Gaussian resummation approximation of the reference spin-reduced second-order density matrix in the Colle-Salvetti model for electron correlation

The Colle-Salvetti functional for electron correlation in closed-shell systems [Theor. Chim. Acta 37, 329 (1975)] is revised by introducing a Gaussian resummation ansatz in order to approximate the higher than second-order terms in the Taylor expansion of the diagonal elements of the reference spin-reduced second-order density matrix. The correlation strength and the correlation energy per electron are revised accordingly; the latter is now analytic everywhere in space and rid of any spurious correlation effects from the asymptotic region. The range of the correlation hole due to the cusp condition is also investigated. We illustrate the proposed modifications as they apply to the helium and beryllium atoms. The revised model does as good a job as the original model in predicting the correlation energy, but there are profound differences with regard to the correlation energy per electron. In the original model, the electronic density is correlated almost uniformly, but we find this not to be the case if the above Gaussian resummation ansatz is employed.