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

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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 − 12[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 ϵx. 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.

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The work on this paper was started during a stay at the Max-Planck Institut für Festkörperforschung Stuttgart, continued during a stay at the Tulane University New Orleans and finished during a stay at the Forschungszentrum Jülich.

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