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 [S. Ragot and P. Cortona, J. Chem. Phys. 121, 7671 (2004)] revisits the initial approach of Colle and Salvetti [Theor. Chim. Acta 37, 329 (1975)] in order to reinstate the kinetic contribution T(c) to the total correlation energy E(c). 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 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 parametrized momentum distributions except at small momenta, where the disagreement reflects the nonrepresentability of the model and restricts to a small fraction of the slowest electrons only.