插值可分密度拟合加速纳米体系光吸收谱和激子能量计算
Accelerating Optical Absorption Spectra and Exciton Energy Computation for Nanosystems via Interpolative Separable Density Fitting
摘要：
我们提出了一种有效的方法来解决贝特萨尔彼得方程（BSE），一个模型的计算吸收光谱的分子和固体，包括电子空穴激发。构造和对角化Bethe-Salpeter哈密顿量的标准方法至少需要$Ø(N_e^5)$运算，其中$N_e$与系统中的电子数成比例，限制了其在小系统中的应用。我们的方法是基于插值可分离密度拟合（ISDF）技术构建低秩近似裸和屏蔽交换算子与BSE哈密顿量。这种方法将哈密顿构造的复杂性降低到具有小得多的前常数的$Ø(N_e^3)$。在这里，我们实现了ISDF方法的BSE计算内的Tamm-Dancoff近似（TDA）的BerkeleyGW软件包。我们表明，ISDF为基础的BSE计算在分子和固体重现准确的激子能量和光学吸收光谱，显着降低计算成本。
英文摘要：
We present an efficient way to solve the Bethe-Salpeter equation (BSE), a model for the computation of absorption spectra in molecules and solids that includes electron-hole excitations. Standard approaches to construct and diagonalize the Bethe-Salpeter Hamiltonian require at least $Ø(N_e^5)$ operations, where $N_e$ is proportional to the number of electrons in the system, limiting its application to small systems. Our approach is based on the interpolative separable density fitting (ISDF) technique to construct low rank approximations to the bare and screened exchange operators associated with the BSE Hamiltonian. This approach reduces the complexity of the Hamiltonian construction to $Ø(N_e^3)$ with a much smaller pre-constant. Here, we implement the ISDF method for the BSE calculations within the Tamm-Dancoff approximation (TDA) in the BerkeleyGW software package. We show that ISDF-based BSE calculations in molecules and solids reproduce accurate exciton energies and optical absorption spectra with significantly reduced computational cost.
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