Hybrid MPI and OpenMP parallel implementation of large-scale linear-response time-dependent density functional theory with plane-wave basis set

High performance computing (HPC) is a powerful tool to accelerate the Kohn-Sham density functional theory (KS-DFT) calculations on modern heterogeneous supercomputers. Here, we describe a massively parallel implementation of large-scale linear-response time-dependent density functional theory (LR-TDDFT) to calculate the excitation energy and wave functions of solids with plane-wave basis set under the periodic boundary condition in the Plane Wave Density Functional Theory (PWDFT) software package. We adopt a two-level parallelization strategy that combines the Message Passing Interface (MPI) with Open Multi-Processing (OpenMP) parallel programming to deal with the matrix operations and data communications of constructing and diagonalizing the LR-TDDFT Hamiltonian matrix. Numerical results illustrate that the LR-TDDFT calculations can scale up to 24,576 processing cores on modern heterogeneous supercomputers to study the excited state properties of bulky silicon systems containing thousands of atoms (4,096 atoms). We prove that the LR-TDDFT calculations can study the photoinduced charge separation of water molecule adsorption on rutile TiO2(110) surface from an excitonic perspective.