Multi-reference configuration interaction method

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. 

Unfortunately, in many situation of interest, both static and dynamic electronic correlation need to be taken into account. This is particularly true for the study of processes involving excited electronic states as in UV spectroscopy or in photochemistry. In this case, methods capable of taking into account the dynamic electronic correlation on top of a multi-determinantal wavefunction of the MCSCF type are needed. These methods are usually called multi-reference methods. The two standard methods that are able to account for both the static and dynamic electronic correlation are the multi-reference configuration interaction (MRCI) and several variants of second-order multi-reference perturbation theory (MRPT). 

Werner H-J 1987 Matrix-formulated direct multiconfigurational self-consistent field and multi reference configuration interaction methods Adv. Chem. Phys. 69 1... 

Grimme, S., Waletzke, M., 1999, A Combination of Kohn-Sham Density Functional Theory and Multi-Reference Configuration Interaction Methods , J. Chem. Phys., Ill, 5645. 

Such a wave function is represented by a linear combination of wave functions for more than one electron configuration, and is called a "multi-configurational" wave function. The consideration of more than one configuration can reduce the correlation error. Such an approach is referred to as the method of configuration interaction (Cl) . 

Grimme S, Waletzke M (1999) A combination of Kohn-Sham density-functional theory and multi-reference configuration interaction methods, J Chem Phys, 111 5645-5655... 

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