The Colle and Salvetti approach [Theoret. Chim. Acta, 37, 329 (1975)] to thecalculation of the correlation energy of a system is modified in order toexplicitly include into the theory the kinetic contribution to the correlationenergy. This is achieved by deducing from a many electrons wave function,including the correlation effects via a Jastrow factor, an approximateexpression of the one-electron reduced density matrix. Applying the latter tothe homogeneous electron gas, an analytic expression of the correlation kineticenergy is derived. The total correlation energy of such a system is thendeduced from its kinetic contribution inverting a standard procedure. Atvariance of the original Colle-Salvetti theory, the parameters entering in boththe kinetic correlation and the total correlation energies are determinedanalytically, leading to a satisfactory agreement with the results of Perdewand Wang [Phys. Rev. B 45, 13244 (1992)]. The resulting (parameter-free)expressions give rise to a modified-local-density approximation that can beused in self-consistent density-functional calculations. We have performed suchcalculations for a large set of atoms and ions and we have found results forthe correlation energies and for the ionization potentials which improve thoseof the standard local-density approximation.
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