# Singularity analysis of fourth-order Møller - Plesset perturbation theory

*David Z. Goodson, Alexey V. Sergeev*

## Abstract

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.

Text of the paper: PDF format.

Results of work at UMassD

Designed by A. Sergeev.