Multi-reference Brillouin-Wigner configuration interaction

Multi-reference Brillouin-Wigner configuration interaction theory... 

Multi-reference Brillouin-Wigner perturbation theory for limited configuration interaction... 

A posteriori corrections can be developed for calculations performed by using the Brillouin-Wigner perturbation expansion. These a posteriori corrections can be obtained for the Brillouin-Wigner perturbation theory itself and, more importantly, for methods, such as limited configuration interaction or multi-reference coupled cluster theory, which can be formulated within the framework of a Brillouin-Wigner perturbation expansion. 

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. 

If j) is a determinant related to one of the reference determinants by a double replacement, then k) involves, at most, quadruple replacements with respect to 1 ) in eq. (4.193). Repeated application of the Lippmann-Schwinger-file equation [160] leads to higher order replacements. If we restrict the degree of replacement admitted in (4.193) then we realize a limited multi-reference configuration interaction method. It is this realization of the multi-reference limited configuration interaction method that we use to obtain an a posteriori correction based on Brillouin-Wigner perturbation theory. 

Equation (4.190) has p roots of which we take only one. The exact energy, q, occurs in the denominator factors in eqs. (4.191) and (4.193). The eq. (4.190) must, therefore, be solved iteratively until self-consistency is achieved. These are the basic equations of the multi-reference configuration interaction method in a Brillouin-Wigner formulation in the case of a p state reference. 

A posteriori Brillouin-Wigner correction to limited multi-reference configuration interaction... 

We are now in a position to develop an a posteriori correction to state-specific limited multi-reference configuration interaction in the case of a p-state reference function. The following identity relates the Brillouin-Wigner and the Rayleigh-Schrodinger denominators [18,76,77] for the ground state (a = 0) ... 

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