Dynamical Correction to the Bethe-Salpeter Equation Beyond the Plasmon-Pole Approximation

TL;DR

This paper introduces a method to improve the accuracy of molecular excitation energy calculations by incorporating a dynamical correction to the Bethe-Salpeter equation, surpassing the plasmon-pole approximation.

Contribution

It presents a novel dynamical correction to the BSE that accounts for frequency-dependent screening beyond the plasmon-pole approximation, enhancing excitation energy predictions.

Findings

Dynamical correction improves agreement with high-level calculations.

Exact dynamical screening surpasses the plasmon-pole approximation.

Enhanced accuracy for both singlet and triplet transitions.

Abstract

The Bethe-Salpeter equation (BSE) formalism is a computationally affordable method for the calculation of accurate optical excitation energies in molecular systems. Similar to the ubiquitous adiabatic approximation of time-dependent density-functional theory, the static approximation, which substitutes a dynamical (i.e., frequency-dependent) kernel by its static limit, is usually enforced in most implementations of the BSE formalism. Here, going beyond the static approximation, we compute the dynamical correction of the electron-hole screening for molecular excitation energies thanks to a renormalized first-order perturbative correction to the static BSE excitation energies. The present dynamical correction goes beyond the plasmon-pole approximation as the dynamical screening of the Coulomb interaction is computed exactly within the random-phase approximation. Our calculations are benchmarked against high-level (coupled-cluster) calculations, allowing to assess the clear improvement brought by the dynamical correction for both singlet and triplet optical transitions.