Resolutions of the Coulomb operator: VI. Computation of auxiliary integrals

TL;DR

This paper presents a new recurrence relation and an efficient algorithm for computing auxiliary integrals involving Coulomb operators in quantum chemistry, improving computational efficiency for Gaussian basis functions.

Contribution

It introduces a novel recurrence relation and a near-optimal algorithm for auxiliary integral computation with arbitrary angular momentum Gaussian functions.

Findings

Enhanced computational efficiency for auxiliary integrals

Applicable to Coulomb and long-range Ewald operators

Supports Gaussian basis functions of arbitrary angular momentum

Abstract

We discuss the efficient computation of the auxiliary integrals that arise when resolutions of two-electron operators (specifically, the Coulomb and long-range Ewald operators) are employed in quantum chemical calculations. We derive a recurrence relation that facilitates the generation of auxiliary integrals for Gaussian basis functions of arbitrary angular momentum and propose a near-optimal algorithm for its use.