Brillouin-Wigner perturbation theory energy components

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 chapter, we come to the central purpose of this volume - the application of Brillouin-Wigner methods to many-body atomic and molecular systems. We have seen in Chapter 2 that Brillouin-Wigner perturbation theory [2-4] leads to energy expressions with denominators which contain the exact energy, . As a consequence of this, the Brillouin-Wigner expansion yields energy components which scale non-linearly with the number of electrons in the system. The method does not have. 

We shall provide an overview of the applications that have been made over the period being review which demonstrate the many-body Brillouin-Wigner approach for each of these methods. By using Brillouin-Wigner methods, any problems associated with intruder states can be avoided. A posteriori corrections can be introduced to remove terms which scale in a non linear fashion with particle number. We shall not, for example, consider in any detail hybrid methods such as the widely used ccsd(t) which employs ccsd theory together with a perturbative estimate of the triple excitation component of the correlation energy. 

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