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

We present an efficient way to solve the Bethe–Salpeter equation (BSE), a method for the computation of optical absorption spectra in molecules and solids that includes electron–hole interactions. Standard approaches to construct and diagonalize the Bethe–Salpeter Hamiltonian require at least \(\mathcal {O}(N_e^5)\) operations, where \(N_e\) is the number of electrons in the system, limiting its application to smaller systems. Our approach is based on the interpolative separable density fitting (ISDF) technique to construct low rank approximations to the bare exchange and screened direct operators associated with the BSE Hamiltonian. This approach reduces the complexity of the Hamiltonian construction to \(\mathcal {O}(N_e^3)\) with a much smaller pre-constant, and allows for a faster solution of the BSE. Here, we implement the ISDF method for BSE calculations within the Tamm–Dancoff approximation (TDA) in the BerkeleyGW software package. We show that this novel approach accurately reproduces exciton energies and optical absorption spectra in molecules and solids with a significantly reduced computational cost.

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