Evaluation of three-center two-electron repulsion integrals over Slater orbitals

TL;DR

This paper presents an analytical method to evaluate three-center two-electron repulsion integrals over Slater orbitals, achieving high precision and laying groundwork for future extensions to more complex molecular configurations.

Contribution

The authors derive an analytical expression for three-center two-electron integrals over Slater orbitals using a linear combination of overlap integrals, with high accuracy and potential for extension.

Findings

Integral converges to 20 decimal digits with 25-30 terms

Method expressed as a linear combination of overlap integrals

Analytical approach applicable to linear conformation of centers

Abstract

The Slater orbitals are the natural basis functions in quantum molecular calculations. Three-center repulsion Coulomb-exchange integrals over Slater orbitals are evaluated analytically with arbitrary orbital exponents, first for linear conformation of the atomic centers. These integrals have been expressed as a linear combination of three-center one-electron overlap integrals, and those have been calculated using auxiliary functions in terms of one-electron auxiliary integrals. Only one infinite expansion has been introduced. The resulting integral converges to 20 decimal digits using about 25-30 terms. Hybrid-exchange three-center repulsion integrals will be investigated next using this method, as well as triangular conformation of the centers.