Approximate treatment of higher excitations in coupled-cluster theory. II. Extension to general single-determinant reference functions and improved approaches for the canonical Hartree-Fock case.

The theory and implementation of approximate coupled-cluster (CC), in particular approximate CC singles, doubles, triples, and quadruples methods, are discussed for general single-determinant reference functions. While the extension of iterative approximate models to the non-Hartree-Fock case is straightforward, the generalization of perturbative approaches is not trivial. In contrast to the corresponding perturbative triples methods, there are additional terms required for non-Hartree-Fock reference functions, and there are several possibilities to derive approximations to these terms. As it turns out impossible to develop an approach that is consistent with the canonical Hartree-Fock-based theory, several new approximations have been implemented and their performance for total energies and heats of formation has been assessed. The numerical results show that the performance of the methods does not depend strongly on the approximations assumed. Furthermore, the new perturbative quadruples methods, when applied to canonical Hartree-Fock reference functions, outperform at least for absolute energies the existing ones without increasing the computational costs.