Different IPM Approximations

In evaluating correlation corrections to one-particle densities and one-electron expectation values, one must realize that single excitations only vanish to first order, but not to higher orders. This implies that the first natural orbitals differ somewhat from the Hartree-Fock orbitals, and since the singly excited configurations enter linearly in their expansion coefficient, they can have more influence on the density than doubly excited ones, even if their coefficients are smaller. 

The admixture of singly excited configurations (with respect to the SCF determinant) via their interaction with doubly excited ones is exactly equivalent to a replacement of Hartree-Fock by Brueckner (best-overlap) orbitals. Expectation values of simple one-electron operators like x, r, (3z — r )j2 etc., have been calculated (35) for H2 in its 

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