Low-rank approximations to accelerate hybrid functional enabled real-time time-dependent density functional theory within plane waves

Real-time time-dependent density functional theory (RT-TDDFT) is a powerful tool for predicting excited-state dynamics. Herein, we combine the adaptively compressed exchange (ACE) operator with interpolative separable density fitting (ISDF) algorithm to accelerate the hybrid functional calculations in RT-TDDFT (hybrid RT-TDDFT) dynamics simulations for molecular and periodic systems within plane waves. Under this low-rank representation, we demonstrate that the ACE-ISDF enabled hybrid RT-TDDFT can yield accurate excited-state dynamics, but much faster than conventional calculations. Furthermore, we describe a massively parallel implementation of ACE-ISDF enabled hybrid RT-TDDFT dynamics simulations containing thousands of atoms (1728 atoms), which can scale up to 3456 central processing unit cores on modern supercomputers.