Diagrams infinite order summations

The relationship between the coupled-electron pair approximation (c.e.p.a.) and the many-body perturbation theory has been discussed in detail by Ahl-richs.149 All of the methods denoted by c.e.p.a. (x) (x=0, 1, 2, 3) may be related to the summation of certain classes of diagrams in the many-body perturbation theory to infinite order. For example, c.e.p.a. (0), which is Cizek s linear approximation or Hurley s c.p.a. (0) ansatz150 is equivalent to the summation of all double-excitation linked diagrams in the perturbation series. This is also denoted d.e.m.b.p.t. (double excitation many-body perturbation theory) by some workers.151 168... 

Above we referred to the development of the CC method by Cizek and Paldus [49-51], The CC method may be viewed as a consistent summation to infinite order of certain type of linked correlation (MBPT, MP) diagrams. Thus, there is a clear relationship between many-body permrbation theory [based on the MP operator of Eq. (Al) in Appendix 37A] and coupled cluster theory. Both are supermolecule methods that give size-extensive energies. 

There are finally attempts to apply diagrammatic techniques of many-body perturbation theory S ), with the summation of certain diagrams to infinite order, to the correlation problem in atoms and molecules. A close relationship between this kind of approach and the independent electron-pair approximation has been demonstrated >. 

In this language, the RPA procedure corresponds to the summation of ring diagrams to infinite order. 

An important technique in diagrammatic perturbation theory is the summation of certain classes of diagrams to infinite order. To illustrate the technique consider our two-state system. The only diagram that contributes in second-order is... 

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