Sec III OK

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Pierre-Francois Loos 2020-06-04 22:13:52 +02:00
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@ -501,7 +501,7 @@ Such an underestimation of the fundamental gap leads to a similar underestimatio
\EgOpt = E_1^{\Nel} - E_0^{\Nel} = \EgFun + \EB,
\end{equation}
where $\EB$ is the excitonic effect, that is, the stabilization implied by the attraction of the excited electron and its hole left behind (see Fig.~\ref{fig:gaps}).
Because of this, we have $\EgOpt < \EgFun$.
%Because of this, we have $\EgOpt < \EgFun$.
Such a residual gap problem can be significantly improved by adopting xc functionals with a tuned amount of exact exchange \cite{Stein_2009,Kronik_2012} that yield a much improved KS gap as a starting point for the $GW$ correction. \cite{Bruneval_2013,Rangel_2016,Knight_2016}
Alternatively, self-consistent schemes such as ev$GW$ and qs$GW$, \cite{Hybertsen_1986,Shishkin_2007,Blase_2011,Faber_2011,Faleev_2004,vanSchilfgaarde_2006,Kotani_2007,Ke_2011} where corrected eigenvalues, and possibly orbitals, are reinjected in the construction of $G$ and $W$, have been shown to lead to a significant improvement of the quasiparticle energies in the case of molecular systems, with the advantage of significantly removing the dependence on the starting point functional. \cite{Rangel_2016,Kaplan_2016,Caruso_2016}