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We implement and benchmark twelve distinct algorithms for the Hartree–Fock (HF) method using the resolution-of-the-identity (RI) approximation, testing them on polyene molecules ranging from C \(_{10}\) H \(_{12}\) to C \(_{60}\) H \(_{62}\) . The three-center electron repulsion integrals employed for this are stored in RAM. We introduce a novel memory layout that accounts for the permutation symmetry of these integrals. This layout allows to eliminate data movement entirely, enabling optimal parallel implementation of the RI-HF method. While highly effective for computing the exchange contribution to the Fock matrix, this approach slightly complicates the Coulomb contribution calculation. All implementations leverage the MKL or OpenBLAS libraries. The version exploiting the proposed memory layout, along with several other variants, outperforms the PySCF quantum chemistry implementation in both serial and parallel execution modes.

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Achieving the Maximum Performance of the Resolution of the Identity Approximation in the Hartree–Fock Method

  • 会议论文

  • 发表日期：

    2026年

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  • Iurii V. Kashpurovich,
  • Alexander V. Oleynichenko,
  • Vladimir V. Stegailov

摘要

We implement and benchmark twelve distinct algorithms for the Hartree–Fock (HF) method using the resolution-of-the-identity (RI) approximation, testing them on polyene molecules ranging from C \(_{10}\) H \(_{12}\) to C \(_{60}\) H \(_{62}\) . The three-center electron repulsion integrals employed for this are stored in RAM. We introduce a novel memory layout that accounts for the permutation symmetry of these integrals. This layout allows to eliminate data movement entirely, enabling optimal parallel implementation of the RI-HF method. While highly effective for computing the exchange contribution to the Fock matrix, this approach slightly complicates the Coulomb contribution calculation. All implementations leverage the MKL or OpenBLAS libraries. The version exploiting the proposed memory layout, along with several other variants, outperforms the PySCF quantum chemistry implementation in both serial and parallel execution modes.