analytical approximation for the observable characteristics of many-electron atoms is developed via a complete and orthonormal hydrogen-like basis with a single-effective charge parameter for all electrons of a given atom. The basis completeness allows us to employ the secondary-quantized representation for the construction of regular perturbation theory, which includes in a natural way correlation effects, converges fast and enables an effective calculation of the subsequent corrections. The hydrogen-like basis set provides a possibility to perform all summations over intermediate states in closed form, including both the discrete and continuous spectra. This is achieved with the help of the decomposition of the multi-particle Green function in a convolution of single-electronic Coulomb Green functions. We demonstrate that our fully analytical zeroth-order approximation describes the whole spectrum of the system, provides accuracy, which is independent of the number of electrons and is important for applications where the Thomas-Fermi model is still utilized. In addition already in second-order perturbation theory our results become comparable with those via a multi-configuration Hartree-Fock approach.

Particle-hole symmetry in many-body theories of electron correlation

NASA Astrophysics Data System (ADS)

Kats, Daniel; Usvyat, Denis; Manby, Frederick R.

2018-06-01

Second-quantised creation and annihilation operators for fermionic particles anticommute, but the same is true for the creation and annihilation operators for holes. This introduces a symmetry into the quantum theory of fermions that is absent for bosons. In ab initio electronic structure theory, it is common to classify methods by the number of electrons for which the method returns exact results: for example Hartree-Fock theory is exact for one-electron systems, whereas coupled-cluster theory with single and double excitations is exact for two-electron systems. Here, we discuss the generalisation: methods based on approximate wavefunctions that are exact for n-particle systems are also exact for n-hole systems. Novel electron correlation methods that attempt to improve on the coupled-cluster framework sometimes retain this property, and sometimes lose it. Here, we argue for retaining particle-hole symmetry as a desirable design criterion of approximate electron correlation methods. Dispensing with it might lead to loss of n-representability of density matrices, and this in turn can lead to spurious long-range behaviour in the correlation energy.

Electronic wave function and binding effects in M-shell ionization of gold by protons

NASA Astrophysics Data System (ADS)

Pajek, M.; Banaś, D.; Jabłoński, Ł.; Mukoyama, T.

2018-02-01

The measured M-X-ray production cross sections for protons, which are used in the particle induced X-ray emission (PIXE) technique, are systematically underestimated for low impact energies by the ECPSSR and ECUSAR theories. These theories, which are based on the plane wave Born approximation (PWBA) and use the screened hydrogenic wave functions, include corrections for the projectile Coulomb deflection and electron relativistic and binding effects. In the present paper, in order to interpret the observed disagreement at low impact energies, the systematic calculations of the M-shell ionization cross sections for gold were performed using the semiclassical (SCA) and the binary encounter (BEA) approximations in order to identify a role of the electronic wave function and electron binding effects. In these calculations the different wave functions, from nonrelativistic hydrogenic to selfconsistent Dirac-Hartree-Fock, were considered and the binding effect was treated within extreme separated- (SA) and united-atoms (UA) limits. The results are discussed in details and the observed discrepancies are attributed to inadequate description of the electron binding effect at the lowest impact energies for which the molecular approach is required.

When Density Functional Approximations Meet Iron Oxides.

PubMed

Meng, Yu; Liu, Xing-Wu; Huo, Chun-Fang; Guo, Wen-Ping; Cao, Dong-Bo; Peng, Qing; Dearden, Albert; Gonze, Xavier; Yang, Yong; Wang, Jianguo; Jiao, Haijun; Li, Yongwang; Wen, Xiao-Dong

2016-10-11

Three density functional approximations (DFAs), PBE, PBE+U, and Heyd-Scuseria-Ernzerhof screened hybrid functional (HSE), were employed to investigate the geometric, electronic, magnetic, and thermodynamic properties of four iron oxides, namely, α-FeOOH, α-Fe 2 O 3 , Fe 3 O 4 , and FeO. Comparing our calculated results with available experimental data, we found that HSE (a = 0.15) (containing 15% "screened" Hartree-Fock exchange) can provide reliable values of lattice constants, Fe magnetic moments, band gaps, and formation energies of all four iron oxides, while standard HSE (a = 0.25) seriously overestimates the band gaps and formation energies. For PBE+U, a suitable U value can give quite good results for the electronic properties of each iron oxide, but it is challenging to accurately get other properties of the four iron oxides using the same U value. Subsequently, we calculated the Gibbs free energies of transformation reactions among iron oxides using the HSE (a = 0.15) functional and plotted the equilibrium phase diagrams of the iron oxide system under various conditions, which provide reliable theoretical insight into the phase transformations of iron oxides.

Relativistic coupled-cluster-theory analysis of energies, hyperfine-structure constants, and dipole polarizabilities of Cd+

NASA Astrophysics Data System (ADS)

Li, Cheng-Bin; Yu, Yan-Mei; Sahoo, B. K.

2018-02-01

Roles of electron correlation effects in the determination of attachment energies, magnetic-dipole hyperfine-structure constants, and electric-dipole (E 1 ) matrix elements of the low-lying states in the singly charged cadmium ion (Cd+) have been analyzed. We employ the singles and doubles approximated relativistic coupled-cluster (RCC) method to calculate these properties. Intermediate results from the Dirac-Hartree-Fock approximation,the second-order many-body perturbation theory, and considering only the linear terms of the RCC method are given to demonstrate propagation of electron correlation effects in this ion. Contributions from important RCC terms are also given to highlight the importance of various correlation effects in the evaluation of these properties. At the end, we also determine E 1 polarizabilities (αE 1) of the ground and 5 p 2P1 /2 ;3 /2 states of Cd+ in the ab initio approach. We estimate them again by replacing some of the E 1 matrix elements and energies from the measurements to reduce their uncertainties so that they can be used in the high-precision experiments of this ion.

The effective local potential method: Implementation for molecules and relation to approximate optimized effective potential techniques

NASA Astrophysics Data System (ADS)

Izmaylov, Artur F.; Staroverov, Viktor N.; Scuseria, Gustavo E.; Davidson, Ernest R.; Stoltz, Gabriel; Cancès, Eric

2007-02-01

We have recently formulated a new approach, named the effective local potential (ELP) method, for calculating local exchange-correlation potentials for orbital-dependent functionals based on minimizing the variance of the difference between a given nonlocal potential and its desired local counterpart [V. N. Staroverov et al., J. Chem. Phys. 125, 081104 (2006)]. Here we show that under a mildly simplifying assumption of frozen molecular orbitals, the equation defining the ELP has a unique analytic solution which is identical with the expression arising in the localized Hartree-Fock (LHF) and common energy denominator approximations (CEDA) to the optimized effective potential. The ELP procedure differs from the CEDA and LHF in that it yields the target potential as an expansion in auxiliary basis functions. We report extensive calculations of atomic and molecular properties using the frozen-orbital ELP method and its iterative generalization to prove that ELP results agree with the corresponding LHF and CEDA values, as they should. Finally, we make the case for extending the iterative frozen-orbital ELP method to full orbital relaxation.

Optimizing phonon space in the phonon-coupling model

NASA Astrophysics Data System (ADS)

Tselyaev, V.; Lyutorovich, N.; Speth, J.; Reinhard, P.-G.

2017-08-01

We present a new scheme to select the most relevant phonons in the phonon-coupling model, named here the time-blocking approximation (TBA). The new criterion, based on the phonon-nucleon coupling strengths rather than on B (E L ) values, is more selective and thus produces much smaller phonon spaces in the TBA. This is beneficial in two respects: first, it curbs the computational cost, and second, it reduces the danger of double counting in the expansion basis of the TBA. We use here the TBA in a form where the coupling strength is regularized to keep the given Hartree-Fock ground state stable. The scheme is implemented in a random-phase approximation and TBA code based on the Skyrme energy functional. We first explore carefully the cutoff dependence with the new criterion and can work out a natural (optimal) cutoff parameter. Then we use the freshly developed and tested scheme for a survey of giant resonances and low-lying collective states in six doubly magic nuclei looking also at the dependence of the results when varying the Skyrme parametrization.

Approximate solution of the mode-mode coupling integral: Application to cytosine and its deuterated derivative.

PubMed

Rasheed, Tabish; Ahmad, Shabbir

2010-10-01

Ab initio Hartree-Fock (HF), density functional theory (DFT) and second-order Møller-Plesset (MP2) methods were used to perform harmonic and anharmonic calculations for the biomolecule cytosine and its deuterated derivative. The anharmonic vibrational spectra were computed using the vibrational self-consistent field (VSCF) and correlation-corrected vibrational self-consistent field (CC-VSCF) methods. Calculated anharmonic frequencies have been compared with the argon matrix spectra reported in literature. The results were analyzed with focus on the properties of anharmonic couplings between pair of modes. A simple and easy to use formula for calculation of mode-mode coupling magnitudes has been derived. The key element in present approach is the approximation that only interactions between pairs of normal modes have been taken into account, while interactions of triples or more are neglected. FTIR and Raman spectra of solid state cytosine have been recorded in the regions 400-4000 cm(-1) and 60-4000 cm(-1), respectively. Vibrational analysis and assignments are based on calculated potential energy distribution (PED) values. Copyright 2010 Elsevier B.V. All rights reserved.

Mulliken's populations and electron momentum densities of transition metal tungstates using LCAO scheme

NASA Astrophysics Data System (ADS)

Meena, B. S.; Heda, N. L.; Ahuja, B. L.

2018-05-01

We have computed the Mulliken's populations (MP) and electron momentum densities (EMDs) for TMWO4 (TM=Co, Ni, Cu and Zn) using linear combination of atomic orbitals (LCAO) scheme. The latest hybridization of Hartree-Fock (HF) and density functional theory (DFT) under the framework of LCAO approximations (so called WC1LYP and B1WC) have been employed. The theoretical EMDs have been compared with the available experimental data which show that WC1LYP scheme gives slightly better agreement with the experimental data for all the reported tungstates. Such trend shows the applicability of Lee-Yang-Parr (LYP) correlation energies within hybrid approximations in predicting the electronic properties of these compounds. Further, the MP data show the charge transfer from Co/Ni/Cu/Zn and W to O atoms. In addition, we have plotted the total EMDs at the same normalized area which show almost similar type of localization of 3d electrons (in real space) of Cu and Zn, which is lower than that of Ni and Co atoms in their tungstates environment.

Self-consistent field calculations of conductance through conjugated molecules at finite bias

NASA Astrophysics Data System (ADS)

Paulsson, Magnus; Stafström, Sven

2001-03-01

Conductance through conjugated molecules have previously been calculated for a large number of systems using the Landauer formula but only a few calculations have included charging effects. In this study we present calculations in the mean field approximation of the conductance of metal-molecule-metal systems using two different kinds of molecules for a large number of configurations and applied biases. The molecules are described in the Pariser-Parr Pople model. Current-voltage (I-V) characteristics and charge distribution of the molecule connected by one dimensional leads to reservoirs is solved within the Hartree-Fock approximation. Charging of the molecule occurs when the chemical potential of the reservoirs approach the resonant tunneling levels. The ensuing potential difference, due to the charging, shifts the tunneling peaks which affects the I-V curves considerably. Asymmetrical interaction with the metal leads, e.g. molecule on a metal surface contacted with an STM-tip, also give asymmetrical I-V curves where the potential of the molecule is shown to more closely follow the potential of the surface. Negative differential conductance is discussed in systems consisting of two weakly coupled molecules.

A meta-GGA level screened range-separated hybrid functional by employing short range Hartree-Fock with a long range semilocal functional.

PubMed

Jana, Subrata; Samal, Prasanjit

2018-03-28

The range-separated hybrid density functionals are very successful in describing a wide range of molecular and solid-state properties accurately. In principle, such functionals are designed from spherically averaged or system averaged as well as reverse engineered exchange holes. In the present attempt, the screened range-separated hybrid functional scheme has been applied to the meta-GGA rung by using the density matrix expansion based semilocal exchange hole (or functional). The hybrid functional proposed here utilizes the spherically averaged density matrix expansion based exchange hole in the range separation scheme. For slowly varying density correction the range separation scheme is employed only through the local density approximation based exchange hole coupled with the corresponding fourth order gradient approximate Tao-Mo enhancement factor. The comprehensive testing and performance of the newly constructed functional indicates its applicability in describing several molecular properties. The most appealing feature of this present screened hybrid functional is that it will be practically very useful in describing solid-state properties at the meta-GGA level.

Calculation of longitudinal polarizability and second hyperpolarizability of polyacetylene with the coupled perturbed Hartree-Fock/Kohn-Sham scheme: Where it is shown how finite oligomer chains tend to the infinite periodic polymer

NASA Astrophysics Data System (ADS)

Lacivita, Valentina; Rèrat, Michel; Orlando, Roberto; Ferrero, Mauro; Dovesi, Roberto

2012-03-01

The longitudinal polarizability, αxx, and second hyperpolarizability, γxxxx, of polyacetylene are evaluated by using the coupled perturbed Hartree-Fock/Kohn-Sham (HF/KS) scheme as implemented in the periodic CRYSTAL code and a split valence type basis set. Four different density functionals, namely local density approximation (LDA) (pure local), Perdew-Becke-Ernzerhof (PBE) (gradient corrected), PBE0, and B3LYP (hybrid), and the Hartree-Fock Hamiltonian are compared. It is shown that very tight computational conditions must be used to obtain well converged results, especially for γxxxx, that is, very sensitive to the number of k points in reciprocal space when the band gap is small (as for LDA and PBE), and to the extension of summations of the exact exchange series (HF and hybrids). The band gap in LDA is only 0.01 eV: at least 300 k points are required to obtain well converged total energy and equilibrium geometry, and 1200 for well converged optical properties. Also, the exchange series convergence is related to the band gap. The PBE0 band gap is as small as 1.4 eV and the exchange summation must extend to about 130 Å from the origin cell. Total energy, band gap, equilibrium geometry, polarizability, and second hyperpolarizability of oligomers -(C2H2)m-, with m up to 50 (202 atoms), and of the polymer have been compared. It turns out that oligomers of that length provide an extremely poor representation of the infinite chain polarizability and hyperpolarizability when the gap is smaller than 0.2 eV (that is, for LDA and PBE). Huge differences are observed on αxx and γxxxx of the polymer when different functionals are used, that is in connection to the well-known density functional theory (DFT) overshoot, reported in the literature about short oligomers: for the infinite model the ratio between LDA (or PBE) and HF becomes even more dramatic (about 500 for αxx and 1010 for γxxxx). On the basis of previous systematic comparisons of results obtained with various approaches including DFT, HF, Moller-Plesset (MP2) and coupled cluster for finite chains, we can argue that, for the infinite chain, the present HF results are the most reliable.

Electron scattering from excited states of hydrogen: Implications for the ionization threshold law

NASA Astrophysics Data System (ADS)

Temkin, A.; Shertzer, J.

2013-05-01

The elastic scattering wave function for electrons scattered from the Nth excited state of hydrogen is the final state of the matrix element for excitation of that state. This paper deals with the solution of that problem primarily in the context of the Temkin-Poet (TP) model [A. Temkin, Phys. Rev.PHRVAO0031-899X10.1103/PhysRev.126.130 126, 130 (1962); R. Poet, J. Phys. BJPAPEH0022-370010.1088/0022-3700/11/17/019 11, 3081 (1978)], wherein only the radial parts of the interaction are included. The relevant potential for the outer electron is dominated by the Hartree potential, VNH(r). In the first part of the paper, VNH(r) is approximated by a potential WN(r), for which the scattering equation can be analytically solved. The results allow formal analytical continuation of N into the continuum, so that the ionization threshold law can be deduced. Because the analytic continuation involves going from N to an imaginary function of the momentum of the inner electron, the threshold law turns out to be an exponentially damped function of the available energy E, in qualitative accord with the result of Macek and Ihra [J. H. Macek and W. Ihra, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.55.2024 55, 2024 (1997)] for the TP model. Thereafter, the scattering equation for the Hartree potential VNH(r) is solved numerically. The numerical aspects of these calculations have proven to be challenging and required several developments for the difficulties to be overcome. The results for VNH(r) show only a simple energy-dependent shift from the approximate potential WN(r), which therefore does not change the analytic continuation and the form of the threshold law. It is concluded that the relevant optical potential must be included in order to compare directly with the analytic result of Macek and Ihra. The paper concludes with discussions of (a) a quantum mechanical interpretation of the result, and (b) the outlook of this approach for the complete problem.

Electric dipole transitions for four-times ionized cerium (Ce V)

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

Usta, Betül Karaçoban, E-mail: bkaracoban@sakarya.edu.tr; Akgün, Elif, E-mail: elif.akgun@ogr.sakarya.edu.tr; Alparslan, Büşra, E-mail: busra.alparslan1@ogr.sakarya.edu.tr

2016-03-25

We have calculated the transition parameters, such as wavelengths, oscillator strengths, and transition probabilities (or rates), for the electric dipole (E1) transitions in four-times ionized cerium (Ce V, Z = 58) by using the multiconfiguration Hartree-Fock method within the framework of Breit-Pauli (MCHF+BP) relativistic corrections and the relativistic Hartree-Fock (HFR) method. The obtained results have been compared with other works available in literature. A discussion of these calculations for Ce V in this study has also been in view of the MCHF+BP and HFR methods.

Second-Order Moller-Plesset Perturbation Theory for Molecular Dirac-Hartree-Fock Wave Functions

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.; Arnold, James O. (Technical Monitor)

1994-01-01

Moller-Plesset perturbation theory is developed to second order for a selection of Kramers restricted Dirac-Hartree-Fock closed and open-shell reference wave functions. The open-shell wave functions considered are limited to those with no more than two electrons in open shells, but include the case of a two-configuration SCF reference. Denominator shifts are included in the style of Davidson's OPT2 method. An implementation which uses unordered integrals with labels is presented, and results are given for a few test cases.

Extension of many-body theory and approximate density functionals to fractional charges and fractional spins.

PubMed

Yang, Weitao; Mori-Sánchez, Paula; Cohen, Aron J

2013-09-14

The exact conditions for density functionals and density matrix functionals in terms of fractional charges and fractional spins are known, and their violation in commonly used functionals has been shown to be the root of many major failures in practical applications. However, approximate functionals are designed for physical systems with integer charges and spins, not in terms of the fractional variables. Here we develop a general framework for extending approximate density functionals and many-electron theory to fractional-charge and fractional-spin systems. Our development allows for the fractional extension of any approximate theory that is a functional of G(0), the one-electron Green's function of the non-interacting reference system. The extension to fractional charge and fractional spin systems is based on the ensemble average of the basic variable, G(0). We demonstrate the fractional extension for the following theories: (1) any explicit functional of the one-electron density, such as the local density approximation and generalized gradient approximations; (2) any explicit functional of the one-electron density matrix of the non-interacting reference system, such as the exact exchange functional (or Hartree-Fock theory) and hybrid functionals; (3) many-body perturbation theory; and (4) random-phase approximations. A general rule for such an extension has also been derived through scaling the orbitals and should be useful for functionals where the link to the Green's function is not obvious. The development thus enables the examination of approximate theories against known exact conditions on the fractional variables and the analysis of their failures in chemical and physical applications in terms of violations of exact conditions of the energy functionals. The present work should facilitate the calculation of chemical potentials and fundamental bandgaps with approximate functionals and many-electron theories through the energy derivatives with respect to the fractional charge. It should play an important role in developing accurate approximate density functionals and many-body theory.

Comparative study of the requantization of the time-dependent mean field for the dynamics of nuclear pairing

NASA Astrophysics Data System (ADS)

Ni, Fang; Nakatsukasa, Takashi

2018-04-01

To describe quantal collective phenomena, it is useful to requantize the time-dependent mean-field dynamics. We study the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory for the two-level pairing Hamiltonian, and compare results of different quantization methods. The one constructing microscopic wave functions, using the TDHFB trajectories fulfilling the Einstein-Brillouin-Keller quantization condition, turns out to be the most accurate. The method is based on the stationary-phase approximation to the path integral. We also examine the performance of the collective model which assumes that the pairing gap parameter is the collective coordinate. The applicability of the collective model is limited for the nuclear pairing with a small number of single-particle levels, because the pairing gap parameter represents only a half of the pairing collective space.

Entanglement and magnetism in high-spin graphene nanodisks

NASA Astrophysics Data System (ADS)

Hagymási, I.; Legeza, Ö.

2018-01-01

We investigate the ground-state properties of triangular graphene nanoflakes with zigzag edge configurations. The description of zero-dimensional nanostructures requires accurate many-body techniques since the widely used density-functional theory with local density approximation or Hartree-Fock methods cannot handle the strong quantum fluctuations. Applying the unbiased density-matrix renormalization group algorithm we calculate the magnetization and entanglement patterns with high accuracy for different interaction strengths and compare them to the mean-field results. With the help of quantum information analysis and subsystem density matrices we reveal that the edges are strongly entangled with each other. We also address the effect of electron and hole doping and demonstrate that the magnetic properties of triangular nanoflakes can be controlled by an electric field, which reveals features of flat-band ferromagnetism. This may open up new avenues in graphene based spintronics.

Dynamical photoionization observables of the CS molecule: The role of electron correlation

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

Ponzi, Aurora; Coriani, Sonia; Decleva, Piero

2014-05-28

Highly correlated calculations are performed on the primary ionic states and the prominent satellite present in the outer valence photoelectron spectrum of carbon monosulfide (CS). Dyson orbitals are coupled to accurate one particle continuum orbitals to provide a correlated description of energy dependent cross sections, asymmetry parameters, branching ratios, and molecular frame photoelectron angular distributions. The comparison with results obtained at the Hartree-Fock and Density Functional Theory level shows the strong sensitivity of these observables to details of the correlation in the bound states. The behaviour of the well characterized satellite state is analyzed in detail, and shows differences frommore » the relevant primary states, revealing the limitations of a simple intensity borrowing mechanism. The results resolve the intensity disagreement with experiment obtained at the level of the sudden approximation.« less

Modulational Instability and Quantum Discrete Breather States of Cold Bosonic Atoms in a Zig-Zag Optical Lattice

NASA Astrophysics Data System (ADS)

Chang, Xia; Xie, Jiayu; Wu, Tianle; Tang, Bing

2018-07-01

A theoretical study on modulational instability and quantum discrete breather states in a system of cold bosonic atoms in zig-zag optical lattices is presented in this work. The time-dependent Hartree approximation is employed to deal with the multiple body problem. By means of a linear stability analysis, we analytically study the modulational instability, and estimate existence conditions of the bright stationary localized solutions for different values of the second-neighbor hopping constant. On the other hand, we get analytical bright stationary localized solutions, and analyze the influence of the second-neighbor hopping on their existence conditions. The predictions of the modulational instability analysis are shown to be reliable. Using these stationary localized single-boson wave functions, the quantum breather states corresponding to the system with different types of nonlinearities are constructed.

Impact of Many-Body Effects on Landau Levels in Graphene

NASA Astrophysics Data System (ADS)

Sonntag, J.; Reichardt, S.; Wirtz, L.; Beschoten, B.; Katsnelson, M. I.; Libisch, F.; Stampfer, C.

2018-05-01

We present magneto-Raman spectroscopy measurements on suspended graphene to investigate the charge carrier density-dependent electron-electron interaction in the presence of Landau levels. Utilizing gate-tunable magnetophonon resonances, we extract the charge carrier density dependence of the Landau level transition energies and the associated effective Fermi velocity vF. In contrast to the logarithmic divergence of vF at zero magnetic field, we find a piecewise linear scaling of vF as a function of the charge carrier density, due to a magnetic-field-induced suppression of the long-range Coulomb interaction. We quantitatively confirm our experimental findings by performing tight-binding calculations on the level of the Hartree-Fock approximation, which also allow us to estimate an excitonic binding energy of ≈6 meV contained in the experimentally extracted Landau level transitions energies.

The Effect of Ionospheric Models on Electromagnetic Pulse Locations

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

Fenimore, Edward E.; Triplett, Laurie A.

2014-07-01

Locations of electromagnetic pulses (EMPs) determined by time-of-arrival (TOA) often have outliers with significantly larger errors than expected. In the past, these errors were thought to arise from high order terms in the Appleton-Hartree equation. We simulated 1000 events randomly spread around the Earth into a constellation of 22 GPS satellites. We used four different ionospheres: “simple” where the time delay goes as the inverse of the frequency-squared, “full Appleton-Hartree”, the “BobRD integrals” and a full raytracing code. The simple and full Appleton-Hartree ionospheres do not show outliers whereas the BobRD and raytracing do. This strongly suggests that the causemore » of the outliers is not additional terms in the Appleton-Hartree equation, but rather is due to the additional path length due to refraction. A method to fix the outliers is suggested based on fitting a time to the delays calculated at the 5 GPS frequencies with BobRD and simple ionospheres. The difference in time is used as a correction to the TOAs.« less

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

Molecular modeling studies of interactions between sodium polyacrylate polymer and calcite surface

NASA Astrophysics Data System (ADS)

Ylikantola, A.; Linnanto, J.; Knuutinen, J.; Oravilahti, A.; Toivakka, M.

2013-07-01

The interactions between calcite pigment and sodium polyacrylate dispersing agent, widely used in papermaking as paper coating components, were investigated using classical force field and quantum chemical approaches. The objective was to understand interactions between the calcite surface and sodium polyacrylate polymer at 300 K using molecular dynamics simulations. A quantum mechanical ab initio Hartree-Fock method was also used to obtain detailed information about the sodium polyacrylate polymer structure. The effect of water molecules (moisture) on the interactions was also examined. Calculations showed that molecular weight, branching and the orientation of sodium polyacrylate polymers influence the interactions between the calcite surface and the polymer. The force field applied, and also water molecules, were found to have an impact on all systems studied. Ab initio Hartree-Fock calculations indicated that there are two types of coordination between sodium atoms and carboxylate groups of the sodium polyacrylate polymer, inter- and intra-carboxylate group coordination. In addition, ab initio Hartree-Fock calculations of the structure of the sodium polyacrylate polymer produced important information regarding interactions between the polymers and carboxylated styrene-butadiene latex particles.

Global Futures: a multithreaded execution model for Global Arrays-based applications

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

Chavarría-Miranda, Daniel; Krishnamoorthy, Sriram; Vishnu, Abhinav

2012-05-31

We present Global Futures (GF), an execution model extension to Global Arrays, which is based on a PGAS-compatible Active Message-based paradigm. We describe the design and implementation of Global Futures and illustrate its use in a computational chemistry application benchmark (Hartree-Fock matrix construction using the Self-Consistent Field method). Our results show how we used GF to increase the scalability of the Hartree-Fock matrix build to up to 6,144 cores of an Infiniband cluster. We also show how GF's multithreaded execution has comparable performance to the traditional process-based SPMD model.

Self-consistent collective coordinate for reaction path and inertial mass

NASA Astrophysics Data System (ADS)

Wen, Kai; Nakatsukasa, Takashi

2016-11-01

We propose a numerical method to determine the optimal collective reaction path for a nucleus-nucleus collision, based on the adiabatic self-consistent collective coordinate (ASCC) method. We use an iterative method, combining the imaginary-time evolution and the finite amplitude method, for the solution of the ASCC coupled equations. It is applied to the simplest case, α -α scattering. We determine the collective path, the potential, and the inertial mass. The results are compared with other methods, such as the constrained Hartree-Fock method, Inglis's cranking formula, and the adiabatic time-dependent Hartree-Fock (ATDHF) method.

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

NASA Technical Reports Server (NTRS)

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

1986-01-01

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

Hartree-Fock studies of hypernuclear properties

NASA Astrophysics Data System (ADS)

Lanskoy, D. E.

1998-08-01

The Skyrme-Hartree-Fock approach is approved as a powerful tool to reproduce general properties of Λ hypernuclear spectra [1-4] and to relate hypernuclear observables to effective interaction features. In this contribution, we consider briefly some less common hypernuclear systems, which appear to be quite sensitive to details of the relevant interactions. Particularly, we address possible manifestations of the polarization of a hypernuclear core (i.e. core distortion due to hyperon addition), which is driven in terms of the Skyrme force mainly by counterbalance between the two-body ΛN force and the three-body ΛNN (or density-dependent ΛN) one.

The Dielectric Permittivity of Crystals in the Reduced Hartree-Fock Approximation

NASA Astrophysics Data System (ADS)

Cancès, Éric; Lewin, Mathieu

2010-07-01

In a recent article (Cancès et al. in Commun Math Phys 281:129-177, 2008), we have rigorously derived, by means of bulk limit arguments, a new variational model to describe the electronic ground state of insulating or semiconducting crystals in the presence of local defects. In this so-called reduced Hartree-Fock model, the ground state electronic density matrix is decomposed as {γ = γ^0_per + Q_{ν,\\varepsilon_F}}, where {γ^0_per} is the ground state density matrix of the host crystal and {Q_{ν,\\varepsilon_F}} the modification of the electronic density matrix generated by a modification ν of the nuclear charge of the host crystal, the Fermi level ɛ F being kept fixed. The purpose of the present article is twofold. First, we study in more detail the mathematical properties of the density matrix {Q_{ν,\\varepsilon_F}} (which is known to be a self-adjoint Hilbert-Schmidt operator on {L^2(mathbb{R}^3)}). We show in particular that if {int_{mathbb{R}^3} ν neq 0, Q_{ν,\\varepsilon_F}} is not trace-class. Moreover, the associated density of charge is not in {L^1(mathbb{R}^3)} if the crystal exhibits anisotropic dielectric properties. These results are obtained by analyzing, for a small defect ν, the linear and nonlinear terms of the resolvent expansion of {Q_{ν,\\varepsilon_F}}. Second, we show that, after an appropriate rescaling, the potential generated by the microscopic total charge (nuclear plus electronic contributions) of the crystal in the presence of the defect converges to a homogenized electrostatic potential solution to a Poisson equation involving the macroscopic dielectric permittivity of the crystal. This provides an alternative (and rigorous) derivation of the Adler-Wiser formula.

A poly-epoxy surface explored by Hartree-Fock ΔSCF simulations of C1s XPS spectra

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

Gavrielides, A.; Duguet, T., E-mail: thomas.duguet@ensiacet.fr, E-mail: Paul.Bagus@unt.edu; Esvan, J.

Whereas poly-epoxy polymers represent a class of materials with a wide range of applications, the structural disorder makes them difficult to model. In the present work, we use good experimental model samples in the sense that they are pure, fully polymerized, flat and smooth, defect-free, and suitable for ultrahigh vacuum x-ray photoelectron spectroscopy, XPS, experiments. In parallel, we perform Hartree-Fock, HF, calculations of the binding energies, BEs, of the C1s electrons in a model molecule composed of the two constituents of the poly-epoxy sample. These C1s BEs were determined using the HF ΔSCF method, which is known to yield accuratemore » values, especially for the shifts of the BEs, ΔBEs. We demonstrate the benefits of combining rigorous theory with careful XPS measurements in order to obtain correct assignments of the C1s XPS spectra of the polymer sample. Both the relative binding energies—by the ΔSCF method—and relative intensities—in the sudden approximation, SA, are calculated. It results in an excellent match with the experimental spectra. We are able to identify 9 different chemical environments under the C1s peak, where an exclusively experimental work would have found only 3 contributions. In addition, we observe that some contributions are localized at discrete binding energies, whereas others allow a much wider range because of the variation of their second neighbor bound polarization. Therefore, HF-ΔSCF simulations significantly increase the spectral resolution of XPS and thus offer a new avenue for the exploration of the surface of polymers.« less

A Hartree-Fock-Bogoliubov mass formula

NASA Astrophysics Data System (ADS)

Samyn, M.; Goriely, S.; Heenen, P.-H.; Pearson, J. M.; Tondeur, F.

2002-03-01

In order to have more reliable predictions of nuclear masses at the neutron drip line, we here go beyond the recent mass formula HFBCS-1 and present a new mass formula, HFB-1, based on the Hartree-Fock-Bogoliubov method. As with the HFBCS-1 mass formula, we use a 10-parameter Skyrme force along with a 4-parameter δ-function pairing force and a 2-parameter phenomenological Wigner term. However, with the original HFBCS-1 Skyrme force (MSk7), the rms error becomes unacceptably large and a new force fit is required. With the isoscalar and isovector effective masses constrained to be equal, the remaining 15 degrees of freedom are fitted to the masses of all the 1754 measured nuclei with A⩾16, | N- Z|>2 given in the 1995 Audi-Wapstra compilation. The rms error with respect to the masses of all the 1888 measured nuclei with Z, N⩾8 is 0.764 MeV. A complete mass table, HFB-1 (available on the Web), has been constructed, giving all nuclei lying between the two drip lines over the range Z, N⩾8 and Z⩽120. A comparison between HFB-1 and HFBCS-1 mass tables shows that the HFBCS model is a very good approximation of the HFB theory, in particular for masses, the extrapolated masses never differing by more than 2 MeV below Z⩽110. We also find that the behaviour of shell gaps far away from the region of beta stability does not depend on whether the HFBCS or HFB methods are used, in particular, no quenching of astrophysical interest arises from replacing the BCS method by the Bogoliubov method.

Effects of structural spin-orbit coupling in two dimensional electron and hole liquids

NASA Astrophysics Data System (ADS)

Chesi, Stefano

The recent interest in spin-dependent phenomena in semiconductor heterostructures motivates our detailed study of the structural spin-orbit coupling present in clean two-dimensional electron and hole liquids. Interesting polarization effects are produced in a system out of equilibrium, as when a finite current flows in the sample. In particular, the consequences of a lateral confinement creating a quasi one-dimensional wire are studied in detail, partially motivated by a recent experimental investigation of the point-contact transmission for two-dimensional holes. We also address the role of the electron-electron interaction in the presence of spin-orbit coupling, which has received little attention in the literature. We discuss the formulation of the Hartree-Fock approximation in the particular case of linear Rashba spin-orbit. We establish the form of the mean-field phase diagram in the homogeneous case, which shows a complex interplay between paramagnetic and ferromagnetic states. The latter can be polarized in the plane or in a transverse direction, and are characterized by a complex spin structure and nontrivial occupation. The generality of the Hartree-Fock method allows a simple treatment of the Pauli spin susceptibility, and the application to different forms of spin-orbit coupling. Correlation corrections can be obtained in an analytic form for particular asymptotic regimes. For linear Rashba spin-orbit we identified the relevance of the large spin-orbit limit, dominated by many-body effects, and explicitly treated the high density limit, in which the system is asymptotically noninteracting. As a special case, we derive a new exact formula for the polarization dependence of the ring-diagram correlation energy.

Neutron densities from a global analysis of medium-energy proton-nucleus elastic scattering

NASA Astrophysics Data System (ADS)

Clark, B. C.; Kerr, L. J.; Hama, S.

2003-05-01

A new method for extracting neutron densities from intermediate-energy elastic proton-nucleus scattering observables uses a global Dirac phenomenological approach based on the relativistic impulse approximation. Datasets for 40Ca, 48Ca, and 208Pb in the energy range from 500 MeV to 1040 MeV are considered. The global fits are successful in reproducing the data and in predicting datasets not included in the analysis. Using this global approach, energy-independent neutron densities are obtained. The vector point proton density distribution ρpv is determined from the empirical charge density after unfolding the proton form factor. The other densities, ρnv, ρps, ρns, are parametrized. This work provides energy-independent values for the rms neutron radius Rn and the neutron skin thickness Sn, in contrast to the energy-dependent values obtained by previous studies. In addition, the results presented in this paper show that the expected rms neutron radius and the skin thickness for 40Ca are accurately reproduced. The values of Rn and Sn obtained from the global fits that we consider to be the most reliable are given as follows: for 40Ca, 3.314>Rn>3.310 fm and -0.063>Sn >-0.067 fm; for 48Ca, 3.459>Rn>3.413 fm and 0.102>Sn>0.056 fm; and for 208Pb, 5.550>Rn>5.522 fm and 0.111>Sn>0.083 fm. These values are in reasonable agreement with nonrelativistic Skyrme-Hartree-Fock models and with relativistic Hartree-Bogoliubov models with density-dependent meson-nucleon couplings. The results from the global fits for 48Ca and 208Pb are generally not in agreement with the usual relativistic mean-field models.

Select-divide-and-conquer method for large-scale configuration interaction

NASA Astrophysics Data System (ADS)

Bunge, Carlos F.; Carbó-Dorca, Ramon

2006-07-01

A select-divide-and-conquer variational method to approximate configuration interaction (CI) is presented. Given an orthonormal set made up of occupied orbitals (Hartree-Fock or similar) and suitable correlation orbitals (natural or localized orbitals), a large N-electron target space S is split into subspaces S0,S1,S2,…,SR. S0, of dimension d0, contains all configurations K with attributes (energy contributions, etc.) above thresholds T0≡{T0egy,T0etc.}; the CI coefficients in S0 remain always free to vary. S1 accommodates Ks with attributes above T1⩽T0. An eigenproblem of dimension d0+d1 for S0+S1 is solved first, after which the last d1 rows and columns are contracted into a single row and column, thus freezing the last d1 CI coefficients hereinafter. The process is repeated with successive Sj(j ⩾2) chosen so that corresponding CI matrices fit random access memory (RAM). Davidson's eigensolver is used R times. The final energy eigenvalue (lowest or excited one) is always above the corresponding exact eigenvalue in S. Threshold values {Tj;j=0,1,2,…,R} regulate accuracy; for large-dimensional S, high accuracy requires S0+S1 to be solved outside RAM. From there on, however, usually a few Davidson iterations in RAM are needed for each step, so that Hamiltonian matrix-element evaluation becomes rate determining. One μhartree accuracy is achieved for an eigenproblem of order 24×106, involving 1.2×1012 nonzero matrix elements, and 8.4×109 Slater determinants.

The nature of excess electrons in anatase and rutile from hybrid DFT and RPA.

PubMed

Spreafico, Clelia; VandeVondele, Joost

2014-12-21

The behavior of excess electrons in undoped and defect free bulk anatase and rutile TiO2 has been investigated by state-of-the-art electronic structure methods including hybrid density functional theory (DFT) and the random phase approximation (RPA). Consistent with experiment, charge trapping and polaron formation is observed in both anatase and rutile. The difference in the anisotropic shape of the polarons is characterized, confirming for anatase the large polaron picture. For anatase, where polaron formation energies are small, charge trapping is observed also with standard hybrid functionals, provided the simulation cell is sufficiently large (864 atoms) to accommodate the lattice relaxation. Even though hybrid orbitals are required as a starting point for RPA in this system, the obtained polaron formation energies are relatively insensitive to the amount of Hartree-Fock exchange employed. The difference in trapping energy between rutile and anatase can be obtained accurately with both hybrid functionals and RPA. Computed activation energies for polaron hopping and delocalization clearly show that anatase and rutile might have different charge transport mechanisms. In rutile, only hopping is likely, whereas in anatase hopping and delocalization are competing. Delocalization will result in conduction-band-like and thus enhanced transport. Anisotropic conduction, in agreement with experimental data, is observed, and results from the tendency to delocalize in the [001] direction in rutile and the (001) plane in anatase. For future work, our calculations serve as a benchmark and suggest RPA on top on hybrid orbitals (PBE0 with 30% Hartree-Fock exchange), as a suitable method to study the rich chemistry and physics of TiO2.

First-principles calculations on anharmonic vibrational frequencies of polyethylene and polyacetylene in the Gamma approximation.

PubMed

Keçeli, Murat; Hirata, So; Yagi, Kiyoshi

2010-07-21

The frequencies of the infrared- and/or Raman-active (k=0) vibrations of polyethylene and polyacetylene are computed by taking account of the anharmonicity in the potential energy surfaces (PESs) and the resulting phonon-phonon couplings explicitly. The electronic part of the calculations is based on Gaussian-basis-set crystalline orbital theory at the Hartree-Fock and second-order Møller-Plesset (MP2) perturbation levels, providing one-, two-, and/or three-dimensional slices of the PES (namely, using the so-called n-mode coupling approximation with n=3), which are in turn expanded in the fourth-order Taylor series with respect to the normal coordinates. The vibrational part uses the vibrational self-consistent field, vibrational MP2, and vibrational truncated configuration-interaction (VCI) methods within the Gamma approximation, which amounts to including only k=0 phonons. It is shown that accounting for both electron correlation and anharmonicity is essential in achieving good agreement (the mean and maximum absolute deviations less than 50 and 90 cm(-1), respectively, for polyethylene and polyacetylene) between computed and observed frequencies. The corresponding values for the calculations including only one of such effects are in excess of 120 and 300 cm(-1), respectively. The VCI calculations also reproduce semiquantitatively the frequency separation and intensity ratio of the Fermi doublet involving the nu(2)(0) fundamental and nu(8)(pi) first overtone in polyethylene.

Time-dependent Gutzwiller theory of magnetic excitations in the Hubbard model

NASA Astrophysics Data System (ADS)

Seibold, G.; Becca, F.; Rubin, P.; Lorenzana, J.

2004-04-01

We use a spin-rotational invariant Gutzwiller energy functional to compute random-phase-approximation-like (RPA) fluctuations on top of the Gutzwiller approximation (GA). The method can be viewed as an extension of the previously developed GA+RPA approach for the charge sector [G. Seibold and J. Lorenzana, Phys. Rev. Lett. 86, 2605 (2001)] with respect to the inclusion of the magnetic excitations. Unlike the charge case, no assumptions about the time evolution of the double occupancy are needed in this case. Interestingly, in a spin-rotational invariant system, we find the correct degeneracy between triplet excitations, showing the consistency of both computations. Since no restrictions are imposed on the symmetry of the underlying saddle-point solution, our approach is suitable for the evaluation of the magnetic susceptibility and dynamical structure factor in strongly correlated inhomogeneous systems. We present a detailed study of the quality of our approach by comparing with exact diagonalization results and show its much higher accuracy compared to the conventional Hartree-Fock+RPA theory. In infinite dimensions, where the GA becomes exact for the Gutzwiller variational energy, we evaluate ferromagnetic and antiferromagnetic instabilities from the transverse magnetic susceptibility. The resulting phase diagram is in complete agreement with previous variational computations.

Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (IV) HFODD (v2.08i): a new version of the program

NASA Astrophysics Data System (ADS)

Dobaczewski, J.; Olbratowski, P.

2004-04-01

We describe the new version (v2.08i) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, all symmetries can be broken, which allows for calculations with angular frequency and angular momentum tilted with respect to the mass distribution. The new version contains an interface to the LAPACK subroutine ZHPEVX. Program summaryTitle of the program:HFODD (v2.08i) Catalogue number: ADTO Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTO Reference in CPC for earlier version of program: J. Dobaczewski and J. Dudek, Comput. Phys. Commun. 131 (2000) 164 (v1.75r) Catalogue number of previous version: ADML Licensing provisions: none Does the new version supersede the previous one: yes Computers on which the program has been tested: SG Power Challenge L, Pentium-II, Pentium-III, AMD-Athlon Operating systems: UNIX, LINUX, Windows-2000 Programming language used: FORTRAN-77 and FORTRAN-90 Memory required to execute with typical data: 10 Mwords No. of bits in a word: The code is written in single-precision for the use on a 64-bit processor. The compiler option -r8 or +autodblpad (or equivalent) has to be used to promote all real and complex single-precision floating-point items to double precision when the code is used on a 32-bit machine. Has the code been vectorised?: Yes No. of bytes in distributed program, including test data, etc.: 265352 No. of lines in distributed program: 52656 Distribution format: tar gzip file Nature of physical problem: The nuclear mean-field and an analysis of its symmetries in realistic cases are the main ingredients of a description of nuclear states. Within the Local Density Approximation, or for a zero-range velocity-dependent Skyrme interaction, the nuclear mean-field is local and velocity dependent. The locality allows for an effective and fast solution of the self-consistent Hartree-Fock equations, even for heavy nuclei, and for various nucleonic (n-particle n-hole) configurations, deformations, excitation energies, or angular momenta. Similar Local Density Approximation in the particle-particle channel, which is equivalent to using a zero-range interaction, allows for a simple implementation of pairing effects within the Hartree-Fock-Bogolyubov method. Method of solution: The program uses the Cartesian harmonic oscillator basis to expand single-particle or single-quasiparticle wave functions of neutrons and protons interacting by means of the Skyrme effective interaction and zero-range pairing interaction. The expansion coefficients are determined by the iterative diagonalization of the mean field Hamiltonians or Routhians which depend non-linearly on the local neutron and proton densities. Suitable constraints are used to obtain states corresponding to a given configuration, deformation or angular momentum. The method of solution has been presented in: J. Dobaczewski, J. Dudek, Comput. Phys. Commun. 102 (1997) 166. Summary of revisions:Two insignificant errors have been corrected. Breaking of all the three plane-reflection symmetries has been implemented. Breaking of all the three time-reversal×plane-reflection symmetries has been implemented. Conservation of parity with simultaneously broken simplex has been implemented. Tilted-axis cranking has been implemented. Cranking with isovector angular frequency has been implemented. Quadratic constraint on tilted angular momentum has been added. Constraint on the vector product of angular frequency and angular momentum has been added. Calculation of surface multipole moments has been added. Constraints on surface multipole moments have been added. Calculation of magnetic moments has been added. Calculation of multipole and surface multipole moments in the center-of-mass reference frame has been added. Calculation of multipole, surface multipole, and magnetic moments in the principal-axes (intrinsic) reference frame has been added. Calculation of angular momenta in the center-of-mass and principal-axes reference frames has been added. New single-particle observables for a diabatic blocking have been added. Solution of the Hartree-Fock-Bogolyubov equations has been implemented. Non-standard spin-orbit energy density has been implemented. Non-standard center-of-mass corrections have been implemented. Definition of the time-odd terms through the Landau parameters has been implemented. Definition of Skyrme forces taken from the literature now includes the force parameters as well as the value of the nucleon mass and the treatment of tensor, spin-orbit, and center-of-mass terms specific to the given force. Interface to the LAPACK subroutine ZHPEVX has been implemented. Computer memory management has been improved by implementing the memory-allocation features available within FORTRAN-90. Restrictions on the complexity of the problem: The main restriction is the CPU time required for calculations of heavy deformed nuclei and for a given precision required. Pairing correlations are only included for even-even nuclei and conserved simplex symmetry. Typical running time: One Hartree-Fock iteration for the superdeformed, rotating, parity conserving state of 15266Dy 86 takes about six seconds on the AMD-Athlon 1600+ processor. Starting from the Woods-Saxon wave functions, about fifty iterations are required to obtain the energy converged within the precision of about 0.1 keV. In case when every value of the angular velocity is converged separately, the complete superdeformed band with precisely determined dynamical moments J(2) can be obtained within forty minutes of CPU on the AMD-Athlon 1600+ processor. This time can be often reduced by a factor of three when a self-consistent solution for a given rotational frequency is used as a starting point for a neighboring rotational frequency. Unusual features of the program: The user must have an access to the NAGLIB subroutine F02AXE, or to the LAPACK subroutines ZHPEV or ZHPEVX, which diagonalize complex hermitian matrices, or provide another subroutine which can perform such a task. The LAPACK subroutines ZHPEV and ZHPEVX can be obtained from the Netlib Repository at University of Tennessee, Knoxville: http://netlib2.cs.utk.edu/cgi-bin/netlibfiles.pl?filename=/lapack/complex16/zhpev.f and http://netlib2.cs.utk.edu/cgi-bin/netlibfiles.pl?filename=/lapack/complex16/zhpevx.f respectively.

Many-body Effects in a Laterally Inhomogeneous Semiconductor Quantum Well

NASA Technical Reports Server (NTRS)

Ning, Cun-Zheng; Li, Jian-Zhong; Biegel, Bryan A. (Technical Monitor)

2002-01-01

Many body effects on conduction and diffusion of electrons and holes in a semiconductor quantum well are studied using a microscopic theory. The roles played by the screened Hartree-Fock (SHE) terms and the scattering terms are examined. It is found that the electron and hole conductivities depend only on the scattering terms, while the two-component electron-hole diffusion coefficients depend on both the SHE part and the scattering part. We show that, in the limit of the ambipolax diffusion approximation, however, the diffusion coefficients for carrier density and temperature are independent of electron-hole scattering. In particular, we found that the SHE terms lead to a reduction of density-diffusion coefficients and an increase in temperature-diffusion coefficients. Such a reduction or increase is explained in terms of a density-and temperature dependent energy landscape created by the bandgap renormalization.

Quantum cluster theory for the polarizable continuum model. I. The CCSD level with analytical first and second derivatives.

PubMed

Cammi, R

2009-10-28

We present a general formulation of the coupled-cluster (CC) theory for a molecular solute described within the framework of the polarizable continuum model (PCM). The PCM-CC theory is derived in its complete form, called PTDE scheme, in which the correlated electronic density is used to have a self-consistent reaction field, and in an approximate form, called PTE scheme, in which the PCM-CC equations are solved assuming the fixed Hartree-Fock solvent reaction field. Explicit forms for the PCM-CC-PTDE equations are derived at the single and double (CCSD) excitation level of the cluster operator. At the same level, explicit equations for the analytical first derivatives of the PCM basic energy functional are presented, and analytical second derivatives are also discussed. The corresponding PCM-CCSD-PTE equations are given as a special case of the full theory.

Is the Pauli exclusion principle the origin of electron localisation?

NASA Astrophysics Data System (ADS)

Rincón, Luis; Torres, F. Javier; Almeida, Rafael

2018-03-01

In this work, we inquire into the origins of the electron localisation as obtained from the information content of the same-spin pair density, γσ, σ(r2∣r1). To this end, we consider systems of non-interacting and interacting identical Fermions contained in two simple 1D potential models: (1) an infinite potential well and (2) the Kronig-Penney periodic potential. The interparticle interaction is considered through the Hartree-Fock approximation as well as the configuration interaction expansion. Morover, the electron localisation is described through the Kullback-Leibler divergence between γσ, σ(r2∣r1) and its associated marginal probability. The results show that, as long as the adopted method properly includes the Pauli principle, the electronic localisation depends only modestly on the interparticle interaction. In view of the latter, one may conclude that the Pauli principle is the main responsible for the electron localisation.

Quantum-chemical investigation of the structures and electronic spectra of the nucleic acid bases at the coupled cluster CC2 level.

PubMed

Fleig, Timo; Knecht, Stefan; Hättig, Christof

2007-06-28

We study the ground-state structures and singlet- and triplet-excited states of the nucleic acid bases by applying the coupled cluster model CC2 in combination with a resolution-of-the-identity approximation for electron interaction integrals. Both basis set effects and the influence of dynamic electron correlation on the molecular structures are elucidated; the latter by comparing CC2 with Hartree-Fock and Møller-Plesset perturbation theory to second order. Furthermore, we investigate basis set and electron correlation effects on the vertical excitation energies and compare our highest-level results with experiment and other theoretical approaches. It is shown that small basis sets are insufficient for obtaining accurate results for excited states of these molecules and that the CC2 approach to dynamic electron correlation is a reliable and efficient tool for electronic structure calculations on medium-sized molecules.

Variational Dirac-Hartree-Fock calculation of the Breit interaction

NASA Astrophysics Data System (ADS)

Goldman, S. P.

1988-04-01

The calculation of the retarded version of the Breit interaction in the context of the VDHF method is discussed. With the use of Slater-type basis functions, all the terms involved can be calculated in closed form. The results are expressed as an expansion in powers of one-electron energy differences and linear combinations of hypergeometric functions. Convergence is fast and high accuracy is obtained with a small number of terms in the expansion even for high values of the nuclear charge. An added advantage is that the lowest order cancellations occurring in the retardation terms are accounted for exactly a priori. A comparison of the number of terms in the total expansion needed for an accuracy of 12 significant digits in the total energy, as well as a comparison of the results with an without retardation and in the local potential approximation, are presented for the carbon isoelectronic sequence.

Pinning of fermionic occupation numbers.

PubMed

Schilling, Christian; Gross, David; Christandl, Matthias

2013-01-25

The Pauli exclusion principle is a constraint on the natural occupation numbers of fermionic states. It has been suspected since at least the 1970s, and only proved very recently, that there is a multitude of further constraints on these numbers, generalizing the Pauli principle. Here, we provide the first analytic analysis of the physical relevance of these constraints. We compute the natural occupation numbers for the ground states of a family of interacting fermions in a harmonic potential. Intriguingly, we find that the occupation numbers are almost, but not exactly, pinned to the boundary of the allowed region (quasipinned). The result suggests that the physics behind the phenomenon is richer than previously appreciated. In particular, it shows that for some models, the generalized Pauli constraints play a role for the ground state, even though they do not limit the ground-state energy. Our findings suggest a generalization of the Hartree-Fock approximation.

Efficient G0W0 using localized basis sets: a benchmark for molecules

NASA Astrophysics Data System (ADS)

Koval, Petr; Per Ljungberg, Mathias; Sanchez-Portal, Daniel

Electronic structure calculations within Hedin's GW approximation are becoming increasingly accessible to the community. In particular, as it has been shown earlier and we confirm by calculations using our MBPT_LCAO package, the computational cost of the so-called G0W0 can be made comparable to the cost of a regular Hartree-Fock calculation. In this work, we study the performance of our new implementation of G0W0 to reproduce the ionization potentials of all 117 closed-shell molecules belonging to the G2/97 test set, using a pseudo-potential starting point provided by the popular density-functional package SIESTA. Moreover, the ionization potentials and electron affinities of a set of 24 acceptor molecules are compared to experiment and to reference all-electron calculations. PK: Guipuzcoa Fellow; PK,ML,DSP: Deutsche Forschungsgemeinschaft (SFB1083); PK,DSP: MINECO MAT2013-46593-C6-2-P.

Electronic reconstruction of doped Mott insulator heterojunctions

NASA Astrophysics Data System (ADS)

Charlebois, M.; Hassan, S. R.; Karan, R.; Dion, M.; Senechal, D.; Tremblay, A.-M. S.

2012-02-01

Correlated electron heterostructures became a possible alternative when thin-film deposition techniques achieved structures with a sharp interface transition [1]. Soon thereafter, Okamoto & Millis introduced the concept of ``electronic reconstruction'' [2]. We study here the electronic reconstruction of doped Mott insulator heterostructures based on a Cluster Dynamical Mean Field Theory (CDMFT) calculations of the Hubbard model in the limit where electrostatic energy dominates over the kinetic energy associated with transport across layers. The grand potential of individual layers is first computed within CDMFT and then the electrostatic potential energy is taken into account in the Hartree approximation. The charge reconstruction in an ensemble of stacked planes of different nature can lead to a distribution of electron charge and to transport properties that are unique to doped-Mott insulators.[4pt] [1] J. Mannhart, D. G. Schlom, Science 327, 1607 (2010).[0pt] [2] S. Okamoto and A. J. Millis, Nature 428, 630 (2004).

A single molecule rectifier with strong push-pull coupling

NASA Astrophysics Data System (ADS)

Saraiva-Souza, Aldilene; Macedo de Souza, Fabricio; Aleixo, Vicente F. P.; Girão, Eduardo Costa; Filho, Josué Mendes; Meunier, Vincent; Sumpter, Bobby G.; Souza Filho, Antônio Gomes; Del Nero, Jordan

2008-11-01

We theoretically investigate the electronic charge transport in a molecular system composed of a donor group (dinitrobenzene) coupled to an acceptor group (dihydrophenazine) via a polyenic chain (unsaturated carbon bridge). Ab initio calculations based on the Hartree-Fock approximations are performed to investigate the distribution of electron states over the molecule in the presence of an external electric field. For small bridge lengths (n =0-3) we find a homogeneous distribution of the frontier molecular orbitals, while for n >3 a strong localization of the lowest unoccupied molecular orbital is found. The localized orbitals in between the donor and acceptor groups act as conduction channels when an external electric field is applied. We also calculate the rectification behavior of this system by evaluating the charge accumulated in the donor and acceptor groups as a function of the external electric field. Finally, we propose a phenomenological model based on nonequilibrium Green's function to rationalize the ab initio findings.

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

NASA Astrophysics Data System (ADS)

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

2015-03-01

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

(1 + 1) resonant enhanced multiphoton ionization via the A2Sigma(+) state of NO - Ionic rotational branching ratios and their intensity dependence

NASA Technical Reports Server (NTRS)

Rudolph, H.; Mckoy, V.; Dixit, S. N.; Huo, W. M.

1988-01-01

Rotational branching ratios resulting from the (1 + 1) resonant enhanced multiphoton ionization spectroscopy of NO via the 0-0 transition of the A-X band for the four possible branches that can be assigned as R(21.5) are explored using calculation performed in the frozen-core approximation at the Hartree-Fock level. The four different branches, of which three are distinctly different in the perturbative limit, have rather different branching ratios. The mixed R12 + Q22(21.5) branch, which is not intense and has the lowest transition energy, appears to give the best agreement with experimental branching ratio for parallel detection. The agreement is less satisfactory for perpendicular detection. Neither the effect of finite-acceptance angle of the photoelectron detector nor high intensities can explain the discrepancy.

Generalized virial theorem for massless electrons in graphene and other Dirac materials

NASA Astrophysics Data System (ADS)

Sokolik, A. A.; Zabolotskiy, A. D.; Lozovik, Yu. E.

2016-05-01

The virial theorem for a system of interacting electrons in a crystal, which is described within the framework of the tight-binding model, is derived. We show that, in the particular case of interacting massless electrons in graphene and other Dirac materials, the conventional virial theorem is violated. Starting from the tight-binding model, we derive the generalized virial theorem for Dirac electron systems, which contains an additional term associated with a momentum cutoff at the bottom of the energy band. Additionally, we derive the generalized virial theorem within the Dirac model using the minimization of the variational energy. The obtained theorem is illustrated by many-body calculations of the ground-state energy of an electron gas in graphene carried out in Hartree-Fock and self-consistent random-phase approximations. Experimental verification of the theorem in the case of graphene is discussed.

Efficient and accurate treatment of electron correlations with correlation matrix renormalization theory

DOE PAGES

Yao, Y. X.; Liu, J.; Liu, C.; ...

2015-08-28

We present an efficient method for calculating the electronic structure and total energy of strongly correlated electron systems. The method extends the traditional Gutzwiller approximation for one-particle operators to the evaluation of the expectation values of two particle operators in the many-electron Hamiltonian. The method is free of adjustable Coulomb parameters, and has no double counting issues in the calculation of total energy, and has the correct atomic limit. We demonstrate that the method describes well the bonding and dissociation behaviors of the hydrogen and nitrogen clusters, as well as the ammonia composed of hydrogen and nitrogen atoms. We alsomore » show that the method can satisfactorily tackle great challenging problems faced by the density functional theory recently discussed in the literature. The computational workload of our method is similar to the Hartree-Fock approach while the results are comparable to high-level quantum chemistry calculations.« less

Shape and energy consistent pseudopotentials for correlated electron systems

PubMed Central

Needs, R. J.

2017-01-01

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

A Hybrid Density Functional Study of Atomic Hydrogen and Oxygen Adsorptions on the (0001) Surface of Non-Magnetic DHCP Americium

NASA Astrophysics Data System (ADS)

Amdani-Moten, Shafaq; Atta-Fynn, Raymond; Ray, Asok

2010-03-01

As our group have recently shown^+, hybrid density functional theory (HDFT) which replaces a fraction (40%) of approximate DFT exchange with exact Hartree-Fock exchange yield structural, magnetic, and electronic properties for Americium-I that are in excellent agreement with experimental data. As a natural progression, ab initio calculations for atomic adsorptions on the (0001) surface of non-magnetic americium have been performed using HDFT. The americium surface is modeled by a seven-layer slab using inversion symmetry consisting of one atom per layer and non-magnetic ABAC stacking arrangement of these layers. Top, bridge, hcp and fcc chemisorption sites have been investigated with energies optimized with respect to the adatom distance from the surface. Details of the chemisorptions processes as well as comparisons of different sites will be presented. ^+ R. Atta-Fynn and A. K. Ray, Chemical Physics Letters, 482, 223-227 (2009).

Nonlocal screening effects on core-level photoemission spectra investigated by large-cluster models

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

Okada, K.; Kotani, A.

1995-08-15

The copper 2{ital p} core-level x-ray photoemission spectrum in CuO{sub 2} plane systems is calculated by means of large-cluster models to investigate in detail the nonlocal screening effects, which were pointed out by van Veenendaal {ital et} {ital al}. [Phys. Rev. B 47, 11 462 (1993)]. Calculating the hole distributions for the initial and final states of photoemission, we show that the atomic coordination in a cluster strongly affects accessible final states. Accordingly, we point out that the interpretation for Cu{sub 3}O{sub 10} given by van Veenendaal {ital et} {ital al}. is not always general. Moreover, it is shown thatmore » the spectrum can be remarkably affected by whether or not the O 2{ital p}{sub {pi}} orbits are taken into account in the calculations. We also introduce a Hartree-Fock approximation in order to treat much larger-cluster models.« less

Calculation of longitudinal polarizability and second hyperpolarizability of polyacetylene with the coupled perturbed Hartree-Fock/Kohn-Sham scheme: where it is shown how finite oligomer chains tend to the infinite periodic polymer.

PubMed

Lacivita, Valentina; Rèrat, Michel; Orlando, Roberto; Ferrero, Mauro; Dovesi, Roberto

2012-03-21

The longitudinal polarizability, α(xx), and second hyperpolarizability, γ(xxxx), of polyacetylene are evaluated by using the coupled perturbed Hartree-Fock/Kohn-Sham (HF/KS) scheme as implemented in the periodic CRYSTAL code and a split valence type basis set. Four different density functionals, namely local density approximation (LDA) (pure local), Perdew-Becke-Ernzerhof (PBE) (gradient corrected), PBE0, and B3LYP (hybrid), and the Hartree-Fock Hamiltonian are compared. It is shown that very tight computational conditions must be used to obtain well converged results, especially for γ(xxxx), that is, very sensitive to the number of k(->) points in reciprocal space when the band gap is small (as for LDA and PBE), and to the extension of summations of the exact exchange series (HF and hybrids). The band gap in LDA is only 0.01 eV: at least 300 k(->) points are required to obtain well converged total energy and equilibrium geometry, and 1200 for well converged optical properties. Also, the exchange series convergence is related to the band gap. The PBE0 band gap is as small as 1.4 eV and the exchange summation must extend to about 130 Å from the origin cell. Total energy, band gap, equilibrium geometry, polarizability, and second hyperpolarizability of oligomers -(C(2)H(2))(m)-, with m up to 50 (202 atoms), and of the polymer have been compared. It turns out that oligomers of that length provide an extremely poor representation of the infinite chain polarizability and hyperpolarizability when the gap is smaller than 0.2 eV (that is, for LDA and PBE). Huge differences are observed on α(xx) and γ(xxxx) of the polymer when different functionals are used, that is in connection to the well-known density functional theory (DFT) overshoot, reported in the literature about short oligomers: for the infinite model the ratio between LDA (or PBE) and HF becomes even more dramatic (about 500 for α(xx) and 10(10) for γ(xxxx)). On the basis of previous systematic comparisons of results obtained with various approaches including DFT, HF, Moller-Plesset (MP2) and coupled cluster for finite chains, we can argue that, for the infinite chain, the present HF results are the most reliable. © 2012 American Institute of Physics

Hartree-Fock investigation of muon trapping in the chemical ferromagnet 4-(/p-chlorobenzylideneamino)-TEMPO

NASA Astrophysics Data System (ADS)

Jeong, Junho; Briere, Tina M.; Sahoo, N.; Das, T. P.; Ohira, Seiko; Nishiyama, K.; Nagamine, K.

2000-08-01

First-principles unrestricted Hartree-Fock theory is used to obtain the trapping sites for muon and muonium in ferromagnetic p-Cl-Ph-CHN-TEMPO (4-( p-chlorobenzylideneamino)- 2,2,6,6-tetramethylpiperidin-1-yloxyl) and the hyperfine interaction tensors for these sites. Using the calculated hyperfine interactions to fit the two experimentally observed muon spin rotation frequencies, it has been concluded that the two most likely candidates for explaining the experimental data are a muon trapped at the chlorine site and a singlet muonium state at the radical oxygen. The direction of the easy axis is also determined.

Predicted NMR properties of noble gas hydride cations RgH +

NASA Astrophysics Data System (ADS)

Cukras, Janusz; Sadlej, Joanna

2008-12-01

The NMR shielding constants and, for the first time, the spin-spin coupling constants of Rg and H in RgH + compounds for Rg = Ne, Ar, Kr, Xe have been investigated by non-relativistic Hartree-Fock (HF) and relativistic Dirac-Hartree-Fock (DHF) methods. Electron-correlation effects have been furthermore calculated using SOPPA and CCSD at the non-relativistic level. The correlation effects are large on both parameters and opposite to the relativistic effects. The results indicate that both the relativistic and correlation effects need to be taken into account in a quantitative computations, especially in the case of the spin-spin coupling constants.

Conserving and gapless Hartree-Fock-Bogoliubov theory for the three-dimensional dilute Bose gas

NASA Astrophysics Data System (ADS)

Zhang, Ya-Hui; Li, Dingping

2013-11-01

The excitation spectrum for the three-dimensional Bose gas in the Bose-Einstein condensation phase is calculated nonperturbatively with the modified Hartree-Fock-Bogoliubov theory, which is both conserving and gapless. From improved Φ-derivable theory, the diagrams needed to preserve the Ward-Takahashi identity are re-summed in a systematic and nonperturbative way. It is valid up to the critical temperature where the dispersion relation of the low-energy excitation spectrum changes from linear to quadratic. Because including the higher-order fluctuation, the results show significant improvement on the calculation of the shift of critical temperature with other conserving and gapless theories.

Hartree-Fock limit values of multipole moments, polarizabilities, and hyperpolarizabilities for atoms and diatomic molecules

NASA Astrophysics Data System (ADS)

Kobus, Jacek

2015-02-01

Recently it has been demonstrated that the finite difference Hartree-Fock method can be used to deliver highly accurate values of electric multipole moments together with polarizabilities αz z,Az ,z z , and hyperpolarizabilities βz z z, γz z z,Bz z ,z z , for the ground states of various atomic and diatomic systems. Since these results can be regarded as de facto Hartree-Fock limit values their quality is of the utmost importance. This paper reexamines the use of the finite field method to calculate these electric properties, discusses its accuracy, and presents an updated list of the properties for the following atoms and diatomic molecules: H-, He, Li, Li+,Li2 +,Li-,Be2 + , Be, B+,C2 + , Ne, Mg2 +, Mg, Al+,Si2 + , Ar, K+,Ca2 +,Rb+,Sr2 +,Zr4 +,He2 , Be2,N2,F2,O2 , HeNe, LiH2 +, LiCl, LiBr, BH, CO, FH, NaCl, and KF. The potential energy curves and the dependence of the electric properties on the internuclear distance is also studied for He2,LiH+,Be2 , and HeNe systems.

Generalization of the Hartree-Fock approach to collision processes

NASA Astrophysics Data System (ADS)

Hahn, Yukap

1997-06-01

The conventional Hartree and Hartree-Fock approaches for bound states are generalized to treat atomic collision processes. All the single-particle orbitals, for both bound and scattering states, are determined simultaneously by requiring full self-consistency. This generalization is achieved by introducing two Ansäauttze: (a) the weak asymptotic boundary condition, which maintains the correct scattering energy and target orbitals with correct number of nodes, and (b) square integrable amputated scattering functions to generate self-consistent field (SCF) potentials for the target orbitals. The exact initial target and final-state asymptotic wave functions are not required and thus need not be specified a priori, as they are determined simultaneously by the SCF iterations. To check the asymptotic behavior of the solution, the theory is applied to elastic electron-hydrogen scattering at low energies. The solution is found to be stable and the weak asymptotic condition is sufficient to produce the correct scattering amplitudes. The SCF potential for the target orbital shows the strong penetration by the projectile electron during the collision, but the exchange term tends to restore the original form. Potential applicabilities of this extension are discussed, including the treatment of ionization and shake-off processes.

Straightening the Hierarchical Staircase for Basis Set Extrapolations: A Low-Cost Approach to High-Accuracy Computational Chemistry

NASA Astrophysics Data System (ADS)

Varandas, António J. C.

2018-04-01

Because the one-electron basis set limit is difficult to reach in correlated post-Hartree-Fock ab initio calculations, the low-cost route of using methods that extrapolate to the estimated basis set limit attracts immediate interest. The situation is somewhat more satisfactory at the Hartree-Fock level because numerical calculation of the energy is often affordable at nearly converged basis set levels. Still, extrapolation schemes for the Hartree-Fock energy are addressed here, although the focus is on the more slowly convergent and computationally demanding correlation energy. Because they are frequently based on the gold-standard coupled-cluster theory with single, double, and perturbative triple excitations [CCSD(T)], correlated calculations are often affordable only with the smallest basis sets, and hence single-level extrapolations from one raw energy could attain maximum usefulness. This possibility is examined. Whenever possible, this review uses raw data from second-order Møller-Plesset perturbation theory, as well as CCSD, CCSD(T), and multireference configuration interaction methods. Inescapably, the emphasis is on work done by the author's research group. Certain issues in need of further research or review are pinpointed.

Self-Attractive Hartree Decomposition: Partitioning Electron Density into Smooth Localized Fragments.

PubMed

Zhu, Tianyu; de Silva, Piotr; Van Voorhis, Troy

2018-01-09

Chemical bonding plays a central role in the description and understanding of chemistry. Many methods have been proposed to extract information about bonding from quantum chemical calculations, the majority of them resorting to molecular orbitals as basic descriptors. Here, we present a method called self-attractive Hartree (SAH) decomposition to unravel pairs of electrons directly from the electron density, which unlike molecular orbitals is a well-defined observable that can be accessed experimentally. The key idea is to partition the density into a sum of one-electron fragments that simultaneously maximize the self-repulsion and maintain regular shapes. This leads to a set of rather unusual equations in which every electron experiences self-attractive Hartree potential in addition to an external potential common for all the electrons. The resulting symmetry breaking and localization are surprisingly consistent with chemical intuition. SAH decomposition is also shown to be effective in visualization of single/multiple bonds, lone pairs, and unusual bonds due to the smooth nature of fragment densities. Furthermore, we demonstrate that it can be used to identify specific chemical bonds in molecular complexes and provides a simple and accurate electrostatic model of hydrogen bonding.

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

Symbolic computation of the Hartree-Fock energy from a chiral EFT three-nucleon interaction at N 2LO

NASA Astrophysics Data System (ADS)

Gebremariam, B.; Bogner, S. K.; Duguet, T.

2010-06-01

We present the first of a two-part Mathematica notebook collection that implements a symbolic approach for the application of the density matrix expansion (DME) to the Hartree-Fock (HF) energy from a chiral effective field theory (EFT) three-nucleon interaction at N 2LO. The final output from the notebooks is a Skyrme-like energy density functional that provides a quasi-local approximation to the non-local HF energy. In this paper, we discuss the derivation of the HF energy and its simplification in terms of the scalar/vector-isoscalar/isovector parts of the one-body density matrix. Furthermore, a set of steps is described and illustrated on how to extend the approach to other three-nucleon interactions. Program summaryProgram title: SymbHFNNN Catalogue identifier: AEGC_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGC_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 96 666 No. of bytes in distributed program, including test data, etc.: 378 083 Distribution format: tar.gz Programming language: Mathematica 7.1 Computer: Any computer running Mathematica 6.0 and later versions Operating system: Windows Xp, Linux/Unix RAM: 256 Mb Classification: 5, 17.16, 17.22 Nature of problem: The calculation of the HF energy from the chiral EFT three-nucleon interaction at N 2LO involves tremendous spin-isospin algebra. The problem is compounded by the need to eventually obtain a quasi-local approximation to the HF energy, which requires the HF energy to be expressed in terms of scalar/vector-isoscalar/isovector parts of the one-body density matrix. The Mathematica notebooks discussed in this paper solve the latter issue. Solution method: The HF energy from the chiral EFT three-nucleon interaction at N 2LO is cast into a form suitable for an automatic simplification of the spin-isospin traces. Several Mathematica functions and symbolic manipulation techniques are used to obtain the result in terms of the scalar/vector-isoscalar/isovector parts of the one-body density matrix. Running time: Several hours

Two-parameter partially correlated ground-state electron density of some light spherical atoms from Hartree-Fock theory with nonintegral nuclear charge

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

Cordero, Nicolas A.; March, Norman H.; Alonso, Julio A.

2007-05-15

Partially correlated ground-state electron densities for some spherical light atoms are calculated, into which nonrelativistic ionization potentials represent essential input data. The nuclear cusp condition of Kato is satisfied precisely. The basic theoretical starting point, however, is Hartree-Fock (HF) theory for the N electrons under consideration but with nonintegral nuclear charge Z{sup '} slightly different from the atomic number Z (=N). This HF density is scaled with a parameter {lambda}, near to unity, to preserve normalization. Finally, some tests are performed on the densities for the atoms Ne and Ar, as well as for Be and Mg.

Multiconfiguration Dirac-Hartree-Fock calculations of energy levels and radiative rates of Fe VII

NASA Astrophysics Data System (ADS)

Li, Yang; Xu, Xiaokai; Li, Bowen; Jönsson, Per; Chen, Ximeng

2018-06-01

Detailed calculations are performed for 134 fine-structure levels of the 3p63d2, 3p63d4s, 3p53d3 and 3p63d4p configurations in Fe VII using the multiconfiguration Dirac-Hartree-Fock (MCDHF) and relativistic configuration interaction (RCI) methods. Important electron correlation effects are systematically accounted for through active space (AS) expansions. Our results compare well with experimental measurements, emphasizing the importance of a careful treatment of electron correlation, and provide some missing data in the NIST atomic database. The data obtained are expected to be useful in astrophysical applications, particularly for the research of the solar coronal plasma.

M sub shell X-ray emission cross section measurements for Pt, Au, Hg, Pb, Th and U at 8 and 10 keV synchrotron photons

NASA Astrophysics Data System (ADS)

Kaur, Gurpreet; Gupta, Sheenu; Tiwari, M. K.; Mittal, Raj

2014-02-01

M sub shell X-ray emission cross sections of Pt, Au, Hg, Pb, Th and U at 8 and 10 keV photon energies have been determined with linearly polarized photon beam from Indus-2 synchrotron source. The measured cross sections have been reported for the first time and were used to check the available theoretical Dirac-Hartree-Slater (DHS) and Dirac-Fock (DF) values reported in literature and also the presently derived Non Relativistic Hartree-Slater (NRHS), DF and DHS values for Mξ, Mδ, Mα, Mβ, Mγ, Mm1 and Mm2 group of X-rays.

Accuracy of Hartree-Fock wave functions for electron-H/sub 2/ scattering calculations

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

Feldt, A.N.

1988-05-01

Recent papers on electron-N/sub 2/ scattering by Rumble, Stevens, and Truhlar (J. Phys. B 17, 3151 (1984)) and Weatherford, Brown, and Temkin (Phys. Rev. A 35, 4561 (1987)) have suggested that Hartree-Fock (HF) wave functions may not be accurate for calculating potentials for use in studying electron-molecule collisions. A comparison of results for electron-H/sub 2/ scattering using both correlated and HF wave functions is presented. It is found that for both elastic and inelastic collisions and for all energies considered (up to 10 eV) the HF wave functions yield results in excellent agreement with those obtained from the more accuratemore » wave functions.« less

Parallel implementation of Hartree-Fock and density functional theory analytical second derivatives

NASA Astrophysics Data System (ADS)

Baker, Jon; Wolinski, Krzysztof; Malagoli, Massimo; Pulay, Peter

2004-01-01

We present an efficient, parallel implementation for the calculation of Hartree-Fock and density functional theory analytical Hessian (force constant, nuclear second derivative) matrices. These are important for the determination of harmonic vibrational frequencies, and to classify stationary points on potential energy surfaces. Our program is designed for modest parallelism (4-16 CPUs) as exemplified by our standard eight-processor QuantumCube™. We can routinely handle systems with up to 100+ atoms and 1000+ basis functions using under 0.5 GB of RAM memory per CPU. Timings are presented for several systems, ranging in size from aspirin (C9H8O4) to nickel octaethylporphyrin (C36H44N4Ni).

An efficient implementation of semi-numerical computation of the Hartree-Fock exchange on the Intel Phi processor

NASA Astrophysics Data System (ADS)

Liu, Fenglai; Kong, Jing

2018-07-01

Unique technical challenges and their solutions for implementing semi-numerical Hartree-Fock exchange on the Phil Processor are discussed, especially concerning the single- instruction-multiple-data type of processing and small cache size. Benchmark calculations on a series of buckyball molecules with various Gaussian basis sets on a Phi processor and a six-core CPU show that the Phi processor provides as much as 12 times of speedup with large basis sets compared with the conventional four-center electron repulsion integration approach performed on the CPU. The accuracy of the semi-numerical scheme is also evaluated and found to be comparable to that of the resolution-of-identity approach.

Asymptotic behavior and interpretation of virtual states: The effects of confinement and of basis sets

NASA Astrophysics Data System (ADS)

Boffi, Nicholas M.; Jain, Manish; Natan, Amir

2016-02-01

A real-space high order finite difference method is used to analyze the effect of spherical domain size on the Hartree-Fock (and density functional theory) virtual eigenstates. We show the domain size dependence of both positive and negative virtual eigenvalues of the Hartree-Fock equations for small molecules. We demonstrate that positive states behave like a particle in spherical well and show how they approach zero. For the negative eigenstates, we show that large domains are needed to get the correct eigenvalues. We compare our results to those of Gaussian basis sets and draw some conclusions for real-space, basis-sets, and plane-waves calculations.

Components of the Bond Energy in Polar Diatomic Molecules, Radicals, and Ions Formed by Group-1 and Group-2 Metal Atoms.

PubMed

Yu, Haoyu; Truhlar, Donald G

2015-07-14

Although many transition metal complexes are known to have high multireference character, the multireference character of main-group closed-shell singlet diatomic molecules like BeF, CaO, and MgO has been less studied. However, many group-1 and group-2 diatomic molecules do have multireference character, and they provide informative systems for studying multireference character because they are simpler than transition metal compounds. The goal of the present work is to understand these multireference systems better so that, ultimately, we can apply what we learn to more complicated multireference systems and to the design of new exchange-correlation functionals for treating multireference systems more adequately. Fourteen main-group diatomic molecules and one triatomic molecule (including radicals, cations, and anions, as well as neutral closed-shell species) have been studied for this article. Eight of these molecules contain a group-1 element, and six contain a group-2 element. Seven of these molecules are multireference systems, and eight of them are single-reference systems. Fifty-three exchange-correlation functionals of 11 types [local spin-density approximation (LSDA), generalized gradient approximation (GGA), nonseparable gradient approximation (NGA), global-hybrid GGA, meta-GGA, meta-NGA, global-hybrid meta GGA, range-separated hybrid GGA, range-separated hybrid meta-GGA, range-separated hybrid meta-NGA, and DFT augmented with molecular mechanics damped dispersion (DFT-D)] and the Hartree-Fock method have been applied to calculate the bond distance, bond dissociation energy (BDE), and dipole moment of these molecules. All of the calculations are converged to a stable solution by allowing the symmetry of the Slater determinant to be broken. A reliable functional should not only predict an accurate BDE but also predict accurate components of the BDE, so each bond dissociation energy has been decomposed into ionization potential (IP) of the electropositive element, electron affinity of the electronegative bonding partner (EA), atomic excitation energy (EE) to prepare the valence states of the interacting partners, and interaction energy (IE) of the valence-prepared states. Adding Hartree-Fock exchange helps to obtain better results for atomic excitation energy, and this leads to improvements in getting the right answer for the right reason. The following functionals are singled out for reasonably good performance on all three of bond distance, BDE, and dipole moment: B97-1, B97-3, MPW1B95, M05, M06, M06-2X, M08-SO, N12-SX, O3LYP, TPSS, τ-HCTHhyb, and GAM; all but two (TPSS and GAM) of these functionals are hybrid functionals.

Equilibration in the time-dependent Hartree-Fock approach probed with the Wigner distribution function

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

Loebl, N.; Maruhn, J. A.; Reinhard, P.-G.

2011-09-15

By calculating the Wigner distribution function in the reaction plane, we are able to probe the phase-space behavior in the time-dependent Hartree-Fock scheme during a heavy-ion collision in a consistent framework. Various expectation values of operators are calculated by evaluating the corresponding integrals over the Wigner function. In this approach, it is straightforward to define and analyze quantities even locally. We compare the Wigner distribution function with the smoothed Husimi distribution function. Different reaction scenarios are presented by analyzing central and noncentral {sup 16}O +{sup 16}O and {sup 96}Zr +{sup 132}Sn collisions. Although we observe strong dissipation in the timemore » evolution of global observables, there is no evidence for complete equilibration in the local analysis of the Wigner function. Because the initial phase-space volumes of the fragments barely merge and mean values of the observables are conserved in fusion reactions over thousands of fm/c, we conclude that the time-dependent Hartree-Fock method provides a good description of the early stage of a heavy-ion collision but does not provide a mechanism to change the phase-space structure in a dramatic way necessary to obtain complete equilibration.« less

Restricted Hartree Fock using complex-valued orbitals: A long-known but neglected tool in electronic structure theory

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

Small, David W.; Sundstrom, Eric J.; Head-Gordon, Martin

2015-01-14

Restricted Hartree Fock using complex-valued orbitals (cRHF) is studied. We introduce an orbital pairing theorem, with which we obtain a concise connection between cRHF and real-valued RHF, and use it to uncover the close relationship between cRHF, unrestricted Hartree Fock, and generalized valence bond perfect pairing. This enables an intuition for cRHF, contrasting with the generally unintuitive nature of complex orbitals. We also describe an efficient computer implementation of cRHF and its corresponding stability analysis. By applying cRHF to the Be + H{sub 2} insertion reaction, a Woodward-Hoffmann violating reaction, and a symmetry-driven conical intersection, we demonstrate in genuine molecularmore » systems that cRHF is capable of removing certain potential energy surface singularities that plague real-valued RHF and related methods. This complements earlier work that showed this capability in a model system. We also describe how cRHF is the preferred RHF method for certain radicaloid systems like singlet oxygen and antiaromatic molecules. For singlet O{sub 2}, we show that standard methods fail even at the equilibrium geometry. An implication of this work is that, regardless of their individual efficacies, cRHF solutions to the HF equations are fairly commonplace.« less

The properties of nuclear matter with lattice NN potential in relativistic Brueckner-Hartree-Fock theory

PubMed Central

Hu, Jinniu; Toki, Hiroshi; Shen, Hong

2016-01-01

We study the properties of nuclear matter with lattice nucleon-nucleon (NN) potential in the relativistic Brueckner-Hartree-Fock (RBHF) theory. To use this potential in such a microscopic many-body theory, we firstly have to construct a one-boson-exchange potential (OBEP) based on the latest lattice NN potential. Three mesons, pion, σ meson, and ω meson, are considered. Their coupling constants and cut-off momenta are determined by fitting the on-shell behaviors and phase shifts of the lattice force, respectively. Therefore, we obtain two parameter sets of the OBEP potential (named as LOBEP1 and LOBEP2) with these two fitting ways. We calculate the properties of symmetric and pure neutron matter with LOBEP1 and LOBEP2. In non-relativistic Brueckner-Hartree-Fock case, the binding energies of symmetric nuclear matter are around −3 and −5 MeV at saturation density, while it becomes −8 and −12 MeV in relativistic framework with 1S0, 3S1, and 3D1 channels using our two parameter sets. For the pure neutron matter, the equations of state in non-relativistic and relativistic cases are very similar due to only consideration 1S0 channel with isospin T = 1 case. PMID:27752124

The properties of nuclear matter with lattice NN potential in relativistic Brueckner-Hartree-Fock theory.

PubMed

Hu, Jinniu; Toki, Hiroshi; Shen, Hong

2016-10-18

We study the properties of nuclear matter with lattice nucleon-nucleon (NN) potential in the relativistic Brueckner-Hartree-Fock (RBHF) theory. To use this potential in such a microscopic many-body theory, we firstly have to construct a one-boson-exchange potential (OBEP) based on the latest lattice NN potential. Three mesons, pion, σ meson, and ω meson, are considered. Their coupling constants and cut-off momenta are determined by fitting the on-shell behaviors and phase shifts of the lattice force, respectively. Therefore, we obtain two parameter sets of the OBEP potential (named as LOBEP1 and LOBEP2) with these two fitting ways. We calculate the properties of symmetric and pure neutron matter with LOBEP1 and LOBEP2. In non-relativistic Brueckner-Hartree-Fock case, the binding energies of symmetric nuclear matter are around -3 and -5 MeV at saturation density, while it becomes -8 and -12 MeV in relativistic framework with 1 S 0 , 3 S 1 , and 3 D 1 channels using our two parameter sets. For the pure neutron matter, the equations of state in non-relativistic and relativistic cases are very similar due to only consideration 1 S 0 channel with isospin T = 1 case.

Limit behavior of mass critical Hartree minimization problems with steep potential wells

NASA Astrophysics Data System (ADS)

Guo, Yujin; Luo, Yong; Wang, Zhi-Qiang

2018-06-01

We consider minimizers of the following mass critical Hartree minimization problem: eλ(N ) ≔inf {u ∈H1(Rd ) , ‖u‖2 2=N } Eλ(u ) , where d ≥ 3, λ > 0, and the Hartree energy functional Eλ(u) is defined by Eλ(u ) ≔∫Rd|∇u (x ) |2d x +λ ∫Rdg (x ) u2(x ) d x -1/2 ∫Rd∫Rdu/2(x ) u2(y ) |x -y |2 d x d y . Here the steep potential g(x) satisfies 0 =g (0 ) =infRdg (x ) ≤g (x ) ≤1 and 1 -g (x ) ∈Ld/2(Rd ) . We prove that there exists a constant N* > 0, independent of λg(x), such that if N ≥ N*, then eλ(N) does not admit minimizers for any λ > 0; if 0 < N < N*, then there exists a constant λ*(N) > 0 such that eλ(N) admits minimizers for any λ > λ*(N) and eλ(N) does not admit minimizers for 0 < λ < λ*(N). For any given 0 < N < N*, the limit behavior of positive minimizers for eλ(N) is also studied as λ → ∞, where the mass concentrates at the bottom of g(x).

Measurement of K to L shell vacancy transfer probabilities for the elements 46≤ Z≤55 by photoionization

NASA Astrophysics Data System (ADS)

Şimşek, Ö.; Karagöz, D.; Ertugrul, M.

2003-10-01

The K to L shell vacancy transfer probabilities for nine elements in the atomic region 46≤ Z≤55 were determined by measuring the L X-ray yields from targets excited by 5.96 and 59.5 keV photons and using the theoretical K and L shell photoionization cross-sections. The L X-rays from different targets were detected with an Ultra-LEGe detector with very thin polymer window. Present experimental results were compared with the semi empirical values tabulated by Rao et al. [Atomic vacancy distributions product by inner shellionization, Phys. Rev. A 5 (1972) 997-1002] and theoretically calculated values using radiative and radiationless transitions. The radiative transitions of these elements were observed from the relativistic Hartree-Slater model, which was proposed by Scofield [Relativistic Hartree-Slater values for K and L shell X-ray emission rates, At. Data Nucl. Data Tables 14 (1974) 121-137]. The radiationless transitions were observed from the Dirac-Hartree-Slater model, which was proposed by Chen et al. [Relativistic radiationless transition probabilities for atomic K- and L-shells, At. Data Nucl. Data Tables 24 (1979) 13-37]. To the best of our knowledge, these vacancy transfer probabilities are reported for the first time.

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

PubMed

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

2014-05-14

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

Exchange potential from the common energy denominator approximation for the Kohn-Sham Green's function: Application to (hyper)polarizabilities of molecular chains

NASA Astrophysics Data System (ADS)

Grüning, M.; Gritsenko, O. V.; Baerends, E. J.

2002-04-01

An approximate Kohn-Sham (KS) exchange potential vxσCEDA is developed, based on the common energy denominator approximation (CEDA) for the static orbital Green's function, which preserves the essential structure of the density response function. vxσCEDA is an explicit functional of the occupied KS orbitals, which has the Slater vSσ and response vrespσCEDA potentials as its components. The latter exhibits the characteristic step structure with "diagonal" contributions from the orbital densities |ψiσ|2, as well as "off-diagonal" ones from the occupied-occupied orbital products ψiσψj(≠1)σ*. Comparison of the results of atomic and molecular ground-state CEDA calculations with those of the Krieger-Li-Iafrate (KLI), exact exchange (EXX), and Hartree-Fock (HF) methods show, that both KLI and CEDA potentials can be considered as very good analytical "closure approximations" to the exact KS exchange potential. The total CEDA and KLI energies nearly coincide with the EXX ones and the corresponding orbital energies ɛiσ are rather close to each other for the light atoms and small molecules considered. The CEDA, KLI, EXX-ɛiσ values provide the qualitatively correct order of ionizations and they give an estimate of VIPs comparable to that of the HF Koopmans' theorem. However, the additional off-diagonal orbital structure of vxσCEDA appears to be essential for the calculated response properties of molecular chains. KLI already considerably improves the calculated (hyper)polarizabilities of the prototype hydrogen chains Hn over local density approximation (LDA) and standard generalized gradient approximations (GGAs), while the CEDA results are definitely an improvement over the KLI ones. The reasons of this success are the specific orbital structures of the CEDA and KLI response potentials, which produce in an external field an ultranonlocal field-counteracting exchange potential.

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

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

We discuss the octupole deformation properties of the recently proposed Barcelona-Catania-Paris (BCP) energy density functionals for two sets of isotopes, those of radium and barium, in which it is believed that octupole deformation plays a role in the description of the ground state. The analysis is carried out in the mean field framework (Hartree-Fock-Bogoliubov approximation) by using the axially symmetric octupole moment as a constraint. The main ingredients entering the octupole collective Hamiltonian are evaluated and the lowest-lying octupole eigenstates are obtained. In this way we restore, in an approximate way, the parity symmetry spontaneously broken by the mean fieldmore » and also incorporate octupole fluctuations around the ground-state solution. For each isotope the energy of the lowest lying 1{sup -} state and the B(E1) and B(E3) transition probabilities have been computed and compared to both the experimental data and the results obtained in the same framework with the Gogny D1S interaction, which are used here as a well-established benchmark. Finally, the octupolarity of the configurations involved in the way down to fission of {sup 240}Pu, which is strongly connected to the asymmetric fragment mass distribution, is studied. We confirm with this thorough study the suitability of the BCP functionals to describe octupole-related phenomena.« less

An atomic mean-field spin-orbit approach within exact two-component theory for a non-perturbative treatment of spin-orbit coupling

NASA Astrophysics Data System (ADS)

Liu, Junzi; Cheng, Lan

2018-04-01

An atomic mean-field (AMF) spin-orbit (SO) approach within exact two-component theory (X2C) is reported, thereby exploiting the exact decoupling scheme of X2C, the one-electron approximation for the scalar-relativistic contributions, the mean-field approximation for the treatment of the two-electron SO contribution, and the local nature of the SO interactions. The Hamiltonian of the proposed SOX2CAMF scheme comprises the one-electron X2C Hamiltonian, the instantaneous two-electron Coulomb interaction, and an AMF SO term derived from spherically averaged Dirac-Coulomb Hartree-Fock calculations of atoms; no molecular relativistic two-electron integrals are required. Benchmark calculations for bond lengths, harmonic frequencies, dipole moments, and electric-field gradients for a set of diatomic molecules containing elements across the periodic table show that the SOX2CAMF scheme offers a balanced treatment for SO and scalar-relativistic effects and appears to be a promising candidate for applications to heavy-element containing systems. SOX2CAMF coupled-cluster calculations of molecular properties for bismuth compounds (BiN, BiP, BiF, BiCl, and BiI) are also presented and compared with experimental results to further demonstrate the accuracy and applicability of the SOX2CAMF scheme.

Electron collisions with small esters: A joint experimental-theoretical investigation

NASA Astrophysics Data System (ADS)

de Souza, G. L. C.; da Silva, L. A.; de Sousa, W. J. C.; Sugohara, R. T.; Iga, I.; dos Santos, A. S.; Machado, L. E.; Homem, M. G. P.; Brescansin, L. M.; Lucchese, R. R.; Lee, M.-T.

2016-03-01

A theoretical and experimental investigation on elastic electron scattering by two small esters, namely, methyl formate and ethyl acetate, is reported. Experimental differential, integral, and momentum-transfer cross sections are given in the 30-1000 eV and 10∘-120∘ ranges. The relative-flow technique was used to determine such quantities. Particularly for methyl formate, a theoretical study was also carried out in the 1-500 eV range. A complex optical potential derived from a Hartree-Fock molecular wave function was used to represent the collision dynamics, whereas the Padé approximation was used to solve the scattering equations. In addition, calculations based on the framework of the independent-atom model (IAM) were also performed for both targets. In general, there is good agreement between our experimental data and the present theoretical results calculated using the Padé approximation. The theoretical results using the IAM also agree well with the experimental data at 200 eV and above. Moreover, for methyl formate, our calculations reveal a 2A'' (π*) resonance at about 3.0 eV and a σ*-type resonance centered at about 8.0 eV in the 2A' scattering channel. The π* resonance is also seen in other targets containing a carbonyl group.

Assessing the performance of the random phase approximation for exchange and superexchange coupling constants in magnetic crystalline solids

NASA Astrophysics Data System (ADS)

Olsen, Thomas

2017-09-01

The random phase approximation (RPA) for total energies has previously been shown to provide a qualitatively correct description of static correlation in molecular systems, where density functional theory (DFT) with local functionals are bound to fail. This immediately poses the question of whether the RPA is also able to capture the correct physics of strongly correlated solids such as Mott insulators. Due to strong electron localization, magnetic interactions in such systems are dominated by superexchange, which in the simplest picture can be regarded as the analog of static correlation for molecules. In this paper, we investigate the performance of the RPA for evaluating both superexchange and direct exchange interactions in the magnetic solids NiO, MnO, Na3Cu2SbO6,Sr2CuO3,Sr2CuTeO6 , and a monolayer of CrI3, which were chosen to represent a broad variety of magnetic interactions. It is found that the RPA can accurately correct the large errors introduced by Hartree-Fock, independent of the input orbitals used for the perturbative expansion. However, in most cases, accuracies similar to RPA can be obtained with DFT+U, which is significantly simpler from a computational point of view.

Separation of Pygmy Dipole and M1 Resonances in Zr90 by a High-Resolution Inelastic Proton Scattering Near 0°

NASA Astrophysics Data System (ADS)

Iwamoto, C.; Utsunomiya, H.; Tamii, A.; Akimune, H.; Nakada, H.; Shima, T.; Yamagata, T.; Kawabata, T.; Fujita, Y.; Matsubara, H.; Shimbara, Y.; Nagashima, M.; Suzuki, T.; Fujita, H.; Sakuda, M.; Mori, T.; Izumi, T.; Okamoto, A.; Kondo, T.; Bilgier, B.; Kozer, H. C.; Lui, Y.-W.; Hatanaka, K.

2012-06-01

A high-resolution measurement of inelastic proton scattering off Zr90 near 0° was performed at 295 MeV with a focus on a pronounced strength previously reported in the low-energy tail of giant dipole resonance. A forest of fine structure was observed in the excitation energy region 7-12 MeV. A multipole decomposition analysis of the angular distribution for the forest was carried out using the ECIS95 distorted-wave Born approximation code with the Hartree-Fock plus random-phase approximation model of E1 and M1 transition densities and inclusion of E1 Coulomb excitation. The analysis separated pygmy dipole and M1 resonances in the forest at EPDR=9.15±0.18MeV with ΓPDR=2.91±0.64MeV and at EM1=9.53±0.06MeV with ΓM1=2.70±0.17MeV in the Lorentzian function, respectively. The B(E1)↑ value for pygmy dipole resonance over 7-11 MeV is 0.75±0.08e2fm2, which corresponds to 2.1±0.2% of the Thomas-Reiche-Kuhn sum rule.

Bose-Einstein condensation of triplons with a weakly broken U(1) symmetry

NASA Astrophysics Data System (ADS)

Khudoyberdiev, Asliddin; Rakhimov, Abdulla; Schilling, Andreas

2017-11-01

The low-temperature properties of certain quantum magnets can be described in terms of a Bose-Einstein condensation (BEC) of magnetic quasiparticles (triplons). Some mean-field approaches (MFA) to describe these systems, based on the standard grand canonical ensemble, do not take the anomalous density into account and leads to an internal inconsistency, as it has been shown by Hohenberg and Martin, and may therefore produce unphysical results. Moreover, an explicit breaking of the U(1) symmetry as observed, for example, in TlCuCl3 makes the application of MFA more complicated. In the present work, we develop a self-consistent MFA approach, similar to the Hartree-Fock-Bogolyubov approximation in the notion of representative statistical ensembles, including the effect of a weakly broken U(1) symmetry. We apply our results on experimental data of the quantum magnet TlCuCl3 and show that magnetization curves and the energy dispersion can be well described within this approximation assuming that the BEC scenario is still valid. We predict that the shift of the critical temperature T c due to a finite exchange anisotropy is rather substantial even when the anisotropy parameter γ is small, e.g., {{Δ }}{T}{c}≈ 10 % of T c in H = 6 T and for γ ≈ 4 μ {eV}.

Relativistic Brueckner-Hartree-Fock theory for neutron drops

NASA Astrophysics Data System (ADS)

Shen, Shihang; Liang, Haozhao; Meng, Jie; Ring, Peter; Zhang, Shuangquan

2018-05-01

Neutron drops confined in an external field are studied in the framework of relativistic Brueckner-Hartree-Fock theory using the bare nucleon-nucleon interaction. The ground-state energies and radii of neutron drops with even numbers from N =4 to N =50 are calculated and compared with results obtained from other nonrelativistic ab initio calculations and from relativistic density functional theory. Special attention has been paid to the magic numbers and to the subshell closures. The single-particle energies are investigated and the monopole effect of the tensor force on the evolutions of the spin-orbit and the pseudospin-orbit splittings is discussed. The results provide interesting insights into neutron-rich systems and can form an important guide for future density functionals.

Constrained Hartree-Fock Theory and Study of Deformed Structures of Closed Shell Nuclei

NASA Astrophysics Data System (ADS)

Praharaj, Choudhury

2016-03-01

We have studied some N or Z = 50 nuclei in a microscopic model with effective interaction in a reasonably large shell model space. Excitation of particles across 50 shell closure leads to well-deformed excited prolate configurations. The potential energy surfaces of nuclei are studied using Hartree-Fock theory with quadrupole constraint to explore the various deformed configurations of N = 50 nuclei 82Ge , 84Se and 86Kr . Energy spectra are calculated from various intrinsic states using Peierls-Yoccoz angular momentum projection technique. Results of spectra and electromagnetic moments and transitions will be presented for N = 50 nuclei and for Z = 50 114Sn nucleus. Supported by Grant No SB/S2/HEP-06/2013 of DST.

Computational Nuclear Physics and Post Hartree-Fock Methods

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

Lietz, Justin; Sam, Novario; Hjorth-Jensen, M.

We present a computational approach to infinite nuclear matter employing Hartree-Fock theory, many-body perturbation theory and coupled cluster theory. These lectures are closely linked with those of chapters 9, 10 and 11 and serve as input for the correlation functions employed in Monte Carlo calculations in chapter 9, the in-medium similarity renormalization group theory of dense fermionic systems of chapter 10 and the Green's function approach in chapter 11. We provide extensive code examples and benchmark calculations, allowing thereby an eventual reader to start writing her/his own codes. We start with an object-oriented serial code and end with discussions onmore » strategies for porting the code to present and planned high-performance computing facilities.« less

All-electron molecular Dirac-Hartree-Fock calculations - The group IV tetrahydrides CH4, SiH4, GeH4, SnH4, and PbH4

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.; Taylor, Peter R.; Faegri, Knut, Jr.; Partridge, Harry

1991-01-01

A basis-set-expansion Dirac-Hartree-Fock program for molecules is described. Bond lengths and harmonic frequencies are presented for the ground states of the group 4 tetrahydrides, CH4, SiH4, GeH4, SnH4, and PbH4. The results are compared with relativistic effective core potential (RECP) calculations, first-order perturbation theory (PT) calculations and with experimental data. The bond lengths are well predicted by first-order perturbation theory for all molecules, but none of the RECP's considered provides a consistent prediction. Perturbation theory overestimates the relativistic correction to the harmonic frequencies; the RECP calculations underestimate the correction.

All-electron molecular Dirac-Hartree-Fock calculations: The group 4 tetrahydrides CH4, SiH4, GeH4, SnH4 and PbH4

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.; Taylor, Peter R.; Faegri, Knut, Jr.; Partridge, Harry

1990-01-01

A basis-set-expansion Dirac-Hartree-Fock program for molecules is described. Bond lengths and harmonic frequencies are presented for the ground states of the group 4 tetrahydrides, CH4, SiH4, GeH4, SnH4, and PbH4. The results are compared with relativistic effective core potential (RECP) calculations, first-order perturbation theory (PT) calculations and with experimental data. The bond lengths are well predicted by first-order perturbation theory for all molecules, but non of the RECP's considered provides a consistent prediction. Perturbation theory overestimates the relativistic correction to the harmonic frequencies; the RECP calculations underestimate the correction.

Near Hartree-Fock quality GTO basis sets for the second-row atoms

NASA Technical Reports Server (NTRS)

Partridge, Harry

1987-01-01

Energy optimized, near Hartree-Fock quality Gaussian basis sets ranging in size from (17s12p) to (20s15p) are presented for the ground states of the second-row atoms for Na(2P), Na(+), Na(-), Mg(3P), P(-), S(-), and Cl(-). In addition, optimized supplementary functions are given for the ground state basis sets to describe the negative ions, and the excited Na(2P) and Mg(3P) atomic states. The ratios of successive orbital exponents describing the inner part of the 1s and 2p orbitals are found to be nearly independent of both nuclear charge and basis set size. This provides a method of obtaining good starting estimates for other basis set optimizations.

Immediate estimation of correlation energy for molecular systems from the partial charges on atoms in the molecule

NASA Astrophysics Data System (ADS)

Kristyán, Sándor

1997-11-01

In the author's previous work (Chem. Phys. Lett. 247 (1995) 101 and Chem. Phys. Lett. 256 (1996) 229) a simple quasi-linear relationship was introduced between the number of electrons, N, participating in any molecular system and the correlation energy: -0.035 ( N - 1) > Ecorr[hartree] > - 0.045( N -1). This relationship was developed to estimate more accurately correlation energy immediately in ab initio calculations by using the partial charges of atoms in the molecule, easily obtained after Hartree-Fock self-consistent field (HF-SCF) calculations. The method is compared to the well-known B3LYP, MP2, CCSD and G2M methods. Correlation energy estimations for negatively (-1) charged atomic ions are also reported.

Interacting Electrons in Graphene: Fermi Velocity Renormalization and Optical Response

NASA Astrophysics Data System (ADS)

Stauber, T.; Parida, P.; Trushin, M.; Ulybyshev, M. V.; Boyda, D. L.; Schliemann, J.

2017-06-01

We have developed a Hartree-Fock theory for electrons on a honeycomb lattice aiming to solve a long-standing problem of the Fermi velocity renormalization in graphene. Our model employs no fitting parameters (like an unknown band cutoff) but relies on a topological invariant (crystal structure function) that makes the Hartree-Fock sublattice spinor independent of the electron-electron interaction. Agreement with the experimental data is obtained assuming static self-screening including local field effects. As an application of the model, we derive an explicit expression for the optical conductivity and discuss the renormalization of the Drude weight. The optical conductivity is also obtained via precise quantum Monte Carlo calculations which compares well to our mean-field approach.

Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.. (VI) HFODD (v2.40h): A new version of the program

NASA Astrophysics Data System (ADS)

Dobaczewski, J.; Satuła, W.; Carlsson, B. G.; Engel, J.; Olbratowski, P.; Powałowski, P.; Sadziak, M.; Sarich, J.; Schunck, N.; Staszczak, A.; Stoitsov, M.; Zalewski, M.; Zduńczuk, H.

2009-11-01

We describe the new version (v2.40h) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented: (i) projection on good angular momentum (for the Hartree-Fock states), (ii) calculation of the GCM kernels, (iii) calculation of matrix elements of the Yukawa interaction, (iv) the BCS solutions for state-dependent pairing gaps, (v) the HFB solutions for broken simplex symmetry, (vi) calculation of Bohr deformation parameters, (vii) constraints on the Schiff moments and scalar multipole moments, (viii) the DT2h transformations and rotations of wave functions, (ix) quasiparticle blocking for the HFB solutions in odd and odd-odd nuclei, (x) the Broyden method to accelerate the convergence, (xi) the Lipkin-Nogami method to treat pairing correlations, (xii) the exact Coulomb exchange term, (xiii) several utility options, and we have corrected three insignificant errors. New version program summaryProgram title: HFODD (v2.40h) Catalogue identifier: ADFL_v2_2 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFL_v2_2.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 79 618 No. of bytes in distributed program, including test data, etc.: 372 548 Distribution format: tar.gz Programming language: FORTRAN-77 and Fortran-90 Computer: Pentium-III, AMD-Athlon, AMD-Opteron Operating system: UNIX, LINUX, Windows XP Has the code been vectorised or parallelized?: Yes, vectorised RAM: 10 Mwords Word size: The code is written in single-precision for use on a 64-bit processor. The compiler option -r8 or +autodblpad (or equivalent) has to be used to promote all real and complex single-precision floating-point items to double precision when the code is used on a 32-bit machine. Classification: 17.22 Catalogue identifier of previous version: ADFL_v2_1 Journal reference of previous version: Comput. Phys. Commun. 167 (2005) 214 External routines: Lapack (http://www.netlib.org/lapack/), Blas (http://www.netlib.org), linpack (http://www.netlib/linpack/) Does the new version supersede the previous version?: Yes Nature of problem: The nuclear mean-field and an analysis of its symmetries in realistic cases are the main ingredients of a description of nuclear states. Within the Local Density Approximation, or for a zero-range velocity-dependent Skyrme interaction, the nuclear mean-field is local and velocity dependent. The locality allows for an effective and fast solution of the self-consistent Hartree-Fock equations, even for heavy nuclei, and for various nucleonic (n-particle n-hole) configurations, deformations, excitation energies, or angular momenta. Similar Local Density Approximation in the particle-particle channel, which is equivalent to using a zero-range interaction, allows for a simple implementation of pairing effects within the Hartree-Fock-Bogolyubov method. Solution method: The program uses the Cartesian harmonic oscillator basis to expand single-particle or single-quasiparticle wave functions of neutrons and protons interacting by means of the Skyrme effective interaction and zero-range pairing interaction. The expansion coefficients are determined by the iterative diagonalization of the mean field Hamiltonians or Routhians which depend non-linearly on the local neutron and proton densities. Suitable constraints are used to obtain states corresponding to a given configuration, deformation or angular momentum. The method of solution has been presented in [1]. Summary of revisions: Projection on good angular momentum (for the Hartree-Fock states) has been implemented. Calculation of the GCM kernels has been implemented. Calculation of matrix elements of the Yukawa interaction has been implemented. The BCS solutions for state-dependent pairing gaps have been implemented. The HFB solutions for broken simplex symmetry have been implemented. Calculation of Bohr deformation parameters has been implemented. Constraints on the Schiff moments and scalar multipole moments have been implemented. The DT2h transformations and rotations of wave functions have been implemented. The quasiparticle blocking for the HFB solutions in odd and odd-odd nuclei has been implemented. The Broyden method to accelerate the convergence has been implemented. The Lipkin-Nogami method to treat pairing correlations has been implemented. The exact Coulomb exchange term has been implemented. Several utility options have been implemented. Three insignificant errors have been corrected. Restrictions: The main restriction is the CPU time required for calculations of heavy deformed nuclei and for a given precision required. Unusual features: The user must have access to an implementation of the BLAS (Basic Linear Algebra Subroutines), the NAGLIB subroutine F02AXE, or LAPACK subroutines ZHPEV, ZHPEVX, or ZHEEVR, which diagonalize complex Hermitian matrices, and the LINPACK subroutines ZGEDI and ZGECO, which invert arbitrary complex matrices and calculate determinants or provide another set of subroutines that can perform such a tasks. The LAPACK and LINPACK subroutines and an unoptimized version of the BLAS can be obtained from the Netlib Repository at the University of Tennessee, Knoxville: http://www.netlib.org/. Running time: One Hartree-Fock iteration for the superdeformed, rotating, parity conserving state of 15266Dy86 takes about six seconds on the AMD-Athlon 1600+ processor. Starting from the Woods-Saxon wave functions, about fifty iterations are required to obtain the energy converged within the precision of about 0.1 keV. In the case where every value of the angular velocity is converged separately, the complete superdeformed band with precisely determined dynamical moments J (2) can be obtained in forty minutes of CPU time on the AMD-Athlon 1600+ processor. This time can be often reduced by a factor of three when a self-consistent solution for a given rotational frequency is used as a starting point for a neighboring rotational frequency. References: J. Dobaczewski, J. Dudek, Comput. Phys. Commun. 102 (1997) 166.

REVIEW ARTICLE: On correlation effects in electron spectroscopies and the GW approximation

NASA Astrophysics Data System (ADS)

Hedin, Lars

1999-10-01

The GW approximation (GWA) extends the well-known Hartree-Fock approximation (HFA) for the self-energy (exchange potential), by replacing the bare Coulomb potential v by the dynamically screened potential W, e.g. Vex = iGv is replaced by icons/Journals/Common/Sigma" ALT="Sigma" ALIGN="TOP"/>GW = iGW. Here G is the one-electron Green's function. The GWA like the HFA is self-consistent, which allows for solutions beyond perturbation theory, like say spin-density waves. In a first approximation, iGW is a sum of a statically screened exchange potential plus a Coulomb hole (equal to the electrostatic energy associated with the charge pushed away around a given electron). The Coulomb hole part is larger in magnitude, but the two parts give comparable contributions to the dispersion of the quasi-particle energy. The GWA can be said to describe an electronic polaron (an electron surrounded by an electronic polarization cloud), which has great similarities to the ordinary polaron (an electron surrounded by a cloud of phonons). The dynamical screening adds new crucial features beyond the HFA. With the GWA not only bandstructures but also spectral functions can be calculated, as well as charge densities, momentum distributions, and total energies. We will discuss the ideas behind the GWA, and generalizations which are necessary to improve on the rather poor GWA satellite structures in the spectral functions. We will further extend the GWA approach to fully describe spectroscopies like photoemission, x-ray absorption, and electron scattering. Finally we will comment on the relation between the GWA and theories for strongly correlated electronic systems. In collecting the material for this review, a number of new results and perspectives became apparent, which have not been published elsewhere.

A Hydrodynamic Theory for Spatially Inhomogeneous Semiconductor Lasers: Microscopic Approach

NASA Technical Reports Server (NTRS)

Li, Jianzhong; Ning, C. Z.; Biegel, Bryan A. (Technical Monitor)

2001-01-01

Starting from the microscopic semiconductor Bloch equations (SBEs) including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell's equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole (e-h) and carrier-LO (c-LO) phonon scatterings are directly used to derive the momentum and energy relaxation rates. These rates expressed as functions of temperatures and densities lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma (EHP) to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-h scattering dominates over c-LO phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-h scattering, even though the diffusion coefficients of individual components depend sensitively on the e-h scattering rates. Our discussions lead to new perspectives into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization which in turn couples to the laser field.

2-D Modeling of Nanoscale MOSFETs: Non-Equilibrium Green's Function Approach

NASA Technical Reports Server (NTRS)

Svizhenko, Alexei; Anantram, M. P.; Govindan, T. R.; Biegel, Bryan

2001-01-01

We have developed physical approximations and computer code capable of realistically simulating 2-D nanoscale transistors, using the non-equilibrium Green's function (NEGF) method. This is the most accurate full quantum model yet applied to 2-D device simulation. Open boundary conditions and oxide tunneling are treated on an equal footing. Electrons in the ellipsoids of the conduction band are treated within the anisotropic effective mass approximation. Electron-electron interaction is treated within Hartree approximation by solving NEGF and Poisson equations self-consistently. For the calculations presented here, parallelization is performed by distributing the solution of NEGF equations to various processors, energy wise. We present simulation of the "benchmark" MIT 25nm and 90nm MOSFETs and compare our results to those from the drift-diffusion simulator and the quantum-corrected results available. In the 25nm MOSFET, the channel length is less than ten times the electron wavelength, and the electron scattering time is comparable to its transit time. Our main results are: (1) Simulated drain subthreshold current characteristics are shown, where the potential profiles are calculated self-consistently by the corresponding simulation methods. The current predicted by our quantum simulation has smaller subthreshold slope of the Vg dependence which results in higher threshold voltage. (2) When gate oxide thickness is less than 2 nm, gate oxide leakage is a primary factor which determines off-current of a MOSFET (3) Using our 2-D NEGF simulator, we found several ways to drastically decrease oxide leakage current without compromising drive current. (4) Quantum mechanically calculated electron density is much smaller than the background doping density in the poly silicon gate region near oxide interface. This creates an additional effective gate voltage. Different ways to. include this effect approximately will be discussed.

A full-dimensional multilayer multiconfiguration time-dependent Hartree study on the ultraviolet absorption spectrum of formaldehyde oxide

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

Meng, Qingyong, E-mail: mengqingyong@dicp.ac.cn; Meyer, Hans-Dieter, E-mail: hans-dieter.meyer@pci.uni-heidelberg.de

2014-09-28

Employing the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method in conjunction with the multistate multimode vibronic coupling Hamiltonian (MMVCH) model, we perform a full dimensional (9D) quantum dynamical study on the simplest Criegee intermediate, formaldehyde oxide, in five lower-lying singlet electronic states. The ultraviolet (UV) spectrum is then simulated by a Fourier transform of the auto-correlation function. The MMVCH model is built based on extensive MRCI(8e,8o)/aug-cc-pVTZ calculations. To ensure a fast convergence of the final calculations, a large number of ML-MCTDH test calculations is performed to find an appropriate multilayer separations (ML-trees) of the ML-MCTDH nuclear wave functions, and the dynamicalmore » calculations are carefully checked to ensure that the calculations are well converged. To compare the computational efficiency, standard MCTDH simulations using the same Hamiltonian are also performed. A comparison of the MCTDH and ML-MCTDH calculations shows that even for the present not-too-large system (9D here) the ML-MCTDH calculations can save a considerable amount of computational resources while producing identical spectra as the MCTDH calculations. Furthermore, the present theoretical B{sup ~} {sup 1}A{sup ′}←X{sup ~} {sup 1}A{sup ′} UV spectral band and the corresponding experimental measurements [J. M. Beames, F. Liu, L. Lu, and M. I. Lester, J. Am. Chem. Soc. 134, 20045–20048 (2012); L. Sheps, J. Phys. Chem. Lett. 4, 4201–4205 (2013); W.-L. Ting, Y.-H. Chen, W. Chao, M. C. Smith, and J. J.-M. Lin, Phys. Chem. Chem. Phys. 16, 10438–10443 (2014)] are discussed. To the best of our knowledge, this is the first theoretical UV spectrum simulated for this molecule including nuclear motion beyond an adiabatic harmonic approximation.« less

Tensor Fermi liquid parameters in nuclear matter from chiral effective field theory

NASA Astrophysics Data System (ADS)

Holt, J. W.; Kaiser, N.; Whitehead, T. R.

2018-05-01

We compute from chiral two- and three-body forces the complete quasiparticle interaction in symmetric nuclear matter up to twice nuclear matter saturation density. Second-order perturbative contributions that account for Pauli blocking and medium polarization are included, allowing for an exploration of the full set of central and noncentral operator structures permitted by symmetries and the long-wavelength limit. At the Hartree-Fock level, the next-to-next-to-leading order three-nucleon force contributes to all noncentral interactions, and their strengths grow approximately linearly with the nucleon density up to that of saturated nuclear matter. Three-body forces are shown to enhance the already strong proton-neutron effective tensor interaction, while the corresponding like-particle tensor force remains small. We also find a large isovector cross-vector interaction but small center-of-mass tensor interactions in the isoscalar and isovector channels. The convergence of the expansion of the noncentral quasiparticle interaction in Landau parameters and Legendre polynomials is studied in detail.

Study on the spin-states of cobalt-based double-layer perovskite Sr2Y0.5Ca0.5Co2O7

NASA Astrophysics Data System (ADS)

He, H.; Zhang, W. Y.

2008-02-01

The spin-states of cobalt based perovskite compounds depend sensitively on the valence state and local crystal environment of Co ions and the rich physical properties arise from strong coupling among charge, spin, and orbital degrees of freedom. While extensive studies have been carried out in the past, most of them concentrated on the isotropic compound LaCoO3. In this paper, using the unrestricted Hartree-Fock approximation and the real-space recursion method, we have investigated the competition of various magnetically ordered spin-states of anisotropic double-layered perovskite Sr2Y0.5Ca0.5Co2O7. The energy comparison among these states shows that the nearest-neighbor high-spin-intermediate-spin ferromagnetically ordered state is the relevant magnetic ground state of the compound. The magnetic structure and sizes of magnetic moments are consistent with the recent experimental observation.

Prediction of surface tension of HFD-like fluids using the Fowler’s approximation

NASA Astrophysics Data System (ADS)

Goharshadi, Elaheh K.; Abbaspour, Mohsen

2006-09-01

The Fowler's expression for calculation of the reduced surface tension has been used for simple fluids using the Hartree-Fock Dispersion (HFD)-like potential (HFD-like fluids) obtained from the inversion of the viscosity collision integrals at zero pressure. In order to obtain the RDFs values needed for calculation of the surface tension, we have performed the MD simulation at different temperatures and densities and then fitted with an expression and compared the resulting RDFs with the experiment. Our results are in excellent accordance with experimental values when the vapor density has been considered, especially at high temperatures. We have also calculated the surface tension using a RDF's expression based on the Lennard-Jones (LJ) potential which was in good agreement with the molecular dynamics simulations. In this work, we have shown that our results based on HFD-like potential can describe the temperature dependence of the surface tension superior than that of LJ potential.

Relativistic semiempirical-core-potential calculations in Ca+,Sr+ , and Ba+ ions on Lagrange meshes

NASA Astrophysics Data System (ADS)

Filippin, Livio; Schiffmann, Sacha; Dohet-Eraly, Jérémy; Baye, Daniel; Godefroid, Michel

2018-01-01

Relativistic atomic structure calculations are carried out in alkaline-earth-metal ions using a semiempirical-core-potential approach. The systems are partitioned into frozen-core electrons and an active valence electron. The core orbitals are defined by a Dirac-Hartree-Fock calculation using the grasp2k package. The valence electron is described by a Dirac-like Hamiltonian involving a core-polarization potential to simulate the core-valence electron correlation. The associated equation is solved with the Lagrange-mesh method, which is an approximate variational approach having the form of a mesh calculation because of the use of a Gauss quadrature to calculate matrix elements. Properties involving the low-lying metastable D 3 /2 ,5 /2 2 states of Ca+, Sr+, and Ba+ are studied, such as polarizabilities, one- and two-photon decay rates, and lifetimes. Good agreement is found with other theory and observation, which is promising for further applications in alkalilike systems.

Equation of state for neutron stars. Some recent developments

NASA Astrophysics Data System (ADS)

Haensel, P.; Fortin, M.

2017-12-01

Calculations using the chiral effective field theory (ChEFT) indicate that the four-body force contribution to the equation of state (EOS) of pure neutron matter (PNM) at the nuclear density n 0 is negligibly small. However, the overall uncertainty in the EOS of PNM at n 0 remains ∼ 20%. Relativistic mean field (RMF) calculations with in-medium scaling, and including hyperons and Δ resonances, can be made consistent with recent nuclear and astrophysical constraints. Dirac-Brueckner-Hartree-Fock calculations with some medium dependence of the nuclear interaction yield neutron star (NS) models with hyperonic cores consistent with 2 M⊙ stars and agreeing with the saturation parameters of nuclear matter. Many unified EOS for the NS crust and core were calculated, and are reviewed here. The effect of the finite size of baryons on the EOS, its treatment via the excluded-volume approximation, and its relevance for the hypothetical hybrid-star twins at ∼ 2 M⊙ are dicussed.

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

PubMed

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

2013-08-21

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

A general range-separated double-hybrid density-functional theory

NASA Astrophysics Data System (ADS)

Kalai, Cairedine; Toulouse, Julien

2018-04-01

A range-separated double-hybrid (RSDH) scheme which generalizes the usual range-separated hybrids and double hybrids is developed. This scheme consistently uses a two-parameter Coulomb-attenuating-method (CAM)-like decomposition of the electron-electron interaction for both exchange and correlation in order to combine Hartree-Fock exchange and second-order Møller-Plesset (MP2) correlation with a density functional. The RSDH scheme relies on an exact theory which is presented in some detail. Several semi-local approximations are developed for the short-range exchange-correlation density functional involved in this scheme. After finding optimal values for the two parameters of the CAM-like decomposition, the RSDH scheme is shown to have a relatively small basis dependence and to provide atomization energies, reaction barrier heights, and weak intermolecular interactions globally more accurate or comparable to range-separated MP2 or standard MP2. The RSDH scheme represents a new family of double hybrids with minimal empiricism which could be useful for general chemical applications.

A new approach to barrier-top fission dynamics

NASA Astrophysics Data System (ADS)

Bertsch, G. F.; Mehlhaff, J. M.

2016-06-01

We proposed a calculational framework for describing induced fission that avoids the Bohr-Wheeler assumption of well-defined fission channels. The building blocks of our approach are configurations that form a discrete, orthogonal basis and can be characterized by both energy and shape. The dynamics is to be determined by interaction matrix elements between the states rather than by a Hill-Wheeler construction of a collective coordinate. Within our approach, several simple limits can be seen: diffusion; quantized conductance; and ordinary decay through channels. The specific proposal for the discrete basis is to use the Kπ quantum numbers of the axially symmetric Hartree-Fock approximation to generate the configurations. Fission paths would be determined by hopping from configuration to configuration via the residual interaction. We show as an example the configurations needed to describe a fictitious fission decay 32S → 16 O + 16 O. We also examine the geometry of the path for fission of 236U, measuring distances by the number of jumps needed to go to a new Kπ partition.

Transient and Sharvin resistances of Luttinger liquids

NASA Astrophysics Data System (ADS)

Kloss, Thomas; Weston, Joseph; Waintal, Xavier

2018-04-01

Although the intrinsic conductance of an interacting one-dimensional system is renormalized by the electron-electron correlations, it has been known for some time that this renormalization is washed out by the presence of the (noninteracting) electrodes to which the wire is connected. Here, we study the transient conductance of such a wire: a finite voltage bias is suddenly applied across the wire and we measure the current before it has enough time to reach its stationary value. These calculations allow us to extract the Sharvin (contact) resistance of Luttinger and Fermi liquids. In particular, we find that a perfect junction between a Fermi liquid electrode and a Luttinger liquid electrode is characterized by a contact resistance that consists of half the quantum of conductance in series with half the intrinsic resistance of an infinite Luttinger liquid. These results were obtained using two different methods: a dynamical Hartree-Fock approach and a self-consistent Boltzmann approach. Although these methods are formally approximate, we find a perfect match with the exact results of Luttinger/Fermi liquid theory.

Optical properties of 3d transition-metal-doped MgAl2O4 spinels

NASA Astrophysics Data System (ADS)

Izumi, K.; Miyazaki, S.; Yoshida, S.; Mizokawa, T.; Hanamura, E.

2007-08-01

Strong emission bands in the visible region are observed in MgAl2O4 crystals doped with transition-metal ions under excitation at the band-to-band transitions. We report optical responses of Cr-, Co-, and Ni-doped MgAl2O4 and present optical models for M -doped MgAl2O4 ( M=Ti , V, Cr, Mn, Co, and Ni) to describe the charge-transfer transitions and the transitions between multiplet levels of 3d electrons, which are observed competitively or coexisting, depending on the number of 3d electrons. While the optical responses of Cr- and Ni-doped MgAl2O4 are dominated by the multiplet-multiplet transitions, those of Ti- and V-doped MgAl2O4 are governed by the charge-transfer transitions. The two kinds of transitions coexist in the Mn- and Co-doped MgAl2O4 . These behaviors are well understood based on the numerical results of unrestricted Hartree-Fock approximation.

Towards an exact correlated orbital theory for electrons

NASA Astrophysics Data System (ADS)

Bartlett, Rodney J.

2009-12-01

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

Photoluminescence and gain/absorption spectra of a driven-dissipative electron-hole-photon condensate

NASA Astrophysics Data System (ADS)

Hanai, Ryo; Littlewood, Peter B.; Ohashi, Yoji

2018-06-01

We investigate theoretically nonequilibrium effects on photoluminescence and gain/absorption spectra of a driven-dissipative exciton-polariton condensate, by employing the combined Hartree-Fock-Bogoliubov theory with the generalized random phase approximation extended to the Keldysh formalism. Our calculated photoluminescence spectra is in semiquantitative agreement with experiments, where features such as a blue shift of the emission from the condensate, the appearance of the dispersionless feature of a diffusive Goldstone mode, and the suppression of the dispersive profile of the mode are obtained. We show that the nonequilibrium nature of the exciton-polariton condensate strongly suppresses the visibility of the Bogoliubov dispersion in the negative energy branch (ghost branch) in photoluminescence spectra. We also show that the trace of this branch can be captured as a hole burning effect in gain/absorption spectra. Our results indicate that the nonequilibrium nature of the exciton-polariton condensate strongly reduces quantum depletion, while a scattering channel to the ghost branch is still present.

Outstanding performance of configuration interaction singles and doubles using exact exchange Kohn-Sham orbitals in real-space numerical grid method

NASA Astrophysics Data System (ADS)

Lim, Jaechang; Choi, Sunghwan; Kim, Jaewook; Kim, Woo Youn

2016-12-01

To assess the performance of multi-configuration methods using exact exchange Kohn-Sham (KS) orbitals, we implemented configuration interaction singles and doubles (CISD) in a real-space numerical grid code. We obtained KS orbitals with the exchange-only optimized effective potential under the Krieger-Li-Iafrate (KLI) approximation. Thanks to the distinctive features of KLI orbitals against Hartree-Fock (HF), such as bound virtual orbitals with compact shapes and orbital energy gaps similar to excitation energies; KLI-CISD for small molecules shows much faster convergence as a function of simulation box size and active space (i.e., the number of virtual orbitals) than HF-CISD. The former also gives more accurate excitation energies with a few dominant configurations than the latter, even with many more configurations. The systematic control of basis set errors is straightforward in grid bases. Therefore, grid-based multi-configuration methods using exact exchange KS orbitals provide a promising new way to make accurate electronic structure calculations.

The AB Initio Mia Method: Theoretical Development and Practical Applications

NASA Astrophysics Data System (ADS)

Peeters, Anik

The bottleneck in conventional ab initio Hartree -Fock calculations is the storage of the electron repulsion integrals because their number increases with the fourth power of the number of basis functions. This problem can be solved by a combination of the multiplicative integral approximation (MIA) and the direct SCF method. The MIA approach was successfully applied in the geometry optimisation of some biologically interesting compounds like the neurolepticum Haloperidol and two TIBO derivatives, inactivators of HIV1. In this thesis the potency of the MIA-method is shown by the application of this method in the calculation of the forces on the nuclei. In addition, the MIA method enabled the development of a new model for performing crystal field studies: the supermolecule model. The results for this model are in better agreement with experimental data than the results for the point charge model. This is illustrated by the study of some small molecules in the solid state: 2,3-diketopiperazine, formamide oxime and two polymorphic forms of glycine, alpha-glycine and beta-glycine.

Weak-interaction rates in stellar conditions

NASA Astrophysics Data System (ADS)

Sarriguren, Pedro

2018-05-01

Weak-interaction rates, including β-decay and electron captures, are studied in several mass regions at various densities and temperatures of astrophysical interest. In particular, we study odd-A nuclei in the pf-shell region, which are involved in presupernova formations. Weak rates are relevant to understand the late stages of the stellar evolution, as well as the nucleosynthesis of heavy nuclei. The nuclear structure involved in the weak processes is studied within a quasiparticle proton-neutron random-phase approximation with residual interactions in both particle-hole and particle-particle channels on top of a deformed Skyrme Hartree-Fock mean field with pairing correlations. First, the energy distributions of the Gamow-Teller strength are discussed and compared with the available experimental information, measured under terrestrial conditions from charge-exchange reactions. Then, the sensitivity of the weak-interaction rates to both astrophysical densities and temperatures is studied. Special attention is paid to the relative contribution to these rates of thermally populated excited states in the decaying nucleus and to the electron captures from the degenerate electron plasma.

Extended Lagrangian Excited State Molecular Dynamics.

PubMed

Bjorgaard, J A; Sheppard, D; Tretiak, S; Niklasson, A M N

2018-02-13

An extended Lagrangian framework for excited state molecular dynamics (XL-ESMD) using time-dependent self-consistent field theory is proposed. The formulation is a generalization of the extended Lagrangian formulations for ground state Born-Oppenheimer molecular dynamics [Phys. Rev. Lett. 2008 100, 123004]. The theory is implemented, demonstrated, and evaluated using a time-dependent semiempirical model, though it should be generally applicable to ab initio theory. The simulations show enhanced energy stability and a significantly reduced computational cost associated with the iterative solutions of both the ground state and the electronically excited states. Relaxed convergence criteria can therefore be used both for the self-consistent ground state optimization and for the iterative subspace diagonalization of the random phase approximation matrix used to calculate the excited state transitions. The XL-ESMD approach is expected to enable numerically efficient excited state molecular dynamics for such methods as time-dependent Hartree-Fock (TD-HF), Configuration Interactions Singles (CIS), and time-dependent density functional theory (TD-DFT).

Communication: A reduced scaling J-engine based reformulation of SOS-MP2 using graphics processing units.

PubMed

Maurer, S A; Kussmann, J; Ochsenfeld, C

2014-08-07

We present a low-prefactor, cubically scaling scaled-opposite-spin second-order Møller-Plesset perturbation theory (SOS-MP2) method which is highly suitable for massively parallel architectures like graphics processing units (GPU). The scaling is reduced from O(N⁵) to O(N³) by a reformulation of the MP2-expression in the atomic orbital basis via Laplace transformation and the resolution-of-the-identity (RI) approximation of the integrals in combination with efficient sparse algebra for the 3-center integral transformation. In contrast to previous works that employ GPUs for post Hartree-Fock calculations, we do not simply employ GPU-based linear algebra libraries to accelerate the conventional algorithm. Instead, our reformulation allows to replace the rate-determining contraction step with a modified J-engine algorithm, that has been proven to be highly efficient on GPUs. Thus, our SOS-MP2 scheme enables us to treat large molecular systems in an accurate and efficient manner on a single GPU-server.

Nuclear relaxation and vibrational contributions to the static electrical properties of polyatomic molecules: beyond the Hartree-Fock approximation

NASA Astrophysics Data System (ADS)

Luis, Josep M.; Martí, Josep; Duran, Miquel; Andrés, JoséL.

1997-04-01

Electronic and nuclear contributions to the static molecular electrical properties, along with the Stark tuning rate ( δνE ) and the infrared cross section changes ( δSE) have been calculated at the SCF level and at different correlated levels of theory, using a TZ2P basis set and finite field techniques. Nuclear contributions to these molecular properties have also been calculated using a recent analytical approach that allow both to check the accuracy of the finite field values, and to evaluate the importance of higher-order derivatives. The HF, CO, H 2O, H 2CO, and CH 4 molecules have been studied and the results compared to experimental date when available. The paper shows that nuclear relaxation and vibrational contributions must be included in order to obtain accurate values of the static electrical properties. Two different, combined approaches are proposed to predict experimental values of the electrical properties to an error smaller than 5%.

Quantum-mechanical predictions of electron-induced ionization cross sections of DNA components

NASA Astrophysics Data System (ADS)

Champion, Christophe

2013-05-01

Ionization of biomolecules remains still today rarely investigated on both the experimental and the theoretical sides. In this context, the present work appears as one of the first quantum mechanical approaches providing a multi-differential description of the electron-induced ionization process of the main DNA components for impact energies ranging from the target ionization threshold up to about 10 keV. The cross section calculations are here performed within the 1st Born approximation framework in which the ejected electron is described by a Coulomb wave whereas the incident and the scattered electrons are both described by a plane wave. The biological targets of interest, namely, the DNA nucleobases and the sugar-phosphate backbone, are here described by means of the GAUSSIAN 09 system using the restricted Hartree-Fock method with geometry optimization. The theoretical predictions also obtained have shown a reasonable agreement with the experimental total ionization cross sections while huge discrepancies have been pointed out with existing theoretical models, mainly developed within a semi-classical framework.

Computation of indirect nuclear spin-spin couplings with reduced complexity in pure and hybrid density functional approximations.

PubMed

Luenser, Arne; Kussmann, Jörg; Ochsenfeld, Christian

2016-09-28

We present a (sub)linear-scaling algorithm to determine indirect nuclear spin-spin coupling constants at the Hartree-Fock and Kohn-Sham density functional levels of theory. Employing efficient integral algorithms and sparse algebra routines, an overall (sub)linear scaling behavior can be obtained for systems with a non-vanishing HOMO-LUMO gap. Calculations on systems with over 1000 atoms and 20 000 basis functions illustrate the performance and accuracy of our reference implementation. Specifically, we demonstrate that linear algebra dominates the runtime of conventional algorithms for 10 000 basis functions and above. Attainable speedups of our method exceed 6 × in total runtime and 10 × in the linear algebra steps for the tested systems. Furthermore, a convergence study of spin-spin couplings of an aminopyrazole peptide upon inclusion of the water environment is presented: using the new method it is shown that large solvent spheres are necessary to converge spin-spin coupling values.

Hybrid configuration mixing model for odd nuclei

NASA Astrophysics Data System (ADS)

Colò, G.; Bortignon, P. F.; Bocchi, G.

2017-03-01

In this work, we introduce a new approach which is meant to be a first step towards complete self-consistent low-lying spectroscopy of odd nuclei. So far, we essentially limit ourselves to the description of a double-magic core plus an extra nucleon. The model does not contain any free adjustable parameter and is instead based on a Hartree-Fock (HF) description of the particle states in the core, together with self-consistent random-phase approximation (RPA) calculations for the core excitations. We include both collective and noncollective excitations, with proper care of the corrections due to the overlap between them (i.e., due to the nonorthonormality of the basis). As a consequence, with respect to traditional particle-vibration coupling calculations in which one can only address single-nucleon states and particle-vibration multiplets, we can also describe states of shell-model types like 2 particle-1 hole. We will report results for 49Ca and 133Sb and discuss future perspectives.

Existence problem of proton semi-bubble structure in the 21 + state of 34Si

NASA Astrophysics Data System (ADS)

Wu, Feng; Bai, C. L.; Yao, J. M.; Zhang, H. Q.; Zhang, X. Z.

2017-09-01

The fully self-consistent Hartree-Fock (HF) plus random phase approximation (RPA) based on Skyrme-type interaction is used to study the existence problem of proton semi-bubble structure in the 21+ state of 34Si. The experimental excitation energy and the transition strength of the 21+ state in 34Si can be reproduced quite well. The tensor effect is also studied. It is shown that the tensor interaction has a notable impact on the excitation energy of the 21+ state and a small effect on the B( E2) value. Besides, its effect on the density distributions in the ground and 21+ state of 34Si is negligible. Our present results with T36 and T44 show that the 21+ state of 34Si is mainly caused by proton transition from π 1d_{5/2} orbit to π 2s_{1/2} orbit, and the existence of a proton semi-bubble structure in this state is very unlikely.

Long-range corrected density functional through the density matrix expansion based semilocal exchange hole.

PubMed

Patra, Bikash; Jana, Subrata; Samal, Prasanjit

2018-03-28

The exchange hole, which is one of the principal constituents of the density functional formalism, can be used to design accurate range-separated hybrid functionals in association with appropriate correlation. In this regard, the exchange hole derived from the density matrix expansion has gained attention due to its fulfillment of some of the desired exact constraints. Thus, the new long-range corrected density functional proposed here combines the meta generalized gradient approximation level exchange functional designed from the density matrix expansion based exchange hole coupled with the ab initio Hartree-Fock exchange through the range separation of the Coulomb interaction operator using the standard error function technique. Then, in association with the Lee-Yang-Parr correlation functional, the assessment and benchmarking of the above newly constructed range-separated functional with various well-known test sets shows its reasonable performance for a broad range of molecular properties, such as thermochemistry, non-covalent interaction and barrier heights of the chemical reactions.

Hartree-Fock mass formulas and extrapolation to new mass data

NASA Astrophysics Data System (ADS)

Goriely, S.; Samyn, M.; Heenen, P.-H.; Pearson, J. M.; Tondeur, F.

2002-08-01

The two previously published Hartree-Fock (HF) mass formulas, HFBCS-1 and HFB-1 (HF-Bogoliubov), are shown to be in poor agreement with new Audi-Wapstra mass data. The problem lies first with the prescription adopted for the cutoff of the single-particle spectrum used with the δ-function pairing force, and second with the Wigner term. We find an optimal mass fit if the spectrum is cut off both above EF+15 MeV and below EF-15 MeV, EF being the Fermi energy of the nucleus in question. In addition to the Wigner term of the form VW exp(-λ|N-Z|/A) already included in the two earlier HF mass formulas, we find that a second Wigner term linear in |N-Z| leads to a significant improvement in lighter nuclei. These two features are incorporated into our new Hartree-Fock-Bogoliubov model, which leads to much improved extrapolations. The 18 parameters of the model are fitted to the 2135 measured masses for N,Z>=8 with an rms error of 0.674 MeV. With this parameter set a complete mass table, labeled HFB-2, has been constructed, going from one drip line to the other, up to Z=120. The new pairing-cutoff prescription favored by the new mass data leads to weaker neutron-shell gaps in neutron-rich nuclei.

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.

Interpretation of the silver L X-ray spectrum

NASA Technical Reports Server (NTRS)

Chen, M. H.; Crasemann, B.; Aoyagi, M.; Mark, H.

1977-01-01

Silver L X-ray energies were calculated using theoretical binding energies from relaxed orbital relativistic Hartree-Fock-Slater calculations. Theoretical X-ray energies are compared with experimental results.

Roothaan-Hartree-Fock ground-state atomic wave functions: Slater-type orbital expansions and expectation values for Z = 2-54

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

Bunge, C.F.; Barrientos, J.A.; Bunge, A.V.

1993-01-01

Roothaan-Hartree-Fock orbitals expressed in a Slater-type basis are reported for the ground states of He through Xe. Energy accuracy ranges between 8 and 10 significant figures, reducing by between 21 and 2,770 times the energy errors of the previous such compilation (E. Clementi and C. Roetti, Atomic Data and Nuclear Data Tables 14, 177, 1974). For each atom, the total energy, kinetic energy, potential energy, virial ratio, electron density at the nucleus, and the Kato cusp are given together with radial expectation values [l angle]r[sup n][r angle] with n from [minus]3 to 2 for each orbital, orbital energies, and orbitalmore » expansion coefficients. 29 refs., 1 tab.« less

Vibrational spectroscopic investigation of p-, m- and o-nitrobenzonitrile by using Hartree-Fock and density functional theory

NASA Astrophysics Data System (ADS)

Sert, Y.; Ucun, F.

2013-08-01

In the present work, the theoretical vibrational spectra of p-, m- and o-nitrobenzonitrile molecules have been analyzed. The harmonic vibrational frequencies and geometric parameters (bond lengths and bond angles) of these molecules have been calculated using ab initio Hartree-Fock and density functional theory methods with 6-311++G(d,p) basis set by Gaussian 03 W, for the first time. Assignments of the vibrational frequencies have been performed by potential energy distribution by using VEDA 4 program. The optimized geometric parameters and harmonic vibrational frequencies have been compared with the corresponding experimental data and seen to be in a good agreement with each other. Also, the highest occupied molecular orbital and lowest unoccupied molecular orbital energies have been obtained.

Ground-state properties of the three-band Hubbard model

NASA Astrophysics Data System (ADS)

Zhang, Shiwei; Vitali, Ettore; Chiciak, Adam; Shi, Hao

The three-band Hubbard model proposed by Emery describes the CuO2 plane in cuprate superconductors by retaining both Cu and O orbitals in a minimal sense. Applying the latest developments in the auxiliary-field quantum Monte Carlo (AFQMC) method, we investigate ground-state properties of this model at half-filling and when lightly (under-)doped. The AFQMC uses generalized Hartree-Fock (GHF) trial wave functions to control the sign problem. A self-consistent constraint is applied. We also determine the unrestricted Hartree-Fock (UHF) and GHF ground states and compare their predictions with those from AFQMC. Similarities and differences between the three-band model and one-band Hubbard model will be discussed. Supported by NSF, and the Simons Foundation. Computing is carried out at the Extreme Science and Engineering Discovery Environment(XSEDE).

Molecular structure and vibrational spectra of three substituted 4-thioflavones by density functional theory and ab initio Hartree-Fock calculations

NASA Astrophysics Data System (ADS)

Li, Xiao-Hong; Liu, Xiang-Ru; Zhang, Xian-Zhou

2011-01-01

The vibrational frequencies of three substituted 4-thioflavones in the ground state have been calculated using the Hartree-Fock and density functional method (B3LYP) with 6-31G* and 6-31+G** basis sets. The structural analysis shows that there exists H-bonding in the selected compounds and the hydrogen bond lengths increase with the augment of the conjugate parameters of the substituent group on the benzene ring. A complete vibrational assignment aided by the theoretical harmonic wavenumber analysis was proposed. The theoretical spectrograms for FT-IR spectra of the title compounds have been constructed. In addition, it is noted that the selected compounds show significant activity against Shigella flexniri. Several electronic properties and thermodynamic parameters were also calculated.

Parallel scalability of Hartree-Fock calculations

NASA Astrophysics Data System (ADS)

Chow, Edmond; Liu, Xing; Smelyanskiy, Mikhail; Hammond, Jeff R.

2015-03-01

Quantum chemistry is increasingly performed using large cluster computers consisting of multiple interconnected nodes. For a fixed molecular problem, the efficiency of a calculation usually decreases as more nodes are used, due to the cost of communication between the nodes. This paper empirically investigates the parallel scalability of Hartree-Fock calculations. The construction of the Fock matrix and the density matrix calculation are analyzed separately. For the former, we use a parallelization of Fock matrix construction based on a static partitioning of work followed by a work stealing phase. For the latter, we use density matrix purification from the linear scaling methods literature, but without using sparsity. When using large numbers of nodes for moderately sized problems, density matrix computations are network-bandwidth bound, making purification methods potentially faster than eigendecomposition methods.

Calculation of the vibrational excited states of malonaldehyde and their tunneling splittings with the multi-configuration time-dependent Hartree method

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

Schröder, Markus, E-mail: Markus.Schroeder@pci.uni-heidelberg.de; Meyer, Hans-Dieter, E-mail: Hans-Dieter.Meyer@pci.uni-heidelberg.de

2014-07-21

We report energies and tunneling splittings of vibrational excited states of malonaldehyde which have been obtained using full dimensional quantum mechanical calculations. To this end we employed the multi configuration time-dependent Hartree method. The results have been obtained using a recently published potential energy surface [Y. Wang, B. J. Braams, J. M. Bowman, S. Carter, and D. P. Tew, J. Chem. Phys. 128, 224314 (2008)] which has been brought into a suitable form by a modified version of the n-mode representation which was used with two different arrangements of coordinates. The relevant terms of the expansion have been identified withmore » a Metropolis algorithm and a diffusion Monte-Carlo technique, respectively.« less

Solution of the Skyrme Hartree Fock Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (V) HFODD(v2.08k)

NASA Astrophysics Data System (ADS)

Dobaczewski, J.; Olbratowski, P.

2005-05-01

We describe the new version (v2.08k) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. Similarly as in the previous version (v2.08i), all symmetries can be broken, which allows for calculations with angular frequency and angular momentum tilted with respect to the mass distribution. In the new version, three minor errors have been corrected. New Version Program SummaryTitle of program: HFODD; version: 2.08k Catalogue number: ADVA Catalogue number of previous version: ADTO (Comput. Phys. Comm. 158 (2004) 158) Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVA Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Does the new version supersede the previous one: yes Computers on which this or another recent version has been tested: SG Power Challenge L, Pentium-II, Pentium-III, AMD-Athlon Operating systems under which the program has been tested: UNIX, LINUX, Windows-2000 Programming language used: Fortran Memory required to execute with typical data: 10M words No. of bits in a word: 64 No. of lines in distributed program, including test data, etc.: 52 631 No. of bytes in distributed program, including test data, etc.: 266 885 Distribution format:tar.gz Nature of physical problem: The nuclear mean-field and an analysis of its symmetries in realistic cases are the main ingredients of a description of nuclear states. Within the Local Density Approximation, or for a zero-range velocity-dependent Skyrme interaction, the nuclear mean-field is local and velocity dependent. The locality allows for an effective and fast solution of the self-consistent Hartree-Fock equations, even for heavy nuclei, and for various nucleonic ( n-particle n-hole) configurations, deformations, excitation energies, or angular momenta. Similar Local Density Approximation in the particle-particle channel, which is equivalent to using a zero-range interaction, allows for a simple implementation of pairing effects within the Hartree-Fock-Bogolyubov method. Solution method: The program uses the Cartesian harmonic-oscillator basis to expand single-particle or single-quasiparticle wave functions of neutrons and protons interacting by means of the Skyrme effective interaction and zero-range pairing interaction. The expansion coefficients are determined by the iterative diagonalization of the mean field Hamiltonians or Routhians which depend non-linearly on the local neutron and proton densities. Suitable constrains are used to obtain states corresponding to a given configuration, deformation or angular momentum. The method of solution has been presented in [J. Dobaczewski, J. Dudek, Comput. Phys. Comm. 102 (1997) 166]. Summary of revisions: 1. Incorrect value of the " t" force parameter for SLY5 has been corrected. 2. Opening of an empty file "FILREC" for IWRIRE=-1 has been removed. 3. Call to subroutine "OLSTOR" has been moved before that to "SPZERO". In this way, correct data transferred to "FLISIG", "FLISIM", "FLISIQ" or "FLISIZ" allow for a correct determination of the candidate states for diabatic blocking. These corrections pertain to the user interface of the code and do not affect results performed for forces other than SLY5. Restrictions on the complexity of the problem: The main restriction is the CPU time required for calculations of heavy deformed nuclei and for a given precision required. Pairing correlations are only included for even-even nuclei and conserved simplex symmetry. Unusual features: The user must have access to the NAGLIB subroutine F02AXE or to the LAPACK subroutines ZHPEV or ZHPEVX, which diagonalize complex Hermitian matrices, or provide another subroutine which can perform such a task. The LAPACK subroutines ZHPEV and ZHPEVX can be obtained from the Netlib Repository at University of Tennessee, Knoxville: http://netlib2.cs.utk.edu/cgi-bin/netlibfiles.pl?filename=/lapack/complex16/zhpev.f and http://netlib2.cs.utk.edu/cgi-bin/netlibfiles.pl?filename=/lapack/complex16/zhpevx.f, respectively. The code is written in single-precision for use on a 64-bit processor. The compiler option -r8 or +autodblpad (or equivalent) has to be used to promote all real and complex single-precision floating-point items to double precision when the code is used on a 32-bit machine. Typical running time: One Hartree-Fock iteration for the superdeformed, rotating, parity conserving state of 15266Dy 86 takes about six seconds on the AMD-Athlon 1600+ processor. Starting from the Woods-Saxon wave functions, about fifty iterations are required to obtain the energy converged within the precision of about 0.1 keV. In the case when every value of the angular velocity is converged separately, the complete superdeformed band with precisely determined dynamical moments J can be obtained within forty minutes of CPU on the AMD-Athlon 1600+ processor. This time can be often reduced by a factor of three when a self-consistent solution for a given rotational frequency is used as a starting point for a neighboring rotational frequency. Additional comments: The actual output files obtained during user's test runs may differ from those provided in the distribution file. The differences may occur because various compilers may produce different results in the following aspects: The initial Nilsson spectrum (the starting point of each run) is Kramers degenerate, and thus the diagonalization routine may return the degenerate states in arbitrary order and in arbitrary mixture. For an odd number of particles, one of these states becomes occupied, and the other one is left empty. Therefore, starting points of such runs can widely vary from compiler to compiler, and these differences cannot be controlled. For axial shapes, two quadrupole moments (with respect to two different axes) become very small and their values reflect only a numerical noise. However, depending on which of these two moments is smaller, the intrinsic-frame Euler axes will differ, most often by 180 degrees. Hence, signs of some moments and angular momenta may vary from compiler to compiler, and these differences cannot be controlled. These differences are insignificant. The final energies do not depend on them, although the intermediate results can.

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.

All-electron molecular Dirac-Hartree-Fock calculations - Properties of the group IV monoxides GeO, SnO, and PbO

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.

1993-01-01

Dirac-Hartree-Fock calculations have been carried out on the ground states of the group IV monoxides GeO, SnO and PbO. Geometries, dipole moments and infrared data are presented. For comparison, nonrelativistic, first-order perturbation and relativistic effective core potential calculations have also been carried out. Where appropriate the results are compared with the experimental data and previous calculations. Spin-orbit effects are of great importance for PbO, where first-order perturbation theory including only the mass-velocity and Darwin terms is inadequate to predict the relativistic corrections to the properties. The relativistic effective core potential results show a larger deviation from the all-electron values than for the hydrides, and confirm the conclusions drawn on the basis of the hydride calculations.

All-electron molecular Dirac-Hartree-Fock calculations: Properties of the group IV monoxides GeO, SnO and PbO

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.

1991-01-01

Dirac-Hartree-Fock calculations have been carried out on the ground states of the group IV monoxides GeO, SnO and PbO. Geometries, dipole moments and infrared data are presented. For comparison, nonrelativistic, first-order perturbation and relativistic effective core potential calculations have also been carried out. Where appropriate the results are compared with the experimental data and previous calculations. Spin-orbit effects are of great importance for PbO, where first-order perturbation theory including only the mass-velocity and Darwin terms is inadequate to predict the relativistic corrections to the properties. The relativistic effective core potential results show a larger deviation from the all-electron values than for the hydrides, and confirm the conclusions drawn on the basis of the hydride calculations.

Electrical transport properties of CuXSn1-X metallic glasses

NASA Astrophysics Data System (ADS)

Vora, A. M.; Gajjar, P. N.

2018-05-01

In the present paper, we report the electrical resistivity (ρ), the thermoelectric power (TEP) and thermal conductivity (σ) of CuXSn1-X metallic glasses computed from Faber-Ziman formulation with Percus-Yevic (PY) hard sphere structure factors of Ashcroft and Langreth. Our well-recognized model potential is used to represent ionic interaction for the first time with seven local field correction functions due to Hartree (H), Hubbard-Sham (HS), Vashishta-Singwi (VS), Taylor (T), Ichimaru-Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) in the present computation and found suitable for such study. The percentile influence of various local field corrections with respect to Hartree (H) is found in the range of 17.35%-71.55%. It is concluded that, the comparison of present and experimental findings of electrical resistivity (ρ) is highly promising.

A long-range-corrected density functional that performs well for both ground-state properties and time-dependent density functional theory excitation energies, including charge-transfer excited states.

PubMed

Rohrdanz, Mary A; Martins, Katie M; Herbert, John M

2009-02-07

We introduce a hybrid density functional that asymptotically incorporates full Hartree-Fock exchange, based on the long-range-corrected exchange-hole model of Henderson et al. [J. Chem. Phys. 128, 194105 (2008)]. The performance of this functional, for ground-state properties and for vertical excitation energies within time-dependent density functional theory, is systematically evaluated, and optimal values are determined for the range-separation parameter, omega, and for the fraction of short-range Hartree-Fock exchange. We denote the new functional as LRC-omegaPBEh, since it reduces to the standard PBEh hybrid functional (also known as PBE0 or PBE1PBE) for a certain choice of its two parameters. Upon optimization of these parameters against a set of ground- and excited-state benchmarks, the LRC-omegaPBEh functional fulfills three important requirements: (i) It outperforms the PBEh hybrid functional for ground-state atomization energies and reaction barrier heights; (ii) it yields statistical errors comparable to PBEh for valence excitation energies in both small and medium-sized molecules; and (iii) its performance for charge-transfer excitations is comparable to its performance for valence excitations. LRC-omegaPBEh, with the parameters determined herein, is the first density functional that satisfies all three criteria. Notably, short-range Hartree-Fock exchange appears to be necessary in order to obtain accurate ground-state properties and vertical excitation energies using the same value of omega.

A finite difference Hartree-Fock program for atoms and diatomic molecules

NASA Astrophysics Data System (ADS)

Kobus, Jacek

2013-03-01

The newest version of the two-dimensional finite difference Hartree-Fock program for atoms and diatomic molecules is presented. This is an updated and extended version of the program published in this journal in 1996. It can be used to obtain reference, Hartree-Fock limit values of total energies and multipole moments for a wide range of diatomic molecules and their ions in order to calibrate existing and develop new basis sets, calculate (hyper)polarizabilities (αzz, βzzz, γzzzz, Az,zz, Bzz,zz) of atoms, homonuclear and heteronuclear diatomic molecules and their ions via the finite field method, perform DFT-type calculations using LDA or B88 exchange functionals and LYP or VWN correlations ones or the self-consistent multiplicative constant method, perform one-particle calculations with (smooth) Coulomb and Krammers-Henneberger potentials and take account of finite nucleus models. The program is easy to install and compile (tarball+configure+make) and can be used to perform calculations within double- or quadruple-precision arithmetic. Catalogue identifier: ADEB_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADEB_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 2 No. of lines in distributed program, including test data, etc.: 171196 No. of bytes in distributed program, including test data, etc.: 9481802 Distribution format: tar.gz Programming language: Fortran 77, C. Computer: any 32- or 64-bit platform. Operating system: Unix/Linux. RAM: Case dependent, from few MB to many GB Classification: 16.1. Catalogue identifier of previous version: ADEB_v1_0 Journal reference of previous version: Comput. Phys. Comm. 98(1996)346 Does the new version supersede the previous version?: Yes Nature of problem: The program finds virtually exact solutions of the Hartree-Fock and density functional theory type equations for atoms, diatomic molecules and their ions. The lowest energy eigenstates of a given irreducible representation and spin can be obtained. The program can be used to perform one-particle calculations with (smooth) Coulomb and Krammers-Henneberger potentials and also DFT-type calculations using LDA or B88 exchange functionals and LYP or VWN correlations ones or the self-consistent multiplicative constant method. Solution method: Single-particle two-dimensional numerical functions (orbitals) are used to construct an antisymmetric many-electron wave function of the restricted open-shell Hartree-Fock model. The orbitals are obtained by solving the Hartree-Fock equations as coupled two-dimensional second-order (elliptic) partial differential equations (PDEs). The Coulomb and exchange potentials are obtained as solutions of the corresponding Poisson equations. The PDEs are discretized by the eighth-order central difference stencil on a two-dimensional single grid, and the resulting large and sparse system of linear equations is solved by the (multicolour) successive overrelaxation ((MC)SOR) method. The self-consistent-field iterations are interwoven with the (MC)SOR ones and orbital energies and normalization factors are used to monitor the convergence. The accuracy of solutions depends mainly on the grid and the system under consideration, which means that within double precision arithmetic one can obtain orbitals and energies having up to 12 significant figures. If more accurate results are needed, quadruple-precision floating-point arithmetic can be used. Reasons for new version: Additional features, many modifications and corrections, improved convergence rate, overhauled code and documentation. Summary of revisions: see ChangeLog found in tar.gz archive Restrictions: The present version of the program is restricted to 60 orbitals. The maximum grid size is determined at compilation time. Unusual features: The program uses two C routines for allocating and deallocating memory. Several BLAS (Basic Linear Algebra System) routines are emulated by the program. When possible they should be replaced by their library equivalents. Additional comments: automake and autoconf tools are required to build and compile the program; checked with f77, gfortran and ifort compilers Running time: Very case dependent - from a few CPU seconds for the H2 defined on a small grid up to several weeks for the Hartree-Fock-limit calculations for 40-50 electron molecules.

On the importance of excited state dynamic response electron correlation in polarizable embedding methods.

PubMed

Eriksen, Janus J; Sauer, Stephan P A; Mikkelsen, Kurt V; Jensen, Hans J Aa; Kongsted, Jacob

2012-09-30

We investigate the effect of including a dynamic reaction field at the lowest possible ab inito wave function level of theory, namely the Hartree-Fock (HF) self-consistent field level within the polarizable embedding (PE) formalism. We formulate HF based PE within the linear response theory picture leading to the PE-random-phase approximation (PE-RPA) and bridge the expressions to a second-order polarization propagator approximation (SOPPA) frame such that dynamic reaction field contributions are included at the RPA level in addition to the static response described at the SOPPA level but with HF induced dipole moments. We conduct calculations on para-nitro-aniline and para-nitro-phenolate using said model in addition to dynamic PE-RPA and PE-CAM-B3LYP. We compare the results to recently published PE-CCSD data and demonstrate how the cost effective SOPPA-based model successfully recovers a great portion of the inherent PE-RPA error when the observable is the solvatochromic shift. We furthermore demonstrate that whenever the change in density resulting from the ground state-excited state electronic transition in the solute is not associated with a significant change in the electric field, dynamic response contributions formulated at the HF level of theory manage to capture the majority of the system response originating from derivative densities. Copyright © 2012 Wiley Periodicals, Inc.

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

PubMed

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

2017-01-10

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

Bose-Einstein condensation in atomic alkali gases

NASA Astrophysics Data System (ADS)

Dodd, Robert J.

1998-05-01

I present a review of the time-independent Gross-Pitaevskii (GP), Bogoliubov, and finite-temperature Hartree-Fock-Bogoliubov (HFB) mean-field theories used to study trapped, Bose-Einstein condensed alkali gases. Numerical solutions of the (zero-temperature) GP equation are presented for attractive (negative scattering length) and repulsive (positive scattering length) interactions. Comparison is made with the Thomas-Fermi and (variational) trial wavefunction appr oximations that are used in the literature to study condensed gases. Numerical calculations of the (zero-temperature) Bogoliubov quasi-particle excitation frequencies are found to be in excellent agreement with the experimental results. The finite-temperature properties of condensed gases are examined using the Popov approximation (of the HFB theory) and a simple two-gas model. Specific, quantitative comparisons are made with experimental results for finite-temperature excitation frequencies. Qualitative comparisons are made between the results of the Popov approximation, two-gas model, and other published models for condensate fraction and thermal density distribution. The time-independent mean-field theories are found to be in excellent agreement with experimental results at relatively low temperatures (high condensate fractions). However, at higher temperatures (and condensate fractions of less than 50%) there are significant discrepancies between experimental data and theoretical calculations. This work was undertaken at the University of Maryland at College Park and was supported in part by the National Science Foundation (PHY-9601261) and the U.S. Office of Naval Research.

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.

Kohn's theorem in a superfluid Fermi gas with a Feshbach resonance

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

Ohashi, Y.

2004-12-01

We investigate the dipole mode in a superfluid gas of Fermi atoms trapped in a harmonic potential. According to Kohn's theorem, the frequency of this collective mode is not affected by an interaction between the atoms and is always equal to the trap frequency. This remarkable property, however, does not necessarily hold in an approximate theory. We explicitly prove that the Hartree-Fock-Bogoliubov generalized random phase approximation (HFB-GRPA), including a coupling between fluctuations in the density and Cooper channels, is consistent with both Kohn's theorem as well as Goldstone's theorem. This proof can be immediately extended to the strong-coupling superfluid theorymore » developed by Nozieres and Schmitt-Rink (NSR), where the effect of superfluid fluctuations is included within the Gaussian level. As a result, the NSR-GRPA formalism can be used to study collective modes in the BCS-BEC crossover region in a manner which is consistent with Kohn's theorem. We also include the effect of a Feshbach resonance and a condensate of the associated molecular bound states. A detailed discussion is given of the unusual nature of the Kohn mode eigenfunctions in a Fermi superfluid, in the presence and absence of a Feshbach resonance. When the molecular bosons feel a different trap frequency from the Fermi atoms, the dipole frequency is shown to depend on the strength of effective interaction associated with the Feshbach resonance.« less

Measurement of the interference structure function R{sub LT} for the {sup 12}C(e,e{sup {prime}}p) reaction in the quasielastic region

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

Holtrop, M.; Jordan, D.; McIlvain, T.

1998-12-01

The coincidence cross section and the interference structure function, R{sub LT}, were measured for the {sup 12}C(e,e{sup {prime}}p)thinsp{sup 11}B reaction at quasielastic kinematics and central momentum transfer of {vert_bar}{rvec q}{vert_bar}=400thinspMeV/c. The measurement was at an opening angle of {theta}{sub pq}=11{degree}, covering a range in missing energy of E{sub m}=0 to 65 MeV. The R{sub LT} structure function is found to be consistent with zero for E{sub m}{gt}50thinspMeV, confirming an earlier study which indicated that R{sub L} vanishes in this region. The integrated strengths of the p- and s-shell are compared with a distorted wave impulse approximation (DWIA) calculation. The s-shellmore » strength and shape are also compared with a Hartree Fock{endash}random phase approximation (HF-RPA) calculation. The DWIA calculation does not succeed in giving a consistent description of both the cross section data and the extracted R{sub LT} response for either shell. The HF-RPA calculation describes the data more consistently, which may be due to the inclusion of 2-body currents in this calculation. {copyright} {ital 1998} {ital The American Physical Society}« less

Evaluation of interatomic potentials for rainbow scattering under axial channeling at KCl(0 0 1) surface by three-dimensional computer simulations based on binary collision approximation

NASA Astrophysics Data System (ADS)

Takeuchi, Wataru

2017-05-01

The rainbow angles corresponding to prominent peaks in the angular distributions of scattered projectiles with small angle, attributed to rainbow scattering (RS), under axial surface channeling conditions are strongly influenced by the interatomic potentials between projectiles and target atoms. The dependence of rainbow angles on normal energy of projectile energy to the target surface, being experimentally obtained by Specht et al. for RS of He, N, Ne and Ar atoms under <1 0 0> and <1 1 0> axial channeling conditions at a KCl(0 0 1) surface with projectile energies of 1-60 keV, was evaluated by the three-dimensional computer simulations using the ACOCT code based on the binary collision approximation with interatomic pair potentials. Good agreement between the ACOCT results using the ZBL pair potential and the individual pair potentials calculated from Hartree-Fock (HF) wave functions and the experimental ones was found for RS of He, N and Ne atoms from the atomic rows along <1 0 0> direction. For <1 1 0> direction, the ACOCT results employing the Moliere pair potential with adjustable screening length of O'Connor-Biersack (OB) formula, the ZBL pair potential and the individual HF pair potentials except for Ar → KCl using the OB pair potential are nearly in agreement with the experimental ones.

A highly optimized code for calculating atomic data at neutron star magnetic field strengths using a doubly self-consistent Hartree-Fock-Roothaan method

NASA Astrophysics Data System (ADS)

Schimeczek, C.; Engel, D.; Wunner, G.

2012-07-01

Our previously published code for calculating energies and bound-bound transitions of medium-Z elements at neutron star magnetic field strengths [D. Engel, M. Klews, G. Wunner, Comput. Phys. Comm. 180 (2009) 302-311] was based on the adiabatic approximation. It assumes a complete decoupling of the (fast) gyration of the electrons under the action of the magnetic field and the (slow) bound motion along the field under the action of the Coulomb forces. For the single-particle orbitals this implied that each is a product of a Landau state and an (unknown) longitudinal wave function whose B-spline coefficients were determined self-consistently by solving the Hartree-Fock equations for the many-electron problem on a finite-element grid. In the present code we go beyond the adiabatic approximation, by allowing the transverse part of each orbital to be a superposition of Landau states, while assuming that the longitudinal part can be approximated by the same wave function in each Landau level. Inserting this ansatz into the energy variational principle leads to a system of coupled equations in which the B-spline coefficients depend on the weights of the individual Landau states, and vice versa, and which therefore has to be solved in a doubly self-consistent manner. The extended ansatz takes into account the back-reaction of the Coulomb motion of the electrons along the field direction on their motion in the plane perpendicular to the field, an effect which cannot be captured by the adiabatic approximation. The new code allows for the inclusion of up to 8 Landau levels. This reduces the relative error of energy values as compared to the adiabatic approximation results by typically a factor of three (1/3 of the original error), and yields accurate results also in regions of lower neutron star magnetic field strengths where the adiabatic approximation fails. Further improvements in the code are a more sophisticated choice of the initial wave functions, which takes into account the shielding of the core potential for outer electrons by inner electrons, and an optimal finite-element decomposition of each individual longitudinal wave function. These measures largely enhance the convergence properties compared to the previous code, and lead to speed-ups by factors up to two orders of magnitude compared with the implementation of the Hartree-Fock-Roothaan method used by Engel and Wunner in [D. Engel, G. Wunner, Phys. Rev. A 78 (2008) 032515]. New version program summaryProgram title: HFFER II Catalogue identifier: AECC_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECC_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: v 55 130 No. of bytes in distributed program, including test data, etc.: 293 700 Distribution format: tar.gz Programming language: Fortran 95 Computer: Cluster of 1-13 HP Compaq dc5750 Operating system: Linux Has the code been vectorized or parallelized?: Yes, parallelized using MPI directives. RAM: 1 GByte per node Classification: 2.1 External routines: MPI/GFortran, LAPACK, BLAS, FMlib (included in the package) Catalogue identifier of previous version: AECC_v1_0 Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 302 Does the new version supersede the previous version?: Yes Nature of problem: Quantitative modellings of features observed in the X-ray spectra of isolated magnetic neutron stars are hampered by the lack of sufficiently large and accurate databases for atoms and ions up to the last fusion product, iron, at strong magnetic field strengths. Our code is intended to provide a powerful tool for calculating energies and oscillator strengths of medium-Z atoms and ions at neutron star magnetic field strengths with sufficient accuracy in a routine way to create such databases. Solution method: The Slater determinants of the atomic wave functions are constructed from single-particle orbitals ψi which are products of a wave function in the z direction (the direction of the magnetic field) and an expansion of the wave function perpendicular to the direction of the magnetic field in terms of Landau states, ψi(ρ,φ,z)=Pi(z)∑n=0NLtinϕni(ρ,φ). The tin are expansion coefficients, and the expansion is cut off at some maximum Landau level quantum number n=NL. In the previous version of the code only the lowest Landau level was included (NL=0), in the new version NL can take values of up to 7. As in the previous version of the code, the longitudinal wave functions are expanded in terms of sixth-order B-splines on finite elements on the z axis, with a combination of equidistant and quadratically widening element borders. Both the B-spline expansion coefficients and the Landau weights tin of all orbitals have to be determined in a doubly self-consistent way: For a given set of Landau weights tin, the system of linear equations for the B-spline expansion coefficients, which is equivalent to the Hartree-Fock equations for the longitudinal wave functions, is solved numerically. In the second step, for frozen B-spline coefficients new Landau weights are determined by minimizing the total energy with respect to the Landau expansion coefficients. Both steps require solving non-linear eigenvalue problems of Roothaan type. The procedure is repeated until convergence of both the B-spline coefficients and the Landau weights is achieved. Reasons for new version: The former version of the code was restricted to the adiabatic approximation, which assumes the quantum dynamics of the electrons in the plane perpendicular to the magnetic field to be fixed in the lowest Landau level, n=0. This approximation is valid only if the magnetic field strengths are large compared to the reference magnetic field BZ, for a nuclear charge Z,BZ=Z24.70108×105 T. Summary of revisions: In the new version, the transverse parts of the orbitals are expanded in terms of Landau states up to n=7, and the expansion coefficients are determined, together with the longitudinal wave functions, in a doubly self-consistent way. Thus the back-reaction of the quantum dynamics along the magnetic field direction on the quantum dynamics in the plane perpendicular to it is taken into account. The new ansatz not only increases the accuracy of the results for energy values and transition strengths obtained so far, but also allows their calculation for magnetic field strengths down to B≳BZ, where the adiabatic approximation fails. Restrictions: Intense magnetic field strengths are required, since the expansion of the transverse single-particle wave functions using 8 Landau levels will no longer produce accurate results if the scaled magnetic field strength parameter βZ=B/BZ becomes much smaller than unity. Unusual features: A huge program speed-up is achieved by making use of pre-calculated binary files. These can be calculated with additional programs provided with this package. Running time: 1-30 min.

Theoretical dissociation energies for ionic molecules

NASA Technical Reports Server (NTRS)

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

1986-01-01

Ab initio calculations at the self-consistent-field and singles plus doubles configuration-interaction level are used to determine accurate spectroscopic parameters for most of the alkali and alkaline-earth fluorides, chlorides, oxides, sulfides, hydroxides, and isocyanides. Numerical Hartree-Fock (NHF) calculations are performed on selected systems to ensure that the extended Slater basis sets employed for the diatomic systems are near the Hartree-Fock limit. Extended Gaussian basis sets of at least triple-zeta plus double polarization equality are employed for the triatomic system. With this model, correlation effects are relatively small, but invariably increase the theoretical dissociation energies. The importance of correlating the electrons on both the anion and the metal is discussed. The theoretical dissociation energies are critically compared with the literature to rule out disparate experimental values. Theoretical (sup 2)Pi - (sup 2)Sigma (sup +) energy separations are presented for the alkali oxides and sulfides.

LoFEx - A local framework for calculating excitation energies: Illustrations using RI-CC2 linear response theory.

PubMed

Baudin, Pablo; Kristensen, Kasper

2016-06-14

We present a local framework for the calculation of coupled cluster excitation energies of large molecules (LoFEx). The method utilizes time-dependent Hartree-Fock information about the transitions of interest through the concept of natural transition orbitals (NTOs). The NTOs are used in combination with localized occupied and virtual Hartree-Fock orbitals to generate a reduced excitation orbital space (XOS) specific to each transition where a standard coupled cluster calculation is carried out. Each XOS is optimized to ensure that the excitation energies are determined to a predefined precision. We apply LoFEx in combination with the RI-CC2 model to calculate the lowest excitation energies of a set of medium-sized organic molecules. The results demonstrate the black-box nature of the LoFEx approach and show that significant computational savings can be gained without affecting the accuracy of CC2 excitation energies.

a HARTREE-FOCK Nuclear Mass Table

NASA Astrophysics Data System (ADS)

Goriely, S.; Tondeur, F.; Pearson, J. M.

2001-03-01

We present the first complete nuclear mass table, HFBCS-1, to be based on the Hartree-Fock-BCS method. The force used, MSk7, is a 10-parameter Skyrme force, along with a 4-parameter δ-function pairing force and a 2-parameter phenomenological Wigner term. Our tabulation presents 9200 nuclei, including all those lying between the drip lines over the range Z, N≥8 and Z≤120. The root-mean-square error of our fit to the 1888 nuclei in this range for which measured masses are given in the 1995 Audi-Wapstra compilation is 0.738 MeV. In addition to the calculated masses, we show the calculated neutron- and proton-separation energies, and beta-decay energies. We also give for each nucleus in the table the calculated values for the deformation parameters and deformation energy (with axial and left-right symmetry assumed), and for the charge radius.

X-ray production cross sections at incident photon energies across the M{sub i} (i=1-5) edges of {sub 90}Th

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

Kaur, Rajnish; Shehla,; Kumar, Anil

2015-08-28

The X-ray production cross sections for the M{sub k} (k= ξ, δ, α, β, ζ, γ, m{sub 1}, m{sub 2}) groups of X-rays have been evaluated at incident photon energies across the M{sub i} (i =1-5) edges of {sub 90}Th using the relativistic Hartree-Fock-Slater model based photoionisation cross sections and recently reported values of the M-shell X-ray emission rates, fluorescence and Coster Kronig yields. Further, the energies of the prominent (M{sub i}-S{sub j}) (S{sub j}=N{sub j}, O{sub j} and i =1-3, j =1-7) resonant Raman scattered (RRS) peaks at different incident photon energies have also been evaluated using the neutral-atommore » electron binding energies (E{sub sj}) based on the relaxed orbital relativistic Hartree-Fock-Slater model.« less

Optimal plane-wave Hartree-Fock states for many-fermion systems

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

de Llano, M.; Plastino, A.; Zabolitzky, J.G.

1979-12-01

The possibility of taking plane-wave orbitals of a Hartree-Fock determinant to fill k space differently from the ''normal'' Fermi sphere is investigated for several two-body potentials including the ''homework'' v/sub 0/, v/sub 1/, and v/sub 2/ - aken from the Reid nucleon-nucleon force - as well as a sum-of-Gaussians potential chosen to fit the deuteron binding and size. A random-search and random-walk numerical algorithm shows that, provided the potential strengths are made large enough, a single-shell ''abnormal'' occupation is always found to be lower in energy than the normal one if sufficient attraction is present in the two-body interaction. Nomore » abnormal occupation is possible for, among other pair interactions, the electron or charged-boson fluid, the repulsive square barrier, and a common form of the He-He interaction.« less

Modeling molecule-plasmon interactions using quantized radiation fields within time-dependent electronic structure theory

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

Nascimento, Daniel R.; DePrince, A. Eugene, E-mail: deprince@chem.fsu.edu

2015-12-07

We present a combined cavity quantum electrodynamics/ab initio electronic structure approach for simulating plasmon-molecule interactions in the time domain. The simple Jaynes-Cummings-type model Hamiltonian typically utilized in such simulations is replaced with one in which the molecular component of the coupled system is treated in a fully ab initio way, resulting in a computationally efficient description of general plasmon-molecule interactions. Mutual polarization effects are easily incorporated within a standard ground-state Hartree-Fock computation, and time-dependent simulations carry the same formal computational scaling as real-time time-dependent Hartree-Fock theory. As a proof of principle, we apply this generalized method to the emergence ofmore » a Fano-like resonance in coupled molecule-plasmon systems; this feature is quite sensitive to the nanoparticle-molecule separation and the orientation of the molecule relative to the polarization of the external electric field.« less

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

PubMed

Vikramaditya, Talapunur; Lin, Shiang-Tai

2017-06-05

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

Linear scaling computation of the Fock matrix. II. Rigorous bounds on exchange integrals and incremental Fock build

NASA Astrophysics Data System (ADS)

Schwegler, Eric; Challacombe, Matt; Head-Gordon, Martin

1997-06-01

A new linear scaling method for computation of the Cartesian Gaussian-based Hartree-Fock exchange matrix is described, which employs a method numerically equivalent to standard direct SCF, and which does not enforce locality of the density matrix. With a previously described method for computing the Coulomb matrix [J. Chem. Phys. 106, 5526 (1997)], linear scaling incremental Fock builds are demonstrated for the first time. Microhartree accuracy and linear scaling are achieved for restricted Hartree-Fock calculations on sequences of water clusters and polyglycine α-helices with the 3-21G and 6-31G basis sets. Eightfold speedups are found relative to our previous method. For systems with a small ionization potential, such as graphitic sheets, the method naturally reverts to the expected quadratic behavior. Also, benchmark 3-21G calculations attaining microhartree accuracy are reported for the P53 tetramerization monomer involving 698 atoms and 3836 basis functions.

Polyatomic molecular Dirac-Hartree-Fock calculations with Gaussian basis sets

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.; Faegri, Knut, Jr.; Taylor, Peter R.

1990-01-01

Numerical methods have been used successfully in atomic Dirac-Hartree-Fock (DHF) calculations for many years. Some DHF calculations using numerical methods have been done on diatomic molecules, but while these serve a useful purpose for calibration, the computational effort in extending this approach to polyatomic molecules is prohibitive. An alternative more in line with traditional quantum chemistry is to use an analytical basis set expansion of the wave function. This approach fell into disrepute in the early 1980's due to problems with variational collapse and intruder states, but has recently been put on firm theoretical foundations. In particular, the problems of variational collapse are well understood, and prescriptions for avoiding the most serious failures have been developed. Consequently, it is now possible to develop reliable molecular programs using basis set methods. This paper describes such a program and reports results of test calculations to demonstrate the convergence and stability of the method.

Theoretical X-ray production cross sections at incident photon energies across Li (i=1-3) absorption edges of Br

NASA Astrophysics Data System (ADS)

Puri, Sanjiv

2015-08-01

The X-ray production (XRP) cross sections, σLk (k = l, η, α, β6, β1, β3, β4, β9,10, γ1,5, γ2,3) have been evaluated at incident photon energies across the Li(i=1-3) absorption edge energies of 35Br using theoretical data sets of different physical parameters, namely, the Li(i=1-3) sub-shell the X-ray emission rates based on the Dirac-Fock (DF) model, the fluorescence and Coster Kronig yields based on the Dirac-Hartree-Slater (DHS) model, and two sets of the photoionisation cross sections based on the relativistic Hartree-Fock-Slater (RHFS) model and the Dirac-Fock (DF) model, in order to highlight the importance of electron exchange effects at photon energies in vicinity of absorption edge energies.

Ab initio study of MF2 (M=Mn, Fe, Co, Ni) rutile-type compounds using the periodic unrestricted Hartree-Fock approach

NASA Astrophysics Data System (ADS)

de P. R. Moreira, Ibério; Dovesi, Roberto; Roetti, Carla; Saunders, Victor R.; Orlando, Roberto

2000-09-01

The ab initio periodic unrestricted Hartree-Fock method has been applied in the investigation of the ground-state structural, electronic, and magnetic properties of the rutile-type compounds MF2 (M=Mn, Fe, Co, and Ni). All electron Gaussian basis sets have been used. The systems turn out to be large band-gap antiferromagnetic insulators; the optimized geometrical parameters are in good agreement with experiment. The calculated most stable electronic state shows an antiferromagnetic order in agreement with that resulting from neutron scattering experiments. The magnetic coupling constants between nearest-neighbor magnetic ions along the [001], [111], and [100] (or [010]) directions have been calculated using several supercells. The resulting ab initio magnetic coupling constants are reasonably satisfactory when compared with available experimental data. The importance of the Jahn-Teller effect in FeF2 and CoF2 is also discussed.

Attractive electron-electron interactions within robust local fitting approximations.

PubMed

Merlot, Patrick; Kjærgaard, Thomas; Helgaker, Trygve; Lindh, Roland; Aquilante, Francesco; Reine, Simen; Pedersen, Thomas Bondo

2013-06-30

An analysis of Dunlap's robust fitting approach reveals that the resulting two-electron integral matrix is not manifestly positive semidefinite when local fitting domains or non-Coulomb fitting metrics are used. We present a highly local approximate method for evaluating four-center two-electron integrals based on the resolution-of-the-identity (RI) approximation and apply it to the construction of the Coulomb and exchange contributions to the Fock matrix. In this pair-atomic resolution-of-the-identity (PARI) approach, atomic-orbital (AO) products are expanded in auxiliary functions centered on the two atoms associated with each product. Numerical tests indicate that in 1% or less of all Hartree-Fock and Kohn-Sham calculations, the indefinite integral matrix causes nonconvergence in the self-consistent-field iterations. In these cases, the two-electron contribution to the total energy becomes negative, meaning that the electronic interaction is effectively attractive, and the total energy is dramatically lower than that obtained with exact integrals. In the vast majority of our test cases, however, the indefiniteness does not interfere with convergence. The total energy accuracy is comparable to that of the standard Coulomb-metric RI method. The speed-up compared with conventional algorithms is similar to the RI method for Coulomb contributions; exchange contributions are accelerated by a factor of up to eight with a triple-zeta quality basis set. A positive semidefinite integral matrix is recovered within PARI by introducing local auxiliary basis functions spanning the full AO product space, as may be achieved by using Cholesky-decomposition techniques. Local completion, however, slows down the algorithm to a level comparable with or below conventional calculations. Copyright © 2013 Wiley Periodicals, Inc.

Physics in Screening Environments

NASA Astrophysics Data System (ADS)

Certik, Ondrej

In the current study, we investigated atoms in screening environments like plasmas. It is common practice to extract physical data, such as temperature and electron densities, from plasma experiments. We present results that address inherent computational difficulties that arise when the screening approach is extended to include the interaction between the atomic electrons. We show that there may arise an ambiguity in the interpretation of physical properties, such as temperature and charge density, from experimental data due to the opposing effects of electron-nucleus screening and electron-electron screening. The focus of the work, however, is on the resolution of inherent computational challenges that appear in the computation of two-particle matrix elements. Those enter already at the Hartree-Fock level. Furthermore, as examples of post Hartree-Fock calculations, we show second-order Green's function results and many body perturbation theory results of second order. A self-contained derivation of all necessary equations has been included. The accuracy of the implementation of the method is established by comparing standard unscreened results for various atoms and molecules against literature for Hartree-Fock as well as Green's function and many body perturbation theory. The main results of the thesis are presented in the chapter called Screened Results, where the behavior of several atomic systems depending on electron-electron and electron-nucleus Debye screening was studied. The computer code that we have developed has been made available for anybody to use. Finally, we present and discuss results obtained for screened interactions. We also examine thoroughly the computational details of the calculations and particular implementations of the method.

Towards a multiconfigurational method of increments

NASA Astrophysics Data System (ADS)

Fertitta, E.; Koch, D.; Paulus, B.; Barcza, G.; Legeza, Ö.

2018-06-01

The method of increments (MoI) allows one to successfully calculate cohesive energies of bulk materials with high accuracy, but it encounters difficulties when calculating dissociation curves. The reason is that its standard formalism is based on a single Hartree-Fock (HF) configuration whose orbitals are localised and used for the many-body expansion. In situations where HF does not allow a size-consistent description of the dissociation, the MoI cannot be guaranteed to yield proper results either. Herein, we address the problem by employing a size-consistent multiconfigurational reference for the MoI formalism. This leads to a matrix equation where a coupling derived by the reference itself is employed. In principle, such an approach allows one to evaluate approximate values for the ground as well as excited states energies. While the latter are accurate close to the avoided crossing only, the ground state results are very promising for the whole dissociation curve, as shown by the comparison with density matrix renormalisation group benchmarks. We tested this two-state constant-coupling MoI on beryllium rings of different sizes and studied the error introduced by the constant coupling.

Calculations of the β-decay half-lives of neutron-deficient nuclei

NASA Astrophysics Data System (ADS)

Tan, Wenjin; Ni, Dongdong; Ren, Zhongzhou

2017-05-01

In this work, β+/EC decays of some medium-mass nuclei are investigated within the extended quasiparticle random-phase approximation (QRPA), where neutron-neutron, proton-proton and neutron-proton (np) pairing correlations are taken into consideration in the specialized Hartree-Fock-Bogoliubov (HFB) transformation. In addition to the pairing interaction, the Brückner G-matrix obtained with the charge-dependent Bonn nucleon-nucleon force is used for the residual particle-particle and particle-hole interactions. Calculations are performed for even-even proton-rich isotopes ranging from Z=24 to Z=34. It is found that the np pairing interaction plays a significant role in β-decay for some nuclei far from stability. Compared with other theoretical calculations, our calculations show good agreement with the available experimental data. Predictions of β-decay half-lives for some very neutron-deficient nuclei are made for reference. Supported by National Nature Science Foundation of China (11535004, 11375086, 11120101005, 11175085 and 11235001), 973 Nation Major State Basic Research and Development of China (2013CB834400) and Science and Technology Development Fund of Macau (020/2014/A1 and 039/2013/A2)

Isoscalar compression modes within fluid dynamic approach

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

Kolomietz, V. M.; Cyclotron Institute, Texas A and M University, College Station, Texas 77843-3366; Shlomo, S.

2000-06-01

We study the nuclear isoscalar monopole and dipole compression modes in nuclei within the fluid dynamic approach (FDA) with and without the effect of relaxation. For a wide region of the medium and heavy nuclei, the FDA predicts that the isoscalar giant monopole resonance (ISGMR) and the isoscalar giant dipole resonance (ISGDR) exhaust about 90% of the corresponding model-independent sum rules. In the case of neglecting the effect of relaxation, the FDA, when adjusted to reproduce the centroid energy E0 of the ISGMR, results with centroid energy E1 of the ISGDR which is in agreement with the predictions of themore » self-consistent Hartree-Fock random-phase approximation calculations and the scaling model but significantly larger than the experimental value. We also show that the FDA leads to the correct hydrodynamic limit for the ratio (E1/E0){sub FDA}. We find that the ratio (E1/E0){sub FDA} depends on the relaxation time and approaches the preliminary experimental value (E1/E0){sub exp}=1.5{+-}0.1 in a short relaxation time limit. (c) 2000 The American Physical Society.« less

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

NASA Astrophysics Data System (ADS)

Jerke, Jonathan; Poirier, Bill

2018-03-01

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

Communication: A reduced scaling J-engine based reformulation of SOS-MP2 using graphics processing units

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

Maurer, S. A.; Kussmann, J.; Ochsenfeld, C., E-mail: Christian.Ochsenfeld@cup.uni-muenchen.de

2014-08-07

We present a low-prefactor, cubically scaling scaled-opposite-spin second-order Møller-Plesset perturbation theory (SOS-MP2) method which is highly suitable for massively parallel architectures like graphics processing units (GPU). The scaling is reduced from O(N{sup 5}) to O(N{sup 3}) by a reformulation of the MP2-expression in the atomic orbital basis via Laplace transformation and the resolution-of-the-identity (RI) approximation of the integrals in combination with efficient sparse algebra for the 3-center integral transformation. In contrast to previous works that employ GPUs for post Hartree-Fock calculations, we do not simply employ GPU-based linear algebra libraries to accelerate the conventional algorithm. Instead, our reformulation allows tomore » replace the rate-determining contraction step with a modified J-engine algorithm, that has been proven to be highly efficient on GPUs. Thus, our SOS-MP2 scheme enables us to treat large molecular systems in an accurate and efficient manner on a single GPU-server.« less

A fermionic de Finetti theorem

NASA Astrophysics Data System (ADS)

Krumnow, Christian; Zimborás, Zoltán; Eisert, Jens

2017-12-01

Quantum versions of de Finetti's theorem are powerful tools, yielding conceptually important insights into the security of key distribution protocols or tomography schemes and allowing one to bound the error made by mean-field approaches. Such theorems link the symmetry of a quantum state under the exchange of subsystems to negligible quantum correlations and are well understood and established in the context of distinguishable particles. In this work, we derive a de Finetti theorem for finite sized Majorana fermionic systems. It is shown, much reflecting the spirit of other quantum de Finetti theorems, that a state which is invariant under certain permutations of modes loses most of its anti-symmetric character and is locally well described by a mode separable state. We discuss the structure of the resulting mode separable states and establish in specific instances a quantitative link to the quality of the Hartree-Fock approximation of quantum systems. We hint at a link to generalized Pauli principles for one-body reduced density operators. Finally, building upon the obtained de Finetti theorem, we generalize and extend the applicability of Hudson's fermionic central limit theorem.

Magnetic states, correlation effects and metal-insulator transition in FCC lattice

NASA Astrophysics Data System (ADS)

Timirgazin, M. A.; Igoshev, P. A.; Arzhnikov, A. K.; Irkhin, V. Yu

2016-12-01

The ground-state magnetic phase diagram (including collinear and spiral states) of the single-band Hubbard model for the face-centered cubic lattice and related metal-insulator transition (MIT) are investigated within the slave-boson approach by Kotliar and Ruckenstein. The correlation-induced electron spectrum narrowing and a comparison with a generalized Hartree-Fock approximation allow one to estimate the strength of correlation effects. This, as well as the MIT scenario, depends dramatically on the ratio of the next-nearest and nearest electron hopping integrals {{t}\\prime}/t . In contrast with metallic state, possessing substantial band narrowing, insulator one is only weakly correlated. The magnetic (Slater) scenario of MIT is found to be superior over the Mott one. Unlike simple and body-centered cubic lattices, MIT is the first order transition (discontinuous) for most {{t}\\prime}/t . The insulator state is type-II or type-III antiferromagnet, and the metallic state is spin-spiral, collinear antiferromagnet or paramagnet depending on {{t}\\prime}/t . The picture of magnetic ordering is compared with that in the standard localized-electron (Heisenberg) model.

Projector Augmented Wave formulation of orbital-dependent exchange-correlation functionals

NASA Astrophysics Data System (ADS)

Xu, Xiao; Holzwarth, N. A. W.

2012-02-01

The use of orbital-dependent exchange-correlation functionals within electronic structure calculations has recently received renewed attention for improving the accuracy of the calculations, especially correcting self-interaction errors. Since the Projector Augmented Wave (PAW) methodootnotetext P. Bl"ochl, Phys. Rev. B 50, 17953 (1994). is an efficient pseudopotential-like scheme which ensures accurate evaluation of all multipole moments of direct and exchange Coulomb integrals, it is a natural choice for implementing orbital-dependent formalisms. Using Fock exchange as an example of an orbital-dependent functional, we developed the formulation and numerical implementation of the approximate optimized effective potential formalism of Kreiger, Li, and Iafrate (KLI)ootnotetext J. B. Krieger, Y. Li, and G. J. Iafrate Phys. Rev. A 45, 101 (1992). within the PAW method, comparing results with the analogous Hartree-Fock treatment.ootnotetext Xiao Xu and N. A. W. Holzwarth, Phys. Rev. B 81, 245105 (2010); 84, 155113 (2011). Test results are presented for ground state properties of two well-known materials -- diamond and LiF. This formalism can be extended to treat orbital-dependent functionals more generally.

Relativistic effects on the bonding and properties of the hydrides of platinum

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.

1993-01-01

The ground state of PtH2 and several low-lying states of PtH(+) and PtH have been studied at the all-electron self-consistent-field level of theory to examine the importance of relativistic effects. The results of calculations based on Dirac-Hartree-Fock theory, nonrelativistic theory, and the spin-free no-pair relativistic approximation of Hess are compared to separate the effects of the spin-free terms and the spin-orbit terms of the Hamiltonian on the relativistic corrections to the molecular properties. Comparison is also made between first-order perturbation theory including the one-electron spin-free terms and the method of Hess to determine the size of effects beyond first order. It is found that the spin-orbit interaction significantly affects the properties and energetics of these molecules because of the participation of the Pt 5d orbitals in the bonding, and that effects beyond first order in perturbation theory are large. Any treatment of Pt compounds will have to include both the spin-free and spin-orbit interactions for an accurate description.

Charge modulation as fingerprints of phase-string triggered interference

NASA Astrophysics Data System (ADS)

Zhu, Zheng; Tian, Chushun; Jiang, Hong-Chen; Qi, Yang; Weng, Zheng-Yu; Zaanen, Jan

2015-07-01

Charge order appears to be an ubiquitous phenomenon in doped Mott insulators, which is currently under intense experimental and theoretical investigations particularly in the high Tc cuprates. This phenomenon is conventionally understood in terms of Hartree-Fock-type mean-field theory. Here we demonstrate a mechanism for charge modulation which is rooted in the many-particle quantum physics arising in the strong coupling limit. Specifically, we consider the problem of a single hole in a bipartite t -J ladder. As a remnant of the fermion signs, the hopping hole picks up subtle phases pending the fluctuating spins, the so-called phase-string effect. We demonstrate the presence of charge modulations in the density matrix renormalization group solutions which disappear when the phase strings are switched off. This form of charge modulation can be understood analytically in a path-integral language with a mean-field-like approximation adopted, showing that the phase strings give rise to constructive interferences leading to self-localization. When the latter occurs, left- and right-moving propagating modes emerge inside the localization volume and their interference is responsible for the real space charge modulation.

A derivation and scalable implementation of the synchronous parallel kinetic Monte Carlo method for simulating long-time dynamics

NASA Astrophysics Data System (ADS)

Byun, Hye Suk; El-Naggar, Mohamed Y.; Kalia, Rajiv K.; Nakano, Aiichiro; Vashishta, Priya

2017-10-01

Kinetic Monte Carlo (KMC) simulations are used to study long-time dynamics of a wide variety of systems. Unfortunately, the conventional KMC algorithm is not scalable to larger systems, since its time scale is inversely proportional to the simulated system size. A promising approach to resolving this issue is the synchronous parallel KMC (SPKMC) algorithm, which makes the time scale size-independent. This paper introduces a formal derivation of the SPKMC algorithm based on local transition-state and time-dependent Hartree approximations, as well as its scalable parallel implementation based on a dual linked-list cell method. The resulting algorithm has achieved a weak-scaling parallel efficiency of 0.935 on 1024 Intel Xeon processors for simulating biological electron transfer dynamics in a 4.2 billion-heme system, as well as decent strong-scaling parallel efficiency. The parallel code has been used to simulate a lattice of cytochrome complexes on a bacterial-membrane nanowire, and it is broadly applicable to other problems such as computational synthesis of new materials.

Electronic response of rare-earth magnetic-refrigeration compounds GdX2 (X = Fe and Co)

NASA Astrophysics Data System (ADS)

Bhatt, Samir; Ahuja, Ushma; Kumar, Kishor; Heda, N. L.

2018-05-01

We present the Compton profiles (CPs) of rare-earth-transition metal compounds GdX2 (X = Fe and Co) using 740 GBq 137Cs Compton spectrometer. To compare the experimental momentum densities, we have also computed the CPs, electronic band structure, density of states (DOS) and Mulliken population (MP) using linear combination of atomic orbitals (LCAO) method. Local density and generalized gradient approximations within density functional theory (DFT) along with the hybridization of Hartree-Fock and DFT (B3LYP and PBE0) have been considered under the framework of LCAO scheme. It is seen that the LCAO-B3LYP based momentum densities give a better agreement with the experimental data for both the compounds. The energy bands and DOS for both the spin-up and spin-down states show metallic like character of the reported intermetallic compounds. The localization of 3d electrons of Co and Fe has also been discussed in terms of equally normalized CPs and MP data. Discussion on magnetization using LCAO method is also included.

Study of electronic structure and Compton profiles of transition metal diborides

NASA Astrophysics Data System (ADS)

Bhatt, Samir; Heda, N. L.; Kumar, Kishor; Ahuja, B. L.

2017-08-01

We report Compton profiles (CPs) of transition metal diborides (MB2; M= Ti and Zr) using a 740 GBq 137Cs Compton spectrometer measured at an intermediate resolution of 0.34 a.u. To validate the experimental momentum densities, we have employed the linear combination of atomic orbitals (LCAO) method to compute the theoretical CPs along with the energy bands, density of states (DOS) and Mulliken's population response. The LCAO computations have been performed in the frame work of density functional theory (DFT) and hybridization of Hartree-Fock and DFT (namely B3LYP and PBE0). For both the diborides, the CPs based on revised Perdew-Burke-Ernzerhof exchange and correlation functions (DFT-PBESol) lead to a better agreement with the experimental momentum densities than other reported approximations. Energy bands, DOS and real space analysis of CPs confirm a metallic-like character of both the borides. Further, a comparison of DFT-PBESol and experimental data on equal-valence-electron-density scale shows more ionicity in ZrB2 than that in TiB2, which is also supported by the Mulliken's population based charge transfer data.

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

PubMed

Jerke, Jonathan; Poirier, Bill

2018-03-14

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

Fermi Surface of Sr_{2}RuO_{4}: Spin-Orbit and Anisotropic Coulomb Interaction Effects.

PubMed

Zhang, Guoren; Gorelov, Evgeny; Sarvestani, Esmaeel; Pavarini, Eva

2016-03-11

The topology of the Fermi surface of Sr_{2}RuO_{4} is well described by local-density approximation calculations with spin-orbit interaction, but the relative size of its different sheets is not. By accounting for many-body effects via dynamical mean-field theory, we show that the standard isotropic Coulomb interaction alone worsens or does not correct this discrepancy. In order to reproduce experiments, it is essential to account for the Coulomb anisotropy. The latter is small but has strong effects; it competes with the Coulomb-enhanced spin-orbit coupling and the isotropic Coulomb term in determining the Fermi surface shape. Its effects are likely sizable in other correlated multiorbital systems. In addition, we find that the low-energy self-energy matrix-responsible for the reshaping of the Fermi surface-sizably differs from the static Hartree-Fock limit. Finally, we find a strong spin-orbital entanglement; this supports the view that the conventional description of Cooper pairs via factorized spin and orbital part might not apply to Sr_{2}RuO_{4}.

Distribution of nuclei in equilibrium stellar matter from the free-energy density in a Wigner-Seitz cell

NASA Astrophysics Data System (ADS)

Grams, G.; Giraud, S.; Fantina, A. F.; Gulminelli, F.

2018-03-01

The aim of the present study is to calculate the nuclear distribution associated at finite temperature to any given equation of state of stellar matter based on the Wigner-Seitz approximation, for direct applications in core-collapse simulations. The Gibbs free energy of the different configurations is explicitly calculated, with special care devoted to the calculation of rearrangement terms, ensuring thermodynamic consistency. The formalism is illustrated with two different applications. First, we work out the nuclear statistical equilibrium cluster distribution for the Lattimer and Swesty equation of state, widely employed in supernova simulations. Secondly, we explore the effect of including shell structure, and consider realistic nuclear mass tables from the Brussels-Montreal Hartree-Fock-Bogoliubov model (specifically, HFB-24). We show that the whole collapse trajectory is dominated by magic nuclei, with extremely spread and even bimodal distributions of the cluster probability around magic numbers, demonstrating the importance of cluster distributions with realistic mass models in core-collapse simulations. Simple analytical expressions are given, allowing further applications of the method to any relativistic or nonrelativistic subsaturation equation of state.

Rovibrational spectroscopy using a kinetic energy operator in Eckart frame and the multi-configuration time-dependent Hartree (MCTDH) approach

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

Sadri, Keyvan, E-mail: keyvan.sadri@pci.uni-heidelberg.de; Meyer, Hans-Dieter, E-mail: hans-dieter.meyer@pci.uni-heidelberg.de; Lauvergnat, David, E-mail: david.lauvergnat@u-psud.fr

2014-09-21

For computational rovibrational spectroscopy the choice of the frame is critical for an approximate separation of overall rotation from internal motions. To minimize the coupling between internal coordinates and rotation, Eckart proposed a condition [“Some studies concerning rotating axes and polyatomic molecules,” Phys. Rev. 47, 552–558 (1935)] and a frame that fulfills this condition is hence called an Eckart frame. A method is developed to introduce in a systematic way the Eckart frame for the expression of the kinetic energy operator (KEO) in the polyspherical approach. The computed energy levels of a water molecule are compared with those obtained usingmore » a KEO in the standard definition of the Body-fixed frame of the polyspherical approach. The KEO in the Eckart frame leads to a faster convergence especially for large J states and vibrationally excited states. To provide an example with more degrees of freedom, rotational states of the vibrational ground state of the trans nitrous acid (HONO) are also investigated.« less

Theoretical investigation of the He4Br2 conformers.

PubMed

Valdés, Álvaro; Prosmiti, Rita; Villarreal, Pablo; Delgado-Barrio, Gerardo

2012-07-05

Full dimensional quantum dynamics calculations of the three lowest isomers of the He(4)Br(2) van der Waals molecule in its ground electronic state are reported. The calculations are performed using the multiconfiguration time-dependent Hartree (MCTDH) method and a realistic potential form that includes the sum of three body ab initio coupled-cluster single double triple [CCSD(T)] He-Br(2) interactions plus the He-He and Br-Br interactions. This potential exhibits several multiple minima, with the three lowest ones lying very close in energy, just within 2 cm(-1). Such small differences are also found in the calculated binding energies of the three most stable conformers, indicating the floppiness of the system and, thus, the need of accurate potential forms and quantum full dynamics methods to treat this kind of complexes. The 12 dimensional results reported in this work present benchmark data and, thus, can serve to evaluate approximate methods aiming to describe higher order rare gas-dihalogen (N > 4) complexes. A comparison with previous studies using different potential forms and approaches to the energetics for the He(4)Br(2) cluster is also presented.

Progesterone and testosterone studies by neutron-scattering methods and quantum chemistry calculations

NASA Astrophysics Data System (ADS)

Holderna-Natkaniec, K.; Szyczewski, A.; Natkaniec, I.; Khavryutchenko, V. D.; Pawlukojc, A.

Inelastic incoherent neutron scattering (IINS) and neutron diffraction spectra of progesterone and testosterone were measured simultaneously on the NERA spectrometer at the IBR-2 pulsed reactor in Dubna. Both studied samples do not indicate any phase transition in the temperature range from 20 to 290K. The IINS spectra have been transformed to the phonon density of states (PDS) in the one-phonon scattering approximation. The PDS spectra display well-resolved peaks of low-frequency internal vibration modes up to 600cm-1. The assignment of these modes was proposed taking into account the results of calculations of the structure and dynamics of isolated molecules of the investigated substances. The quantum chemistry calculations were performed by the semi-empirical PM3 method and at the restricted Hartree-Fock level with the 6-31* basis set. The lower internal modes assigned to torsional vibration of the androstane skeleton mix with the lattice vibrations. The intense bands in the PDS spectra in the frequency range from 150 to 300cm-1 are related to librations of structurally inequivalent methyl groups.

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

Zhu, Zheng; Tian, Chushun; Jiang, Hong-Chen

Charge order appears to be an ubiquitous phenomenon in doped Mott insulators, which is currently under intense experimental and theoretical investigations particularly in the high T c cuprates. This phenomenon is conventionally understood in terms of Hartree-Fock-type mean-field theory. Here we demonstrate a mechanism for charge modulation which is rooted in the many-particle quantum physics arising in the strong coupling limit. Specifically, we consider the problem of a single hole in a bipartite t - J ladder. As a remnant of the fermion signs, the hopping hole picks up subtle phases pending the fluctuating spins, the so-called phase-string effect. Wemore » demonstrate the presence of charge modulations in the density matrix renormalization group solutions which disappear when the phase strings are switched off. This form of charge modulation can be understood analytically in a path-integral language with a mean-field-like approximation adopted, showing that the phase strings give rise to constructive interferences leading to self-localization. When the latter occurs, left- and right-moving propagating modes emerge inside the localization volume and their interference is responsible for the real space charge modulation.« less

Quasiparticle energies and lifetimes in a metallic chain model of a tunnel junction.

PubMed

Szepieniec, Mark; Yeriskin, Irene; Greer, J C

2013-04-14

As electronics devices scale to sub-10 nm lengths, the distinction between "device" and "electrodes" becomes blurred. Here, we study a simple model of a molecular tunnel junction, consisting of an atomic gold chain partitioned into left and right electrodes, and a central "molecule." Using a complex absorbing potential, we are able to reproduce the single-particle energy levels of the device region including a description of the effects of the semi-infinite electrodes. We then use the method of configuration interaction to explore the effect of correlations on the system's quasiparticle peaks. We find that when excitations on the leads are excluded, the device's highest occupied molecular orbital and lowest unoccupied molecular orbital quasiparticle states when including correlation are bracketed by their respective values in the Hartree-Fock (Koopmans) and ΔSCF approximations. In contrast, when excitations on the leads are included, the bracketing property no longer holds, and both the positions and the lifetimes of the quasiparticle levels change considerably, indicating that the combined effect of coupling and correlation is to alter the quasiparticle spectrum significantly relative to an isolated molecule.

The effect of exchange interaction on quasiparticle Landau levels in narrow-gap quantum well heterostructures.

PubMed

Krishtopenko, S S; Gavrilenko, V I; Goiran, M

2012-04-04

Using the 'screened' Hartree-Fock approximation based on the eight-band k·p Hamiltonian, we have extended our previous work (Krishtopenko et al 2011 J. Phys.: Condens. Matter 23 385601) on exchange enhancement of the g-factor in narrow-gap quantum well heterostructures by calculating the exchange renormalization of quasiparticle energies, the density of states at the Fermi level and the quasiparticle g-factor for different Landau levels overlapping. We demonstrate that exchange interaction yields more pronounced Zeeman splitting of the density of states at the Fermi level and leads to the appearance of peak-shaped features in the dependence of the Landau level energies on the magnetic field at integer filling factors. We also find that the quasiparticle g-factor does not reach the maximum value at odd filling factors in the presence of large overlapping of spin-split Landau levels. We advance an argument that the behavior of the quasiparticle g-factor in weak magnetic fields is defined by a random potential of impurities in narrow-gap heterostructures. © 2012 IOP Publishing Ltd

Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.. (VII) HFODD (v2.49t): A new version of the program

NASA Astrophysics Data System (ADS)

Schunck, N.; Dobaczewski, J.; McDonnell, J.; Satuła, W.; Sheikh, J. A.; Staszczak, A.; Stoitsov, M.; Toivanen, P.

2012-01-01

We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite-temperature formalism for the HFB and HF + BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex-breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected. New version program summaryProgram title:HFODD (v2.49t) Catalogue identifier: ADFL_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFL_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence v3 No. of lines in distributed program, including test data, etc.: 190 614 No. of bytes in distributed program, including test data, etc.: 985 898 Distribution format: tar.gz Programming language: FORTRAN-90 Computer: Intel Pentium-III, Intel Xeon, AMD-Athlon, AMD-Opteron, Cray XT4, Cray XT5 Operating system: UNIX, LINUX, Windows XP Has the code been vectorized or parallelized?: Yes, parallelized using MPI RAM: 10 Mwords Word size: The code is written in single-precision for the use on a 64-bit processor. The compiler option -r8 or +autodblpad (or equivalent) has to be used to promote all real and complex single-precision floating-point items to double precision when the code is used on a 32-bit machine. Classification: 17.22 Catalogue identifier of previous version: ADFL_v2_2 Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 2361 External routines: The user must have access to the NAGLIB subroutine f02axe, or LAPACK subroutines zhpev, zhpevx, zheevr, or zheevd, which diagonalize complex hermitian matrices, the LAPACK subroutines dgetri and dgetrf which invert arbitrary real matrices, the LAPACK subroutines dsyevd, dsytrf and dsytri which compute eigenvalues and eigenfunctions of real symmetric matrices, the LINPACK subroutines zgedi and zgeco, which invert arbitrary complex matrices and calculate determinants, the BLAS routines dcopy, dscal, dgeem and dgemv for double-precision linear algebra and zcopy, zdscal, zgeem and zgemv for complex linear algebra, or provide another set of subroutines that can perform such tasks. The BLAS and LAPACK subroutines can be obtained from the Netlib Repository at the University of Tennessee, Knoxville: http://netlib2.cs.utk.edu/. Does the new version supersede the previous version?: Yes Nature of problem: The nuclear mean field and an analysis of its symmetries in realistic cases are the main ingredients of a description of nuclear states. Within the Local Density Approximation, or for a zero-range velocity-dependent Skyrme interaction, the nuclear mean field is local and velocity dependent. The locality allows for an effective and fast solution of the self-consistent Hartree-Fock equations, even for heavy nuclei, and for various nucleonic ( n-particle- n-hole) configurations, deformations, excitation energies, or angular momenta. Similarly, Local Density Approximation in the particle-particle channel, which is equivalent to using a zero-range interaction, allows for a simple implementation of pairing effects within the Hartree-Fock-Bogolyubov method. Solution method: The program uses the Cartesian harmonic oscillator basis to expand single-particle or single-quasiparticle wave functions of neutrons and protons interacting by means of the Skyrme effective interaction and zero-range pairing interaction. The expansion coefficients are determined by the iterative diagonalization of the mean-field Hamiltonians or Routhians which depend non-linearly on the local neutron and proton densities. Suitable constraints are used to obtain states corresponding to a given configuration, deformation or angular momentum. The method of solution has been presented in: [J. Dobaczewski, J. Dudek, Comput. Phys. Commun. 102 (1997) 166]. Reasons for new version: Version 2.49s of HFODD provides a number of new options such as the isospin mixing and projection of the Skyrme functional, the finite-temperature HF and HFB formalism and optimized methods to perform multi-constrained calculations. It is also the first version of HFODD to contain threading and parallel capabilities. Summary of revisions: Isospin mixing and projection of the HF states has been implemented. The finite-temperature formalism for the HFB equations has been implemented. The Lipkin translational energy correction method has been implemented. Calculation of the shell correction has been implemented. The two-basis method for the solution to the HFB equations has been implemented. The Augmented Lagrangian Method (ALM) for calculations with multiple constraints has been implemented. The linear constraint method based on the cranking approximation of the RPA matrix has been implemented. An interface between HFODD and the axially-symmetric and parity-conserving code HFBTHO has been implemented. The mixing of the matrix elements of the HF or HFB matrix has been implemented. A parallel interface using the MPI library has been implemented. A scalable model for reading input data has been implemented. OpenMP pragmas have been implemented in three subroutines. The diagonalization of the HFB matrix in the simplex-breaking case has been parallelized using the ScaLAPACK library. Several little significant errors of the previous published version were corrected. Running time: In serial mode, running 6 HFB iterations for 152Dy for conserved parity and signature symmetries in a full spherical basis of N=14 shells takes approximately 8 min on an AMD Opteron processor at 2.6 GHz, assuming standard BLAS and LAPACK libraries. As a rule of thumb, runtime for HFB calculations for parity and signature conserved symmetries roughly increases as N, where N is the number of full HO shells. Using custom-built optimized BLAS and LAPACK libraries (such as in the ATLAS implementation) can bring down the execution time by 60%. Using the threaded version of the code with 12 threads and threaded BLAS libraries can bring an additional factor 2 speed-up, so that the same 6 HFB iterations now take of the order of 2 min 30 s.

Time-dependent theoretical treatments of the dynamics of electrons and nuclei in molecular systems

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

Deumens, E.; Diz, A.; Longo, R.

1994-07-01

An overview is presented of methods for time-dependent treatments of molecules as systems of electrons and nuclei. The theoretical details of these methods are reviewed and contrasted in the light of a recently developed time-dependent method called electron-nuclear dynamics. Electron-nuclear dynamics (END) is a formulation of the complete dynamics of electrons and nuclei of a molecular system that eliminates the necessity of constructing potential-energy surfaces. Because of its general formulation, it encompasses many aspects found in other formulations and can serve as a didactic device for clarifying many of the principles and approximations relevant in time-dependent treatments of molecular systems.more » The END equations are derived from the time-dependent variational principle applied to a chosen family of efficiently parametrized approximate state vectors. A detailed analysis of the END equations is given for the case of a single-determinantal state for the electrons and a classical treatment of the nuclei. The approach leads to a simple formulation of the fully nonlinear time-dependent Hartree-Fock theory including nuclear dynamics. The nonlinear END equations with the [ital ab] [ital initio] Coulomb Hamiltonian have been implemented at this level of theory in a computer program, ENDyne, and have been shown feasible for the study of small molecular systems. Implementation of the Austin Model 1 semiempirical Hamiltonian is discussed as a route to large molecular systems. The linearized END equations at this level of theory are shown to lead to the random-phase approximation for the coupled system of electrons and nuclei. The qualitative features of the general nonlinear solution are analyzed using the results of the linearized equations as a first approximation. Some specific applications of END are presented, and the comparison with experiment and other theoretical approaches is discussed.« less

SU-E-I-43: Photoelectric Cross Section Revisited

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

Haga, A; Nakagawa, K; Kotoku, J

2015-06-15

Purpose: The importance of the precision in photoelectric cross-section value increases for recent developed technology such as dual energy computed tomography, in which some reconstruction algorithms require the energy dependence of the photo-absorption in each material composition of human being. In this study, we revisited the photoelectric cross-section calculation by self-consistent relativistic Hartree-Fock (HF) atomic model and compared with that widely distributed as “XCOM database” in National Institute of Standards and Technology, which was evaluated with localdensity approximation for electron-exchange (Fock)z potential. Methods: The photoelectric cross section can be calculated with the electron wave functions in initial atomic state (boundmore » electron) and final continuum state (photoelectron). These electron states were constructed based on the selfconsistent HF calculation, where the repulsive Coulomb potential from the electron charge distribution (Hartree term) and the electron exchange potential with full electromagnetic interaction (Fock term) were included for the electron-electron interaction. The photoelectric cross sections were evaluated for He (Z=2), Be (Z=4), C (Z=6), O (Z=8), and Ne (Z=10) in energy range of 10keV to 1MeV. The Result was compared with XCOM database. Results: The difference of the photoelectric cross section between the present calculation and XCOM database was 8% at a maximum (in 10keV for Be). The agreement tends to be better as the atomic number increases. The contribution from each atomic shell has a considerable discrepancy with XCOM database except for K-shell. However, because the photoelectric cross section arising from K-shell is dominant, the net photoelectric cross section was almost insensitive to the different handling in Fock potential. Conclusion: The photoelectric cross-section program has been developed based on the fully self-consistent relativistic HF atomic model. Due to small effect on the Fock potential for K-shell electrons, the difference from XCOM database was limited: 1% to 8% for low-Z elements in 10keV-1MeV energy ranges. This work was partly supported by the JSPS Core-to-Core Program (No. 23003)« less

Fingerprints of spin-orbital polarons and of their disorder in the photoemission spectra of doped Mott insulators with orbital degeneracy

NASA Astrophysics Data System (ADS)

Avella, Adolfo; Oleś, Andrzej M.; Horsch, Peter

2018-04-01

We explore the effects of disordered charged defects on the electronic excitations observed in the photoemission spectra of doped transition metal oxides in the Mott insulating regime by the example of the R1 -xCaxVO3 perovskites, where R = La, ⋯, Lu. A fundamental characteristic of these vanadium d2 compounds with partly filled t2 g valence orbitals is the persistence of spin and orbital order up to high doping, in contrast to the loss of magnetic order in high-Tc cuprates at low defect concentration. We study the disordered electronic structure of such doped Mott-Hubbard insulators within the unrestricted Hartree-Fock approximation and, as a result, manage to explain the spectral features that occur in photoemission and inverse photoemission. In particular, (i) the atomic multiplet excitations in the inverse photoemission spectra and the various defect-related states and satellites are qualitatively well reproduced, (ii) a robust Mott gap survives up to large doping, and (iii) we show that the defect states inside the Mott gap develop a soft gap at the Fermi energy. The soft defect-states gap, which separates the highest occupied from the lowest unoccupied states, can be characterized by a shape and a scale parameter extracted from a Weibull statistical sampling of the density of states near the chemical potential. These parameters provide a criterion and a comprehensive schematization for the insulator-metal transition in disordered systems. Our results provide clear indications that doped holes are bound to charged defects and form small spin-orbital polarons whose internal kinetic energy is responsible for the opening of the soft defect-states gap. We show that this kinetic gap survives disorder fluctuations of defects and is amplified by the long-range electron-electron interactions, whereas we observe a Coulomb singularity in the atomic limit. The small size of spin-orbital polarons is inferred by an analysis of the inverse participation ratio and by means of a complementary many-body polaron theory, which yields a similar robust spin and orbital order as the Hartree-Fock approximation. Using realistic parameters for the vanadium perovskite La1 -xCaxVO3 , we show that its soft gap is reproduced as well as the marginal doping dependence of the position of the chemical potential relative to the center of the lower Hubbard band. The present theory uncovers also the reasons why the d1→d0 satellite excitations, which directly probe the effect of the random defect fields on the polaron state, are not well resolved in the available experimental photoemission spectra for La1 -xCaxVO3 .

Topological Phase Transitions in Zinc-Blende Semimetals Driven Exclusively by Electronic Temperature

NASA Astrophysics Data System (ADS)

Trushin, Egor; Görling, Andreas

2018-04-01

We show that electronic phase transitions in zinc-blende semimetals with quadratic band touching (QBT) at the center of the Brillouin zone, like GaBi, InBi, or HgTe, can occur exclusively due to a change of the electronic temperature without the need to involve structural transformations or electron-phonon coupling. The commonly used Kohn-Sham density-functional methods based on local and semilocal density functionals employing the local density approximation (LDA) or generalized gradient approximations (GGAs), however, are not capable of describing such phenomena because they lack an intrinsic temperature dependence and account for temperature only via the occupation of bands, which essentially leads only to a shift of the Fermi level without changing the shape or topology of bands. Kohn-Sham methods using the exact temperature-dependent exchange potential, not to be confused with the Hartree-Fock exchange potential, on the other hand, describe such phase transitions. A simple modeling of correlation effects can be achieved by screening of the exchange. In the considered zinc-blende compounds the QBT is unstable at low temperatures and a transition to electronic states without QBT takes place. In the case of HgTe and GaBi Weyl points of type I and type II, respectively, emerge during the transitions. This demonstrates that Kohn-Sham methods can describe such topological phase transitions provided they are based on functionals more accurate than those within the LDA or GGA. Moreover, the electronic temperature is identified as a handle to tune topological materials.

First-order symmetry-adapted perturbation theory for multiplet splittings.

PubMed

Patkowski, Konrad; Żuchowski, Piotr S; Smith, Daniel G A

2018-04-28

We present a symmetry-adapted perturbation theory (SAPT) for the interaction of two high-spin open-shell molecules (described by their restricted open-shell Hartree-Fock determinants) resulting in low-spin states of the complex. The previously available SAPT formalisms, except for some system-specific studies for few-electron complexes, were restricted to the high-spin state of the interacting system. Thus, the new approach provides, for the first time, a SAPT-based estimate of the splittings between different spin states of the complex. We have derived and implemented the lowest-order SAPT term responsible for these splittings, that is, the first-order exchange energy. We show that within the so-called S 2 approximation commonly used in SAPT (neglecting effects that vanish as fourth or higher powers of intermolecular overlap integrals), the first-order exchange energies for all multiplets are linear combinations of two matrix elements: a diagonal exchange term that determines the spin-averaged effect and a spin-flip term responsible for the splittings between the states. The numerical factors in this linear combination are determined solely by the Clebsch-Gordan coefficients: accordingly, the S 2 approximation implies a Heisenberg Hamiltonian picture with a single coupling strength parameter determining all the splittings. The new approach is cast into both molecular-orbital and atomic-orbital expressions: the latter enable an efficient density-fitted implementation. We test the newly developed formalism on several open-shell complexes ranging from diatomic systems (Li⋯H, Mn⋯Mn, …) to the phenalenyl dimer.

First-order symmetry-adapted perturbation theory for multiplet splittings

NASA Astrophysics Data System (ADS)

Patkowski, Konrad; Żuchowski, Piotr S.; Smith, Daniel G. A.

2018-04-01

We present a symmetry-adapted perturbation theory (SAPT) for the interaction of two high-spin open-shell molecules (described by their restricted open-shell Hartree-Fock determinants) resulting in low-spin states of the complex. The previously available SAPT formalisms, except for some system-specific studies for few-electron complexes, were restricted to the high-spin state of the interacting system. Thus, the new approach provides, for the first time, a SAPT-based estimate of the splittings between different spin states of the complex. We have derived and implemented the lowest-order SAPT term responsible for these splittings, that is, the first-order exchange energy. We show that within the so-called S2 approximation commonly used in SAPT (neglecting effects that vanish as fourth or higher powers of intermolecular overlap integrals), the first-order exchange energies for all multiplets are linear combinations of two matrix elements: a diagonal exchange term that determines the spin-averaged effect and a spin-flip term responsible for the splittings between the states. The numerical factors in this linear combination are determined solely by the Clebsch-Gordan coefficients: accordingly, the S2 approximation implies a Heisenberg Hamiltonian picture with a single coupling strength parameter determining all the splittings. The new approach is cast into both molecular-orbital and atomic-orbital expressions: the latter enable an efficient density-fitted implementation. We test the newly developed formalism on several open-shell complexes ranging from diatomic systems (Li⋯H, Mn⋯Mn, …) to the phenalenyl dimer.

Exploring the limits of the self-consistent Born approximation for inelastic electronic transport

NASA Astrophysics Data System (ADS)

Lee, William; Jean, Nicola; Sanvito, Stefano

2009-02-01

The nonequilibrium Green’s function formalism is today the standard computational method for describing elastic transport in molecular devices. This can be extended to include inelastic scattering by the so-called self-consistent Born approximation (SCBA), where the interaction of the electrons with the vibrations of the molecule is assumed to be weak and it is treated perturbatively. The validity of such assumption and therefore of the SCBA is difficult to establish with certainty. In this work we explore the limitations of the SCBA by using a simple tight-binding model with the electron-phonon coupling strength α chosen as a free parameter. As model devices we consider Au monatomic chains and a H2 molecule sandwiched between Pt electrodes. In both cases, our self-consistent calculations demonstrate a breakdown of the SCBA for large α and we identify a weak and a strong-coupling regime. For weak coupling our SCBA results compare closely with those obtained with exact scattering theory. However in the strong-coupling regime large deviations are found. In particular we demonstrate that there is a critical coupling strength, characteristic of the materials system, beyond which multiple self-consistent solutions can be found depending on the initial conditions in the simulation. These are entirely due to the large contribution of the Hartree self-energy and completely disappear when this is neglected. We attribute this feature to the breakdown of the perturbative expansion leading to the SCBA.

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

Witte, Jonathon; Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720; Neaton, Jeffrey B., E-mail: jbneaton@lbl.gov

Adsorption of gas molecules in metal-organic frameworks is governed by many factors, the most dominant of which are the interaction of the gas with open metal sites, and the interaction of the gas with the ligands. Herein, we examine the latter class of interaction in the context of CO{sub 2} binding to benzene. We begin by clarifying the geometry of the CO{sub 2}–benzene complex. We then generate a benchmark binding curve using a coupled-cluster approach with single, double, and perturbative triple excitations [CCSD(T)] at the complete basis set (CBS) limit. Against this ΔCCSD(T)/CBS standard, we evaluate a plethora of electronicmore » structure approximations: Hartree-Fock, second-order Møller-Plesset perturbation theory (MP2) with the resolution-of-the-identity approximation, attenuated MP2, and a number of density functionals with and without different empirical and nonempirical van der Waals corrections. We find that finite-basis MP2 significantly overbinds the complex. On the other hand, even the simplest empirical correction to standard density functionals is sufficient to bring the binding energies to well within 1 kJ/mol of the benchmark, corresponding to an error of less than 10%; PBE-D in particular performs well. Methods that explicitly include nonlocal correlation kernels, such as VV10, vdW-DF2, and ωB97X-V, perform with similar accuracy for this system, as do ωB97X and M06-L.« less

Significance of distinct electron-correlation effects in determining the (P ,T )-odd electric dipole moment of 171Yb

NASA Astrophysics Data System (ADS)

Sahoo, B. K.; Singh, Yashpal

2017-06-01

The parity and time-reversal violating electric dipole moment (EDM) of 171Yb is calculated accounting for the electron-correlation effects over the Dirac-Hartree-Fock method in the relativistic Rayleigh-Schrödinger many-body perturbation theory, with the second- [MBPT(2) method] and third-order [MBPT(3) method] approximations, and two variants of all-order relativistic many-body approaches, in the random phase approximation (RPA) and coupled-cluster (CC) method with singles and doubles (CCSD method) framework. We consider electron-nucleus tensor-pseudotensor (T-PT) and nuclear Schiff moment (NSM) interactions as the predominant sources that induce EDM in a diamagnetic atomic system. Our results from the CCSD method to EDM (da) of 171Yb due to the T-PT and NSM interactions are found to be da=4.85 (6 ) ×10-20<σ > CT|e | cm and da=2.89 (4 ) ×10-17S /(|e |fm3) , respectively, where CT is the T-PT coupling constant and S is the NSM. These values differ significantly from the earlier calculations. The reason for the same has been attributed to large correlation effects arising through non-RPA type of interactions among the electrons in this atom that are observed by analyzing the differences in the RPA and CCSD results. This has been further scrutinized from the MBPT(2) and MBPT(3) results and their roles have been demonstrated explicitly.

Simultaneous analytical optimization of variational parameters in Gaussian-type functions with full configuration interaction of multicomponent molecular orbital method by elimination of translational and rotational motions: application to isotopomers of the hydrogen molecule.

PubMed

Ishimoto, Takayoshi; Tachikawa, Masanori; Nagashima, Umpei

2008-04-28

We have extended the multicomponent molecular orbital (MCMO) method to the full-configuration interaction (full-CI) fully variational molecular orbital method by elimination of translational and rotational motion components from total Hamiltonian. In the MCMO scheme, the quantum effects of protons and deuterons as well as electrons can be directly taken into account. All variational parameters in the full-CI scheme, i.e., exponents and centers (alpha and R) in the Gaussian-type function (GTF) basis set as well as the CI coefficients, are simultaneously optimized by using their analytical gradients. The total energy of the H(2) molecule calculated using the electronic [6s3p2d1f] and nuclear [1s1p1d1f] GTFs is -1.161 726 hartree, which can be compared to the energy of -1.164 025 hartree reported using a 512 term-explicitly correlated GTF calculation. Although the d- and f-type nuclear GTFs contribute to the improvement of energy convergence, the convergence of electron-nucleus correlation energy is slower than that of electron-electron one. The nuclear wave functions are delocalized due to the electron-nucleus correlation effect compared to the result of Hartree-Fock level of MCMO method. In addition, the average internuclear distances of all diatomic molecules are within 0.001 A of the previously reported experimental results. The dipole moment of the HD molecule estimated by our method is 8.4 x 10(-4) D, which is in excellent agreement with the experimental result of (8-10) x 10(-4) D.

Toward a muon-specific electronic structure theory: effective electronic Hartree-Fock equations for muonic molecules.

PubMed

Rayka, Milad; Goli, Mohammad; Shahbazian, Shant

2018-02-07

An effective set of Hartree-Fock (HF) equations are derived for electrons of muonic systems, i.e., molecules containing a positively charged muon, conceiving the muon as a quantum oscillator, which are completely equivalent to the usual two-component HF equations used to derive stationary states of the muonic molecules. In these effective equations, a non-Coulombic potential is added to the orthodox coulomb and exchange potential energy terms, which describes the interaction of the muon and the electrons effectively and is optimized during the self-consistent field cycles. While in the two-component HF equations a muon is treated as a quantum particle, in the effective HF equations it is absorbed into the effective potential and practically transformed into an effective potential field experienced by electrons. The explicit form of the effective potential depends on the nature of muon's vibrations and is derivable from the basis set used to expand the muonic spatial orbital. The resulting effective Hartree-Fock equations are implemented computationally and used successfully, as a proof of concept, in a series of muonic molecules containing all atoms from the second and third rows of the Periodic Table. To solve the algebraic version of the equations muon-specific Gaussian basis sets are designed for both muon and surrounding electrons and it is demonstrated that the optimized exponents are quite distinct from those derived for the hydrogen isotopes. The developed effective HF theory is quite general and in principle can be used for any muonic system while it is the starting point for a general effective electronic structure theory that incorporates various types of quantum correlations into the muonic systems beyond the HF equations.

Photoionization of Atoms and Molecules using a Configuration-Average Distorted-Wave Method

NASA Astrophysics Data System (ADS)

Pindzola, M. S.; Balance, C. P.; Loch, S. D.; Ludlow, J. A.

2011-05-01

A configuration-average distorted-wave method is applied to calculate the photoionization cross section for the outer subshells of the C atom and the C2 diatomic molecule. Comparisions are made with previous R-matrix and Hartree- Fock distorted-wave calculations.

Automatic Differentiation in Quantum Chemistry with Applications to Fully Variational Hartree-Fock.

PubMed

Tamayo-Mendoza, Teresa; Kreisbeck, Christoph; Lindh, Roland; Aspuru-Guzik, Alán

2018-05-23

Automatic differentiation (AD) is a powerful tool that allows calculating derivatives of implemented algorithms with respect to all of their parameters up to machine precision, without the need to explicitly add any additional functions. Thus, AD has great potential in quantum chemistry, where gradients are omnipresent but also difficult to obtain, and researchers typically spend a considerable amount of time finding suitable analytical forms when implementing derivatives. Here, we demonstrate that AD can be used to compute gradients with respect to any parameter throughout a complete quantum chemistry method. We present DiffiQult , a Hartree-Fock implementation, entirely differentiated with the use of AD tools. DiffiQult is a software package written in plain Python with minimal deviation from standard code which illustrates the capability of AD to save human effort and time in implementations of exact gradients in quantum chemistry. We leverage the obtained gradients to optimize the parameters of one-particle basis sets in the context of the floating Gaussian framework.

Optimized norm-conserving Hartree-Fock pseudopotentials for plane-wave calculations

NASA Astrophysics Data System (ADS)

Al-Saidi, W. A.; Walter, E. J.; Rappe, A. M.

2008-02-01

We report Hartree-Fock (HF)-based pseudopotentials suitable for plane-wave calculations. Unlike typical effective core potentials, the present pseudopotentials are finite at the origin and exhibit rapid convergence in a plane-wave basis; the optimized pseudopotential method [A. M. Rappe , Phys. Rev. B 41, 1227 (1990)] improves plane-wave convergence. Norm-conserving HF pseudopotentials are found to develop long-range non-Coulombic behavior which does not decay faster than 1/r , and is nonlocal. This behavior, which stems from the nonlocality of the exchange potential, is remedied using a recently developed self-consistent procedure [J. R. Trail and R. J. Needs, J. Chem. Phys. 122, 014112 (2005)]. The resulting pseudopotentials slightly violate the norm conservation of the core charge. We calculated several atomic properties using these pseudopotentials, and the results are in good agreement with all-electron HF values. The dissociation energies, equilibrium bond lengths, and frequencies of vibration of several dimers obtained with these HF pseudopotentials and plane waves are also in good agreement with all-electron results.

Analytic energy gradient of projected Hartree-Fock within projection after variation

NASA Astrophysics Data System (ADS)

Uejima, Motoyuki; Ten-no, Seiichiro

2017-03-01

We develop a geometrical optimization technique for the projection-after-variation (PAV) scheme of the recently refined projected Hartree-Fock (PHF) as a fast alternative to the variation-after-projection (VAP) approach for optimizing the structures of molecules/clusters in symmetry-adapted electronic states at the mean-field computational cost. PHF handles the nondynamic correlation effects by restoring the symmetry of a broken-symmetry single reference wavefunction and moreover enables a black-box treatment of orbital selections. Using HF orbitals instead of PHF orbitals, our approach saves the computational cost for the orbital optimization, avoiding the convergence problem that sometimes emerges in the VAP scheme. We show that PAV-PHF provides geometries comparable to those of the complete active space self-consistent field and VAP-PHF for the tested systems, namely, CH2, O3, and the [Cu2O2 ] 2 + core, where nondynamic correlation is abundant. The proposed approach is useful for large systems mainly dominated by nondynamic correlation to find stable structures in many symmetry-adapted states.

Positive semidefinite tensor factorizations of the two-electron integral matrix for low-scaling ab initio electronic structure.

PubMed

Hoy, Erik P; Mazziotti, David A

2015-08-14

Tensor factorization of the 2-electron integral matrix is a well-known technique for reducing the computational scaling of ab initio electronic structure methods toward that of Hartree-Fock and density functional theories. The simplest factorization that maintains the positive semidefinite character of the 2-electron integral matrix is the Cholesky factorization. In this paper, we introduce a family of positive semidefinite factorizations that generalize the Cholesky factorization. Using an implementation of the factorization within the parametric 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)], we study several inorganic molecules, alkane chains, and potential energy curves and find that this generalized factorization retains the accuracy and size extensivity of the Cholesky factorization, even in the presence of multi-reference correlation. The generalized family of positive semidefinite factorizations has potential applications to low-scaling ab initio electronic structure methods that treat electron correlation with a computational cost approaching that of the Hartree-Fock method or density functional theory.

Influence of the plasma environment on atomic structure using an ion-sphere model

DOE PAGES

Belkhiri, Madeny Jean; Fontes, Christopher John; Poirier, Michel

2015-09-03

Plasma environment effects on atomic structure are analyzed using various atomic structure codes. To monitor the effect of high free-electron density or low temperatures, Fermi-Dirac and Maxwell-Boltzmann statistics are compared. After a discussion of the implementation of the Fermi-Dirac approach within the ion-sphere model, several applications are considered. In order to check the consistency of the modifications brought here to extant codes, calculations have been performed using the Los Alamos Cowan Atomic Structure (cats) code in its Hartree-Fock or Hartree-Fock-Slater form and the parametric potential Flexible Atomic Code (fac). The ground-state energy shifts due to the plasma effects for themore » six most ionized aluminum ions have been calculated using the fac and cats codes and fairly agree. For the intercombination resonance line in Fe 22+, the plasma effect within the uniform electron gas model results in a positive shift that agrees with the MCDF value of B. Saha et al.« less

Influence of the plasma environment on atomic structure using an ion-sphere model

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

Belkhiri, Madeny Jean; Fontes, Christopher John; Poirier, Michel

Plasma environment effects on atomic structure are analyzed using various atomic structure codes. To monitor the effect of high free-electron density or low temperatures, Fermi-Dirac and Maxwell-Boltzmann statistics are compared. After a discussion of the implementation of the Fermi-Dirac approach within the ion-sphere model, several applications are considered. In order to check the consistency of the modifications brought here to extant codes, calculations have been performed using the Los Alamos Cowan Atomic Structure (cats) code in its Hartree-Fock or Hartree-Fock-Slater form and the parametric potential Flexible Atomic Code (fac). The ground-state energy shifts due to the plasma effects for themore » six most ionized aluminum ions have been calculated using the fac and cats codes and fairly agree. For the intercombination resonance line in Fe 22+, the plasma effect within the uniform electron gas model results in a positive shift that agrees with the MCDF value of B. Saha et al.« less

The multi-layer multi-configuration time-dependent Hartree method for bosons: theory, implementation, and applications.

PubMed

Cao, Lushuai; Krönke, Sven; Vendrell, Oriol; Schmelcher, Peter

2013-10-07

We develop the multi-layer multi-configuration time-dependent Hartree method for bosons (ML-MCTDHB), a variational numerically exact ab initio method for studying the quantum dynamics and stationary properties of general bosonic systems. ML-MCTDHB takes advantage of the permutation symmetry of identical bosons, which allows for investigations of the quantum dynamics from few to many-body systems. Moreover, the multi-layer feature enables ML-MCTDHB to describe mixed bosonic systems consisting of arbitrary many species. Multi-dimensional as well as mixed-dimensional systems can be accurately and efficiently simulated via the multi-layer expansion scheme. We provide a detailed account of the underlying theory and the corresponding implementation. We also demonstrate the superior performance by applying the method to the tunneling dynamics of bosonic ensembles in a one-dimensional double well potential, where a single-species bosonic ensemble of various correlation strengths and a weakly interacting two-species bosonic ensemble are considered.

The Hartree Equation for Infinitely Many Particles I. Well-Posedness Theory

NASA Astrophysics Data System (ADS)

Lewin, Mathieu; Sabin, Julien

2015-02-01

We show local and global well-posedness results for the Hartree equation where γ is a bounded self-adjoint operator on , ρ γ ( x) = γ( x, x) and w is a smooth short-range interaction potential. The initial datum γ(0) is assumed to be a perturbation of a translation-invariant state γ f = f(-Δ) which describes a quantum system with an infinite number of particles, such as the Fermi sea at zero temperature, or the Fermi-Dirac and Bose-Einstein gases at positive temperature. Global well-posedness follows from the conservation of the relative (free) energy of the state γ( t), counted relatively to the stationary state γ f . We indeed use a general notion of relative entropy, which allows us to treat a wide class of stationary states f(-Δ). Our results are based on a Lieb-Thirring inequality at positive density and on a recent Strichartz inequality for orthonormal functions, which are both due to Frank, Lieb, Seiringer and the first author of this article.

Quantum supercharger library: hyper-parallelism of the Hartree-Fock method.

PubMed

Fernandes, Kyle D; Renison, C Alicia; Naidoo, Kevin J

2015-07-05

We present here a set of algorithms that completely rewrites the Hartree-Fock (HF) computations common to many legacy electronic structure packages (such as GAMESS-US, GAMESS-UK, and NWChem) into a massively parallel compute scheme that takes advantage of hardware accelerators such as Graphical Processing Units (GPUs). The HF compute algorithm is core to a library of routines that we name the Quantum Supercharger Library (QSL). We briefly evaluate the QSL's performance and report that it accelerates a HF 6-31G Self-Consistent Field (SCF) computation by up to 20 times for medium sized molecules (such as a buckyball) when compared with mature Central Processing Unit algorithms available in the legacy codes in regular use by researchers. It achieves this acceleration by massive parallelization of the one- and two-electron integrals and optimization of the SCF and Direct Inversion in the Iterative Subspace routines through the use of GPU linear algebra libraries. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

Theoretical X-ray production cross sections at incident photon energies across L{sub i} (i=1-3) absorption edges of Br

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

Puri, Sanjiv

The X-ray production (XRP) cross sections, σ{sub Lk} (k = l, η, α, β{sub 6}, β{sub 1}, β{sub 3}, β{sub 4}, β{sub 9,10}, γ{sub 1,5}, γ{sub 2,3}) have been evaluated at incident photon energies across the L{sub i}(i=1-3) absorption edge energies of {sub 35}Br using theoretical data sets of different physical parameters, namely, the L{sub i}(i=1-3) sub-shell the X-ray emission rates based on the Dirac-Fock (DF) model, the fluorescence and Coster Kronig yields based on the Dirac-Hartree-Slater (DHS) model, and two sets of the photoionisation cross sections based on the relativistic Hartree-Fock-Slater (RHFS) model and the Dirac-Fock (DF) model, inmore » order to highlight the importance of electron exchange effects at photon energies in vicinity of absorption edge energies.« less

Zn Coordination Chemistry:  Development of Benchmark Suites for Geometries, Dipole Moments, and Bond Dissociation Energies and Their Use To Test and Validate Density Functionals and Molecular Orbital Theory.

PubMed

Amin, Elizabeth A; Truhlar, Donald G

2008-01-01

We present nonrelativistic and relativistic benchmark databases (obtained by coupled cluster calculations) of 10 Zn-ligand bond distances, 8 dipole moments, and 12 bond dissociation energies in Zn coordination compounds with O, S, NH3, H2O, OH, SCH3, and H ligands. These are used to test the predictions of 39 density functionals, Hartree-Fock theory, and seven more approximate molecular orbital theories. In the nonrelativisitic case, the M05-2X, B97-2, and mPW1PW functionals emerge as the most accurate ones for this test data, with unitless balanced mean unsigned errors (BMUEs) of 0.33, 0.38, and 0.43, respectively. The best local functionals (i.e., functionals with no Hartree-Fock exchange) are M06-L and τ-HCTH with BMUEs of 0.54 and 0.60, respectively. The popular B3LYP functional has a BMUE of 0.51, only slightly better than the value of 0.54 for the best local functional, which is less expensive. Hartree-Fock theory itself has a BMUE of 1.22. The M05-2X functional has a mean unsigned error of 0.008 Å for bond lengths, 0.19 D for dipole moments, and 4.30 kcal/mol for bond energies. The X3LYP functional has a smaller mean unsigned error (0.007 Å) for bond lengths but has mean unsigned errors of 0.43 D for dipole moments and 5.6 kcal/mol for bond energies. The M06-2X functional has a smaller mean unsigned error (3.3 kcal/mol) for bond energies but has mean unsigned errors of 0.017 Å for bond lengths and 0.37 D for dipole moments. The best of the semiempirical molecular orbital theories are PM3 and PM6, with BMUEs of 1.96 and 2.02, respectively. The ten most accurate functionals from the nonrelativistic benchmark analysis are then tested in relativistic calculations against new benchmarks obtained with coupled-cluster calculations and a relativistic effective core potential, resulting in M05-2X (BMUE = 0.895), PW6B95 (BMUE = 0.90), and B97-2 (BMUE = 0.93) as the top three functionals. We find significant relativistic effects (∼0.01 Å in bond lengths, ∼0.2 D in dipole moments, and ∼4 kcal/mol in Zn-ligand bond energies) that cannot be neglected for accurate modeling, but the same density functionals that do well in all-electron nonrelativistic calculations do well with relativistic effective core potentials. Although most tests are carried out with augmented polarized triple-ζ basis sets, we also carried out some tests with an augmented polarized double-ζ basis set, and we found, on average, that with the smaller basis set DFT has no loss in accuracy for dipole moments and only ∼10% less accurate bond lengths.

Toroidal high-spin isomers in the nucleus 304120

NASA Astrophysics Data System (ADS)

Staszczak, A.; Wong, Cheuk-Yin; Kosior, A.

2017-05-01

Background: Strongly deformed oblate superheavy nuclei form an intriguing region where the toroidal nuclear structures may bifurcate from the oblate spheroidal shape. The bifurcation may be facilitated when the nucleus is endowed with a large angular moment about the symmetry axis with I =Iz . The toroidal high-K isomeric states at their local energy minima can be theoretically predicted using the cranked self-consistent Skyrme-Hartree-Fock method. Purpose: We use the cranked Skyrme-Hartree-Fock method to predict the properties of the toroidal high-spin isomers in the superheavy nucleus 120304184. Method: Our method consists of three steps: First, we use the deformation-constrained Skyrme-Hartree-Fock-Bogoliubov approach to search for the nuclear density distributions with toroidal shapes. Next, using these toroidal distributions as starting configurations, we apply an additional cranking constraint of a large angular momentum I =Iz about the symmetry z axis and search for the energy minima of the system as a function of the deformation. In the last step, if a local energy minimum with I =Iz is found, we perform at this point the cranked symmetry- and deformation-unconstrained Skyrme-Hartree-Fock calculations to locate a stable toroidal high-spin isomeric state in free convergence. Results: We have theoretically located two toroidal high-spin isomeric states of 120304184 with an angular momentum I =Iz=81 ℏ (proton 2p-2h, neutron 4p-4h excitation) and I =Iz=208 ℏ (proton 5p-5h, neutron 8p-8h) at the quadrupole moment deformations Q20=-297.7 b and Q20=-300.8 b with energies 79.2 and 101.6 MeV above the spherical ground state, respectively. The nuclear density distributions of the toroidal high-spin isomers 120304184(Iz=81 ℏ and 208 ℏ ) have the maximum density close to the nuclear matter density, 0.16 fm-3, and a torus major to minor radius aspect ratio R /d =3.25 . Conclusions: We demonstrate that aligned angular momenta of Iz=81 ℏ and 208 ℏ arising from multiparticle-multihole excitations in the toroidal system of 120304184 can lead to high-spin isomeric states, even though the toroidal shape of 120304184 without spin is unstable. Toroidal energy minima without spin may be possible for superheavy nuclei with higher atomic numbers, Z ≳122 , as reported previously [7 A. Staszczak and C. Y. Wong, Acta Phys. Pol. B 40, 753 (2008)].

Toroidal high-spin isomers in the nucleus 120 304

DOE PAGES

Staszczak, A.; Wong, Cheuk-Yin; Kosior, A.

2017-05-22

Strongly deformed oblate superheavy nuclei form an intriguing region where the toroidal nuclear structures may bifurcate from the oblate spheroidal shape. The bifurcation may be facilitated when the nucleus is endowed with a large angular moment about the symmetry axis withmore » $$I=I_{z}$$. The toroidal high-$K$ isomeric states at their local energy minima can be theoretically predicted using the cranked self-consistent Skyrme-Hartree-Fock method. We use the cranked Skyrme-Hartree-Fock method to predict the properties of the toroidal high-spin isomers in the superheavy nucleus $$^{304}{120}_{184}$$. This method consists of three steps: first, we use the deformation-constrained Skyrme-Hartree-Fock-Bogoliubov approach to search for the nuclear density distributions with toroidal shapes. Next, using these toroidal distributions as starting configurations we apply an additional cranking constraint of a large angular momentum $$I=I_{z}$$ about the symmetry $z$-axis and search for the energy minima of the system as a function of the deformation. In the last step, if a local energy minimum with $$I=I_{z}$$ is found, we perform at this point the cranked symmetry- and deformation-unconstrained Skyrme-Hartree-Fock calculations to locate a stable toroidal high-spin isomeric state in free convergence. Furthemore, we have theoretically located two toroidal high-spin isomeric states of $$^{304}{120}_{184}$$ with an angular momentum $I$=$$I_z$$=81$$\\hbar$$ (proton 2p-2h, neutron 4p-4h excitation) and $I$=$$I_z$$=208$$\\hbar$$ (proton 5p-5h, neutron 8p-8h) at the quadrupole moment deformations $$Q_{20}=-297.7$$~b and $$Q_{20}=-300.8$$~b with energies 79.2 MeV and 101.6 MeV above the spherical ground state, respectively. The nuclear density distributions of the toroidal high-spin isomers $$^{304}{120}_{184}(I_z$$=81$$\\hbar$$ and 208$$\\hbar$$) have the maximum density close to the nuclear matter density, 0.16 fm$$^{-3}$$, and a torus major to minor radius aspect ratio $R/d=3.25$. Here, we demonstrate that aligned angular momenta of $$I_z$$=81$$\\hbar$$ and 208$$\\hbar$$ arising from multi-particle-multi-hole excitations in the toroidal system of $$^{304}{120}_{184}$$ can lead to high-spin isomeric states, even though the toroidal shape of $$^{304}120_{184}$$ without spin is unstable. Toroidal energy minima without spin may be possible for superheavy nuclei with higher atomic numbers, $$Z\\gtrsim$$122, as reported previously [A. Staszczak and C. Y. Wong,Acta Phys. Pol. B 40 , 753 (2008)].« less

COMPARATIVE DOCKING STUDIES OF THE BINDING OF POLYCYCLIC AROMATIC HYDROCARBONS TO THE ESTROGEN RECEPTOR

EPA Science Inventory

The interactions of several PAHs, and some of their possible metabolites, with the ligand binding domain of the estrogen receptor have been examined using molecular docking and quantum mechanical methods. The geometries of the PAHs were optimized at the Hartree-Fock level and the...

Effective Collision Strengths for Fine-structure Transitions in Si VII

NASA Astrophysics Data System (ADS)

Sossah, A. M.; Tayal, S. S.

2014-05-01

The effective collision strengths for electron-impact excitation of fine-structure transitions in Si VII are calculated as a function of electron temperature in the range 5000-2,000,000 K. The B-spline Breit-Pauli R-matrix method has been used to calculate collision strengths by electron impact. The target wave functions have been obtained using the multi-configuration Hartree-Fock method with term-dependent non-orthogonal orbitals. The 92 fine-structure levels belonging to the 46 LS states of 2s 22p 4, 2s2p 5, 2p 6, 2s 22p 33s, 2s 22p 33p, 2s 22p 33d, and 2s2p 43s configurations are included in our calculations of oscillator strengths and collision strengths. There are 4186 possible fine-structure allowed and forbidden transitions among the 92 levels. The present excitation energies, oscillator strengths, and collision strengths have been compared with previous theoretical results and available experimental data. Generally, a good agreement is found with the 6 LS-state close-coupling approximation results of Butler & Zeippen and the 44 LS-state distorted wave calculation of Bhatia & Landi.

An ab initio CASSCF study of zero field splitting fluctuations in the octet ground state of aqueous [Gd(iii)(HPDO3A)(H2O)

NASA Astrophysics Data System (ADS)

Khan, Shehryar; Pollet, Rodolphe; Vuilleumier, Rodolphe; Kowalewski, Jozef; Odelius, Michael

2017-12-01

In this work, we present ab initio calculations of the zero-field splitting (ZFS) of a gadolinium complex [Gd(iii)(HPDO3A)(H2O)] sampled from an ab initio molecular dynamics (AIMD) simulation. We perform both post-Hartree-Fock (complete active space self-consistent field—CASSCF) and density functional theory (DFT) calculations of the ZFS and compare and contrast the methods with experimental data. Two different density functional approximations (TPSS and LC-BLYP) were investigated. The magnitude of the ZFS from the CASSCF calculations is in good agreement with experiment, whereas the DFT results in varying degrees overestimate the magnitude of the ZFS for both functionals and exhibit a strong functional dependence. It was found in the sampling over the AIMD trajectory that the fluctuations in the transient ZFS tensor derived from DFT are not correlated with those of CASSCF nor does the magnitude of the ZFS from CASSCF and DFT correlate. From the fluctuations in the ZFS tensor, we extract a correlation time of the transient ZFS which is on the sub-picosecond time scale, showing a faster decay than experimental estimates.

The time-resolved photoelectron spectrum of toluene using a perturbation theory approach

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

Richings, Gareth W.; Worth, Graham A., E-mail: g.a.worth@bham.ac.uk

A theoretical study of the intra-molecular vibrational-energy redistribution of toluene using time-resolved photo-electron spectra calculated using nuclear quantum dynamics and a simple, two-mode model is presented. Calculations have been carried out using the multi-configuration time-dependent Hartree method, using three levels of approximation for the calculation of the spectra. The first is a full quantum dynamics simulation with a discretisation of the continuum wavefunction of the ejected electron, whilst the second uses first-order perturbation theory to calculate the wavefunction of the ion. Both methods rely on the explicit inclusion of both the pump and probe laser pulses. The third method includesmore » only the pump pulse and generates the photo-electron spectrum by projection of the pumped wavepacket onto the ion potential energy surface, followed by evaluation of the Fourier transform of the autocorrelation function of the subsequently propagated wavepacket. The calculations performed have been used to study the periodic population flow between the 6a and 10b16b modes in the S{sub 1} excited state, and compared to recent experimental data. We obtain results in excellent agreement with the experiment and note the efficiency of the perturbation method.« less

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

NASA Astrophysics Data System (ADS)

Qian, Guo-Xin

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

Rotational excitations in para-H2+para-H2 collisions: full- and reduced-dimensional quantum wave packet studies comparing different potential energy surfaces.

PubMed

Otto, Frank; Gatti, Fabien; Meyer, Hans-Dieter

2008-02-14

We study the process of rotational excitation in the collisions of para-H(2) with para-H(2) by propagating wave packets with the multiconfiguration time-dependent Hartree (MCTDH) algorithm. Transition probabilities are then calculated by the method of Tannor and Weeks based on time-correlation functions. Calculations were carried out up to a total angular momentum of J=70 to compute integral cross sections up to 1.2 eV in collision energy and thermal rate coefficients from 100 to 3000 K. The process is studied on the full-dimensional potential energy surface of Boothroyd-Martin-Keogh-Peterson (BMKP) as well as on the rigid rotor surface of Diep and Johnson. We test the validity of the rigid rotor approximation by also considering two rigid rotor restrictions of the BMKP potential energy surface (PES). Additionally, we investigate a variant of the BMKP PES suggested by Pogrebnya and Clary [Chem. Phys. Lett. 363, 523 (2002)] with reduced anisotropy. We compare our results with previous theoretical data for the cross sections and with experimental data for the rate coefficients at low temperatures.

Quantum Chemistry in Great Britain: Developing a Mathematical Framework for Quantum Chemistry

NASA Astrophysics Data System (ADS)

Simões, Ana; Gavroglu, Kostas

By 1935 quantum chemistry was already delineated as a distinct sub-discipline due to the contributions of Fritz London, Walter Heitler, Friedrich Hund, Erich Hückel, Robert Mulliken, Linus Pauling, John van Vleck and John Slater. These people are credited with showing that the application of quantum mechanics to the solution of chemical problems was, indeed, possible, especially so after the introduction of a number of new concepts and the adoption of certain approximation methods. And though a number of chemists had started talking of the formation of theoretical or, even, mathematical chemistry, a fully developed mathematical framework of quantum chemistry was still wanting. The work of three persons in particular-of John E. Lennard-Jones, Douglas R. Hartree, and Charles Alfred Coulson-has been absolutely crucial in the development of such a framework. In this paper we shall discuss the work of these three researchers who started their careers in the Cambridge tradition of mathematical physics and who at some point of their careers all became professors of applied mathematics. We shall argue that their work consisted of decisive contributions to the development of such a mathematical framework for quantum chemistry.

Ultrafast dynamics induced by the interaction of molecules with electromagnetic fields: Several quantum, semiclassical, and classical approaches.

PubMed

Antipov, Sergey V; Bhattacharyya, Swarnendu; El Hage, Krystel; Xu, Zhen-Hao; Meuwly, Markus; Rothlisberger, Ursula; Vaníček, Jiří

2017-11-01

Several strategies for simulating the ultrafast dynamics of molecules induced by interactions with electromagnetic fields are presented. After a brief overview of the theory of molecule-field interaction, we present several representative examples of quantum, semiclassical, and classical approaches to describe the ultrafast molecular dynamics, including the multiconfiguration time-dependent Hartree method, Bohmian dynamics, local control theory, semiclassical thawed Gaussian approximation, phase averaging, dephasing representation, molecular mechanics with proton transfer, and multipolar force fields. In addition to the general overview, some focus is given to the description of nuclear quantum effects and to the direct dynamics, in which the ab initio energies and forces acting on the nuclei are evaluated on the fly. Several practical applications, performed within the framework of the Swiss National Center of Competence in Research "Molecular Ultrafast Science and Technology," are presented: These include Bohmian dynamics description of the collision of H with H 2 , local control theory applied to the photoinduced ultrafast intramolecular proton transfer, semiclassical evaluation of vibrationally resolved electronic absorption, emission, photoelectron, and time-resolved stimulated emission spectra, infrared spectroscopy of H-bonding systems, and multipolar force fields applications in the condensed phase.

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

Spin-density functional theory treatment of He+-He collisions

NASA Astrophysics Data System (ADS)

Baxter, Matthew; Kirchner, Tom; Engel, Eberhard

2016-09-01

The He+-He collision system presents an interesting challenge to theory. On one hand, a full treatment of the three-electron dynamics constitutes a massive computational problem that has not been attempted yet; on the other hand, simplified independent-particle-model based descriptions may only provide partial information on either the transitions of the initial target electrons or on the transitions of the projectile electron, depending on the choice of atomic model potentials. We address the He+-He system within the spin-density functional theory framework on the exchange-only level. The Krieger-Li-Iafrate (KLI) approximation is used to calculate the exchange potentials for the spin-up and spin-down electrons, which ensures the correct asymptotic behavior of the effective (Kohn-Sham) potential consisting of exchange, Hartree and nuclear Coulomb potentials. The orbitals are propagated with the two-center basis generator method. In each time step, simplified versions of them are fed into the KLI equations to calculate the Kohn-Sham potential, which, in turn, is used to generate the orbitals in the next time step. First results for the transitions of all electrons and the resulting charge-changing total cross sections will be presented at the conference. Work supported by NSERC, Canada.

Probing electronic wave functions of sodium-doped clusters: Dyson orbitals, anisotropy parameters, and ionization cross-sections

DOE PAGES

Gunina, Anastasia O.; Krylov, Anna I.

2016-11-14

We apply high-level ab initio methods to describe the electronic structure of small clusters of ammonia and dimethylether (DME) doped with sodium, which provide a model for solvated electrons. We investigate the effect of the solvent and cluster size on the electronic states. We consider both energies and properties, with a focus on the shape of the electronic wave function and the related experimental observables such as photoelectron angular distributions. The central quantity in modeling photoionization experiments is the Dyson orbital, which describes the difference between the initial N-electron and final (N-1)-electron states of a system. Dyson orbitals enter themore » expression of the photoelectron matrix element, which determines total and partial photoionization cross-sections. We compute Dyson orbitals for the Na(NH3)n and Na(DME)m clusters using correlated wave functions (obtained with equation-of-motion coupled-cluster model for electron attachment with single and double substitutions) and compare them with more approximate Hartree-Fock and Kohn-Sham orbitals. As a result, we also analyze the effect of correlation and basis sets on the shapes of Dyson orbitals and the experimental observables.« less

Ultrafast dynamics induced by the interaction of molecules with electromagnetic fields: Several quantum, semiclassical, and classical approaches

PubMed Central

Antipov, Sergey V.; Bhattacharyya, Swarnendu; El Hage, Krystel; Xu, Zhen-Hao; Meuwly, Markus; Rothlisberger, Ursula; Vaníček, Jiří

2018-01-01

Several strategies for simulating the ultrafast dynamics of molecules induced by interactions with electromagnetic fields are presented. After a brief overview of the theory of molecule-field interaction, we present several representative examples of quantum, semiclassical, and classical approaches to describe the ultrafast molecular dynamics, including the multiconfiguration time-dependent Hartree method, Bohmian dynamics, local control theory, semiclassical thawed Gaussian approximation, phase averaging, dephasing representation, molecular mechanics with proton transfer, and multipolar force fields. In addition to the general overview, some focus is given to the description of nuclear quantum effects and to the direct dynamics, in which the ab initio energies and forces acting on the nuclei are evaluated on the fly. Several practical applications, performed within the framework of the Swiss National Center of Competence in Research “Molecular Ultrafast Science and Technology,” are presented: These include Bohmian dynamics description of the collision of H with H2, local control theory applied to the photoinduced ultrafast intramolecular proton transfer, semiclassical evaluation of vibrationally resolved electronic absorption, emission, photoelectron, and time-resolved stimulated emission spectra, infrared spectroscopy of H-bonding systems, and multipolar force fields applications in the condensed phase. PMID:29376107

Communication: Localized molecular orbital analysis of the effect of electron correlation on the anomalous isotope effect in the NMR spin-spin coupling constant in methane

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

Zarycz, M. Natalia C., E-mail: mnzarycz@gmail.com; Provasi, Patricio F., E-mail: patricio@unne.edu.ar; Sauer, Stephan P. A., E-mail: sauer@kiku.dk

2014-10-21

We discuss the effect of electron correlation on the unexpected differential sensitivity (UDS) in the {sup 1}J(C–H) coupling constant of CH{sub 4} using a decomposition into contributions from localized molecular orbitals and compare with the {sup 1}J(N–H) coupling constant in NH{sub 3}. In particular, we discuss the well known fact that uncorrelated coupled Hartree-Fock (CHF) calculations are not able to reproduce the UDS in methane. For this purpose we have implemented for the first time a localized molecular orbital analysis for the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes—SOPPA(CCSD) in the DALTON program. Comparing themore » changes in the localized orbital contributions at the correlated SOPPA and SOPPA(CCSD) levels and at the uncorrelated CHF level, we find that the latter overestimates the effect of stretching the bond between the coupled atoms on the contribution to the coupling from the localized bonding orbital between these atoms. This disturbs the subtle balance between the molecular orbital contributions, which lead to the UDS in methane.« less

Collective properties of low-lying octupole excitations in 20882Pb126, 6020Ca40 and 288O20

NASA Astrophysics Data System (ADS)

Zhou, X. R.; Zhao, E. G.; Dong, B. G.; Zhang, X. Z.; Long, G. L.

2003-08-01

The octupole strengths of three nuclei: β-stable nucleus 20882Pb 126, neutron skin nucleus 6020Ca 40 and neutron drip line nucleus 288O 20 are studied by using the self-consistent Hartree-Fock calculation with the random phase approximation. The collective properties of low-lying excitations are analyzed by particle-vibration coupling. The results show that there is the coexistence of the collective excitations and the decoupled strong continuum strength near the threshold in the lowest isoscalar states in 6020Ca 40 and 288O 20. For these three nuclei, both the low-lying isoscalar states and giant isoscalar resonance carry isovector strength. The ratio B(IV)/ B(IS) is checked and it is found that, for 20882Pb 126, the ratio is equal to (( N- Z)/ A) 2 in good accuracy, while for 6020Ca 40 and 288O 20, the ratios are much larger than (( N- Z)/ A) 2. The study shows that the enhancement of the ratio is due to the excess neutrons that have small binding energies in 6020Ca 40 and 288O 20.

Neural-network Kohn-Sham exchange-correlation potential and its out-of-training transferability

NASA Astrophysics Data System (ADS)

Nagai, Ryo; Akashi, Ryosuke; Sasaki, Shu; Tsuneyuki, Shinji

2018-06-01

We incorporate in the Kohn-Sham self-consistent equation a trained neural-network projection from the charge density distribution to the Hartree-exchange-correlation potential n → VHxc for a possible numerical approach to the exact Kohn-Sham scheme. The potential trained through a newly developed scheme enables us to evaluate the total energy without explicitly treating the formula of the exchange-correlation energy. With a case study of a simple model, we show that the well-trained neural-network VHxc achieves accuracy for the charge density and total energy out of the model parameter range used for the training, indicating that the property of the elusive ideal functional form of VHxc can approximately be encapsulated by the machine-learning construction. We also exemplify a factor that crucially limits the transferability—the boundary in the model parameter space where the number of the one-particle bound states changes—and see that this is cured by setting the training parameter range across that boundary. The training scheme and insights from the model study apply to more general systems, opening a novel path to numerically efficient Kohn-Sham potential.

Fluctuations in non-ideal pion gas with dynamically fixed particle number

NASA Astrophysics Data System (ADS)

Kolomeitsev, E. E.; Voskresensky, D. N.

2018-05-01

We consider a non-ideal hot pion gas with the dynamically fixed number of particles in the model with the λϕ4 interaction. The effective Lagrangian for the description of such a system is obtained after dropping the terms responsible for the change of the total particle number. Reactions π+π- ↔π0π0, which determine the isospin balance of the medium, are permitted. Within the self-consistent Hartree approximation we compute the effective pion mass, thermodynamic characteristics of the system and the variance of the particle number at temperatures above the critical point of the induced Bose-Einstein condensation when the pion chemical potential reaches the value of the effective pion mass. We analyze conditions for the condensate formation in the process of thermalization of an initially non-equilibrium pion gas. The normalized variance of the particle number increases with a temperature decrease but remains finite in the critical point of the Bose-Einstein condensation. This is due to the non-perturbative account of the interaction and is in contrast to the ideal-gas case. In the kinetic regime of the condensate formation the variance is shown to stay finite also.

Electronic structure of vitamin B12 within the framework of the Haldane-Anderson impurity model

NASA Astrophysics Data System (ADS)

Kandemir, Zafer; Mayda, Selma; Bulut, Nejat

2015-03-01

We study the electronic structure of vitamin B12 (cyanocobalamine C63H88CoN14O14P) by using the framework of the multi-orbital single-impurity Haldane-Anderson model of a transition-metal impurity in a semiconductor host. Here, our purpose is to understand the many-body effects originating from the transition-metal impurity. In this approach, the cobalt 3 d orbitals are treated as the impurity states placed in a semiconductor host which consists of the rest of the molecule. The parameters of the resulting effective Haldane-Anderson model are obtained within the Hartree-Fock approximation for the electronic structure of the molecule. The quantum Monte Carlo technique is then used to calculate the one-electron and magnetic correlation functions of this effective Haldane-Anderson model for vitamin B12. We find that new states form inside the semiconductor gap due to the on-site Coulomb interaction at the impurity 3 d orbitals and that these states become the highest occupied molecular orbitals. In addition, we present results on the charge distribution and spin correlations around the Co atom. We compare the results of this approach with those obtained by the density-functional theory calculations.

Spin Contamination Error in Optimized Geometry of Singlet Carbene (1A1) by Broken-Symmetry Method

NASA Astrophysics Data System (ADS)

Kitagawa, Yasutaka; Saito, Toru; Nakanishi, Yasuyuki; Kataoka, Yusuke; Matsui, Toru; Kawakami, Takashi; Okumura, Mitsutaka; Yamaguchi, Kizashi

2009-10-01

Spin contamination errors of a broken-symmetry (BS) method in optimized structural parameters of the singlet methylene (1A1) molecule are quantitatively estimated for the Hartree-Fock (HF) method, post-HF methods (CID, CCD, MP2, MP3, MP4(SDQ)), and a hybrid DFT (B3LYP) method. For the purpose, the optimized geometry by the BS method is compared with that of an approximate spin projection (AP) method. The difference between the BS and the AP methods is about 10-20° in the HCH angle. In order to examine the basis set dependency of the spin contamination error, calculated results by STO-3G, 6-31G*, and 6-311++G** are compared. The error depends on the basis sets, but the tendencies of each method are classified into two types. Calculated energy splitting values between the triplet and the singlet states (ST gap) indicate that the contamination of the stable triplet state makes the BS singlet solution stable and the ST gap becomes small. The energy order of the spin contamination error in the ST gap is estimated to be 10-1 eV.

First-principles investigation of quantum transport through an endohedral N@C60 in the Coulomb blockade regime.

PubMed

Yu, Zhizhou; Chen, Jian; Zhang, Lei; Wang, Jian

2013-12-11

We report an investigation of Coulomb blockade transport through an endohedral N@C60 weakly coupled with aluminum leads, employing the first-principles method combined with the Keldysh non-equilibrium Green's function derived from the equation of motion beyond the Hartree-Fock approximation. The differential conductance characteristics of the molecular device are calculated within the Coulomb blockade regime, which shows the Coulomb diamond as observed experimentally. When the gate voltage is less than that of the degeneracy point, there are two peaks in the differential conductance with an excited state induced by the change of the exchange interaction between the spin of C60 and the encapsulated nitrogen atom due to the transition from N@C(1-)(60) to N@C(2-)(60), while for a gate voltage larger than that of the degeneracy point, no excited state is available due to the quenching of exchange energy. As a result, there is only one Coulomb blockade peak in the differential conductance from the electron tunneling through the highest energy level below the Fermi level. Our first-principles results are in good agreement with experimental data obtained by an endohedral N@C60 molecular device.

Interplay of quasiparticle-vibration coupling and pairing correlations on β-decay half-lives

NASA Astrophysics Data System (ADS)

Niu, Y. F.; Niu, Z. M.; Colò, G.; Vigezzi, E.

2018-05-01

The nuclear β-decay half-lives of Ni and Sn isotopes, around the closed shell nuclei 78Ni and 132Sn, are investigated by computing the distribution of the Gamow-Teller strength using the Quasiparticle Random Phase Approximation (QRPA) with quasiparticle-vibration coupling (QPVC), based on ground-state properties obtained by Hartree-Fock-Bogoliubov (HFB) calculations. We employ the effective interaction SkM* and a zero-range effective pairing force. The half-lives are strongly reduced by including the QPVC. We study in detail the effects of isovector (IV) and isoscalar (IS) pairing. Increasing the IV strength tends to increase the lifetime for nuclei in the proximity of, but lighter than, the closed-shell ones in QRPA calculations, while the effect is significantly reduced by taking into account the QPVC. On the contrary, the IS pairing mainly plays a role for nuclei after the shell closure. Increasing its strength decreases the half-lives, and the effect at QRPA and QRPA+QPVC level is comparable. The effect of IS pairing is particularly pronounced in the case of the Sn isotopes, where it turns out to be instrumental to obtain good agreement with experimental data.

Neural network approach to quantum-chemistry data: accurate prediction of density functional theory energies.

PubMed

Balabin, Roman M; Lomakina, Ekaterina I

2009-08-21

Artificial neural network (ANN) approach has been applied to estimate the density functional theory (DFT) energy with large basis set using lower-level energy values and molecular descriptors. A total of 208 different molecules were used for the ANN training, cross validation, and testing by applying BLYP, B3LYP, and BMK density functionals. Hartree-Fock results were reported for comparison. Furthermore, constitutional molecular descriptor (CD) and quantum-chemical molecular descriptor (QD) were used for building the calibration model. The neural network structure optimization, leading to four to five hidden neurons, was also carried out. The usage of several low-level energy values was found to greatly reduce the prediction error. An expected error, mean absolute deviation, for ANN approximation to DFT energies was 0.6+/-0.2 kcal mol(-1). In addition, the comparison of the different density functionals with the basis sets and the comparison of multiple linear regression results were also provided. The CDs were found to overcome limitation of the QD. Furthermore, the effective ANN model for DFT/6-311G(3df,3pd) and DFT/6-311G(2df,2pd) energy estimation was developed, and the benchmark results were provided.

Electronic and spectroscopic properties of early 3d metal atoms on a graphite surface

NASA Astrophysics Data System (ADS)

Rakotomahevitra, A.; Garreau, G.; Demangeat, C.; Parlebas, J. C.

1995-07-01

High-sensitivity magneto-optic Kerr effect experiments failed to detect manifestations of magnetism in epitaxial films of V on Ag(100) substrates. More recently V 3s XPS of freshly evaporated V clusters on graphite exhibited the appearance of a satellite structure which has then been interpreted by the effect of surface magnetic moments on V. It is the absence of unambiguous results on the electronic properties of early 3d supported metals that prompts us to examine the problem. Our purpose is twofold. In a first part, after a total energy calculation within a tight-binding method which yields the equilibrium position of a given adatom, we use the Hartree-Fock approximation to find out a possible magnetic solution of V (or Cr) upon graphite for a reasonable value of the exchange integral Jdd. In a second part the informations given by the density of states of the graphite surface as well as the additional states of the adsorbed atom are taken into account through a generalised impurity Anderson Hamiltonian which incorporates the various Coulomb and exchange interactions necessary to analyse the 3s XPS results.

Theory of g-factor enhancement in narrow-gap quantum well heterostructures.

PubMed

Krishtopenko, S S; Gavrilenko, V I; Goiran, M

2011-09-28

We report on the study of the exchange enhancement of the g-factor in the two-dimensional (2D) electron gas in n-type narrow-gap semiconductor heterostructures. Our approach is based on the eight-band k⋅p Hamiltonian and takes into account the band nonparabolicity, the lattice deformation, the spin-orbit coupling and the Landau level broadening in the δ-correlated random potential model. Using the 'screened' Hartree-Fock approximation we demonstrate that the exchange g-factor enhancement not only shows maxima at odd values of Landau level filling factors but, due to the conduction band nonparabolicity, persists at even filling factor values as well. The magnitude of the exchange enhancement, the amplitude and the shape of the g-factor oscillations are determined by both the screening of the electron-electron interaction and the Landau level width. The 'enhanced' g-factor values calculated for the 2D electron gas in InAs/AlSb quantum well heterostructures are compared with our earlier experimental data and with those obtained by Mendez et al (1993 Phys. Rev. B 47 13937) in magnetic fields up to 30 T.

Charge and pairing dynamics in the attractive Hubbard model: Mode coupling and the validity of linear-response theory

NASA Astrophysics Data System (ADS)

Bünemann, Jörg; Seibold, Götz

2017-12-01

Pump-probe experiments have turned out as a powerful tool in order to study the dynamics of competing orders in a large variety of materials. The corresponding analysis of the data often relies on standard linear-response theory generalized to nonequilibrium situations. Here we examine the validity of such an approach for the charge and pairing response of systems with charge-density wave and (or) superconducting (SC) order. Our investigations are based on the attractive Hubbard model which we study within the time-dependent Hartree-Fock approximation. In particular, we calculate the quench and pump-probe dynamics for SC and charge order parameters in order to analyze the frequency spectra and the coupling of the probe field to the specific excitations. Our calculations reveal that the "linear-response assumption" is justified for small to moderate nonequilibrium situations (i.e., pump pulses) in the case of a purely charge-ordered ground state. However, the pump-probe dynamics on top of a superconducting ground state is determined by phase and amplitude modes which get coupled far from the equilibrium state indicating the failure of the linear-response assumption.

Accurate and efficient calculation of excitation energies with the active-space particle-particle random phase approximation

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

Zhang, Du; Yang, Weitao

An efficient method for calculating excitation energies based on the particle-particle random phase approximation (ppRPA) is presented. Neglecting the contributions from the high-lying virtual states and the low-lying core states leads to the significantly smaller active-space ppRPA matrix while keeping the error to within 0.05 eV from the corresponding full ppRPA excitation energies. The resulting computational cost is significantly reduced and becomes less than the construction of the non-local Fock exchange potential matrix in the self-consistent-field (SCF) procedure. With only a modest number of active orbitals, the original ppRPA singlet-triplet (ST) gaps as well as the low-lying single and doublemore » excitation energies can be accurately reproduced at much reduced computational costs, up to 100 times faster than the iterative Davidson diagonalization of the original full ppRPA matrix. For high-lying Rydberg excitations where the Davidson algorithm fails, the computational savings of active-space ppRPA with respect to the direct diagonalization is even more dramatic. The virtues of the underlying full ppRPA combined with the significantly lower computational cost of the active-space approach will significantly expand the applicability of the ppRPA method to calculate excitation energies at a cost of O(K^{4}), with a prefactor much smaller than a single SCF Hartree-Fock (HF)/hybrid functional calculation, thus opening up new possibilities for the quantum mechanical study of excited state electronic structure of large systems.« less

Physical Meaning of Virtual Kohn-Sham Orbitals and Orbital Energies: An Ideal Basis for the Description of Molecular Excitations.

PubMed

van Meer, R; Gritsenko, O V; Baerends, E J

2014-10-14

In recent years, several benchmark studies on the performance of large sets of functionals in time-dependent density functional theory (TDDFT) calculations of excitation energies have been performed. The tested functionals do not approximate exact Kohn-Sham orbitals and orbital energies closely. We highlight the advantages of (close to) exact Kohn-Sham orbitals and orbital energies for a simple description, very often as just a single orbital-to-orbital transition, of molecular excitations. Benchmark calculations are performed for the statistical average of orbital potentials (SAOP) functional for the potential [J. Chem. Phys. 2000, 112, 1344; 2001, 114, 652], which approximates the true Kohn-Sham potential much better than LDA, GGA, mGGA, and hybrid potentials do. An accurate Kohn-Sham potential does not only perform satisfactorily for calculated vertical excitation energies of both valence and Rydberg transitions but also exhibits appealing properties of the KS orbitals including occupied orbital energies close to ionization energies, virtual-occupied orbital energy gaps very close to excitation energies, realistic shapes of virtual orbitals, leading to straightforward interpretation of most excitations as single orbital transitions. We stress that such advantages are completely lost in time-dependent Hartree-Fock and partly in hybrid approaches. Many excitations and excitation energies calculated with local density, generalized gradient, and hybrid functionals are spurious. There is, with an accurate KS, or even the LDA or GGA potentials, nothing problematic about the "band gap" in molecules: the HOMO-LUMO gap is close to the first excitation energy (the optical gap).

On extending Kohn-Sham density functionals to systems with fractional number of electrons.

PubMed

Li, Chen; Lu, Jianfeng; Yang, Weitao

2017-06-07

We analyze four ways of formulating the Kohn-Sham (KS) density functionals with a fractional number of electrons, through extending the constrained search space from the Kohn-Sham and the generalized Kohn-Sham (GKS) non-interacting v-representable density domain for integer systems to four different sets of densities for fractional systems. In particular, these density sets are (I) ensemble interacting N-representable densities, (II) ensemble non-interacting N-representable densities, (III) non-interacting densities by the Janak construction, and (IV) non-interacting densities whose composing orbitals satisfy the Aufbau occupation principle. By proving the equivalence of the underlying first order reduced density matrices associated with these densities, we show that sets (I), (II), and (III) are equivalent, and all reduce to the Janak construction. Moreover, for functionals with the ensemble v-representable assumption at the minimizer, (III) reduces to (IV) and thus justifies the previous use of the Aufbau protocol within the (G)KS framework in the study of the ground state of fractional electron systems, as defined in the grand canonical ensemble at zero temperature. By further analyzing the Aufbau solution for different density functional approximations (DFAs) in the (G)KS scheme, we rigorously prove that there can be one and only one fractional occupation for the Hartree Fock functional, while there can be multiple fractional occupations for general DFAs in the presence of degeneracy. This has been confirmed by numerical calculations using the local density approximation as a representative of general DFAs. This work thus clarifies important issues on density functional theory calculations for fractional electron systems.

Accurate and efficient calculation of excitation energies with the active-space particle-particle random phase approximation

DOE PAGES

Zhang, Du; Yang, Weitao

2016-10-13

An efficient method for calculating excitation energies based on the particle-particle random phase approximation (ppRPA) is presented. Neglecting the contributions from the high-lying virtual states and the low-lying core states leads to the significantly smaller active-space ppRPA matrix while keeping the error to within 0.05 eV from the corresponding full ppRPA excitation energies. The resulting computational cost is significantly reduced and becomes less than the construction of the non-local Fock exchange potential matrix in the self-consistent-field (SCF) procedure. With only a modest number of active orbitals, the original ppRPA singlet-triplet (ST) gaps as well as the low-lying single and doublemore » excitation energies can be accurately reproduced at much reduced computational costs, up to 100 times faster than the iterative Davidson diagonalization of the original full ppRPA matrix. For high-lying Rydberg excitations where the Davidson algorithm fails, the computational savings of active-space ppRPA with respect to the direct diagonalization is even more dramatic. The virtues of the underlying full ppRPA combined with the significantly lower computational cost of the active-space approach will significantly expand the applicability of the ppRPA method to calculate excitation energies at a cost of O(K^{4}), with a prefactor much smaller than a single SCF Hartree-Fock (HF)/hybrid functional calculation, thus opening up new possibilities for the quantum mechanical study of excited state electronic structure of large systems.« less

Optimized effective potential model for the double perovskites Sr2 - xYxVMoO6 and Sr2 - xYxVTcO6

NASA Astrophysics Data System (ADS)

Solovyev, I. V.

2011-08-01

In an attempt to explore half-metallic properties of the double perovskites Sr2 - xYxVMoO6 and Sr2 - xYxVTcO6, we construct an effective low-energy model, which describes the behavior of the t2g states of these compounds. All parameters of such a model are derived rigorously on the basis of first-principles electronic structure calculations. In order to solve this model, we employ the optimized effective potential method and treat the correlation interactions in the random phase approximation. Although correlation interactions considerably reduce the intraatomic exchange splitting in comparison with the Hartree-Fock approach, this splitting still substantially exceeds the typical values obtained in the local-spin-density approximation (LSDA), which alters many predictions based on the LSDA. Our main results are summarized as follows. (i) All ferromagnetic states are expected to be half-metallic. However, their energies are generally higher than those of the ferrimagnetic ordering between V and Mo/Tc sites (except Sr2VMoO6). (ii) All ferrimagnetic states are metallic (except fully insulating Y2VTcO6) and no half-metallic antiferromagnetism has been found. (iii) Moreover, many of the ferrimagnetic structures appear to be unstable with respect to the spin-spiral alignment. Thus, the true magnetic ground state of these systems is expected to be more complex. In addition, we discuss several methodological issues related to nonuniqueness of the effective potential for the half-metallic and magnetic insulating states.

Pairwise additivity of energy components in protein-ligand binding: The HIV II protease-Indinavir case

NASA Astrophysics Data System (ADS)

Ucisik, Melek N.; Dashti, Danial S.; Faver, John C.; Merz, Kenneth M.

2011-08-01

An energy expansion (binding energy decomposition into n-body interaction terms for n ≥ 2) to express the receptor-ligand binding energy for the fragmented HIV II protease-Indinavir system is described to address the role of cooperativity in ligand binding. The outcome of this energy expansion is compared to the total receptor-ligand binding energy at the Hartree-Fock, density functional theory, and semiempirical levels of theory. We find that the sum of the pairwise interaction energies approximates the total binding energy to ˜82% for HF and to >95% for both the M06-L density functional and PM6-DH2 semiempirical method. The contribution of the three-body interactions amounts to 18.7%, 3.8%, and 1.4% for HF, M06-L, and PM6-DH2, respectively. We find that the expansion can be safely truncated after n = 3. That is, the contribution of the interactions involving more than three parties to the total binding energy of Indinavir to the HIV II protease receptor is negligible. Overall, we find that the two-body terms represent a good approximation to the total binding energy of the system, which points to pairwise additivity in the present case. This basic principle of pairwise additivity is utilized in fragment-based drug design approaches and our results support its continued use. The present results can also aid in the validation of non-bonded terms contained within common force fields and in the correction of systematic errors in physics-based score functions.

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

Semiempirical and DFT Investigations of the Dissociation of Alkyl Halides

ERIC Educational Resources Information Center

Waas, Jack R.

2006-01-01

Enthalpy changes corresponding to the gas phase heats of dissociation of 12 organic halides were calculated using two semiempirical methods, the Hartree-Fock method, and two DFT methods. These calculated values were compared to experimental values where possible. All five methods agreed generally with the expected empirically known trends in the…

Charge and Spin Currents in Open-Shell Molecules:  A Unified Description of NMR and EPR Observables.

PubMed

Soncini, Alessandro

2007-11-01

The theory of EPR hyperfine coupling tensors and NMR nuclear magnetic shielding tensors of open-shell molecules in the limit of vanishing spin-orbit coupling (e.g., for organic radicals) is analyzed in terms of spin and charge current density vector fields. The ab initio calculation of the spin and charge current density response has been implemented at the Restricted Open-Shell Hartree-Fock, Unrestricted Hartree-Fock, and unrestricted GGA-DFT level of theory. On the basis of this formalism, we introduce the definition of nuclear hyperfine coupling density, a scalar function of position providing a partition of the EPR observable over the molecular domain. Ab initio maps of spin and charge current density and hyperfine coupling density for small radicals are presented and discussed in order to illustrate the interpretative advantages of the newly introduced approach. Recent NMR experiments providing evidence for the existence of diatropic ring currents in the open-shell singlet pancake-bonded dimer of the neutral phenalenyl radical are directly assessed via the visualization of the induced current density.

A multireference perturbation method using non-orthogonal Hartree-Fock determinants for ground and excited states

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

Yost, Shane R.; Kowalczyk, Tim; Van Voorhis, Troy, E-mail: tvan@mit.edu

2013-11-07

In this article we propose the ΔSCF(2) framework, a multireference strategy based on second-order perturbation theory, for ground and excited electronic states. Unlike the complete active space family of methods, ΔSCF(2) employs a set of self-consistent Hartree-Fock determinants, also known as ΔSCF states. Each ΔSCF electronic state is modified by a first-order correction from Møller-Plesset perturbation theory and used to construct a Hamiltonian in a configuration interactions like framework. We present formulas for the resulting matrix elements between nonorthogonal states that scale as N{sub occ}{sup 2}N{sub virt}{sup 3}. Unlike most active space methods, ΔSCF(2) treats the ground and excited statemore » determinants even-handedly. We apply ΔSCF(2) to the H{sub 2}, hydrogen fluoride, and H{sub 4} systems and show that the method provides accurate descriptions of ground- and excited-state potential energy surfaces with no single active space containing more than 10 ΔSCF states.« less

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.

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.

The unrestricted Hartree-Fock self consistent field calculation for spin density wave state in metallic carbon nanotube

NASA Astrophysics Data System (ADS)

Kobayashi, Katsushi

1997-06-01

The possibility of a spin density wave (SDW) state in a metallic carbon nanotube (CN) and its electronic properties are investigated within the Hartree-Fock self consistent field (SCF) energy-band calculation. Two kinds of spatial SDW states are assumed in this study. Each assumed SDW on the wave function is constructed with the degenerate π orbital in the metallic CN system. The results calculated for the one SDW model of CN always have a relative stability (˜ 0.1 eV/cell) in SCF total energy compared with the original model in which no SDW is assumed. All the results calculated for another SDW model are completely equal to the original one. Moreover, in the energy dispersion of the former stable SDW model, the degenerate π level found in the original model disappears and the band gap (3-5 eV) occurs around at the Fermi level. The energetic stability and the band gap are also found in the π-electron band calculation within the Hubbard Hamiltonian.

Holomorphic Hartree-Fock Theory: The Nature of Two-Electron Problems.

PubMed

Burton, Hugh G A; Gross, Mark; Thom, Alex J W

2018-02-13

We explore the existence and behavior of holomorphic restricted Hartree-Fock (h-RHF) solutions for two-electron problems. Through algebraic geometry, the exact number of solutions with n basis functions is rigorously identified as 1 / 2 (3 n - 1), proving that states must exist for all molecular geometries. A detailed study on the h-RHF states of HZ (STO-3G) then demonstrates both the conservation of holomorphic solutions as geometry or atomic charges are varied and the emergence of complex h-RHF solutions at coalescence points. Using catastrophe theory, the nature of these coalescence points is described, highlighting the influence of molecular symmetry. The h-RHF states of HHeH 2+ and HHeH (STO-3G) are then compared, illustrating the isomorphism between systems with two electrons and two electron holes. Finally, we explore the h-RHF states of ethene (STO-3G) by considering the π electrons as a two-electron problem and employ NOCI to identify a crossing of the lowest energy singlet and triplet states at the perpendicular geometry.

Wavepacket dynamics and the multi-configurational time-dependent Hartree approach

NASA Astrophysics Data System (ADS)

Manthe, Uwe

2017-06-01

Multi-configurational time-dependent Hartree (MCTDH) based approaches are efficient, accurate, and versatile methods for high-dimensional quantum dynamics simulations. Applications range from detailed investigations of polyatomic reaction processes in the gas phase to high-dimensional simulations studying the dynamics of condensed phase systems described by typical solid state physics model Hamiltonians. The present article presents an overview of the different areas of application and provides a comprehensive review of the underlying theory. The concepts and guiding ideas underlying the MCTDH approach and its multi-mode and multi-layer extensions are discussed in detail. The general structure of the equations of motion is highlighted. The representation of the Hamiltonian and the correlated discrete variable representation (CDVR), which provides an efficient multi-dimensional quadrature in MCTDH calculations, are discussed. Methods which facilitate the calculation of eigenstates, the evaluation of correlation functions, and the efficient representation of thermal ensembles in MCTDH calculations are described. Different schemes for the treatment of indistinguishable particles in MCTDH calculations and recent developments towards a unified multi-layer MCTDH theory for systems including bosons and fermions are discussed.

Can model Hamiltonians describe the electron-electron interaction in π-conjugated systems?: PAH and graphene

NASA Astrophysics Data System (ADS)

Chiappe, G.; Louis, E.; San-Fabián, E.; Vergés, J. A.

2015-11-01

Model Hamiltonians have been, and still are, a valuable tool for investigating the electronic structure of systems for which mean field theories work poorly. This review will concentrate on the application of Pariser-Parr-Pople (PPP) and Hubbard Hamiltonians to investigate some relevant properties of polycyclic aromatic hydrocarbons (PAH) and graphene. When presenting these two Hamiltonians we will resort to second quantisation which, although not the way chosen in its original proposal of the former, is much clearer. We will not attempt to be comprehensive, but rather our objective will be to try to provide the reader with information on what kinds of problems they will encounter and what tools they will need to solve them. One of the key issues concerning model Hamiltonians that will be treated in detail is the choice of model parameters. Although model Hamiltonians reduce the complexity of the original Hamiltonian, they cannot be solved in most cases exactly. So, we shall first consider the Hartree-Fock approximation, still the only tool for handling large systems, besides density functional theory (DFT) approaches. We proceed by discussing to what extent one may exactly solve model Hamiltonians and the Lanczos approach. We shall describe the configuration interaction (CI) method, a common technology in quantum chemistry but one rarely used to solve model Hamiltonians. In particular, we propose a variant of the Lanczos method, inspired by CI, that has the novelty of using as the seed of the Lanczos process a mean field (Hartree-Fock) determinant (the method will be named LCI). Two questions of interest related to model Hamiltonians will be discussed: (i) when including long-range interactions, how crucial is including in the Hamiltonian the electronic charge that compensates ion charges? (ii) Is it possible to reduce a Hamiltonian incorporating Coulomb interactions (PPP) to an ‘effective’ Hamiltonian including only on-site interactions (Hubbard)? The performance of CI will be checked on small molecules. The electronic structure of azulene and fused azulene will be used to illustrate several aspects of the method. As regards graphene, several questions will be considered: (i) paramagnetic versus antiferromagnetic solutions, (ii) forbidden gap versus dot size, (iii) graphene nano-ribbons, and (iv) optical properties.

Selection of active spaces for multiconfigurational wavefunctions

NASA Astrophysics Data System (ADS)

Keller, Sebastian; Boguslawski, Katharina; Janowski, Tomasz; Reiher, Markus; Pulay, Peter

2015-06-01

The efficient and accurate description of the electronic structure of strongly correlated systems is still a largely unsolved problem. The usual procedures start with a multiconfigurational (usually a Complete Active Space, CAS) wavefunction which accounts for static correlation and add dynamical correlation by perturbation theory, configuration interaction, or coupled cluster expansion. This procedure requires the correct selection of the active space. Intuitive methods are unreliable for complex systems. The inexpensive black-box unrestricted natural orbital (UNO) criterion postulates that the Unrestricted Hartree-Fock (UHF) charge natural orbitals with fractional occupancy (e.g., between 0.02 and 1.98) constitute the active space. UNOs generally approximate the CAS orbitals so well that the orbital optimization in CAS Self-Consistent Field (CASSCF) may be omitted, resulting in the inexpensive UNO-CAS method. A rigorous testing of the UNO criterion requires comparison with approximate full configuration interaction wavefunctions. This became feasible with the advent of Density Matrix Renormalization Group (DMRG) methods which can approximate highly correlated wavefunctions at affordable cost. We have compared active orbital occupancies in UNO-CAS and CASSCF calculations with DMRG in a number of strongly correlated molecules: compounds of electronegative atoms (F2, ozone, and NO2), polyenes, aromatic molecules (naphthalene, azulene, anthracene, and nitrobenzene), radicals (phenoxy and benzyl), diradicals (o-, m-, and p-benzyne), and transition metal compounds (nickel-acetylene and Cr2). The UNO criterion works well in these cases. Other symmetry breaking solutions, with the possible exception of spatial symmetry, do not appear to be essential to generate the correct active space. In the case of multiple UHF solutions, the natural orbitals of the average UHF density should be used. The problems of the UNO criterion and their potential solutions are discussed: finding the UHF solutions, discontinuities on potential energy surfaces, and inclusion of dynamical electron correlation and generalization to excited states.

Configuration-constrained cranking Hartree-Fock pairing calculations for sidebands of nuclei

NASA Astrophysics Data System (ADS)

Liang, W. Y.; Jiao, C. F.; Wu, Q.; Fu, X. M.; Xu, F. R.

2015-12-01

Background: Nuclear collective rotations have been successfully described by the cranking Hartree-Fock-Bogoliubov (HFB) model. However, for rotational sidebands which are built on intrinsic excited configurations, it may not be easy to find converged cranking HFB solutions. The nonconservation of the particle number in the BCS pairing is another shortcoming. To improve the pairing treatment, a particle-number-conserving (PNC) pairing method was suggested. But the existing PNC calculations were performed within a phenomenological one-body potential (e.g., Nilsson or Woods-Saxon) in which one has to deal the double-counting problem. Purpose: The present work aims at an improved description of nuclear rotations, particularly for the rotations of excited configurations, i.e., sidebands. Methods: We developed a configuration-constrained cranking Skyrme Hartree-Fock (SHF) calculation with the pairing correlation treated by the PNC method. The PNC pairing takes the philosophy of the shell model which diagonalizes the Hamiltonian in a truncated model space. The cranked deformed SHF basis provides a small but efficient model space for the PNC diagonalization. Results: We have applied the present method to the calculations of collective rotations of hafnium isotopes for both ground-state bands and sidebands, reproducing well experimental observations. The first up-bendings observed in the yrast bands of the hafnium isotopes are reproduced, and the second up-bendings are predicted. Calculations for rotational bands built on broken-pair excited configurations agree well with experimental data. The band-mixing between two Kπ=6+ bands observed in 176Hf and the K purity of the 178Hf rotational state built on the famous 31 yr Kπ=16+ isomer are discussed. Conclusions: The developed configuration-constrained cranking calculation has been proved to be a powerful tool to describe both the yrast bands and sidebands of deformed nuclei. The analyses of rotational moments of inertia help to understand the structures of nuclei, including rotational alignments, configurations, and competitions between collective and single-particle excitations.

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.

Flexibility of "polyunsaturated fatty acid chains" and peptide backbones: A comparative ab initio study.

PubMed

Law, Jacqueline M S; Setiadi, David H; Chass, Gregory A; Csizmadia, Imre G; Viskolcz, Béla

2005-01-27

The conformational properties of omega-3 type of polyunsaturated fatty acid (PUFA) chains and their fragments were studied using Hartree-Fock (RHF/3-21G) and DFT (B3LYP/6-31G(d)) methods. Comparisons between a unit (U) fragment of the PUFA chain and a mono N-Ac-glycine-NHMe residue show that both structures have the same sequence of sp2-sp3-sp2 atoms. The flexibility of PUFA originates in the internal rotation about the above pairs of sigma bonds. Therefore, potential energy surfaces (PESs) were generated by a scan around the terminal dihedral angles (phi t1 and phi t2) as well as the phi 1 and psi 1 dihedrals of both 1U congeners (Me-CHCH-CH2-CHCHMe and MeCONH-CH2-CONHMe) at the RHF/3-21G level of theory. An interesting similarity was found in the flexibility between the cis allylic structure and the trans peptide models. A flat landscape can be seen in the cis 1U (hepta-2,5-diene) surface, implying that several conformations are expected to be found in this (PES). An exhaustive search carried out on the 1U and 2U models revealed that straight chain structures such as trans and cis beta (phi 1 approximately psi 1 approximately 120 degrees; phi 2 approximately psi 2 approximately -120 degrees) or trans and cis extended (phi 1 approximately psi 1 approximately phi 2 approximately psi 2 approximately 120 degrees) can be formed at the lowest energy of both isomers. However, forming helical structures, such as trans helix (phi 1 approximately -120 degrees, psi 1 approximately 12 degrees; phi 2 approximately -120 degrees, psi 2 approximately 12 degrees) or cis helix (phi 1 approximately -130 degrees, psi 1 approximately 90 degrees; phi 2 approximately -145 degrees, psi 2 approximately 90 degrees) will require more energy. These six conformations, found in 2U, were selected to construct longer chains such as 3U, 4U, 5U, and 6U to obtain the thermochemistry of secondary structures. The variation in the extension or compression of the chain length turned out to be a factor of 2 between the helical and nonhelical structures. The inside diameter of the "tube" of cis helix turned out to be 3.5 A after discounting the internal H atoms. Thermodynamic functions were computed at the B3LYP/6-311+G(2d,p)//B3LYP/6-31G(d). The cis-trans isomerization energy of 1.7 +/- 0.2 kcal mol(-1) unit(-1) for all structure pairs indicates that the conformer selection was consistent. A folding energy of 0.5 +/- 0.1 kcal mol(-1) unit(-1) has been extracted from the energy comparison of the helices and most extended nonhelical structures. The entropy change associated with the folding (Delta S(folding)) is decreases faster with the degree of polymerization (n) for the cis than for the trans isomer. As a consequence, the linear relationships between (Delta G(folding)) and n for the cis and trans isomer crossed at about n = 3. This suggested that the naturally occurring cis isomer less ready to fold than the trans isomer since a greater degree of organization is exhibited by the cis isomer during the folding process. The result of this work leads to the question within the group additivity rule: could the method applied in our study of the folding of polyallylic hydrocarbons be useful in investigating the thermochemistry of protein folding?

Exploring Do-It-Yourself Approaches in Computational Quantum Chemistry: The Pedagogical Benefits of the Classical Boys Algorithm

ERIC Educational Resources Information Center

Orsini, Gabriele

2015-01-01

The ever-increasing impact of molecular quantum calculations over chemical sciences implies a strong and urgent need for the elaboration of proper teaching strategies in university curricula. In such perspective, this paper proposes an extensive project for a student-driven, cooperative, from-scratch implementation of a general Hartree-Fock…

Average Nuclear Potentials from Selfconsistent Semiclassical Calculations

NASA Astrophysics Data System (ADS)

Bartel, J.

1999-03-01

Using the selfconsistent semiclassical Extended Thomas-Fermi (ETF) method up to 4th order in connection with Skyrme forces it is demonstrated that the neutron and proton average potentials obtained using the semiclassical functionals τ (ETF)[ρ] and vec {J}(ETF)[ρ] reproduce the corresponding Hartree-Fock fields extremely well, except for shell oscillations in the nuclear center.

On the accuracy of density functional theory and wave function methods for calculating vertical ionization energies

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

McKechnie, Scott; Booth, George H.; Cohen, Aron J.

The best practice in computational methods for determining vertical ionization energies (VIEs) is assessed, via reference to experimentally determined VIEs that are corroborated by highly accurate coupled-cluster calculations. These reference values are used to benchmark the performance of density-functional theory (DFT) and wave function methods: Hartree-Fock theory (HF), second-order Møller-Plesset perturbation theory (MP2) and Electron Propagator Theory (EPT). The core test set consists of 147 small molecules. An extended set of six larger molecules, from benzene to hexacene, is also considered to investigate the dependence of the results on molecule size. The closest agreement with experiment is found for ionizationmore » energies obtained from total energy diff calculations. In particular, DFT calculations using exchange-correlation functionals with either a large amount of exact exchange or long-range correction perform best. The results from these functionals are also the least sensitive to an increase in molecule size. In general, ionization energies calculated directly from the orbital energies of the neutral species are less accurate and more sensitive to an increase in molecule size. For the single-calculation approach, the EPT calculations are in closest agreement for both sets of molecules. For the orbital energies from DFT functionals, only those with long-range correction give quantitative agreement with dramatic failing for all other functionals considered. The results offer a practical hierarchy of approximations for the calculation of vertical ionization energies. In addition, the experimental and computational reference values can be used as a standardized set of benchmarks, against which other approximate methods can be compared.« less

Real-Space Multiple-Scattering Theory and Its Applications at Exascale

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

Eisenbach, Markus; Wang, Yang

In recent decades, the ab initio methods based on density functional theory (DFT) (Hohenberg and Kohn 1964, Kohn and Sham 1965) have become a widely used tool in computational materials science, which allows theoretical prediction of physical properties of materials from the first principles and theoretical interpretation of new physical phenomena found in experiments. In the framework of DFT, the original problem that requires solving a quantum mechanical equation for a many-electron system is reduced to a one-electron problem that involves an electron moving in an effective field, while the effective field potential is made up of an electrostatic potential,more » also known as Hartree potential, arising from the electronic and ion charge distribution in space and an exchange–correlation potential, which is a function of the electron density and encapsulates the exchange and correlation effects of the many-electron system. Even though the exact functional form of the exchange-correlation potential is formally unknown, a local density approximation (LDA) or a generalized gradient approximation (GGA) is usually applied so that the calculation of the exchange–correlation potential, as well as the exchange–correlation energy, becomes tractable while a required accuracy is retained. Based on DFT, ab initio electronic structure calculations for a material generally involve a self-consistent process that iterates between two computational tasks: (1) solving an one-electron Schrödinger equation, also known as Kohn–Sham equation, to obtain the electron density and, if needed, the magnetic moment density, and (2) solving the Poisson equation to obtain the electrostatic potential corresponding to the electron density and constructing the effective potential by adding the exchange–correlation potential to the electrostatic potential. This self-consistent process proceeds until a convergence criteria is reached.« less

Variational and perturbative formulations of quantum mechanical/molecular mechanical free energy with mean-field embedding and its analytical gradients.

PubMed

Yamamoto, Takeshi

2008-12-28

Conventional quantum chemical solvation theories are based on the mean-field embedding approximation. That is, the electronic wavefunction is calculated in the presence of the mean field of the environment. In this paper a direct quantum mechanical/molecular mechanical (QM/MM) analog of such a mean-field theory is formulated based on variational and perturbative frameworks. In the variational framework, an appropriate QM/MM free energy functional is defined and is minimized in terms of the trial wavefunction that best approximates the true QM wavefunction in a statistically averaged sense. Analytical free energy gradient is obtained, which takes the form of the gradient of effective QM energy calculated in the averaged MM potential. In the perturbative framework, the above variational procedure is shown to be equivalent to the first-order expansion of the QM energy (in the exact free energy expression) about the self-consistent reference field. This helps understand the relation between the variational procedure and the exact QM/MM free energy as well as existing QM/MM theories. Based on this, several ways are discussed for evaluating non-mean-field effects (i.e., statistical fluctuations of the QM wavefunction) that are neglected in the mean-field calculation. As an illustration, the method is applied to an S(N)2 Menshutkin reaction in water, NH(3)+CH(3)Cl-->NH(3)CH(3) (+)+Cl(-), for which free energy profiles are obtained at the Hartree-Fock, MP2, B3LYP, and BHHLYP levels by integrating the free energy gradient. Non-mean-field effects are evaluated to be <0.5 kcal/mol using a Gaussian fluctuation model for the environment, which suggests that those effects are rather small for the present reaction in water.

Phase diagram of an extended Agassi model

NASA Astrophysics Data System (ADS)

García-Ramos, J. E.; Dukelsky, J.; Pérez-Fernández, P.; Arias, J. M.

2018-05-01

Background: The Agassi model [D. Agassi, Nucl. Phys. A 116, 49 (1968), 10.1016/0375-9474(68)90482-X] is an extension of the Lipkin-Meshkov-Glick (LMG) model [H. J. Lipkin, N. Meshkov, and A. J. Glick, Nucl. Phys. 62, 188 (1965), 10.1016/0029-5582(65)90862-X] that incorporates the pairing interaction. It is a schematic model that describes the interplay between particle-hole and pair correlations. It was proposed in the 1960s by D. Agassi as a model to simulate the properties of the quadrupole plus pairing model. Purpose: The aim of this work is to extend a previous study by Davis and Heiss [J. Phys. G: Nucl. Phys. 12, 805 (1986), 10.1088/0305-4616/12/9/006] generalizing the Agassi model and analyze in detail the phase diagram of the model as well as the different regions with coexistence of several phases. Method: We solve the model Hamiltonian through the Hartree-Fock-Bogoliubov (HFB) approximation, introducing two variational parameters that play the role of order parameters. We also compare the HFB calculations with the exact ones. Results: We obtain the phase diagram of the model and classify the order of the different quantum phase transitions appearing in the diagram. The phase diagram presents broad regions where several phases, up to three, coexist. Moreover, there is also a line and a point where four and five phases are degenerated, respectively. Conclusions: The phase diagram of the extended Agassi model presents a rich variety of phases. Phase coexistence is present in extended areas of the parameter space. The model could be an important tool for benchmarking novel many-body approximations.

VizieR Online Data Catalog: Energy levels & transition rates for F-like ions (Si+, 2016)

NASA Astrophysics Data System (ADS)

Si, R.; Li, S.; Guo, X. L.; Chen, Z. B.; Brage, T.; Jonsson, P.; Wang, K.; Yan, J.; Chen, C. Y.; Zou, Y. M.

2017-01-01

For the multiconfiguration Dirac-Hartree-Fock (MCDHF) calculation we use the latest version of the GRASP2K code (Jonsson+ 2013CoPhC.184.2197J), while the many-body perturbation theory (MBPT) calculation is performed using the Flexible Atomic Code (FAC; Gu 2008CaJPh..86..675G). (2 data files).

The limits of the nuclear landscape explored by the relativistic continuum Hartree-Bogoliubov theory

NASA Astrophysics Data System (ADS)

Xia, X. W.; Lim, Y.; Zhao, P. W.; Liang, H. Z.; Qu, X. Y.; Chen, Y.; Liu, H.; Zhang, L. F.; Zhang, S. Q.; Kim, Y.; Meng, J.

2018-05-01

The ground-state properties of nuclei with 8 ⩽ Z ⩽ 120 from the proton drip line to the neutron drip line have been investigated using the spherical relativistic continuum Hartree-Bogoliubov (RCHB) theory with the relativistic density functional PC-PK1. With the effects of the continuum included, there are totally 9035 nuclei predicted to be bound, which largely extends the existing nuclear landscapes predicted with other methods. The calculated binding energies, separation energies, neutron and proton Fermi surfaces, root-mean-square (rms) radii of neutron, proton, matter, and charge distributions, ground-state spins and parities are tabulated. The extension of the nuclear landscape obtained with RCHB is discussed in detail, in particular for the neutron-rich side, in comparison with the relativistic mean field calculations without pairing correlations and also other predicted landscapes. It is found that the coupling between the bound states and the continuum due to the pairing correlations plays an essential role in extending the nuclear landscape. The systematics of the separation energies, radii, densities, potentials and pairing energies of the RCHB calculations are also discussed. In addition, the α-decay energies and proton emitters based on the RCHB calculations are investigated.

Molecular wave function and effective adiabatic potentials calculated by extended multi-configuration time-dependent Hartree-Fock method

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

Kato, Tsuyoshi; Ide, Yoshihiro; Yamanouchi, Kaoru

We first calculate the ground-state molecular wave function of 1D model H{sub 2} molecule by solving the coupled equations of motion formulated in the extended multi-configuration time-dependent Hartree-Fock (MCTDHF) method by the imaginary time propagation. From the comparisons with the results obtained by the Born-Huang (BH) expansion method as well as with the exact wave function, we observe that the memory size required in the extended MCTDHF method is about two orders of magnitude smaller than in the BH expansion method to achieve the same accuracy for the total energy. Second, in order to provide a theoretical means to understandmore » dynamical behavior of the wave function, we propose to define effective adiabatic potential functions and compare them with the conventional adiabatic electronic potentials, although the notion of the adiabatic potentials is not used in the extended MCTDHF approach. From the comparison, we conclude that by calculating the effective potentials we may be able to predict the energy differences among electronic states even for a time-dependent system, e.g., time-dependent excitation energies, which would be difficult to be estimated within the BH expansion approach.« less

Direct Quantum Dynamics Using Grid-Based Wave Function Propagation and Machine-Learned Potential Energy Surfaces.

PubMed

Richings, Gareth W; Habershon, Scott

2017-09-12

We describe a method for performing nuclear quantum dynamics calculations using standard, grid-based algorithms, including the multiconfiguration time-dependent Hartree (MCTDH) method, where the potential energy surface (PES) is calculated "on-the-fly". The method of Gaussian process regression (GPR) is used to construct a global representation of the PES using values of the energy at points distributed in molecular configuration space during the course of the wavepacket propagation. We demonstrate this direct dynamics approach for both an analytical PES function describing 3-dimensional proton transfer dynamics in malonaldehyde and for 2- and 6-dimensional quantum dynamics simulations of proton transfer in salicylaldimine. In the case of salicylaldimine we also perform calculations in which the PES is constructed using Hartree-Fock calculations through an interface to an ab initio electronic structure code. In all cases, the results of the quantum dynamics simulations are in excellent agreement with previous simulations of both systems yet do not require prior fitting of a PES at any stage. Our approach (implemented in a development version of the Quantics package) opens a route to performing accurate quantum dynamics simulations via wave function propagation of many-dimensional molecular systems in a direct and efficient manner.

Linear-scaling implementation of molecular response theory in self-consistent field electronic-structure theory.

PubMed

Coriani, Sonia; Høst, Stinne; Jansík, Branislav; Thøgersen, Lea; Olsen, Jeppe; Jørgensen, Poul; Reine, Simen; Pawłowski, Filip; Helgaker, Trygve; Sałek, Paweł

2007-04-21

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field theories for the calculation of frequency-dependent molecular response properties and excitation energies is presented, based on a nonredundant exponential parametrization of the one-electron density matrix in the atomic-orbital basis, avoiding the use of canonical orbitals. The response equations are solved iteratively, by an atomic-orbital subspace method equivalent to that of molecular-orbital theory. Important features of the subspace method are the use of paired trial vectors (to preserve the algebraic structure of the response equations), a nondiagonal preconditioner (for rapid convergence), and the generation of good initial guesses (for robust solution). As a result, the performance of the iterative method is the same as in canonical molecular-orbital theory, with five to ten iterations needed for convergence. As in traditional direct Hartree-Fock and Kohn-Sham theories, the calculations are dominated by the construction of the effective Fock/Kohn-Sham matrix, once in each iteration. Linear complexity is achieved by using sparse-matrix algebra, as illustrated in calculations of excitation energies and frequency-dependent polarizabilities of polyalanine peptides containing up to 1400 atoms.

Importance sampling studies of helium using the Feynman-Kac path integral method

NASA Astrophysics Data System (ADS)

Datta, S.; Rejcek, J. M.

2018-05-01

In the Feynman-Kac path integral approach the eigenvalues of a quantum system can be computed using Wiener measure which uses Brownian particle motion. In our previous work on such systems we have observed that the Wiener process numerically converges slowly for dimensions greater than two because almost all trajectories will escape to infinity. One can speed up this process by using a generalized Feynman-Kac (GFK) method, in which the new measure associated with the trial function is stationary, so that the convergence rate becomes much faster. We thus achieve an example of "importance sampling" and, in the present work, we apply it to the Feynman-Kac (FK) path integrals for the ground and first few excited-state energies for He to speed up the convergence rate. We calculate the path integrals using space averaging rather than the time averaging as done in the past. The best previous calculations from variational computations report precisions of 10-16 Hartrees, whereas in most cases our path integral results obtained for the ground and first excited states of He are lower than these results by about 10-6 Hartrees or more.

Efficient method of evaluation for Gaussian Hartree-Fock exchange operator for Gau-PBE functional

NASA Astrophysics Data System (ADS)

Song, Jong-Won; Hirao, Kimihiko

2015-07-01

We previously developed an efficient screened hybrid functional called Gaussian-Perdew-Burke-Ernzerhof (Gau-PBE) [Song et al., J. Chem. Phys. 135, 071103 (2011)] for large molecules and extended systems, which is characterized by the usage of a Gaussian function as a modified Coulomb potential for the Hartree-Fock (HF) exchange. We found that the adoption of a Gaussian HF exchange operator considerably decreases the calculation time cost of periodic systems while improving the reproducibility of the bandgaps of semiconductors. We present a distance-based screening scheme here that is tailored for the Gaussian HF exchange integral that utilizes multipole expansion for the Gaussian two-electron integrals. We found a new multipole screening scheme helps to save the time cost for the HF exchange integration by efficiently decreasing the number of integrals of, specifically, the near field region without incurring substantial changes in total energy. In our assessment on the periodic systems of seven semiconductors, the Gau-PBE hybrid functional with a new screening scheme has 1.56 times the time cost of a pure functional while the previous Gau-PBE was 1.84 times and HSE06 was 3.34 times.

On regularizing the MCTDH equations of motion

NASA Astrophysics Data System (ADS)

Meyer, Hans-Dieter; Wang, Haobin

2018-03-01

The Multiconfiguration Time-Dependent Hartree (MCTDH) approach leads to equations of motion (EOM) which become singular when there are unoccupied so-called single-particle functions (SPFs). Starting from a Hartree product, all SPFs, except the first one, are unoccupied initially. To solve the MCTDH-EOMs numerically, one therefore has to remove the singularity by a regularization procedure. Usually the inverse of a density matrix is regularized. Here we argue and show that regularizing the coefficient tensor, which in turn regularizes the density matrix as well, leads to an improved performance of the EOMs. The initially unoccupied SPFs are rotated faster into their "correct direction" in Hilbert space and the final results are less sensitive to the choice of the value of the regularization parameter. For a particular example (a spin-boson system studied with a transformed Hamiltonian), we could even show that only with the new regularization scheme could one obtain correct results. Finally, in Appendix A, a new integration scheme for the MCTDH-EOMs developed by Lubich and co-workers is discussed. It is argued that this scheme does not solve the problem of the unoccupied natural orbitals because this scheme ignores the latter and does not propagate them at all.

Bubble nuclei within the self-consistent Hartree-Fock mean field plus pairing approach

NASA Astrophysics Data System (ADS)

Phuc, L. Tan; Hung, N. Quang; Dang, N. Dinh

2018-02-01

The depletion of the nuclear density at its center, called the nuclear bubble, is studied within the Skyrme Hartree-Fock mean field consistently incorporating the superfluid pairing. The latter is obtained within the finite-temperature Bardeen-Cooper-Schrieffer theory and within the approach using the exact pairing. The numerical calculations are carried out for 22O and 34Si nuclei, whose bubble structures, caused by a very low occupancy of the 2 s1 /2 level, were previously predicted at T =0 . Among 24 Skyrme interactions under consideration, the MSk3 is the only one which reproduces the experimentally measured occupancy of the 2 s1 /2 proton level as well as the binding energy, and consequently produces the most pronounced bubble structure in 34Si. As compared to the approaches employing the same BSk14 interaction, our approach with exact pairing predicts a pairing effect which is stronger in 22O and weaker in 34Si. The increase in temperature depletes the bubble structure and completely washes it out when the temperature reaches a critical value, at which the factor measuring the depletion of the nucleon density vanishes.

Efficient method of evaluation for Gaussian Hartree-Fock exchange operator for Gau-PBE functional

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

Song, Jong-Won; Hirao, Kimihiko, E-mail: hirao@riken.jp

2015-07-14

We previously developed an efficient screened hybrid functional called Gaussian-Perdew–Burke–Ernzerhof (Gau-PBE) [Song et al., J. Chem. Phys. 135, 071103 (2011)] for large molecules and extended systems, which is characterized by the usage of a Gaussian function as a modified Coulomb potential for the Hartree-Fock (HF) exchange. We found that the adoption of a Gaussian HF exchange operator considerably decreases the calculation time cost of periodic systems while improving the reproducibility of the bandgaps of semiconductors. We present a distance-based screening scheme here that is tailored for the Gaussian HF exchange integral that utilizes multipole expansion for the Gaussian two-electron integrals.more » We found a new multipole screening scheme helps to save the time cost for the HF exchange integration by efficiently decreasing the number of integrals of, specifically, the near field region without incurring substantial changes in total energy. In our assessment on the periodic systems of seven semiconductors, the Gau-PBE hybrid functional with a new screening scheme has 1.56 times the time cost of a pure functional while the previous Gau-PBE was 1.84 times and HSE06 was 3.34 times.« less

L i ( i = 1-3) subshell X-ray production cross sections and fluorescence yields for some elements with 56 ⩽ Z ⩽ 68 at 22.6 keV

NASA Astrophysics Data System (ADS)

Chauhan, Yogeshwar; Tiwari, M. K.; Puri, Sanjiv

2008-01-01

The L k ( k = l, α, β 1,4, β 3,6, β 2,15,9,10,7, γ 1,5 and γ 2,3,4) X-ray production (XRP) cross sections have been measured for six elements with 56 ⩽ Z ⩽ 68 at 22.6 keV incident photon energy using the EDXRF spectrometer. The incident photon intensity, detector efficiency and geometrical factors have been determined from the K X-ray yields emitted from elemental targets with 22 ⩽ Z ⩽ 42 in the same geometrical setup and from knowledge of the K XRP cross sections. The L 1 and L 2 subshell fluorescence yields have been deduced from the present measured L k XRP cross sections using the relativistic Hartree-Fock-Slater (HFS) model based photoionization cross sections. The present deduced ω1 (exp) values have been found to be, on an average, higher by 15% and 20% than those based on the Dirac-Hartree-Slater (DHS) model and the semi-empirical values compiled by Krause, respectively, for elements with 60 ⩽ Z ⩽ 68.

M ξ, M αβ, M γ and M m X-ray production cross-sections for elements with 71⩽ z⩽92 at 5.96 keV photon energy

NASA Astrophysics Data System (ADS)

Sharma, Manju; Sharma, Veena; Kumar, Sanjeev; Puri, S.; Singh, Nirmal

2006-11-01

The M ξ, M αβ, M γ and M m X-ray production (XRP) cross-sections have been measured for the elements with 71⩽ Z⩽92 at 5.96 keV incident photon energy satisfying EM1< Einc< EL3, where EM1(L3) is the M 1(L 3) subshell binding energy. These XRP cross-sections have been calculated using photoionization cross-sections based on the relativistic Dirac-Hartree-Slater (RDHS) model with three sets of X-ray emission rates, fluorescence, Coster-Kronig and super Coster-Kronig yields based on (i) the non-relativistic Hartree-Slater (NRHS) potential model, (ii) the RDHS model and (iii) the relativistic Dirac-Fock (RDF) model. For the third set, the M i ( i=1-5) subshell fluorescence yields have been calculated using the RDF model-based X-ray emission rates and total widths reevaluated to incorporate the RDF model-based radiative widths. The measured cross-sections have been compared with the calculated values to check the applicability of the physical parameters based on different models.

Theory of Valence Transition

NASA Astrophysics Data System (ADS)

Misawa, S.; Takano, F.

1981-01-01

The valence transition phenomena occurring in rare-earth compounds are studied by using the periodic Anderson model with the electron-phonon coupling. This electron-phonon interaction G is treated in the Hartree-Fock approximation. The Coulomb repulsion U between f-electrons on the same site is taken to be ∞, and the decoupling method of Roth is used for the higher order Green function considering the mixing interaction to be small. We put the condition that the total number of electrons is a constant, and calculate the numbers of f- and d-electrons as functions of the original energy of f-electron by using the Green functions. The first order transition is shown to occur if G ≳ (1/2)W, where W is the width of the original d-band. The energy of f-electron at which the insulator and the metallic phase have the same ground state energy is calculated asɛc ≃ (1/2)(G-(1/2)W) + (2V^2/W) log |(G-W/2)/(G+W/2)|- (V^2/8W) log | (G-W/2)(G-(3/2)W) |. The magnetic susceptibilities of both phases are also calculated, but the result is not good, showing the decoupling method used here is not appropriate for the calculation of magnetic properties.

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.

Constraints on the nuclear equation of state from nuclear masses and radii in a Thomas-Fermi meta-modeling approach

NASA Astrophysics Data System (ADS)

Chatterjee, D.; Gulminelli, F.; Raduta, Ad. R.; Margueron, J.

2017-12-01

The question of correlations among empirical equation of state (EoS) parameters constrained by nuclear observables is addressed in a Thomas-Fermi meta-modeling approach. A recently proposed meta-modeling for the nuclear EoS in nuclear matter is augmented with a single finite size term to produce a minimal unified EoS functional able to describe the smooth part of the nuclear ground state properties. This meta-model can reproduce the predictions of a large variety of models, and interpolate continuously between them. An analytical approximation to the full Thomas-Fermi integrals is further proposed giving a fully analytical meta-model for nuclear masses. The parameter space is sampled and filtered through the constraint of nuclear mass reproduction with Bayesian statistical tools. We show that this simple analytical meta-modeling has a predictive power on masses, radii, and skins comparable to full Hartree-Fock or extended Thomas-Fermi calculations with realistic energy functionals. The covariance analysis on the posterior distribution shows that no physical correlation is present between the different EoS parameters. Concerning nuclear observables, a strong correlation between the slope of the symmetry energy and the neutron skin is observed, in agreement with previous studies.

The nature of three-body interactions in DFT: Exchange and polarization effects

NASA Astrophysics Data System (ADS)

Hapka, Michał; Rajchel, Łukasz; Modrzejewski, Marcin; Schäffer, Rainer; Chałasiński, Grzegorz; Szcześniak, Małgorzata M.

2017-08-01

We propose a physically motivated decomposition of density functional theory (DFT) 3-body nonadditive interaction energies into the exchange and density-deformation (polarization) components. The exchange component represents the effect of the Pauli exclusion in the wave function of the trimer and is found to be challenging for density functional approximations (DFAs). The remaining density-deformation nonadditivity is less dependent upon the DFAs. Numerical demonstration is carried out for rare gas atom trimers, Ar2-HX (X = F, Cl) complexes, and small hydrogen-bonded and van der Waals molecular systems. None of the tested semilocal, hybrid, and range-separated DFAs properly accounts for the nonadditive exchange in dispersion-bonded trimers. By contrast, for hydrogen-bonded systems, range-separated DFAs achieve a qualitative agreement to within 20% of the reference exchange energy. A reliable performance for all systems is obtained only when the monomers interact through the Hartree-Fock potential in the dispersion-free Pauli blockade scheme. Additionally, we identify the nonadditive second-order exchange-dispersion energy as an important but overlooked contribution in force-field-like dispersion corrections. Our results suggest that range-separated functionals do not include this component, although semilocal and global hybrid DFAs appear to imitate it in the short range.

Particle Number Conserving Approach to the Collective States in a Small Fermi-System

NASA Astrophysics Data System (ADS)

Glick, Jennifer; Zelevinsky, Vladimir

2014-03-01

The standard Bardeen-Cooper-Schrieffer (BCS) description of pairing theory, random phase approximation (RPA) and Hartree-Fock-Bogoliubov (HFB) methods, routinely used in macroscopic many-body physics when the dimension of the Hamiltonian matrix is prohibitively large, include features which are not well suited to describe mesoscopic systems such as nuclei or cold atoms in traps. Two important disadvantages are the non-conservation of exact particle number through the introduction of quasiparticles, and the absence of a non-trivial paired solution in the discrete spectrum with weak pairing. We develop the pairing theory based on the exact particle number conservation, whose first applications to the ground state physics presented in [A. Volya and V. Zelevinsky, in 50 Years of Nuclear BCS, World Scientific, 2012] demonstrated that such an approach avoids well known deficiencies of the standard treatment, especially in the region of weak pairing. Now, we use the method for low-lying collective excitations which in many cases are even more sensitive to conservation laws. We show that the RPA version based on solving the operator equations of motion is reduced to the set of recurrence relations for neighboring systems which precisely conserve the exact particle number. Supported by the NSF grant PHY-1068217.

Probe-type of superconductivity by impurity in materials with short coherence length: the s-wave and η-wave phases study

NASA Astrophysics Data System (ADS)

Ptok, Andrzej; Jerzy Kapcia, Konrad

2015-04-01

The effects of a single non-magnetic impurity on superconducting states in the Penson-Kolb-Hubbard model have been analyzed. The investigations have been performed within the Hartree-Fock mean field approximation in two steps: (i) the homogeneous system is analysed using the Bogoliubov transformation, whereas (ii) the inhomogeneous system is investigated by self-consistent Bogoliubov-de Gennes equations (with the exact diagonalization and the kernel polynomial method). We analysed both signs of the pair hopping, which correspond to s-wave and η-wave superconductivity. Our results show that an enhancement of the local superconducting gap at the impurity-site occurs for both cases. We obtained that Cooper pairs are scattered (at the impurity site) into the states which are from the neighborhoods of the states, which are commensurate ones with the crystal lattice. Additionally, in the η-phase there are peaks in the local-energy gap (in momentum space), which are connected with long-range oscillations in the spatial distribution of the energy gap, superconducting order parameter (SOP), as well as effective pairing potential. Our results can be contrasted with the experiment and predicts how to experimentally differentiate these two different symmetries of SOP by the scanning tunneling microscopy technique.

Electronic Band Structure of Helical Polyisocyanides.

PubMed

Champagne, Benoît; Liégeois, Vincent; Fripiat, Joseph G; Harris, Frank E

2017-10-19

Restricted Hartree-Fock computations are reported for a methyl isocyanide polymer (repeating unit -C═N-CH 3 ), whose most stable conformation is expected to be a helical chain. The computations used a standard contracted Gaussian orbital set at the computational levels STO-3G, 3-21G, 6-31G, and 6-31G**, and studies were made for two line-group configurations motivated by earlier work and by studies of space-filling molecular models: (1) A structure of line-group symmetry L9 5 , containing a 9-fold screw axis with atoms displaced in the axial direction by 5/9 times the lattice constant, and (2) a structure of symmetry L4 1 that had been proposed, containing a 4-fold screw axis with translation by 1/4 of the lattice constant. Full use of the line-group symmetry was employed to cause most of the computational complexity to depend only on the size of the asymmetric repeating unit. Data reported include computed bond properties, atomic charge distribution, longitudinal polarizability, band structure, and the convoluted density of states. Most features of the description were found to be insensitive to the level of computational approximation. The work also illustrates the importance of exploiting line-group symmetry to extend the range of polymer structural problems that can be treated computationally.

Spin-orbit ZORA and four-component Dirac-Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble gas dimers.

PubMed

Jankowska, Marzena; Kupka, Teobald; Stobiński, Leszek; Faber, Rasmus; Lacerda, Evanildo G; Sauer, Stephan P A

2016-02-05

Hartree-Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange-correlation functionals were used for nonrelativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton, and xenon dimers and free atoms. Relativistic corrections were calculated with the scalar and spin-orbit zeroth-order regular approximation Hamiltonian in combination with the large Slater-type basis set QZ4P as well as with the four-component Dirac-Coulomb Hamiltonian using Dyall's acv4z basis sets. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts are combined with nonrelativistic coupled cluster singles and doubles with noniterative triple excitations [CCSD(T)] calculations using the very large polarization-consistent basis sets aug-pcSseg-4 for He, Ne and Ar, aug-pcSseg-3 for Kr, and the AQZP basis set for Xe. For the dimers also, zero-point vibrational (ZPV) corrections are obtained at the CCSD(T) level with the same basis sets were added. Best estimates of the dimer chemical shifts are generated from these nuclear magnetic shieldings and the relative importance of electron correlation, ZPV, and relativistic corrections for the shieldings and chemical shifts is analyzed. © 2015 Wiley Periodicals, Inc.

Third-Order Incremental Dual-Basis Set Zero-Buffer Approach: An Accurate and Efficient Way To Obtain CCSD and CCSD(T) Energies.

PubMed

Zhang, Jun; Dolg, Michael

2013-07-09

An efficient way to obtain accurate CCSD and CCSD(T) energies for large systems, i.e., the third-order incremental dual-basis set zero-buffer approach (inc3-db-B0), has been developed and tested. This approach combines the powerful incremental scheme with the dual-basis set method, and along with the new proposed K-means clustering (KM) method and zero-buffer (B0) approximation, can obtain very accurate absolute and relative energies efficiently. We tested the approach for 10 systems of different chemical nature, i.e., intermolecular interactions including hydrogen bonding, dispersion interaction, and halogen bonding; an intramolecular rearrangement reaction; aliphatic and conjugated hydrocarbon chains; three compact covalent molecules; and a water cluster. The results show that the errors for relative energies are <1.94 kJ/mol (or 0.46 kcal/mol), for absolute energies of <0.0026 hartree. By parallelization, our approach can be applied to molecules of more than 30 atoms and more than 100 correlated electrons with high-quality basis set such as cc-pVDZ or cc-pVTZ, saving computational cost by a factor of more than 10-20, compared to traditional implementation. The physical reasons of the success of the inc3-db-B0 approach are also analyzed.

Analytic first derivatives for a spin-adapted open-shell coupled cluster theory: Evaluation of first-order electrical properties

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

Datta, Dipayan, E-mail: datta@uni-mainz.de; Gauss, Jürgen, E-mail: gauss@uni-mainz.de

2014-09-14

An analytic scheme is presented for the evaluation of first derivatives of the energy for a unitary group based spin-adapted coupled cluster (CC) theory, namely, the combinatoric open-shell CC (COSCC) approach within the singles and doubles approximation. The widely used Lagrange multiplier approach is employed for the derivation of an analytical expression for the first derivative of the energy, which in combination with the well-established density-matrix formulation, is used for the computation of first-order electrical properties. Derivations of the spin-adapted lambda equations for determining the Lagrange multipliers and the expressions for the spin-free effective density matrices for the COSCC approachmore » are presented. Orbital-relaxation effects due to the electric-field perturbation are treated via the Z-vector technique. We present calculations of the dipole moments for a number of doublet radicals in their ground states using restricted open-shell Hartree-Fock (ROHF) and quasi-restricted HF (QRHF) orbitals in order to demonstrate the applicability of our analytic scheme for computing energy derivatives. We also report calculations of the chlorine electric-field gradients and nuclear quadrupole-coupling constants for the CCl, CH{sub 2}Cl, ClO{sub 2}, and SiCl radicals.« less

Use of Two-Body Correlated Basis Functions with van der Waals Interaction to Study the Shape-Independent Approximation for a Large Number of Trapped Interacting Bosons

NASA Astrophysics Data System (ADS)

Lekala, M. L.; Chakrabarti, B.; Das, T. K.; Rampho, G. J.; Sofianos, S. A.; Adam, R. M.; Haldar, S. K.

2017-05-01

We study the ground-state and the low-lying excitations of a trapped Bose gas in an isotropic harmonic potential for very small (˜ 3) to very large (˜ 10^7) particle numbers. We use the two-body correlated basis functions and the shape-dependent van der Waals interaction in our many-body calculations. We present an exhaustive study of the effect of inter-atomic correlations and the accuracy of the mean-field equations considering a wide range of particle numbers. We calculate the ground-state energy and the one-body density for different values of the van der Waals parameter C6. We compare our results with those of the modified Gross-Pitaevskii results, the correlated Hartree hypernetted-chain equations (which also utilize the two-body correlated basis functions), as well as of the diffusion Monte Carlo for hard sphere interactions. We observe the effect of the attractive tail of the van der Waals potential in the calculations of the one-body density over the truly repulsive zero-range potential as used in the Gross-Pitaevskii equation and discuss the finite-size effects. We also present the low-lying collective excitations which are well described by a hydrodynamic model in the large particle limit.

Testing the single-state dominance hypothesis

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

Álvarez-Rodríguez, R.; Moreno, O.; Moya de Guerra, E.

2013-12-30

We present a theoretical analysis of the single-state dominance hypothesis for the two-neutrino double-beta decay process. The theoretical framework is a proton-neutron QRPA based on a deformed Hartree-Fock mean field with BCS pairing correlations. We focus on the decays of {sup 100}Mo, {sup 116}Cd and {sup 128}Te. We do not find clear evidences for single-state dominance within the present approach.

Electronic Structure and Absorption Spectra of Sodium 2-Hydroxy-5-({2-Methoxy-4[(4-Sulfophenyl)Diazenyl]Phenyl}Diazenyl)Benzoate

NASA Astrophysics Data System (ADS)

Almodarresiyeh, H. A.; Shahab, S. N.; Zelenkovsky, V. M.; Agabekov, V. E.

2014-03-01

The electronic structure and geometry of the synthesized azodye sodium 2-hydroxy-5-({2-methoxy-4[(4-sulfophenyl) diazenyl]phenyl}diazenyl)benzoate (M12) were calculated theoretically by an ab initio Hartree-Fock method in basis set 6-31G. The nature of absorption bands in the visible and near-UV spectral regions was interpreted.

Dynamical description of the fission process using the TD-BCS theory

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

Scamps, Guillaume, E-mail: scamps@nucl.phys.tohoku.ac.jp; Simenel, Cédric; Lacroix, Denis

2015-10-15

The description of fission remains a challenge for nuclear microscopic theories. The time-dependent Hartree-Fock approach with BCS pairing is applied to study the last stage of the fission process. A good agreement is found for the one-body observables: the total kinetic energy and the average mass asymmetry. The non-physical dependence of two-body observables with the initial shape is discussed.

Weak interactions in Graphane/BN systems under static electric fields—A periodic ab-initio study.

PubMed

Steinkasserer, Lukas Eugen Marsoner; Gaston, Nicola; Paulus, Beate

2015-04-21

Ab-initio calculations via periodic Hartree-Fock (HF) and local second-order Møller-Plesset perturbation theory (LMP2) are used to investigate the adsorption properties of combined Graphane/boron nitride systems and their response to static electric fields. It is shown how the latter can be used to alter both structural as well as electronic properties of these systems.

Calculation of UV, IR, and NMR Spectra of Diethyl 2,2'-[(1,1'-Biphenyl)-4,4'-Diylbis(Azanediyl)]Diacetate

NASA Astrophysics Data System (ADS)

Almodarresiyeh, H. A.; Shahab, S. N.; Zelenkovsky, V. M.; Ariko, N. G.; Filippovich, L. N.; Agabekov, V. E.

2014-03-01

The new substance diethyl 2,2'-[(1,1'-biphenyl)-4,4'-diylbis(azanediyl)]diacetate (M13) was modeled using the Hartree-Fock and density functional theory methods and then synthesized. The electronic absorption spectrum of M13 in dimethylformamide solution was calculated. The UV, IR, and NMR spectra of M13 were presented.

A minimal multiconfigurational technique.

PubMed

Fernández Rico, J; Paniagua, M; GarcíA De La Vega, J M; Fernández-Alonso, J I; Fantucci, P

1986-04-01

A direct minimization method previously presented by the authors is applied here to biconfigurational wave functions. A very moderate increasing in the time by iteration with respect to the one-determinant calculation and good convergence properties have been found. So qualitatively correct studies on singlet systems with strong biradical character can be performed with a cost similar to that required by Hartree-Fock calculations. Copyright © 1986 John Wiley & Sons, Inc.

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

Ünlü, Hilmi, E-mail: hunlu@itu.edu.tr

We propose a non-orthogonal sp{sup 3} hybrid bond orbital model to determine the electronic properties of semiconductor heterostructures. The model considers the non-orthogonality of sp{sup 3} hybrid states of nearest neighboring adjacent atoms using the intra-atomic Coulomb interactions corrected Hartree-Fock atomic energies and metallic contribution to calculate the valence band width energies of group IV elemental and group III-V and II-VI compound semiconductors without any adjustable parameter.

Ab initio molecular orbital studies of the positive muon and muonium in 4-arylmethyleneamino-TEMPO derivatives

NASA Astrophysics Data System (ADS)

Briere, T. M.; Jeong, J.; Das, T. P.; Ohira, S.; Nagamine, K.

2000-08-01

The muon and muonium bonding sites of the 4-arylmethyleneamino-2,2,6,6-tetramethylpiperidin-1-yloxyl radical crystals with aryl groups consisting of biphenyl and 4-pyridyl were studied via ab initio Hartree-Fock theory. The hyperfine fields, including both intramolecular and intermolecular interactions, were calculated at the sites of interest and compared to zero field μSR results.

Non-expanded dispersion energies and damping functions for Ar 2 and Li 2

NASA Astrophysics Data System (ADS)

Knowles, Peter J.; Meath, William J.

1986-02-01

The non-expanded second-order dispersion energies and damping functions associated with the long-range dispersion energies varying as R-6, R-8and R-10 have been calculated for Ar 2 and Li 2 with the time-dependent Hartree-Fock method, using extended Gaussian basis sets. These results are used to discuss the difficulties associated with ab initio computations of these quantities.

Vibrational Spectral Studies of Gemfibrozil

NASA Astrophysics Data System (ADS)

Benitta, T. Asenath; Balendiran, G. K.; James, C.

2008-11-01

The Fourier Transform Raman and infrared spectra of the crystallized drug molecule 5-(2,5-Dimethylphenoxy)-2,2-dimethylpentanoic acid (Gemfibrozil) have been recorded and analyzed. Quantum chemical computational methods have been employed using Gaussian 03 software package based on Hartree Fock method for theoretically modeling the grown molecule. The optimized geometry and vibrational frequencies have been predicted. Observed vibrational modes have been assigned with the aid of normal coordinate analysis.

Toroidal high-spin isomers in light nuclei with N ≠ Z

NASA Astrophysics Data System (ADS)

Staszczak, A.; Wong, Cheuk-Yin

2015-11-01

The combined considerations of both the bulk liquid-drop-type behavior and the quantized aligned rotation with cranked Skyrme-Hartree-Fock approach revealed previously (Staszczak and Wong 2014 Phys. Lett. B 738 401) that even-even, N = Z, toroidal high-spin isomeric states have general occurrences for light nuclei with 28≤slant A≤slant 52. We find that in this mass region there are in addition N\

Analytic gradient for second order Møller-Plesset perturbation theory with the polarizable continuum model based on the fragment molecular orbital method.

PubMed

Nagata, Takeshi; Fedorov, Dmitri G; Li, Hui; Kitaura, Kazuo

2012-05-28

A new energy expression is proposed for the fragment molecular orbital method interfaced with the polarizable continuum model (FMO/PCM). The solvation free energy is shown to be more accurate on a set of representative polypeptides with neutral and charged residues, in comparison to the original formulation at the same level of the many-body expansion of the electrostatic potential determining the apparent surface charges. The analytic first derivative of the energy with respect to nuclear coordinates is formulated at the second-order Møller-Plesset (MP2) perturbation theory level combined with PCM, for which we derived coupled perturbed Hartree-Fock equations. The accuracy of the analytic gradient is demonstrated on test calculations in comparison to numeric gradient. Geometry optimization of the small Trp-cage protein (PDB: 1L2Y) is performed with FMO/PCM/6-31(+)G(d) at the MP2 and restricted Hartree-Fock with empirical dispersion (RHF/D). The root mean square deviations between the FMO optimized and NMR experimental structure are found to be 0.414 and 0.426 Å for RHF/D and MP2, respectively. The details of the hydrogen bond network in the Trp-cage protein are revealed.

Analytic gradient for second order Møller-Plesset perturbation theory with the polarizable continuum model based on the fragment molecular orbital method

NASA Astrophysics Data System (ADS)

Nagata, Takeshi; Fedorov, Dmitri G.; Li, Hui; Kitaura, Kazuo

2012-05-01

A new energy expression is proposed for the fragment molecular orbital method interfaced with the polarizable continuum model (FMO/PCM). The solvation free energy is shown to be more accurate on a set of representative polypeptides with neutral and charged residues, in comparison to the original formulation at the same level of the many-body expansion of the electrostatic potential determining the apparent surface charges. The analytic first derivative of the energy with respect to nuclear coordinates is formulated at the second-order Møller-Plesset (MP2) perturbation theory level combined with PCM, for which we derived coupled perturbed Hartree-Fock equations. The accuracy of the analytic gradient is demonstrated on test calculations in comparison to numeric gradient. Geometry optimization of the small Trp-cage protein (PDB: 1L2Y) is performed with FMO/PCM/6-31(+)G(d) at the MP2 and restricted Hartree-Fock with empirical dispersion (RHF/D). The root mean square deviations between the FMO optimized and NMR experimental structure are found to be 0.414 and 0.426 Å for RHF/D and MP2, respectively. The details of the hydrogen bond network in the Trp-cage protein are revealed.

Using a pruned, nondirect product basis in conjunction with the multi-configuration time-dependent Hartree (MCTDH) method

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

Wodraszka, Robert, E-mail: Robert.Wodraszka@chem.queensu.ca; Carrington, Tucker, E-mail: Tucker.Carrington@queensu.ca

In this paper, we propose a pruned, nondirect product multi-configuration time dependent Hartree (MCTDH) method for solving the Schrödinger equation. MCTDH uses optimized 1D basis functions, called single particle functions, but the size of the standard direct product MCTDH basis scales exponentially with D, the number of coordinates. We compare the pruned approach to standard MCTDH calculations for basis sizes small enough that the latter are possible and demonstrate that pruning the basis reduces the CPU cost of computing vibrational energy levels of acetonitrile (D = 12) by more than two orders of magnitude. Using the pruned method, it ismore » possible to do calculations with larger bases, for which the cost of standard MCTDH calculations is prohibitive. Pruning the basis complicates the evaluation of matrix-vector products. In this paper, they are done term by term for a sum-of-products Hamiltonian. When no attempt is made to exploit the fact that matrices representing some of the factors of a term are identity matrices, one needs only to carefully constrain indices. In this paper, we develop new ideas that make it possible to further reduce the CPU time by exploiting identity matrices.« less

M sub-shell X-ray fluorescence cross-section measurements for six elements in the range Z = 78-92 at tuned synchrotron photon energies 5, 7 and 9 keV.

NASA Astrophysics Data System (ADS)

Bansal, Himani; Tiwari, M. K.; Mittal, Raj

2018-01-01

M sub-shell X-ray fluorescence cross-sections of elements Pt, Au, Hg, Pb, Th and U have been measured with linearly polarized photon beams from Indus-II synchrotron source at Raja Ramanna Centre for Advanced Technology (RRCAT), India at tuned 5, 7 and 9 keV energies less than the L3 edge energy of elements. Measurements at present energies and elements are not available in literature. Therefore, measured cross-sections for Mξ, Mδ, Mα, Mβ, Mγ, Mm1 and Mm2 group of X-rays were compared with calculated theoretical values based upon Non Relativistic Hartree-Slater (NRHS) and relativistic Dirac-Fork (DF) and Dirac-Hartree-Slater (DHS) models. The measured cross-sections along with our earlier quoted measurements at 8 and 10 keV by Kaur et al. [Nucl. Instrum. Meth. B, 2014; 320: 37] are found in good agreement with DF and DHS values around 20% deviations and are highly deviated from NRHS values. Most of the spots of observed high deviations in measured and theoretical cross-sections are found to coincide with the presence of crisscrosses/sharp variations in contributing physical parameters photo-ionization cross-sections σMi's and Coster-Kronig yields fij's with Zs.