Singularity analysis of fourth-order Møller - Plesset perturbation theory

David Z. Goodson, Alexey V. Sergeev


A method is developed for determining the singularity structure of Møller-Plesset many-body perturbation theory from fourth-order perturbation series, using a quadratic approximant with a bilinear conformal mapping. Optimal mappings are determined from extremum conditions. Comparison with accurate singularity positions determined from high-order series for the ground-state electronic energy for a variety of small atoms and molecules shows that the fourth-order method gives a reliable estimate of the singularity structure in the positive half plane, which in practice is usually the singularity structure that most affects the accuracy of summation approximants, and a reasonable estimate of the singularity structure in the negative half plane.

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Results of work at UMassD

Designed by A. Sergeev.