GPU ‐Accelerated One‐Electron Integral Computation for Quantum Chemistry

ABSTRACT In Quantum chemical computation, numerical schemes such as the Hartree–Fock (HF) and density functional theory (DFT) are widely used to solve the Schrödinger equation numerically, to realize experiment‐free prediction and analysis of key molecular properties such as structure and energy. Computing one‐electron integrals, such as kinetic energy integrals and nuclear attraction integrals, is essential in both HF and DFT to characterize the molecular electronic states. However, as molecules of practical interest grow in size and angular momentum, computing one‐electron orbitals becomes computationally expensive in most cases. Although computing kinetic energy integrals on CPUs is straightforward, bottlenecks in CPU‐GPU data transfer have often been overlooked. In this study, we propose an efficient method to compute both the kinetic‐energy and nuclear‐attractive integrals on GPUs. First, we explicitly and symbolically expand recurrence relations based on the Obara–Saika and McMurchie–Davidson methods to eliminate redundant operations, thus improving computational efficiency. Second, we implemented a hybrid method that selects the best/fastest of both methods depending on the integration task. Third, we achieved further speedups by using CUDA streams to parallelize the execution of multiple kernels and efficiently utilize multiprocessor resources on the GPU. Computational experiments using NVIDIA A100 GPUs and Intel Xeon Gold 6338 CPU on relevant molecules of interest demonstrated the superiority of our one‐electron integral GPU implementations, achieving a speedup of 20.2 times over PySCF, and a speedup of 132.6 times over GPU4PySCF.