Quasidegenerate perturbation theories. A canonical van Vleck formalism and its relationship to other approaches

Three forms of quasidegenerate perturbation theory are discussed and compared in terms of a common general formulation based on a similarity transformation which decouples the model space and complementary space components of the Hamiltonian. The discussion is limited to formal, rather than many-body (diagrammatic), aspects. Particular attention is focused on a ’’canonical’’ form of van Vleck perturbation theory, for which new and highly compact formulas are obtained. Detailed comparisons are made with the Kirtman–Certain–Hirschfelder form of the van Vleck approach and with the approach based on intermediate normalization which has been used as the basis for most of the diagrammatic formulations of quasidegenerate perturbation theory.