Koopmans Meets Bethe-Salpeter: Excitonic Optical Spectra without GW

TL;DR

This paper introduces a new first-principles method for calculating optical spectra that bypasses the costly GW step by using Koopmans-compliant functionals and a direct minimization scheme, enabling larger system simulations.

Contribution

The work develops a novel approach combining Koopmans-compliant functionals with a direct minimization scheme to compute excitonic spectra without GW calculations.

Findings

Accurately reproduces low-lying excited states of molecules.

Matches trends of quantum chemical methods and previous TD-DFT or GW-BSE results.

Reduces parameter complexity, enabling larger system simulations.

Abstract

The Bethe-Salpeter Equation (BSE) can be applied to compute from first-principles optical spectra that include the effects of screened electron-hole interactions. As input, BSE calculations require single-particle states, quasiparticle energy levels and the screened Coulomb interaction, which are typically obtained with many-body perturbation theory, whose cost limits the scope of possible applications. This work tries to address this practical limitation, instead deriving spectral energies from Koopmans-compliant functionals and introducing a new methodology for handling the screened Coulomb interaction. The explicit calculation of the $W$ matrix is bypassed via a direct minimization scheme applied on top of a maximally localised Wannier function basis. We validate and benchmark this approach by computing the low-lying excited states of the molecules in Thiel's set, and the optical absorption spectrum of a $\text{C}_{60}$ fullerene. The results show the same trends as quantum chemical methods and are in excellent agreement with previous simulations carried out at the TD-DFT or $G_{0}W_{0}$-\text{BSE} level. Conveniently, the new framework reduces the parameter space controlling the accuracy of the calculation, thereby simplifying the simulation of charge-neutral excitations, offering the potential to expand the applicability of first-principles spectroscopies to larger systems of applied interest.