Intermediate Hamiltonian Formulations of the Fock-Space Coupled-Cluster Method: Details, Comparisons, Examples

Abstract

The single-reference approaches such as many-body perturbation expansions and coupled-cluster methods, have been very successful in describing many-particle systems. Their applicability is, however, limited to the cases when the degree of quasi-degeneracy is rather weak. Unfortunately, their generalization to multi-reference cases, that would enable us to deal efficiently with quasi-degenerate and open-shell systems turned out nontrivial. The difficulties that have been encountered are of both theoretical and numerical nature. In spite of tremendous progress that has been made the problem still remains one of the main challenges for theoretical physics and quantum chemistry. In this paper we present one of the developments that, in our opinion, is very promising. It concerns one of the two basic multi-reference coupled-cluster formulations, namely, the so-called Fock-space coupled-cluster method. We would like to show that by employing the intermediate Hamiltonian technique it is possible to overcome many of the problems the standard effective Hamiltonian formulations have to face. The approach is presented in a broader context, relations with other methods of similar type are discussed and some numerical examples showing the effectiveness of the method are presented.