Calculation of Araki-Sucher correction for many-electron systems

TL;DR

This paper presents a new method for calculating the Araki-Sucher correction in many-electron systems using Gaussian basis sets, with verified convergence and applicability to complex atoms and molecules.

Contribution

It introduces a general approach for evaluating the Araki-Sucher correction in many-electron systems, extending beyond few-electron cases with verified convergence properties.

Findings

Method accurately computes Araki-Sucher correction for small systems.

Convergence rate of the method is analytically derived and numerically verified.

Applicable to complex many-electron atoms and molecules.

Abstract

In this paper we consider the evaluation of the Araki-Sucher correction for arbitrary many-electron atomic and molecular systems. This contribution appears in the leading order quantum electrodynamics corrections to the energy of a bound state. The conventional one-electron basis set of Gaussian-type orbitals (GTOs) is adopted; this leads to two-electron matrix elements which are evaluated with help of generalised the McMurchie-Davidson scheme. We also consider the convergence of the results towards the complete basis set. A rigorous analytic result for the convergence rate is obtained and verified by comparing with independent numerical values for the helium atom. Finally, we present a selection of numerical examples and compare our results with the available reference data for small systems. In contrast with other methods used for the evaluation of the Araki-Sucher correction, our method is not restricted to few-electron atoms or molecules. This is illustrated by calculations for several many-electron atoms and molecules.