Brillouin-Wigner perturbation theory and limited configuration interaction

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

The lowest (ground state) non-degenerate energy is given by the expression [8,17, 161] 

Expression (4.143) was used by Huba5 and Neogrady [6,8] in their development of Brillouin-Wigner coupled cluster theory. It is important to recognize that expression 

Since Ki is a two-particle operator, the configuration d i) involves, at most, a double replacement with respect to o)- Thus, given the matrix elements ( j Vb Po), 

Now we can see that Pi) involves, at most, quadruple replacements with respect to the reference configuration, o)- Repeated application of eq. (4.140) leads to higher order replacements in the configuration i). If we restrict our attention to double replacements in eq. (4.146), then eq. (4.145) and (4.146) provide a computational scheme which realizes the limited configuration interaction method in its ci sd form [7,8]. 

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See also in sourсe #XX -- [ ]

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