Accelerating Excitation Energy Computation in Molecules and Solids within Linear-Response Time-Dependent Density Functional Theory via Interpolative Separable Density Fitting Decomposition.

We present an efficient way to compute the excitation energies in molecules and solids within linear-response time-dependent density functional theory (LR-TDDFT). Conventional methods to construct and diagonalize the LR-TDDFT Hamiltonian require ultrahigh computational cost, limiting its optoelectronic applications to small systems. Our new method is based on the interpolative separable density fitting (ISDF) decomposition combined with implicitly constructing and iteratively diagonalizing the LR-TDDFT Hamiltonian and only requires low computational cost to accelerate the LR-TDDFT calculations in the plane-wave basis sets under the periodic boundary condition. We show that this method accurately reproduces excitation energies in a fullerene (C60) molecule and bulk silicon Si64 system with significantly reduced computational cost compared to conventional direct and iterative calculations. The efficiency of this ISDF method enables us to investigate the excited-state properties of liquid water absorption on MoS2 and phosphorene by using the LR-TDDFT calculations. Our computational results show that an aqueous environment has a weak effect on low excitation energies but a strong effect on high excitation energies of 2D semiconductors for photocatalytic water splitting.