Analytic form of the correlation energy of the uniform electron gas

Abstract

An expression for the correlation energy density of the uniform electron gas is derived based on the adiabatic connection method. It covers with a single form the transition between high-density and low-density regions in the range $0.1\ensuremath{\leqslant}{r}_{s}\ensuremath{\leqslant}30$, parsing the entire spin-polarization range $0\ensuremath{\leqslant}\ensuremath{\xi}\ensuremath{\leqslant}1$. The pair-correlation function used to generate the result has been used previously to describe mainly finite systems. We argue that the universality implied by the short-wavelength hypothesis goes both ways, and a model that works well for finite systems may be adapted to describe the uniform electron gas as well.