Analytical expressions for the local-field factor G(q) and the exchange-correlation kernel K_{xc}(r) of the homogeneous electron gas

TL;DR

This paper provides an analytical expression for the local field factor G(q) and the exchange-correlation kernel K_{xc}(r) of the homogeneous electron gas, matching Quantum Monte Carlo data and known asymptotic behaviors, facilitating numerical applications.

Contribution

It introduces a new analytical formula for G(q) that accurately reproduces Quantum Monte Carlo data and known asymptotics, enabling explicit expressions for K_{xc} in real and reciprocal spaces.

Findings

Accurately reproduces Quantum Monte Carlo data

Reflects known asymptotic behaviors for small and large q

Allows analytical expression of K_{xc} in real and reciprocal spaces

Abstract

We present an analytical expression for the local field factor G(q) of the homogeneous electron gas which reproduces recently published Quantum Monte--Carlo data by S. Moroni, D.M. Ceperley, and G. Senatore [Phys. Rev. Lett. 75, 689 (1995)], reflects the theoretically known asymptotic behaviours for both small and large q limits, and allows to express the exchange-correlation kernel K_{xc} analytically in both the direct and reciprocal spaces. The last property is particularly useful in numerical applications to real solids