A proposal of an orbital-dependent correlation energy functional for energy-band calculations

TL;DR

This paper proposes an orbital-dependent correlation energy functional for energy-band calculations, incorporating an effective interaction to account for correlations beyond second-order perturbation theory, applicable to various electron systems.

Contribution

It introduces a novel orbital-dependent correlation functional using an effective interaction derived from the electron liquid, improving accuracy over traditional local density approximations.

Findings

Functional closely resembles second-order perturbation terms

Effective interaction captures long-, intermediate-, and short-range correlations

Applicable to both tightly-binding and nearly-free electrons

Abstract

An explicitly orbital-dependent correlation energy functional is proposed, which is to be used in combination with the orbital-dependent exchange energy functional in energy-band calculations. It bears a close resemblance to the second-order direct and exchange perturbation terms calculated with Kohn-Sham orbitals and Kohn-Sham energies except that one of the two Coulomb interactions entering each term is replaced by an effective interaction which contains information about long-, intermediate-, and short-range correlations beyond second-order perturbation theory. Such an effective interaction can rigorously be defined for the correlation energy of the uniform electron liquid and is evaluated with high accuracy in order to apply to the orbital-dependent correlation energy functional. The coupling-constant-averaged spin-parallel and spin-antiparallel pair correlation functions are also evaluated with high accuracy for the electron liquid. The present orbital-dependent correlation energy functional with the effective interaction borrowed from the electron liquid is valid for tightly-binding electrons as well as for nearly-free electrons in marked contrast with the conventional local density approximation.