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.

中文翻译：

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通过插值可分离的密度拟合分解，在线性响应时间相关的密度泛函理论中加速分子和固体中的激发能计算。

我们提出一种有效的方法来计算线性响应时间相关的密度泛函理论（LR-TDDFT）中的分子和固体中的激发能。构造和对角化LR-TDDFT哈密顿量的常规方法需要超高的计算成本，从而将其光电应用限制在小型系统中。我们的新方法基于插值可分离密度拟合（ISDF）分解，结合隐式构造和迭代对角化LR-TDDFT哈密顿量，并且仅需较低的计算成本即可在周期下的平面波基集中加速LR-TDDFT计算边界条件。我们表明，与传统的直接和迭代计算相比，该方法可在富勒烯（C60）分子和体硅Si64系统中准确地再现激发能，并显着降低了计算成本。这种ISDF方法的效率使我们能够通过LR-TDDFT计算研究液态水在MoS2和磷上的吸收的激发态性质。我们的计算结果表明，水性环境对光催化水分解的2D半导体的低激发能具有微弱的影响，但对高激发能具有强的影响。