Gaussian geminals in explicitly correlated coupled cluster theory including single and double excitations

The coupled cluster method with single and double excitations has been form ulated in a basis set independent language of first quantization. In this f ormulation the excitation operators are represented in terms of one- and tw o-electron cluster functions satisfying a set of integrodifferential equati ons and the strong orthogonality conditions. These equations are solved ite ratively by minimizing appropriate Hylleraas-type functionals. During the i teration process correlation energies of up to fourth order in the Moller-P lesset perturbation operator are extracted. A slight modification of the co upled cluster equations leads to an explicitly correlated formulation of th e configuration interaction theory. The method was tested in applications t o two- and four-electron systems: He, Li+, H-2, Be, Li-, and LiH. The two- electron cluster functions were expanded using explicitly correlated Gaussi an geminal bases optimized in the lowest order of perturbation theory. Most of the correlation energies computed at various levels of the coupled clus ter and perturbation theory represent the most accurate values to date. (C) 1999 American Institute of Physics. [S0021-9606(99)30709-1].