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Pierre-Francois Loos 2023-02-08 21:44:03 +01:00
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Manuscript/SRGGW.tex
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@ -502,8 +502,7 @@ It is worth noting the close similarity of the first-order elements with the one
%%% FIG 1 %%% %%% FIG 1 %%%
\begin{figure*} \begin{figure*}
\centering \includegraphics[width=0.8\linewidth]{fig1.pdf}
\includegraphics[width=\linewidth]{fig1.pdf}
\caption{ \caption{
Functional form of the qs$GW$ self-energy (left) for $\eta = 1$ and the SRG-qs$GW$ self-energy (right) for $s = 1/(2\eta^2) = 1/2$. Functional form of the qs$GW$ self-energy (left) for $\eta = 1$ and the SRG-qs$GW$ self-energy (right) for $s = 1/(2\eta^2) = 1/2$.
\label{fig:plot}} \label{fig:plot}}
@ -563,7 +562,7 @@ while the dynamic part of the self-energy [see Eq.~\eqref{eq:srg_sigma}] tends t
Therefore, the SRG flow continuously transforms the dynamical self-energy $\widetilde{\bSig}(\omega; s)$ into a static correction $\widetilde{\bF}^{(2)}(s)$. Therefore, the SRG flow continuously transforms the dynamical self-energy $\widetilde{\bSig}(\omega; s)$ into a static correction $\widetilde{\bF}^{(2)}(s)$.
As illustrated in Fig.~\ref{fig:flow}, this transformation is done gradually starting from the states that have the largest denominators in Eq.~\eqref{eq:static_F2}. As illustrated in Fig.~\ref{fig:flow}, this transformation is done gradually starting from the states that have the largest denominators in Eq.~\eqref{eq:static_F2}.
%%% FIG 1 %%% %%% FIG 2 %%%
\begin{figure} \begin{figure}
\centering \centering
\includegraphics[width=\linewidth]{flow} \includegraphics[width=\linewidth]{flow}
@ -647,7 +646,6 @@ Then the accuracy of the IP yielded by the traditional and SRG schemes will be s
%%% FIG 2 %%% %%% FIG 2 %%%
\begin{figure} \begin{figure}
\centering
\includegraphics[width=\linewidth]{fig2.pdf} \includegraphics[width=\linewidth]{fig2.pdf}
\caption{ \caption{
Principal IP of the water molecule in the aug-cc-pVTZ basis set as a function of the flow parameter $s$ for the SRG-qs$GW$ method with and without TDA. Principal IP of the water molecule in the aug-cc-pVTZ basis set as a function of the flow parameter $s$ for the SRG-qs$GW$ method with and without TDA.
@ -658,7 +656,6 @@ Then the accuracy of the IP yielded by the traditional and SRG schemes will be s
%%% FIG 3 %%% %%% FIG 3 %%%
\begin{figure*} \begin{figure*}
\centering
\includegraphics[width=\linewidth]{fig3.pdf} \includegraphics[width=\linewidth]{fig3.pdf}
\caption{ \caption{
Principal IP of the \ce{Li2}, \ce{LiH} and \ce{BeO} in the aug-cc-pVTZ basis set as a function of the flow parameter $s$ for the SRG-qs$GW$ method with and without TDA. Principal IP of the \ce{Li2}, \ce{LiH} and \ce{BeO} in the aug-cc-pVTZ basis set as a function of the flow parameter $s$ for the SRG-qs$GW$ method with and without TDA.
@ -717,7 +714,6 @@ Also, the SRG-qs$GW_\TDA$ is better than qs$GW_\TDA$ in the three cases of Fig.~
Therefore, it seems that the effect of the TDA can not be systematically predicted. Therefore, it seems that the effect of the TDA can not be systematically predicted.
\begin{table} \begin{table}
\centering
\caption{First ionization potential in eV calculated using $\Delta$CCSD(T) (reference), HF, $G_0W_0$@HF, qs$GW$ and SRG-qs$GW$. The statistical descriptors are computed for the errors with respect to the reference.} \caption{First ionization potential in eV calculated using $\Delta$CCSD(T) (reference), HF, $G_0W_0$@HF, qs$GW$ and SRG-qs$GW$. The statistical descriptors are computed for the errors with respect to the reference.}
\label{tab:tab1} \label{tab:tab1}
\begin{ruledtabular} \begin{ruledtabular}
@ -764,7 +760,6 @@ Therefore, it seems that the effect of the TDA can not be systematically predict
%%% FIG 4 %%% %%% FIG 4 %%%
\begin{figure*} \begin{figure*}
\centering
\includegraphics[width=\linewidth]{fig4.pdf} \includegraphics[width=\linewidth]{fig4.pdf}
\caption{ \caption{
Histogram of the errors (with respect to $\Delta$CCSD(T)) for the first ionization potential calculated using HF, $G_0W_0$@HF, qs$GW$ and SRG-qs$GW$. Histogram of the errors (with respect to $\Delta$CCSD(T)) for the first ionization potential calculated using HF, $G_0W_0$@HF, qs$GW$ and SRG-qs$GW$.
@ -806,7 +801,6 @@ Maybe that would be nice to add SRG G0W0 to see if it mitigates the outliers of
That would be nice to understand clearly why qsGWTDHF is worse (screening, gap, etc) That would be nice to understand clearly why qsGWTDHF is worse (screening, gap, etc)
\begin{table} \begin{table}
\centering
\caption{First ionization potential in eV calculated using $G_0W_0^{\text{TDA}x}$@HF, qs$GW^{\text{TDA}}$ and SRG-qs$GW^{\text{TDA}}$. The statistical descriptors are computed for the errors with respect to the reference.} \caption{First ionization potential in eV calculated using $G_0W_0^{\text{TDA}x}$@HF, qs$GW^{\text{TDA}}$ and SRG-qs$GW^{\text{TDA}}$. The statistical descriptors are computed for the errors with respect to the reference.}
\label{tab:tab1} \label{tab:tab1}
\begin{ruledtabular} \begin{ruledtabular}