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We present an efficient way to solve the Bethe-Salpeter equation (BSE), amodel for the computation of absorption spectra in molecules and solids thatincludes electron-hole excitations. Standard approaches to construct anddiagonalize the Bethe-Salpeter Hamiltonian require at least $\O(N_e^5)$operations, where $N_e$ is proportional to the number of electrons in thesystem, limiting its application to small systems. Our approach is based on theinterpolative separable density fitting (ISDF) technique to construct low rankapproximations to the bare and screened exchange operators associated with theBSE Hamiltonian. This approach reduces the complexity of the Hamiltonianconstruction to $\O(N_e^3)$ with a much smaller pre-constant. Here, weimplement the ISDF method for the BSE calculations within the Tamm-Dancoffapproximation (TDA) in the BerkeleyGW software package. We show that ISDF-basedBSE calculations in molecules and solids reproduce accurate exciton energiesand optical absorption spectra with significantly reduced computational cost.

Accelerating Optical Absorption Spectra and Exciton Energy Computation for Nanosystems via Interpolative Separable Density Fitting