Algebraic Approach to Coupled Cluster Theory

Abstract

With the advancement of our ability to account for many-electron correlation effects in atomic and molecular electronic structure calculations, particularly when exploring systems undergoing chemical reactions or other dissociative or associative processes, more and more emphasis is being placed on a proper size-extensive (or size-consistent) behavior of the theories employed. The requirement of size-extensivity (i.e., an exact additivity of the energy when applied to non-interacting systems) is, of course, absolutely crucial when we deal with extended systems. This is why this characteristic was automatically required in earlier developments of the general many-body perturbation theory (MBPT) by Brueckner (1955), Goldstone (1957), Hugen-holtz (1957), and others, since its primary domains of application at that time were an infinite nuclear matter (e.g., de Shalit and Feshbach, 1974; Eisenberg and Greiner, 1972) and various models of solid state physics (Hubbard, 1957,1958), notably the electron gas model (Gell-Mann and Brueckner, 1957; Quinn and Ferrell, 1958). The importance of size-extensivity in finite atomic and molecular systems was first recognized by Primas (1965), even though the term itself was coined and employed only later (Pople et al. 1976,1977,1978; Bartlett and Purvis, 1978,1980). Although both terms are often used interchangeably, we shall understand by the size-extensivity the additivity of energy for noninteracting systems or, equivalently, proportionality of the energy to the number of noninteracting systems (electrons, atoms, diatomics, etc.) involved.