  The Colle and Salvetti approach [Theoret. Chim. Acta, 37, 329 (1975)] to the
calculation of the correlation energy of a system is modified in order to
explicitly include into the theory the kinetic contribution to the correlation
energy. This is achieved by deducing from a many electrons wave function,
including the correlation effects via a Jastrow factor, an approximate
expression of the one-electron reduced density matrix. Applying the latter to
the homogeneous electron gas, an analytic expression of the correlation kinetic
energy is derived. The total correlation energy of such a system is then
deduced from its kinetic contribution inverting a standard procedure. At
variance of the original Colle-Salvetti theory, the parameters entering in both
the kinetic correlation and the total correlation energies are determined
analytically, leading to a satisfactory agreement with the results of Perdew
and Wang [Phys. Rev. B 45, 13244 (1992)]. The resulting (parameter-free)
expressions give rise to a modified-local-density approximation that can be
used in self-consistent density-functional calculations. We have performed such
calculations for a large set of atoms and ions and we have found results for
the correlation energies and for the ionization potentials which improve those
of the standard local-density approximation.
