Approximate account of the connected quadruply excited clusters in the coupled-pair many-electron theory

Abstract

In nondegenerate systems, the tetraexcited clusters are well approximated by products of disconnected pair clusters and the connected quadruply excited component is negligible. In contrast, when the reference state becomes quasidegenerate with the lowest biexcited configuration(s), the connected quadruply excited clusters become very important. To extend the applicability of the coupled-pair many-electron theory to such situations, we approximate the connected tetraexcited contribution in the form suggested by the unrestricted Hartree-Fock-type wave function, or one of its projected versions, such as the alternant molecular-orbital method. We show that the incorporation of the connected quadruply excited clusters into the coupled-pair equations effectively cancels certain nonlinear terms, originating from disconnected quadruple excitations, so that the resulting equations are very similar (up to a numerical factor) to the approximate coupled-pair theory, in which only those nonlinear terms which factorize with respect to the hole-electron pairs are considered. This fact shows in turn why various approximate coupled-pair approaches can often provide better results than the full coupled-pair many-electron theory.