TDDFT Gradients and Nonadiabatic Couplings with Minimal Auxiliary Basis Set Approximation for Fewest-Switches Surface Hopping Dynamics

The electronic structure calculations remain a major bottleneck in ab initio nonadiabatic molecular dynamics. We develop an efficient TDDFT-based FSSH implementation in the GPU4PySCF package for medium-sized molecular systems. Our approach combines density fitting, TDDFT with minimal auxiliary basis sets (TDDFT-ris), and an approximate Z-vector solver to reduce the computational cost of TDDFT excited states and derivative coupling calculations. These approximations introduce modest changes in the relaxation time scales while maintaining high computational efficiency. Benchmark results show that, for 73-atom systems with a triple-ζ basis set, individual electronic structure calculations are completed within 1 min on a single NVIDIA A100 GPU.