Single reference Brillouin-Wigner expansions

In section 6.1 we briefly describe the single reference Brillouin-Wigner coupled cluster expansions. The multireference case is considered in more detail in section 6.2. 

SINGLE REFERENCE BRILLOUIN-WIGNER COUPLED CLUSTER EXPANSIONS... 

SINGLE REFERENCE BRILLOUIN-WIGNER CONFIGURATION INTERACTION EXPANSION... 

In this section, we present Brillouin-Wigner perturbation theory in both its single reference and its multireference form. This will serve both to emphasize the similarity of single reference and multireference formulations of Brillouin-Wigner perturbation theory and to establish notation for later sections. In section 3.1, we define the basic concepts of any perturbation theory. The definition of single and multireference spaces is considered in section 3.2 and the model wave function is described in section 3.3. The Brillouin-Wigner expansion is developed in section 3.4. 

Abstract The partitioning technique is described in some detail. The concept of a model space is introduced and the wave operator and the reaction operator are defined. Using these ideas, both the Rayleigh-Schrodinger and the Brillouin-Wigner expansions are developed, first for the case of a single-reference function and then for the multi-reference case. 

In the previous section, we have given the Brillouin-Wigner perturbation expansion for the exact wave function for state a developed with respect to some single reference or multireference model function In this section, we define the Brillouin-Wigner wave operator and the corresponding Bloch-like equation [64]. 

Abstract The Brillouin-Wigner many-body problem in atomic and molecular physics and in quantum chemistry is described. The use of coupled cluster expansions, configuration interaction and perturbation series is considered both for the single-reference function case and for those cases requiring the use of a multi-reference formalism. 

By following procedures similar to those employed in the case of a single-reference function, the exact wave function f o, for a = 1,2,. .., d, in the Brillouin-Wigner perturbation theory can be written as the expansion... 

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