High performance computing is a powerful tool to accelerate the Kohn–Sham density functional theory 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 energies and wave functions of solids with plane-wave basis set. We adopt a two-level parallelization strategy that combines the message passing interface with open multi-processing 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 demonstrate that the LR-TDDFT calculations can be used to investigate the photoinduced charge separation of water molecule adsorption on rutile TiO₂(110) surface from an excitonic perspective.

高性能计算是在现代异构超级计算机上加速 Kohn-Sham 密度泛函理论计算的强大工具。在这里，我们描述了大规模线性响应时间相关密度泛函理论 (LR-TDDFT) 的大规模并行实现，以计算具有平面波基组的固体的激发能量和波函数。我们采用两级并行化策略，将消息传递接口与开放的多处理并行编程相结合，以处理构造和对角化LR-TDDFT哈密顿矩阵的矩阵运算和数据通信。数值结果表明，LR-TDDFT 计算可以在现代异构超级计算机上扩展到 24 576 个处理核心，以研究包含数千个原子（4,096 个原子）的庞大硅系统的激发态特性。我们证明了 LR-TDDFT 计算可用于研究水分子在金红石 TiO2 上吸附的光致电荷分离从激子的角度看₂ (110) 表面。