GPU-accelerated analytic Hartree–Fock gradients

Analytic nuclear gradients underpin much of computational quantum chemistry, driving geometry optimization and supplying the forces of ab initio molecular dynamics. Yet on graphics processing units (GPUs) the gradient has received far less attention than the selfconsistent field (SCF) procedure it accompanies. In current production codes its construction can cost as much as the entire preceding SCF. Here we present a novel, high-performance GPU implementation of the analytic Hartree–Fock energy gradient. The Coulomb and exchange gradients are evaluated by separate engines to exploit their markedly different sparsity. The exchange gradient retains the full eightfold integral symmetry through an in-kernel ring-buffer compaction that eliminates warp divergence. A hybrid Head-Gordon–Pople/Rys quadrature scheme, translational invariance and GPU-resident shell-pair batch construction further accelerate the evaluation. Benchmarked on NVIDIA H200 GPUs across double-and triple-ζ basis sets against TeraChem, GPU4PySCF, QUICK and VeloxChem, EXESS is the fastest code for every system and basis set tested, with average speedups of 12.2×, 15.4×, 222× and 176× respectively on molecules ranging up to ubiquitin (11,577 basis functions).