High-performance evaluation of high angular momentum 4-center Gaussian integrals on modern accelerated processors

TL;DR

This paper introduces a GPU-accelerated method for efficiently computing high angular momentum 4-center Gaussian integrals, significantly outperforming traditional CPU-based implementations and enabling faster quantum chemistry calculations.

Contribution

The authors develop a high-performance GPU implementation of 4-center Gaussian integrals using McMurchie-Davidson recurrences, achieving over 1000x speedup for high angular momentum cases.

Findings

GPU implementation outperforms CPU by over 1000x

Achieves nearly 50% of GPU peak FLOPS

Supports high angular momentum Gaussian integrals

Abstract

We present a high-performance evaluation method for 4-center 2-particle integrals over Gaussian atomic orbitals with high angular momenta ($l\geq4$) and arbitrary contraction degrees on graphical processing units (GPUs) and other accelerators. The implementation uses the matrix form of McMurchie-Davidson recurrences. Evaluation of the 4-center integrals over four $l=6$ ($i$) Gaussian AOs in the double precision (FP64) on an NVIDIA V100 GPU outperforms the reference implementation of the Obara-Saika recurrences (${\tt Libint}$) running on a single Intel Xeon core by more than a factor of 1000, easily exceeding the 73:1 ratio of the respective hardware peak FLOP rates while reaching almost 50\% of the V100 peak. The approach can be extended to support AOs with even higher angular momenta; for lower angular momenta ($l\leq3$) additional improvements will be reported elsewhere. The implementation is part of an open-source ${\tt LibintX}$ library feely available at https://github.com/ValeevGroup/LibintX.