Brillouin-Wigner expansions

Rayleigh-Schrodinger Perturbation Theory.—In Rayleigh-Schrodinger perturbation theory the unknown energy in the denominators of the Lennard-Jones Brillouin Wigner expansion is avoided. This enables a size-consistent theory to be derived. 

This should be compared with the energy coefficients in the Lennard-Jones, Brillouin, Wigner expansion (23) which can be re-written in the form... 

We do not proposed to describe here the theoretical details of many-body Brillouin-Wigner methodology. They can be found in our book Brillouin-Wigner Methods for Many-Body Systems. Here we concentrate on applications of Brillouin-Wigner methods to many-body systems in chemistry and physics. Previous reviews can be found in our article in the Encyclopedia of Computational Chemistry [49] and in our review entitled Brillouin-Wigner expansions in quantum chemistry Bloch-... 

Brillouin- Wigner expansions in quantum chemistry Bloch-like and Lippmanri-Schwinger-like equations... 

BRILLOUIN-WIGNER EXPANSIONS IN QUANTUM CHEMISTRY BLOCH-LIKE AND LIPPMANN-SCHWINGER-LIKE EQUATIONS... 

In 1967, Brandow [69] used the Brillouin-Wigner expansion in his derivation of a multireference many-body (Rayleigh-Schrodinger) perturbation theory. In the abstract to his paper entitled Tinked-Cluster expansions for the nuclear many-body problem Brandow writes ... 

Brandow employed the Brillouin-Wigner expansion as a theoretical tool in developing a linked-cluster expansion for the many-body problem. 

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. 

Comparing equation (34), which defines the wave operator, with equation (32), which is the Brillouin-Wigner expansion for the exact wave function, we can write the wave operator in Brillouin-Wigner form as... 

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