Atomic and molecular correlation energies with explicitly correlated Gaussian geminals. III. Coupled cluster treatment for He, Be, H2, and LiH

Čižek’s coupled-pair, many-electron theory is formulated in a first-quantized, basis set independent way. The resulting set of coupled integro-differential equations for symmetry-adapted spinless pair functions is then solved variationally using the basis set of explicitly correlated Gaussian geminals. In this way, accurate values of the correlation energies in both the linear and quadratic versions of the coupled-pair theory are obtained for He, Be, H2, and LiH. These values are expected to be saturated up to within a fraction of 1%. For Be our results are practically identical with the basis set independent coupled-pair energies obtained recently by Lindgren and Salomonson using an extensive partial-wave expansion, two-dimensional numerical integrations, and extrapolation techniques. For LiH, at the equilibrium separation of the nuclei, the correlation energy obtained using the complete coupled-pair theory amounts to −81.5 mhartrees. Since the leading (fourth-order) perturbation correction to this result is negative, this value can be viewed as a ‘‘perturbative’’ upper bound to the true nonrelativistic correlation energy. The linear coupled-pair theory gives −82.7 mhartrees for the correlation energy of LiH; this value cannot be considered as an upper bound, however. The above results are to be compared with the estimated experimental correlation energy of LiH amounting to −83.2±0.1 mhartree. A simplified theory obtained by neglecting all four-electron integrals in the quadratic part of the coupled-pair equations has been tested. For both Be and LiH the correlation energies obtained differ by only a few hundredths of a mhartree from the complete coupled-pair results.