Leading-order behavior of the correlation energy in the uniform electron gas

TL;DR

This paper derives the leading-order behavior of the correlation energy in the high-density limit of the uniform electron gas, revealing a logarithmic dependence that contradicts previous results.

Contribution

It provides a new derivation of the high-density limit of the correlation energy, showing a logarithmic dependence that corrects earlier assumptions.

Findings

Correlation energy per electron scales as π^{-2}(1 - ln 2) ln r_s in high-density limit

Contradicts previous derivation suggesting O(ln|ln r_s|) behavior

Clarifies the reason for discrepancy in theoretical predictions

Abstract

We show that, in the high-density limit, restricted M{\o}ller-Plesset (RMP) perturbation theory yields $E_{\text{RMP}}^{(2)} = \pi^{-2}(1-\ln 2) \ln r_s + O(r_s^0)$ for the correlation energy per electron in the uniform electron gas, where $r_s$ is the Seitz radius. This contradicts an earlier derivation which yielded $E_{\text{RMP}}^{(2)} = O(\ln|\ln r_s|)$. The reason for the discrepancy is explained.