Very-Large-Scale\nGPU-Accelerated Nuclear Gradient\nof Time-Dependent Density Functional Theory with Tamm–Dancoff\nApproximation and Range-Separated Hybrid Functionals

Modern graphics processing units (GPUs) provide an unprecedented\nlevel of computing power. In this study, we present a high-performance,\nmulti-GPU implementation of the analytical nuclear gradient for Kohn–Sham\ntime-dependent density functional theory (TDDFT), employing the Tamm–Dancoff\napproximation (TDA) and Gaussian-type atomic orbitals as basis functions.\nWe discuss GPU-efficient algorithms for the derivatives of electron\nrepulsion integrals and exchange–correlation functionals within\nthe range-separated scheme. As an illustrative example, we calculate\nthe TDA-TDDFT gradient of the S<sub>1</sub> state of a full-scale\ngreen fluorescent protein with explicit water solvent molecules, totaling\n4353 atoms, at the ωB97X/def2-SVP level of theory. Our algorithm\ndemonstrates favorable parallel efficiencies on a high-speed distributed\nsystem equipped with 256 Nvidia A100 GPUs, achieving >70% with\nup\nto 64 GPUs and 31% with 256 GPUs, effectively leveraging the capabilities\nof modern high-performance computing systems.