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Pierre-Francois Loos 2020-12-09 20:42:32 +01:00
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Manuscript/sfBSE.tex
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\begin{abstract} \begin{abstract}
Like adiabatic time-dependent density-functional theory (TD-DFT), the Bethe-Salpeter equation (BSE) formalism in its static approximation is ``blind'' to double (and higher) excitations, which are, for example, ubiquitous in conjugated molecules like polyenes. Like adiabatic time-dependent density-functional theory (TD-DFT), the Bethe-Salpeter equation (BSE) formalism in its static approximation is ``blind'' to double (and higher) excitations, which are, for example, ubiquitous in conjugated molecules like polyenes.
Here, we apply the spin-flip technique to the BSE formalism of many-body perturbation theory in order to access double excitations. Here, we apply the spin-flip technique (which consists in considering the lowest triplet state as the reference configuration instead of the singlet ground state) to the BSE formalism of many-body perturbation theory in order to access 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. 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. 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 the vertical excitation energies of the beryllium atom, the hydrogen molecule, and cyclobutadiene. The performance of the present spin-flip BSE formalism is illustrated by computing the vertical excitation energies of the beryllium atom, the hydrogen molecule at various bond lengths, and cyclobutadiene.
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