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

We show that, in the high-density limit, restricted Møller-Plesset (RMP) perturbation theory yields E _RMP ⁽²⁾ = π ^-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 _RMP ⁽²⁾ = O(ln|ln r _s|). The reason for the discrepancy is explained.