Dynamically Corrected Bethe–Salpeter Equation Solver for Self-Consistent GW Reference on the Matsubara Frequency Axis

Abstract

We present a Bethe–Salpeter equation (BSE) solver based on a self-consistent GW reference evaluated on the Matsubara frequency axis, referred to as BSE@scGW. The self-consistent GW starting point provides a robust quasiparticle description and reduces sensitivity to the initial mean-field reference compared to one-shot GW-based approaches. We further introduce a dynamical correction to the static Casida formulation via a plasmon-pole model. This scheme incorporates simple dynamical screening effects while retaining the efficiency of an effective eigenvalue problem. The resulting dynamically corrected BSE@scGW yields excitation energies in close agreement with high-level wave function-based benchmarks for both singlet and triplet excitations of small molecules. Overall, the accuracy of the dynamic BSE@scGW approach arises from the combination of a well-converged single-particle reference and the inclusion of frequency-dependent screening effects.