Parallel GPU Computation of Nuclear Attraction Integrals in Quantum Chemistry

In quantum chemical calculations, methods such as Hartree-Fock and density functional theory are used to numerically solve the Schrödinger equation. These methods require the pre-computation of nuclear attraction integrals, which represent the integrals over the attraction of an electron from all nuclei. This study presents a novel approach to accelerate the calculation of nuclear attraction integrals using Graphics Processing Units (GPUs). To optimize GPU performance, we employ three main strategies. First, we enhance the recursive relations of the Obara-Saika and McMurchie-Davidson methods, which are commonly used algorithms for these calculations, to leverage GPU acceleration. Second, we implement a hybrid approach, selecting either the Obara-Saika or McMurchie-Davidson method based on the specific types of computed integrals. Finally, we utilize the CUDA stream to parallelize the execution of GPU kernels, efficiently utilizing the available multicore processors on the GPU. Experimental results on various molecules demonstrate that our proposed method achieves up to 1635 times faster computation than a CPU implementation.