Abstract
The Colle-Salvetti functional for correlation energy has given remarkably good results. It is based on approximating the second order density matrix with a particularly judicious form and using the constraining equation between the first order and second order reduced density matrices. We have used an exactly soluble N-body problem to study some aspects of the functional approximation. This has been done by calculating the reduced density matrices exactly and comparing them to the approximate form proposed by Colle and Salvetti and by comparing the expectation values of physical quantities using the approximate and exact density matrices.
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