Various formulations of the Fock-space coupled-cluster method: Advantages and disadvantages in their practical implementations

The single-reference coupled-cluster method is one of the most efficient approaches to the problem of describing electron correlation effects in situations when a single determinant gives reliable zeroth-order description of a system. Its multi-reference generalizations have not been, however, so successful mainly because of their effective Hamiltonian formulation. In this paper we present attempts that have been made to reformulate the Fock-space coupled-cluster method in order to obtain more efficient and dependable computational schemes allowing more extensive use of the approach. The first one is known as the eigenvalue independent partitioning version of the Fock-space coupled-cluster method. This approach has been an inspiration for other formulations of this type. The new formulations require to take a new look at the use of the connected diagram theorem since the theorem cannot be applied in such a straightforward manner as in the standard version. Another problem is posed by approximate schemes and noniterative corrections that are so popular within the single-reference coupled-cluster framework. These are not so easy to implement when the standard effective Hamiltonian formulation is abandoned. Fortunately, it looks that noniterative corrections can be relatively easily implemented. In the paper we discuss these issues trying to show advantages and disadvantages of different approaches.

Two attempts, that have been made to reformulate the Fock-space coupled-cluster method in order to obtain more efficient and dependable computational schemes, are discussed.