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Pierre-Francois Loos 2022-02-24 10:48:58 +01:00
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Manuscript/ufGW.tex
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@ -396,7 +396,7 @@ The regularized solutions $\reps{p,s}{\GW}$ are then obtained by solving the fol
\eps{p}{\HF} + \rSigC{p}(\omega;\eta) - \omega = 0 \eps{p}{\HF} + \rSigC{p}(\omega;\eta) - \omega = 0
\end{equation} \end{equation}
The most common and well-established way of regularizing $\Sigma$ is via the simple regularizer $f_\eta(\Delta) = (\Delta \pm \eta)^{-1}$, a strategy somehow related to the imaginary shift used in multiconfigurational perturbation theory. \cite{Forsberg_1997} The most common and well-established way of regularizing $\Sigma$ is via the simple regularizer $f_\eta(\Delta) = (\Delta \pm \ii \eta)^{-1}$, a strategy somehow related to the imaginary shift used in multiconfigurational perturbation theory. \cite{Forsberg_1997}
Other choices are legitimate like the regularizers considered by Head-Gordon and coworkers within orbital-optimized second-order M{\o}ller-Plesset theory. \cite{Lee_2018a,Shee_2021} Other choices are legitimate like the regularizers considered by Head-Gordon and coworkers within orbital-optimized second-order M{\o}ller-Plesset theory. \cite{Lee_2018a,Shee_2021}
Our investigations have shown that the following regularizer Our investigations have shown that the following regularizer