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

TL;DR

This paper introduces an efficient method using interpolative separable density fitting to accelerate the computation of optical absorption spectra and exciton energies in nanosystems, significantly reducing computational complexity.

Contribution

The paper develops and implements an ISDF-based approach to construct low-rank approximations for BSE Hamiltonian, lowering computational cost from O(N_e^5) to O(N_e^3).

Findings

Accurately reproduces exciton energies and spectra.

Reduces computational cost significantly.

Applicable to molecules and solids.

Abstract

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 $\O(N_e^5)$ 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 $\O(N_e^3)$ 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.