Development of Strategies for Parallel Implementation of the Hartree–Fock Theory in Resolution-of-the-Identity Approximation

Twelve variants of algorithm implementations in the resolution-of-the-identity (RI) approximation of the Hartree–Fock (HF) method have been developed and analyzed, using the embedded capabilities of parallelism of high-performance linear algebra software libraries. A new parallel algorithm for calculating three-center electron repulsion integrals, based on known libraries for Gaussian function integration, has also been proposed and implemented using the OpenMP technology. The relationship between methods for storing the array of integrals in computer RAM and performing efficient parallel computations was analyzed in detail. Specifically, a new technique has been proposed for storing three-center electron repulsion integrals in computer RAM with allowance for their permutation symmetry. The approaches considered demonstrate how the number of accesses to the computing device’s RAM can be minimized and serve as a basis for creating efficient scalable algorithms for the Hartree–Fock method in the resolution-of-identity approximation. Software implementations of the method were tested on a set of polyene $${{{\text{C}}}_{N}}{{{\text{H}}}_{{N + 2}}}$$ molecules for N = 10–60 and on the chlorophyll C55H72O5N4Mg molecule, and the parallel algorithm for integral calculation was tested on the (C55H72O5N4Mg)2 dimer. The developed software implementations demonstrate computational efficiency comparable to implementations of similar algorithms in the PySCF quantum chemistry package.