Coupled Cluster Theory

Abstract

The necessity to account for many-electron correlation effects in atomic and molecular electronic structure calculations was realized in the sixties, when the first attempts to compute dissociation or activation energies of simple chemical processes (e. g., Wahl, 1964; Schaefer, 1971, 1972) and various molecular properties (e. g., Huo, 1965) were made. The initial hope that the configuration interaction (CI) approach limited to doubly excited configurations, originating from a single reference state, will provide a satisfactory description of correlation effects soon had to be given up (see, e. g., Bender and Davidson, 1968, 1969; Barr and Davidson, 1970; Davidson, 1974). By that time the basic structure of correlated wavefunctions (Hubbard, 1957, 1958) and the problem of size extensivity (Brueckner, 1955; Goldstone, 1957; Primas, 1965) were well understood [although this term was employed only later (Bartlett and Purvis, 1978)], thanks to the developments in solid state (e. g., Gell-Mann and Brueckner, 1957; Quinn and Ferrell, 1958) and nuclear (e. g., deShalit and Feshbach, 1974; Eisenberg and Greiner, 1972) physics. In particular, the linked cluster theorem of the many-body perturbation theory (MBPT) and the connected cluster structure of the exact wavefunctions (Hubbard, 1958b) were firmly established. The exponential ansatz for the wave operator, implied by Hubbard’s (1958b) work, was exploited in the context of the nuclear correlation problem by Coester (1958) and Coester and Kümmel (1960).