Limited configuration interaction perturbation theory

The exact FCI (frill configuration interaction) solution of the PPP or Hubbard model is possible for molecules with up to about 16 atoms in the pi system. Any of the standard methods for performing approximate ab initio calculations, such as limited configuration interaction, Moeller-Plesset perturbation theory, or coupled cluster theory, may be applied to these models as well. All are expected to be very accurate at low order when U is small, but all will have to be pushed to higher order as U increases. 

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. 

Extended articles on the most common electron correlation methods such as limited configuration interaction (Cl see Configuration Interaction), M0ller-Plesset many-body perturbation theory (MBPT see M0ller Plesset Perturbation Theory), variation-perturbation methods (such as PCILO see Complete Active Space Self-consistent Field (CASSCF) Second-order Perturbation Theory (CASPT2) and Configuration Interaction), and coupled cluster theory (CC see Coupled-cluster Theory), as well as on explicitly ri2-dependent wave functions (see rxi Dependent Wave functions), can be found elsewhere. 

Brillouin-Wigner perturbation theory and limited configuration interaction Let us write the exact Schrodinger equation as... 

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

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. 

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