Correlation kinetic energy of many-electron systems: a modified Colle-Salvetti approach

TL;DR

This paper modifies the Colle-Salvetti approach to explicitly include kinetic correlation energy, deriving an analytic, parameter-free expression that improves correlation energy calculations in density functional theory.

Contribution

The authors introduce a modified Colle-Salvetti method that explicitly accounts for kinetic correlation energy with analytic parameters, enhancing density functional calculations.

Findings

Improved correlation energy estimates for atoms and ions.

Enhanced ionization potential predictions.

Analytic expressions align well with established results.

Abstract

The Colle and Salvetti approach [Theoret. Chim. Acta, 37, 329 (1975)] to the calculation of the correlation energy of a system is modified in order to explicitly include into the theory the kinetic contribution to the correlation energy. This is achieved by deducing from a many electrons wave function, including the correlation effects via a Jastrow factor, an approximate expression of the one-electron reduced density matrix. Applying the latter to the homogeneous electron gas, an analytic expression of the correlation kinetic energy is derived. The total correlation energy of such a system is then deduced from its kinetic contribution inverting a standard procedure. At variance of the original Colle-Salvetti theory, the parameters entering in both the kinetic correlation and the total correlation energies are determined analytically, leading to a satisfactory agreement with the results of Perdew and Wang [Phys. Rev. B 45, 13244 (1992)]. The resulting (parameter-free) expressions give rise to a modified-local-density approximation that can be used in self-consistent density-functional calculations. We have performed such calculations for a large set of atoms and ions and we have found results for the correlation energies and for the ionization potentials which improve those of the standard local-density approximation.