MPI+OpenMP implementation of resolution-of-the-identity Hartree-Fock method exploiting permutational symmetry of three-center electron repulsion integrals

Supercomputing Frontiers and Innovations. 2026. Vol. 13. No. 1. P. 52–73.

Kashpurovich I., Oleynichenko A., Stegailov V.

We report a high-performance implementation of the resolution-of-the-identity Hartree–Fock method that fully exploits the permutational symmetry of three-center electron repulsion integrals (ERI). The present implementation adopts a hybrid MPI+OpenMP parallelization strategy. Two different algorithmic approaches (with and without the pre-transformation of ERIs) are compared. A custom data layout introduced previously is employed. Designed to efficiently leverage the permutational symmetry of ERIs, it reduces both inter-node communication and local memory traffic. Extensive low-level and algorithmic optimizations are proposed and discussed. Reasonable parallel scaling is demonstrated by performance benchmarks on a chlorophyll dimer in aqueous environment (322 atoms, 3700 and 11896 functions in main and auxiliary basis sets, respectively). A peak speedups of 84x and 71x on 128 threads are achieved for ERIs calculation and the exchange matrix construction within the algorithm using the pre-transformation.

Keywords: OpenMP, MPI, density fitting, resolution-of-the-identity, three-center electron repulsion integrals, Restricted Hartree-Fock method

Publication based on the results of: Advanced materials and technologies (2025)