Spin-Conserved and Spin-Flip Optical Excitations From the Bethe-Salpeter Equation Formalism

TL;DR

This paper introduces a spin-flip Bethe-Salpeter equation approach to access double excitations in molecules, extending the formalism's capabilities beyond traditional limitations, and demonstrates its effectiveness on atomic and molecular systems.

Contribution

It develops a spin-flip BSE method with a spin-unrestricted $GW$ approximation and dynamical corrections, enabling the calculation of double excitations in molecular systems.

Findings

Accurate excited-state energies for beryllium atom.

Effective description of hydrogen molecule at various bond lengths.

Successful modeling of cyclobutadiene geometries.

Abstract

Like adiabatic time-dependent density-functional theory (TD-DFT), the Bethe-Salpeter equation (BSE) formalism of many-body perturbation theory, in its static approximation, is "blind" to double (and higher) excitations, which are ubiquitous, for example, in conjugated molecules like polyenes. Here, we apply the spin-flip \textit{ansatz} (which considers the lowest triplet state as the reference configuration instead of the singlet ground state) to the BSE formalism in order to access, in particular, double excitations. The present scheme is based on a spin-unrestricted version of the $GW$ approximation employed to compute the charged excitations and screened Coulomb potential required for the BSE calculations. Dynamical corrections to the static BSE optical excitations are taken into account via an unrestricted generalization of our recently developed (renormalized) perturbative treatment. The performance of the present spin-flip BSE formalism is illustrated by computing excited-state energies of the beryllium atom, the hydrogen molecule at various bond lengths, and cyclobutadiene in its rectangular and square-planar geometries.