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Title: Exact exchange-correlation potential and approximate exchange potential in terms of density matrices

Abstract

An exact expression in terms of density matrices (DM) is derived for [delta][ital F][[ital n]]/[delta][ital n]([ital r]), the functional derivative of the Hohenberg-Kohn functional. The derivation starts from the differential form of the virial theorem, obtained here for an electron system with arbitrary interactions, and leads to an expression taking the form of an integral over a path that can be chosen arbitrarily. After applying this approach to the equivalent system of noninteracting electrons (Slater-Kohn-Sham scheme) and combining the corresponding result with the previous one, an exact expression for the exchange-correlation potential [ital v][sub xc]([bold r]) is obtained which is analogous in character to that for [delta][ital F][[ital n]]/[delta][ital n]([ital r]), but involving, besides the interacting-system DMs, also the noninteracitng DMs. Equating the former DMs to the latter ones, we reduce the result for the exact [ital v][sub xc]([bold r]) to that for an approximate exchange-only potential [ital v][sub [ital x]]([bold r]). This leads naturally to the Harbola-Sahni exchange-only potential.

Authors:
 [1];  [2]
  1. Institute of Physical Chemistry of the Polish Academy of Sciences, 44/52 Kasprzaka, 01-224 Warsaw (Poland)
  2. Theoretical Chemistry Department, University of Oxford, 5 South Parks Road, Oxford OX1 3UB (United Kingdom)
Publication Date:
OSTI Identifier:
6585188
Resource Type:
Journal Article
Journal Name:
Physical Review A; (United States)
Additional Journal Information:
Journal Volume: 51:3; Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; ATOMS; ELECTRONIC STRUCTURE; SPIN EXCHANGE; DENSITY MATRIX; ELECTRON CORRELATION; ELECTRON-ELECTRON INTERACTIONS; VIRIAL THEOREM; CORRELATIONS; INTERACTIONS; LEPTON-LEPTON INTERACTIONS; MATRICES; PARTICLE INTERACTIONS; 664100* - Theory of Electronic Structure of Atoms & Molecules- (1992-)

Citation Formats

Holas, A, and March, N H. Exact exchange-correlation potential and approximate exchange potential in terms of density matrices. United States: N. p., 1995. Web. doi:10.1103/PhysRevA.51.2040.
Holas, A, & March, N H. Exact exchange-correlation potential and approximate exchange potential in terms of density matrices. United States. https://doi.org/10.1103/PhysRevA.51.2040
Holas, A, and March, N H. 1995. "Exact exchange-correlation potential and approximate exchange potential in terms of density matrices". United States. https://doi.org/10.1103/PhysRevA.51.2040.
@article{osti_6585188,
title = {Exact exchange-correlation potential and approximate exchange potential in terms of density matrices},
author = {Holas, A and March, N H},
abstractNote = {An exact expression in terms of density matrices (DM) is derived for [delta][ital F][[ital n]]/[delta][ital n]([ital r]), the functional derivative of the Hohenberg-Kohn functional. The derivation starts from the differential form of the virial theorem, obtained here for an electron system with arbitrary interactions, and leads to an expression taking the form of an integral over a path that can be chosen arbitrarily. After applying this approach to the equivalent system of noninteracting electrons (Slater-Kohn-Sham scheme) and combining the corresponding result with the previous one, an exact expression for the exchange-correlation potential [ital v][sub xc]([bold r]) is obtained which is analogous in character to that for [delta][ital F][[ital n]]/[delta][ital n]([ital r]), but involving, besides the interacting-system DMs, also the noninteracitng DMs. Equating the former DMs to the latter ones, we reduce the result for the exact [ital v][sub xc]([bold r]) to that for an approximate exchange-only potential [ital v][sub [ital x]]([bold r]). This leads naturally to the Harbola-Sahni exchange-only potential.},
doi = {10.1103/PhysRevA.51.2040},
url = {https://www.osti.gov/biblio/6585188}, journal = {Physical Review A; (United States)},
issn = {1050-2947},
number = ,
volume = 51:3,
place = {United States},
year = {1995},
month = {3}
}