Abstract
Full fifth-order MOller-Plesset perturbation theory of electron correlation is presented in algebraic form and used to compare the behavior of other approximate methods that are size-consistent and exact for two electrons. Considering only single and double substitutions, quadratic configuration interaction (QCISD), coupled cluster (CCSD), and Brueckner doubles (BD) theories are shown to deviate from each other in fifth order. The BD method contains the most parts of the fifth-order energy in a correct manner. The corresponding methods with noniterative triples corrections QCISD(T), CCSD(T), and BD(T) are also analyzed. These methods are all correct in those parts of the fifth-order energy that are linear in the higher (triple, quadruple) substitutions
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