# Singularity structure of Møller - Plesset perturbation theory

*D. Z. Goodson and A. V. Sergeev*

## Abstract

Møller-Plesset perturbation theory expresses the energy as a function
*E*(*z*) of a perturbation parameter, *z*. This function contains
singular points in the complex *z*-plane that affect the convergence
of the perturbation series. A review is given of what is known in
advance about the singularity structure of *E*(*z*) from functional
analysis of the Schrödinger equation, and of techniques for empirically
analyzing the singularity structure using large-order perturbation series.
The physical significance of the singularities is discussed. They fall
into two classes, which behave differently in response to changes in
basis set or molecular geometry. One class consists of complex-conjugate
square-root branch points that connect the ground state to a low-lying
excited state. The other class consists of a critical point on the
negative real $z$-axis, corresponding to an autoionization phenomenon.
These two kinds of singularities are characterized and contrasted using
quadratic summation approximants. A new classification scheme for
Møller-Plesset perturbation series is proposed, based on the
relative positions in the *z*-plane of the two classes of singularities.
Possible applications of this singularity analysis to practical problems
in quantum chemistry are described.

Text of the paper: PDF format, TeX file.

Results of work at UMassD

Designed by A. Sergeev.