3-center and 4-center 2-particle Gaussian AO integrals on modern accelerated processors

TL;DR

This paper presents an efficient GPU implementation of the McMurchie-Davidson algorithm for 3-center and 4-center Gaussian AO integrals, achieving high performance and supporting high angular momenta for large basis sets.

Contribution

It introduces a novel GPU-optimized implementation of the MD algorithm for Gaussian AO integrals with high angular momentum and varying contraction degrees, including preliminary Hartree-Fock exchange integration.

Findings

Achieves 25-70% of hardware peak performance in double precision.

Supports integrals over AOs with angular momentum up to 6.

Includes a preliminary implementation of the Hartree-Fock exchange operator.

Abstract

We report an implementation of the McMurchie-Davidson (MD) algorithm for 3-center and 4-center 2-particle integrals over Gaussian atomic orbitals (AOs) with low and high angular momenta $l$ and varying degrees of contraction for graphical processing units (GPUs). This work builds upon our recent implementation of a matrix form of the MD algorithm that is efficient for GPU evaluation of 4-center 2-particle integrals over Gaussian AOs of high angular momenta ($l\geq 4$) [$\mathit{J. Phys. Chem. A}\ \mathbf{127}$, 10889 (2023)]. The use of unconventional data layouts and three variants of the MD algorithm allow to evaluate integrals in double precision with sustained performance between 25% and 70% of the theoretical hardware peak. Performance assessment includes integrals over AOs with $l\leq 6$ (higher $l$ is supported). Preliminary implementation of the Hartree-Fock exchange operator is presented and assessed for computations with up to quadruple-zeta basis and more than 20,000 AOs. The corresponding C++ code is a part of the experimental open-source $\mathtt{LibintX}$ library available at $\mathbf{github.com:ValeevGroup/LibintX}$.