Multicenter integrals involving complex Gaussian type functions

TL;DR

This paper develops an analytical method to evaluate multicenter integrals involving complex Gaussian functions, enabling accurate quantum chemistry calculations of ionization processes with multicentric states.

Contribution

It extends previous monocentric approaches to multicentric cases using complex Gaussian functions, validated through numerical tests.

Findings

Analytical evaluation of multicenter integrals with complex Gaussians.

Method applicable in spherical and Cartesian coordinates.

Validated accuracy through numerical tests.

Abstract

Multicentric integrals that involve a continuum state cannot be evaluated with the usual quantum chemistry tools and require a special treatment. We consider an initial molecular bound state described by multicenter spherical or cartesian Gaussian functions. An electron ejected through an ionization process will be described by an oscillating continuum wavefunction that enters the matrix element necessary for cross section calculations. Within a monocentric approach, we have recently shown how such integrals can be evaluated analytically by using a representation of the continuum state by a set of complex Gaussian functions. In this work we tackle the multicentric situation. The method, developed in either spherical or cartesian coordinates, and validated by numerical tests, makes use of existing mathematical tools extended to the complex plane.