Uniform electron gas from the Colle-Salvetti functional: Missing long-range correlations

Colle and Salvetti [Theor. Chim. Acta 37, 329 (1975)] approximated the correlation energy of a many-electron system as a functional of the Hartree-Fock one-particle density matrix. The most fundamental and least approximate version of this functional [their Eq. (9)] is found to yield only 25% of the true correlation energy of a uniform electron gas, and not 100% as previously believed. While short-range correlations are described surprisingly well by this approach, important long-range correlations are missing. Such correlations are energetically negligible in atoms, but cannot be ignored in more extended systems, including solids as well as molecules.