Dynamic Schwarz Screening for <scp>GPU</scp> ‐Accelerated Fock Matrix Computation

ABSTRACT In quantum chemistry, fundamental molecular orbital methods such as the Hartree–Fock theory are pragmatically constrained by the computational complexity behind two‐electron repulsion integrals (ERIs) encoding electron Coulomb interactions. Although the computational cost of ERIs roughly scales with the fourth power of the atom count in the target molecule, it can be reduced by screening techniques based on the Schwarz inequality. However, the Schwarz screening involves evaluating the necessity of computation for individual ERIs based on their upper bounds, which results in substantial overhead consuming most of the total computation time, especially for large‐sized molecules. To tackle this bottleneck, we propose a new dynamic screening algorithm and its efficient GPU implementation, which drastically reduces the number of upper bound evaluations. Our parallel algorithm can discard numerically insignificant ERIs without even evaluating their upper bounds by dynamic scheduling of thread blocks, allowing to traverse only the significant ERIs. The merits and performance of our GPU implementation has been evaluated through computational experiments using an NVIDIA A100/H200 GPU with a relevant set of low and medium molecular‐weight compounds. As a result, our dynamic screening reduces the Schwarz upper bound evaluations by up to and achieves a speedup of up to compared to examining the necessity of computation for all ERIs. Our work has the potential to further enhance the performance frontiers of GPU‐based large‐scale molecular quantum chemistry calculations.