Rayleigh-Schrodinger perturbation theory size-extensivity

Since both these models represent extended systems, the exploitation of the shell-model or Cl-type variational methods was a priori excluded. This placed emphasis on the development of perturbative approaches for this type of problem. It was soon realized that the most efficient methodological approach must be based on a mathematical formalism that was originally developed in quantum field theory. Moreover, in view of the extended character of the studied systems, it was absolutely essential that the method employed yields energies that are linearly proportional to the particle number N in the system or, in today s parlance, that it must be size extensive, so that the limiting procedure when N->-oo makes sense. In terms of MBPT, this imphes that only the connected or finked energy terms be present in the perturbation series, a requirement that automatically leads to the Rayleigh-Schrodinger PT. 

Elimination of the size-extensivity error in the MRBWCC theory was suggested by Hubac and Wilson [68]. The Brillouin-Wigner perturbation theory has been known notoriously as a method not furnishing size extensivity. There was therefore every reason to believe that the size-extensivity error in MR BWCCSD originated from the use of the Brillouin-Wigner type resolvent (15) instead of the Rayleigh-Schrodinger... 

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