Efficient evaluation of the Fourier Transform over products of Slater-type orbitals on different centers

TL;DR

This paper presents a new, stable, and efficient method for computing the Fourier transform of products of Slater-type orbitals on different centers, with broad applicability and detailed benchmarking.

Contribution

A compact, numerically stable formula for Fourier transforms of Slater-type orbital products using the shift-operator technique is introduced.

Findings

The new method is numerically stable across various parameters.

Benchmark data demonstrate the efficiency of the scheme.

Comparison shows advantages over existing algorithms.

Abstract

Using the shift-operator technique, a compact formula for the Fourier transform of a product of two Slater-type orbitals located on different atomic centers is derived. The result is valid for arbitrary quantum numbers and was found to be numerically stable for a wide range of geometrical parameters and momenta. Details of the implementation are presented together with benchmark data for representative integrals. We also discuss the assets and drawbacks of alternative algorithms available and analyze the numerical efficiency of the new scheme.