Direct evaluation of overlap integrals between Slater-type-orbitals

TL;DR

This paper presents a new direct numerical method for evaluating overlap integrals between Slater-type orbitals, simplifying previous approaches and demonstrating high accuracy in computational chemistry applications.

Contribution

It introduces a single-stage numerical evaluation method for overlap integrals that replaces complex sums over special functions, applicable in quantum chemistry calculations.

Findings

Achieves 8-digit agreement with literature results

Implemented in Mathematica and Maple, demonstrating practical usability

Potential for integration as an intrinsic function in quantum chemistry software

Abstract

We derive direct single-stage numerical evaluation of the electronic overlap integral between arbitrary atomic orbitals (including STOs). Integration is over cartesian co-ordinates, and replaces previous sums over 'special' functions. The results, in Mathematica 10 and Maple 18, agree with the literature to 8 digits. We briefly discuss possible use in quantum chemistry, including accuracy, algorithmic suitability and operating-system machine-implementation as an intrinsic function.