Multi-reference second-order Brillouin-Wigner perturbation theory

We turn, in this section, to the multi-reference Brillouin-Wigner perturbation theory. We divide our discussion into two parts. In Section 4.4.2.1, we survey the basic theoretical apparatus of multi-reference second-order Brillouin-Wigner perturbation theory. In Section 4.4.3, we describe an a posteriori correction to multi-reference Brillouin-Wigner perturbation theory. 

Multi-reference second-order Brillouin-Wigner perturbation theory... 

If we restrict the order of perturbation admitted in (4.241) then we realize a finite order multi-reference Brillouin-Wigner perturbation theory. Specifically, if we neglect terms of order A are higher, we are led immediately to the second-order theory for which the matrix elements of the effective Hamiltonian (4.239) take the form ... 

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