Definition of exchange based on cumulant expansion: Correlation induced narrowing of the exchange hole

Abstract

Abstract Under the assumption, that the cumulant expansion of the reduced density matrices has a fundamental meaning, a corresponding decomposition of the pair distribution function of the homogeneous electron gas is considered: g(r) = 1 − 1 2 [f(r)] 2 −h(r) . Here the one-particle density matrix n(r, r′) = nf(|r-r′|) arises from the correlated momentum distribution function n(k) and h(r) is the irreducible part of g(r). In comparison with [f°(r)]2 arising from the uncorrelated Hartree-Fock momentum distribution function n°(k) the corresponding correlated function [f(r)]2 is slightly narrowed leading to a reduction of the exchange energy ϵ x . Normalization condition and virial theorem contain the mutual density dependence of the different parts of the total pair distribution function hole 1 - g(r). The situation is illustrated with the help of a simple model for the correlated momentum distribution function.