A hybrid CPU/GPU method for Hartree–Fock self-consistent-field calculation.

The article focuses on the development and evaluation of a hybrid CPU/GPU method to accelerate the calculation of two-electron repulsion integrals (ERIs) in Hartree–Fock (HF) quantum chemistry computations. By organizing ERI tasks based on angular momentum and dynamically scheduling them between CPUs and GPUs using OpenMP, the method leverages the strengths of both processors to improve computational efficiency. Test results using the Wuhan Electronic Structure Package (WESP) demonstrate that the hybrid approach outperforms GPU-only methods when CPU and GPU computing powers are comparable and all ERI tasks can be executed on GPUs, particularly for basis sets involving s, p, and d orbitals. However, as the number of GPUs increases or when higher angular momentum orbitals (f and above) are involved, the advantage of the hybrid method diminishes due to load imbalance and limited GPU efficiency for certain ERI classes. The study also compares WESP’s performance with the GPU-accelerated software TeraChem, finding that WESP is competitive for smaller systems and fewer GPUs but less efficient for larger molecules with multiple GPUs. Future improvements suggested include finer-grained GPU task partitioning, enhanced GPU algorithms for high-angular-momentum ERIs, and incorporation of linear-scaling methods to better handle large systems.