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

Abstract

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 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 termmore » falls off at least as fast as 1/r{sup 4} for large r.« less

Authors:
 [1]
  1. School of Physics, University of the Witwatersrand, PO Wits 2050, Johannesburg (South Africa)
Publication Date:
OSTI Identifier:
21020709
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 76; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevA.76.042503; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; CORRECTIONS; DENSITY; DENSITY FUNCTIONAL METHOD; DISTURBANCES; ELECTRONS; EQUATIONS; GREEN FUNCTION; HAMILTONIANS; HARTREE-FOCK METHOD; MEAN-FIELD THEORY; NONLOCAL POTENTIAL; PERTURBATION THEORY; WAVE FUNCTIONS

Citation Formats

Joubert, D P. Alternative derivation of an exchange-only density-functional optimized effective potential. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.76.042503.
Joubert, D P. Alternative derivation of an exchange-only density-functional optimized effective potential. United States. https://doi.org/10.1103/PHYSREVA.76.042503
Joubert, D P. 2007. "Alternative derivation of an exchange-only density-functional optimized effective potential". United States. https://doi.org/10.1103/PHYSREVA.76.042503.
@article{osti_21020709,
title = {Alternative derivation of an exchange-only density-functional optimized effective potential},
author = {Joubert, D P},
abstractNote = {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 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/r{sup 4} for large r.},
doi = {10.1103/PHYSREVA.76.042503},
url = {https://www.osti.gov/biblio/21020709}, journal = {Physical Review. A},
issn = {1050-2947},
number = 4,
volume = 76,
place = {United States},
year = {Mon Oct 15 00:00:00 EDT 2007},
month = {Mon Oct 15 00:00:00 EDT 2007}
}