Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density

TLDR

The Colle–Salvetti correlation‑energy formula, originally expressed via the electron density and the Laplacian of the second‑order Hartree–Fock density matrix, is reformulated in terms of the density and local kinetic‑energy density. By inserting gradient expansions for the local kinetic‑energy density, the authors derive density‑functional expressions for the correlation energy and potential. Numerical tests on atoms, ions, and molecules show that the new formulas reproduce correlation energies within a few percent, comparable to the original Colle–Salvetti results. Chim.

Abstract

A correlation-energy formula due to Colle and Salvetti [Theor. Chim. Acta 37, 329 (1975)], in which the correlation energy density is expressed in terms of the electron density and a Laplacian of the second-order Hartree-Fock density matrix, is restated as a formula involving the density and local kinetic-energy density. On insertion of gradient expansions for the local kinetic-energy density, density-functional formulas for the correlation energy and correlation potential are then obtained. Through numerical calculations on a number of atoms, positive ions, and molecules, of both open- and closed-shell type, it is demonstrated that these formulas, like the original Colle-Salvetti formulas, give correlation energies within a few percent.