Diagrammatic formulation of the second-order many-body multipartitioning perturbation theory

The second-order multireference perturbation theory employing multiple partitioning of the many-electron Hamiltonian into a zero-order part and a perturbation is formulated in terms of many-body diagrams. The essential difference from the standard diagrammatic technique of Hose and Kaldor concerns the rules of evaluation of energy denominators which take into account the dependence of the Hamiltonian partitioning on the bra and ket determinantal vectors of a given matrix element, as well as the presence of several two-particle terms in zero-order operators. The novel formulation naturally gives rise to a sum-over-orbital procedure of correlation calculations on molecular electronic states, particularly efficient in treating the problems with large number of correlated electrons and extensive one-electron bases.