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Masahiko Higuchi - One of the best experts on this subject based on the ideXlab platform.
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kinetic Energy contribution to the exchange Correlation Energy functional of the extended constrained search theory
Physical Review A, 2009Co-Authors: Katsuhiko Higuchi, Masahiko HiguchiAbstract:We present the kinetic Energy contribution to the exchange-Correlation Energy functional of the extended constrained-search (ECS) theory by means of the generalized Bauer's relation. Due to the nature of the exchange-Correlation Energy functional being a function of the Bohr radius and ${e}^{2}$, three kinds of expressions for the kinetic Energy contribution are obtained. These can be utilized as constraints in developing and/or evaluating the approximate form of the exchange-Correlation Energy functional of the ECS theory. Furthermore, by combining three expressions with the virial relation, we derive other useful relations that include not the kinetic Energy contribution but only the exchange-Correlation Energy functional.
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vorticity expansion approximation of the exchange Correlation Energy functional in current density functional theory
Physical Review B, 2006Co-Authors: Katsuhiko Higuchi, Masahiko HiguchiAbstract:We propose the vorticity expansion approximation VEA formulas of the exchange and Correlation Energy functionals of the current density functional theory CDFT. They have a form of the second-order expansion with respect to the vorticity. Expansion coefficients are determined by requiring them to satisfy exact relations that have been derived from scaling properties of exchange and Correlation Energy functionals. Resultant VEA formulas satisfy a larger number of exact relations than those of the local-density approximation of the CDFT. Due to the well-behaved forms, the VEA formulas can be in quite good agreement with the exchange and Correlation energies of the homogeneous electron liquid under a uniform magnetic field.
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exchange Correlation Energy functional and virial theorem in the extended constrained search theory
Physical Review B, 2005Co-Authors: Katsuhiko Higuchi, Masahiko HiguchiAbstract:The coupling-constant expression and virial relation for the exchange-Correlation Energy functional of the extended-constrained search theory [M. Higuchi and K. Higuchi, Phys. Rev. B 69, 035113 (2004)] are derived. These provide the guideline for developing and testing the approximate form of the exchange-Correlation Energy functional.
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exchange and Correlation Energy functional in the current density functional theory
Physica B-condensed Matter, 2002Co-Authors: Katsuhiko Higuchi, Masahiko HiguchiAbstract:Abstract The exact conditions fulfilled by the exchange–Correlation Energy functional E xc [ρ, j p ] of the current-density functional theory (CDFT) are investigated for the purpose of developing the approximate form of E xc [ρ, j p ] . A set of new exact conditions is obtained by considering the behavior of the Correlation Energy functional under a nonuniform coordinate scaling of electrons. We also compile certain known exact conditions for E xc [ρ, j p ] of the CDFT. By using some of the exact conditions as the constraint, we newly derive the approximation of the exchange Energy functional in the form of the second-order vorticity expansion.
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band theory for strongly correlated electron systems an orbital dependent exchange and Correlation Energy functional
Physica B-condensed Matter, 2002Co-Authors: Masahiko Higuchi, Hiroshi YasuharaAbstract:An explicitly orbital-dependent Correlation Energy functional is proposed in a form of the modified second-order perturbation terms. The expression encourages the hybridization between the different kinds of orbitals in the vicinity of the Fermi level. We incorporate the present Correlation Energy functional into the relativistic linear augmented-plane-wave method in view of the application to the strongly correlated electron systems.
Hiromi Nakai - One of the best experts on this subject based on the ideXlab platform.
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machine learned electron Correlation model based on Correlation Energy density at complete basis set limit
Journal of Chemical Physics, 2019Co-Authors: Takuro Nudejima, Yasuhiro Ikabata, Junji Seino, Takeshi Yoshikawa, Hiromi NakaiAbstract:We propose a machine-learned Correlation model that is built using the regression between density variables such as electron density and Correlation Energy density. The Correlation Energy density of coupled cluster singles, doubles, and perturbative triples [CCSD(T)] is derived based on grid-based Energy density analysis. The complete basis set (CBS) limit is estimated using the composite method, which has been reported to calculate the total Correlation Energy. The numerical examination revealed that the Correlation Energy density of the CCSD(T)/CBS level is appropriate for the response variable of machine learning. In addition to the density variables used in the exchange-Correlation functionals of the density functional theory, the Hartree−Fock (HF) exchange Energy density and electron density based on the fractional occupation number of molecular orbitals were employed as explanatory variables. Numerical assessments confirmed the accuracy and efficiency of the present Correlation model. Consequently, the present protocol, namely, learning the CCSD(T)/CBS Correlation Energy density using density variables obtained by the HF calculation with a small basis set, yields an efficient Correlation model.We propose a machine-learned Correlation model that is built using the regression between density variables such as electron density and Correlation Energy density. The Correlation Energy density of coupled cluster singles, doubles, and perturbative triples [CCSD(T)] is derived based on grid-based Energy density analysis. The complete basis set (CBS) limit is estimated using the composite method, which has been reported to calculate the total Correlation Energy. The numerical examination revealed that the Correlation Energy density of the CCSD(T)/CBS level is appropriate for the response variable of machine learning. In addition to the density variables used in the exchange-Correlation functionals of the density functional theory, the Hartree−Fock (HF) exchange Energy density and electron density based on the fractional occupation number of molecular orbitals were employed as explanatory variables. Numerical assessments confirmed the accuracy and efficiency of the present Correlation model. Consequently, ...
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machine learned electron Correlation model based on Correlation Energy density at complete basis set limit
Journal of Chemical Physics, 2019Co-Authors: Takuro Nudejima, Yasuhiro Ikabata, Junji Seino, Takeshi Yoshikawa, Hiromi NakaiAbstract:We propose a machine-learned Correlation model that is built using the regression between density variables such as electron density and Correlation Energy density. The Correlation Energy density of coupled cluster singles, doubles, and perturbative triples [CCSD(T)] is derived based on grid-based Energy density analysis. The complete basis set (CBS) limit is estimated using the composite method, which has been reported to calculate the total Correlation Energy. The numerical examination revealed that the Correlation Energy density of the CCSD(T)/CBS level is appropriate for the response variable of machine learning. In addition to the density variables used in the exchange-Correlation functionals of the density functional theory, the Hartree-Fock (HF) exchange Energy density and electron density based on the fractional occupation number of molecular orbitals were employed as explanatory variables. Numerical assessments confirmed the accuracy and efficiency of the present Correlation model. Consequently, the present protocol, namely, learning the CCSD(T)/CBS Correlation Energy density using density variables obtained by the HF calculation with a small basis set, yields an efficient Correlation model.
Andreas Savin - One of the best experts on this subject based on the ideXlab platform.
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alternative representations of the Correlation Energy in density functional theory a kinetic Energy based adiabatic connection
Journal of The Chinese Chemical Society, 2016Co-Authors: Trygve Helgaker, Andrew M Teale, Andreas SavinAbstract:The adiabatic-connection framework has been widely used to explore the properties of the Correlation Energy in density-functional theory. The integrand in this formula may be expressed in terms of the electron–electron interactions directly, involving intrinsically two-particle expectation values. Alternatively, it may be expressed in terms of the kinetic Energy, involving only one-particle quantities. In this work, we explore this alternative representation for the Correlation Energy and highlight some of its potential for the construction of new density functional approximations. The kinetic-Energy based integrand is effective in concentrating static Correlation effects to the low interaction strength regime and approaches zero asymptotically, offering interesting new possibilities for modeling the Correlation Energy in density-functional theory
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properties of short range and long range Correlation Energy density functionals from electron electron coalescence
Physical Review A, 2006Co-Authors: Paola Gorigiorgi, Andreas SavinAbstract:The combination of density-functional theory with other approaches to the many-electron problem through the separation of the electron-electron interaction into a short-range and a long-range contribution is a promising method, which is raising more and more interest in recent years. In this work some properties of the corresponding Correlation Energy functionals are derived by studying the electron-electron coalescence condition for a modified (long-range-only) interaction. A general relation for the on-top (zero electron-electron distance) pair density is derived, and its usefulness is discussed with some examples. For the special case of the uniform electron gas, a simple parametrization of the on-top pair density for a long-range only interaction is presented and supported by calculations within the ''extended Overhauser model.'' The results of this work can be used to build self-interaction corrected short-range Correlation Energy functionals.
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short range exchange Correlation Energy of a uniform electron gas with modified electron electron interaction
International Journal of Quantum Chemistry, 2004Co-Authors: Julien Toulouse, Andreas Savin, Heinz-juergen FladAbstract:We calculate the short-range exchange-Correlation Energy of the uniform electron gas with two modified electron- electron interactions. While the short- range exchange functionals are calculated analytically, coupled-cluster and Fermi- hypernetted-chain calculations are carried out for the Correlation Energy and the results are fitted to an analytical parametrization. These data enable us to construct the local density approximation corresponding to these modified interactions. © 2004 Wiley
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Short-range exchange-Correlation Energy of a uniform electron gas with modified electron-electron interaction
International Journal of Quantum Chemistry, 2004Co-Authors: Julien Toulouse, Andreas Savin, Heinz-juergen FladAbstract:We calculate the short-range exchange-Correlation Energy of the uniform electron gas with two modified electron-electron interactions. While the short-range exchange functionals are calculated analytically, coupled-cluster and Fermi hypernetted-chain calculations are carried out for the Correlation Energy and the results are fitted to an analytical parametrization. These data enable us to construct the local density approximation corresponding to these modified interactions.
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Correlation Energy per particle from the coupling constant integration
Physical Review A, 2003Co-Authors: Francois Colonna, Daniel Maynau, Andreas SavinAbstract:The adiabatic connection can be used in density functional theory to define the unknown (exchange and) Correlation density functional. Using conventional wave-function techniques, accurate estimates of thus defined (exchange and) Correlation Energy densities can be obtained for specified systems. In this paper, numerical results are presented for the He and the Be atom, as well as the isoelectron Ne ions. A generalized gradient approximation is tested against these results. The comparison shows that the generalized gradient approximation has the ability to detect local features (the shell structure). In one case $({\mathrm{Ne}}^{6+}),$ however, it turns out that the accurate Correlation Energy per particle is lower than that obtained within the local-density approximation, and thus not properly corrected by the generalized gradient approximation.
Katsuhiko Higuchi - One of the best experts on this subject based on the ideXlab platform.
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kinetic Energy contribution to the exchange Correlation Energy functional of the extended constrained search theory
Physical Review A, 2009Co-Authors: Katsuhiko Higuchi, Masahiko HiguchiAbstract:We present the kinetic Energy contribution to the exchange-Correlation Energy functional of the extended constrained-search (ECS) theory by means of the generalized Bauer's relation. Due to the nature of the exchange-Correlation Energy functional being a function of the Bohr radius and ${e}^{2}$, three kinds of expressions for the kinetic Energy contribution are obtained. These can be utilized as constraints in developing and/or evaluating the approximate form of the exchange-Correlation Energy functional of the ECS theory. Furthermore, by combining three expressions with the virial relation, we derive other useful relations that include not the kinetic Energy contribution but only the exchange-Correlation Energy functional.
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vorticity expansion approximation of the exchange Correlation Energy functional in current density functional theory
Physical Review B, 2006Co-Authors: Katsuhiko Higuchi, Masahiko HiguchiAbstract:We propose the vorticity expansion approximation VEA formulas of the exchange and Correlation Energy functionals of the current density functional theory CDFT. They have a form of the second-order expansion with respect to the vorticity. Expansion coefficients are determined by requiring them to satisfy exact relations that have been derived from scaling properties of exchange and Correlation Energy functionals. Resultant VEA formulas satisfy a larger number of exact relations than those of the local-density approximation of the CDFT. Due to the well-behaved forms, the VEA formulas can be in quite good agreement with the exchange and Correlation energies of the homogeneous electron liquid under a uniform magnetic field.
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exchange Correlation Energy functional and virial theorem in the extended constrained search theory
Physical Review B, 2005Co-Authors: Katsuhiko Higuchi, Masahiko HiguchiAbstract:The coupling-constant expression and virial relation for the exchange-Correlation Energy functional of the extended-constrained search theory [M. Higuchi and K. Higuchi, Phys. Rev. B 69, 035113 (2004)] are derived. These provide the guideline for developing and testing the approximate form of the exchange-Correlation Energy functional.
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exchange and Correlation Energy functional in the current density functional theory
Physica B-condensed Matter, 2002Co-Authors: Katsuhiko Higuchi, Masahiko HiguchiAbstract:Abstract The exact conditions fulfilled by the exchange–Correlation Energy functional E xc [ρ, j p ] of the current-density functional theory (CDFT) are investigated for the purpose of developing the approximate form of E xc [ρ, j p ] . A set of new exact conditions is obtained by considering the behavior of the Correlation Energy functional under a nonuniform coordinate scaling of electrons. We also compile certain known exact conditions for E xc [ρ, j p ] of the CDFT. By using some of the exact conditions as the constraint, we newly derive the approximation of the exchange Energy functional in the form of the second-order vorticity expansion.
John P Perdew - One of the best experts on this subject based on the ideXlab platform.
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exchange Correlation Energy functional based on the airy gas reference system
Physical Review B, 2009Co-Authors: Lucian A Constantin, Adrienn Ruzsinszky, John P PerdewAbstract:In recent work, generalized gradient approximations (GGAs) have been constructed from the Energy density of the Airy gas for exchange but not for Correlation. We report the random-phase approximation (RPA) conventional Correlation Energy density of the Airy gas, the simplest edge electron gas, in which the auxiliary noninteracting electrons experience a linear potential. By fitting the Airy-gas RPA exchange-Correlation Energy density and making an accurate short-range correction to RPA, we propose a simple beyond RPA GGA density functional (``$\text{ARPA}+$'') for the exchange-Correlation Energy. Our functional, tested for jellium surfaces, atoms, molecules, and solids, improves mildly over the local spin-density approximation for atomization energies and lattice constants without much worsening the already good surface exchange-Correlation energies.
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exchange Correlation Energy functional based on the airy gas reference system
arXiv: Materials Science, 2009Co-Authors: Lucian A Constantin, Adrienn Ruzsinszky, John P PerdewAbstract:In recent work, generalized gradient approximations (GGA's) have been constructed from the Energy density of the Airy gas for exchange but not for Correlation. We report the random phase approximation (RPA) conventional Correlation Energy density of the Airy gas, the simplest edge electron gas, in which the auxiliary noninteracting electrons experience a linear potential. By fitting the Airy-gas RPA exchange-Correlation Energy density and making an accurate short-range correction to RPA, we propose a simple beyond-RPA GGA density functional ("ARPA+") for the exchange-Correlation Energy. Our functional, tested for jellium surfaces, atoms, molecules and solids, improves mildly over the local spin density approximation for atomization energies and lattice constants without much worsening the already-good surface exchange-Correlation energies.
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uniform density limit of exchange Correlation Energy functionals
ACS symposium series, 2007Co-Authors: John P Perdew, Jianmin Tao, Stephan KummelAbstract:We present theoretical and practical reasons why a density functional for the exchange-Correlation Energy should be essentially exact in the uniform density limit. In this limit, the exchange Energy is known exactly, and the Correlation Energy is known to within less than 1 millihartree in the range of valence-electron or lower densities. Some density functionals perform well in this limit, while others do not. Functionals with many parameters fitted to chemical data tend to fail in this limit, and also for real solids. The spin resolution of the Correlation Energy of the spin-unpolarized uniform electron gas seems simple but unlike that of the widely-used ansatz of Stoll et al., and its low-density limit brings a surprise: a positive parallel-spin contribution in the spin-unpolarized case.
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spin resolution of the electron gas Correlation Energy positive same spin contributions
Physical Review B, 2004Co-Authors: Paola Gorigiorgi, John P PerdewAbstract:The negative Correlation Energy ǫc(rs, ζ) per particle of a uniform electron gas of density parameter rs and spin polarization ζ is well known, but its spin resolution into "#, "", and ## contributions is not. Widely-used estimates are incorrect, and hamper the development of reliable density functionals and pair distribution functions. For the spin resolution, we present interpolations between high- and low-density limits that agree with available Quantum Monte Carlo data. In the low-density limit for ζ = 0, we find that the same-spin Correlation Energy is unexpectedly positive, and we explain why. We also estimate the " and # contributions to the kinetic Energy of Correlation. The uniform electron gas is a paradigm for density functional theory, 1,2,3 the most widely-used method for electronic structure calculations in both condensed matter physics and quantum chemistry. The effects of exchange and Correlation can be evaluated and understood in the uniform-density limit, and then transferred to realistic systems. This is done not only in the local spin density (LSD) approximation but also beyond LSD in generalized gradient approximations (GGA’s), meta-GGA’s, and hybrid functionals. 3 The Correlation Energy ǫc(rs, ζ) per particle in a uniform gas of density parameter rs = (4πna 3 /3) −1/3 and spin polarization ζ
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role of the exchange Correlation Energy nature s glue
International Journal of Quantum Chemistry, 2000Co-Authors: S Kurth, John P PerdewAbstract:In the Kohn-Sham density functional theory of ground-state electronic structure, only the exchange-Correlation Energy Exc must be approximated. Although Exc is not typically a large component of the total Energy, it is the principal ingredient of the glue that binds atoms together to form molecules and solids. To illustrate this fact, we present self-consistent results for atomization energies of molecules and for surface energies and work functions of jellium, calculated within the "Hartree" approximation, which neglects Exc. The Hartree world displays weak bonding between atoms, low or negative surface energies, and work functions that are close to zero. Other aspects of the Hartree world can be deduced from known size-effect relationships. The mechanism behind the glue role of exchange and Correlation is the suppression of Hartree charge fluctuations. c 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 814-818, 2000
