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The single-reference coupled-cluster (CC) method is one of the most efficient approaches for describing electron correlation effects in atoms and molecules but its successful application is limited to states dominated by a single Slater determinant. In cases where several determinants dominate the wave function expansion, the multi-reference (MR) CC formulations are required. They usually use the effective Hamiltonian formalism which allows dealing with two types of electron correlation appearing in the MR cases: nondynamic and dynamic. There are two MR-CC formulations of this type: the Hilbert space CC method and the Fock-space (FS) one. In the paper, a version of the FS-CC method designated for the description of systems with three-valence electrons is being considered. The idea of the intermediate Hamiltonian (IH) reformulation of the standard FS-CC method, which simplifies the calculations and avoids the intruder state problem, is discussed in this context. A new IH-FS-CC approach is presented which takes advantage of the redefinition of the normal ordering of the FS cluster expansion introduced by Lindgren. The redefinition significantly simplifies the IH-FS-CC formalism and lowers the computational cost of the calculations. The advantages of the new IH formulation are discussed in detail for the case of the FS-CC method in which the lowest-order cluster operators are included in all sectors of the Fock-space, including the three-valence one.

A new intermediate Hamiltonian Fock-space coupled-cluster formalism for the three-valence sector