Appendix to “Studies in Perturbation Theory”: The Problem of Partitioning

Abstract

The problem of partitioning in perturbation theory is reviewed starting from the classical works by Epstein and Nesbet or by Møller and Piesset, up to optimized partitionings introduced recently. Equations for optimal sets of level shift parameters are presented. Attention is paid to the specific problems appearing if the zero order solution is not a single Slater determinant. A special formalism for multi-configurational perturbation theories is outlined. It is shown that divergent perturbation series, like that of an anharmonic oscillator, can be converted to a convergent series by an appropriate redefinition of the zero order Hamiltonian via level shifts. The possible use of effective one-particle energies in many-body perturbation theory is also discussed. Partitioning optimization in a constant denominator perturbation theory leads to second order correction familiar from connected moment expansion techniques. Ionization potentials, computed perturbatively, are found sensitive to the choice of partitioning, and ordinary approximations are improved upon level shift optimization.KeywordsPerturbation theoryPartitioningOptimal PartitioningMulti-configurational Perturbation Theory