Assessment of an analytical density-matrix derived from a modified Colle-Salvetti approach to the electron gas

TL;DR

This paper derives a parameter-free, density-matrix-based model for the electron gas that improves the understanding of local correlation energy, capturing key physical properties despite non-representability issues.

Contribution

It provides a fully derived, closed-form density-matrix from a modified Colle-Salvetti approach, incorporating kinetic contributions to correlation energy.

Findings

Density-matrix has correct short- and long-range expansions.

Momentum-space distribution qualitatively matches known data.

Model is non-N-representable but captures essential features.

Abstract

The Ragot-Cortona model of local correlation energy (J. Chem. Phys. 121, 7671 (2004)) revisits the initial approach of Colle and Salvetti [Theo. Chim. Acta 37, 329 (1975)] in order to reinstate the kinetic contribution Tc to the total correlation energy Ec. In this work, the one-electron reduced density-matrix underlying the amended model is fully derived in closed-form. By construction, the said density-matrix is parameter-free but not N-representable, owing to a series of approximations used in the Ragot-Cortona approach. However, the resulting density-matrix is shown to have formally correct short- and long-range expansions. Furthermore, its momentum-space counterpart qualitatively agrees with known parameterized momentum distributions except at small momenta, where the disagreement reflects the non-representability of the model and restricts to a small fraction of the slowest electrons only.