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Pierre-Francois Loos 2020-05-19 13:20:03 +02:00
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BSEdyn.tex
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\affiliation{\NEEL}
\begin{abstract}
This is the abstract
Similarly to the ubiquitous adiabatic approximation in time-dependent density-functional theory, the static approximation, which substitutes a dynamical (\ie, frequency-dependent) kernel by its static limit, is usually enforced in most implementations of the Bethe-Salpeter equation (BSE) formalism.
Here, going beyond the static approximation, we compute molecular excitation energies thanks to a renormalized first-order perturbative correction to the static BSE excitation energies.
The present correction goes beyond the plasmon-pole approximation as the dynamical screening of the Coulomb interaction is computed exactly.
Moreover, we investigate quantitatively the effect of the Tamm-Dancoff approximation by computing both the resonant and anti-resonant dynamical corrections to the BSE excitation energies.
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@ -243,7 +246,7 @@ In the two latter studies, they also followed a perturbative approach within the
It is important to note that, although these studies are clearly going beyond the static approximation of BSE, they are not able to recover double excitations as the perturbative treatment makes ultimately the BSE kernel static.
However, it does permit to recover additional relaxation effects coming from the higher excitations which would be present by ``unfolding'' the dynamical BSE kernel in order to recover a linear eigenvalue problem.
Finally, let us also mentioned the work of Romaniello and coworkers, \cite{Romaniello_2009b,Sangalli_2011} in which the authors genuinely accessed double excitations by solving the non-linear, frequency-dependent eigenvalue problem.
Finally, let us also mentioned the work of Romaniello and coworkers, \cite{Romaniello_2009b,Sangalli_2011} in which the authors genuinely accessed additional excitations by solving the non-linear, frequency-dependent eigenvalue problem.
However, it is based on a rather simple model (the Hubbard dimer) which permits to analytically solve the dynamical equations.
In the present study, we extend the work of Rohlfing and coworkers \cite{Rohlfing_2000,Ma_2009} by proposing a renormalized first-order perturbative correction to the static neutral excitation energy.