Implementation of McMurchie–Davidson Algorithm for Gaussian AO Integrals Suited for SIMD Processors

Asadchev, Andrey; Valeev, Edward F.

doi:10.1021/acs.jpca.5c04136

Implementation of McMurchie–Davidson Algorithm for Gaussian AO Integrals Suited for SIMD Processors

Journal Article · Mon Oct 13 00:00:00 EDT 2025 · The Journal of Physical Chemistry A

DOI:https://doi.org/10.1021/acs.jpca.5c04136· OSTI ID:3000380

Asadchev, Andrey ^[1]; ^[1]

Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

We report an implementation of the McMurchie− Davidson evaluation scheme for 1- and 2-particle Gaussian AO integrals designed for processors with Single Instruction Multiple Data (SIMD) instruction sets. Like in our recent MD implementation for graphical processing units (GPUs) [Asadchev, A.; Valeev, E. F.. J. Chem. Phys. 2024, 160, 244109.], variable-sized batches of shellsets of integrals are evaluated at a time. By optimizing for the floating point instruction throughput rather than minimizing the number of operations, this approach achieves up to 50% of the theoretical hardware peak FP64 performance for many common SIMD-equipped platforms (AVX2, AVX512, NEON), which translates to speedups of up to 30 over the state-of-the-art one-shellset-at-a-time implementation of Obara−Saika-type schemes in Libint for a variety of primitive and contracted integrals. As with our previous work, we rely on the standard C++ programming language such as the std::simd standard library feature to be included in the 2026 ISO C++ standard without any explicit code generation to keep the code base small and portable. The implementation is part of the open source LibintX library freely available at https://github.com/ValeevGroup/libintx.

View Accepted Manuscript (DOE)

Research Organization:: Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0022327

OSTI ID:: 3000380

Journal Information:: The Journal of Physical Chemistry A, Journal Name: The Journal of Physical Chemistry A Journal Issue: 42 Vol. 129; ISSN 1089-5639; ISSN 1520-5215

Publisher:: American Chemical Society (ACS)Copyright Statement

Country of Publication:: United States

Language:: English

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