On the calculations of the variational correlation energy using Møller—Plesset first-order wavefunctions

A method is developed, based on first-order symmetry-adapted pair functions obtained within the framework of the Rayleigh—Schrödinger Hartree—Fock perturbation theory, for obtaining a variational upper bound to the correlation energy in the form of pair increments. The correlation-energy functional obtained is written in terms of second- and third-order energy increments of Møller—Plesset perturbation theory. Application of the procedure to the ground states of the Ne-like systems yields energies of greater accuracy than those obtained from CI calculations using very extensive sets of singly and doubly excited configurations. Our pair energies and the total correlation energy obtained for Zn²⁺ represent the most accurate variational results reported so far for atomic systems containing 3d-electrons.