Brillouin-Wigner theory, advantages

One of the drawbacks of Brillouin-Wigner perturbation theory is that the expressions for the energy components in second order and beyond contain the exact energy in the denominator factors. The equations must therefore be solved iteratively until self-consistency is achieved. The generalized Brillouin-Wigner perturbation theory [21] has the advantage that the denominators can be factored from the sum-over-states formulae. 

In this section, we shall first provide an elementary derivation of the Brillouin-Wigner perturbation theory and then present a comparable introduction to the Rayleigh-Schrodinger perturbation theory. The section concludes with a comparison of the advantages and disadvantages of the two theories. 

We consider the advantages of the Brillouin-Wigner perturbation theory on the basis of the elementary derivations given in Sections 1.3.1 and 1.3.2. 

Brillouin-Wigner perturbation theory has five main advantages over the Rayleigh-Schrodinger perturbation theory. These are ... 

This advantage of the Brillouin-Wigner perturbation theory was recognized in the original papers by Lennard-Jones [37] and of Brillouin [40]. It is also described in the review by Dalgarno [38]. 

Wigner [41] noted this advantage of the Brillouin-Wigner perturbation theory in his 1935 paper. Dalgarno [38] also identified this advantage of Brillouin-Wigner perturbation theory in his 1961 review. 

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