Analytical evaluation of relativistic molecular integrals. II. Computational aspect for relativistic molecular auxiliary functions

TL;DR

This paper investigates computational methods to efficiently evaluate relativistic molecular integrals involving Slater-type orbitals with non-integer quantum numbers, enabling accurate and efficient molecular electronic structure calculations.

Contribution

It presents a computational approach that improves efficiency in evaluating complex relativistic molecular integrals with non-integer quantum numbers.

Findings

Evaluation time is competitive with integer quantum number cases.

The method enhances computational efficiency for relativistic molecular integrals.

Accurate results are achievable without restrictions on quantum numbers.

Abstract

The Slater-type orbital basis with non-integer principal quantum numbers is a physically and mathematically motivated choice for molecular electronic structure calculations in both non-relativistic and relativistic theory. The non-analyticity of these orbitals at $r=0$, however, requires analytical relations for multi-center integrals to be derived. This is nearly insurmountable. Previous papers by present authors eliminated this difficulty. Highly accurate results can be achieved by the procedure described in these papers, which place no restrictions on quantum numbers in all ranges of orbital parameters. The purpose of this work is to investigate computational aspects of the formulae given in the previous paper. It is to present a method which helps to increase computational efficiency. In terms of the processing time, evaluation of integrals over Slater-type orbitals with non-integer principal quantum numbers are competitive with those over Slater-type orbitals with integer principal quantum numbers.