Assessment of an analytical density-matrix derived from a modified Colle-Salvetti approach to the electron gas

The Ragot-Cortona model of local correlation energy (J. Chem. Phys. 121, 7671 (2004)) revisits the initial approach of Colle and Salvetti [Theo. Chim. Acta 37, 329 (1975)] in order to reinstate the kinetic contribution Tc to the total correlation energy Ec. In this work, the one-electron reduced density-matrix underlying the amended model is fully derived in closed-form. By construction, the said density-matrix is parameter-free but not N-representable, owing to a series of approximations used in the Ragot-Cortona approach. However, the resulting density-matrix is shown to have formally correct short- and long-range expansions. Furthermore, its momentum-space counterpart qualitatively agrees with known parameterized momentum distributions except at small momenta, where the disagreement reflects the non-representability of the model and restricts to a small fraction of the slowest electrons only.