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

Abstract

We show that, in the high-density limit, restricted Møller-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.

4 pages, accepted for publication in Int. J. Quantum Chem