Multi-GPU RI-HF Energies and Analytic Gradients $-$ Towards High Throughput Ab Initio Molecular Dynamics

This article presents an optimized algorithm and implementation for calculating resolution-of-the-identity Hartree-Fock (RI-HF) energies and analytic gradients using multiple Graphics Processing Units (GPUs). The algorithm is especially designed for high throughput \emph{ab initio} molecular dynamics simulations of small and medium size molecules (10-100 atoms). Key innovations of this work include the exploitation of multi-GPU parallelism and a workload balancing scheme that efficiently distributes computational tasks among GPUs. Our implementation also employs techniques for symmetry utilization, integral screening and leveraging sparsity to optimize memory usage and computational efficiency. Computational results show that the implementation achieves significant performance improvements, including over $3\times$ speedups in single GPU AIMD throughput compared to previous GPU-accelerated RI-HF and traditional HF methods. Furthermore, utilizing multiple GPUs can provide super-linear speedup when the additional aggregate GPU memory allows for the storage of decompressed three-center integrals. Additionally, we report strong scaling efficiencies for systems up to 1000 basis functions and demonstrate practical applications through extensive performance benchmarks on up to quadruple-$\zeta$ primary basis sets, achieving floating-point performance of up to 47\% of the theoretical peak on a 4$\times$A100 GPU node.