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Non‐local relation between kinetic and exchange energy densities in Hartree–Fock theory
Author(s) -
March N. H.,
Santamaria R.
Publication year - 1991
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560390405
Subject(s) - kinetic energy , fermi gas , generalization , hartree–fock method , density matrix , density functional theory , orbital free density functional theory , fermi energy , electron density , exchange interaction , thomas–fermi model , electron , local density approximation , chemistry , quantum mechanics , physics , mathematics , mathematical analysis , quantum , ferromagnetism
A non‐local generalization K ( r, r' ) of the kinetic energy t ( r ) such that t ( r ) = ∫ K ( r, r' ) dr' is defined using the idempotency property of the Hartree–Fock first‐order density matrix. This is, in turn, related by means of an explicit differential equation to the non‐local exchange energy density X ( r, r' ). The relationship is illustrated for a couple of examples: with the Fermi‐hole in a uniform electron gas, of importance in the local density version of density functional theory, and with inhomogeneous electron systems.