push for Enzo

Manuscript/ufGW-SI.tex

@@ -59,57 +59,35 @@
 
 \maketitle
 
-%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Energy differences}
-%%%%%%%%%%%%%%%%%%%%%%%%
-
-\subsection{$\eta$ shift}
+\begin{figure}
+	\includegraphics[width=0.33\linewidth]{eta_0_1}
+	\includegraphics[width=0.33\linewidth]{eta_1}
+	\includegraphics[width=0.33\linewidth]{eta_10}
+	\caption{Difference between non-regularized and regularized quasiparticle energies $\eps{p}{\GW}-\reps{p}{\GW}$ computed with $\eta = 0.1$ (left), $\eta = 1$ (center), and  $\eta = 10$ (right) as functions of the internuclear distance $\RHH$ (in \si{\angstrom}) of \ce{H2} at the {\GOWO}@HF/6-31G level. }
+\end{figure}		
 
 \begin{figure}
-	\includegraphics[width=0.6\linewidth]{eta_0_1}
-	\caption{Difference between non-regularized and regularized quasiparticle energies $\eps{p}{\GW}-\reps{p}{\GW}$ computed with $\eta = 0.1$ as functions of the internuclear distance $\RHH$ (in \si{\angstrom}) of \ce{H2} at the {\GOWO}@HF/6-31G level. }
+	\includegraphics[width=0.33\linewidth]{kappa_0_1}
+	\includegraphics[width=0.33\linewidth]{kappa_1}
+	\includegraphics[width=0.33\linewidth]{kappa_10}
+	\caption{Difference between non-regularized and regularized quasiparticle energies $\eps{p}{\GW}-\reps{p}{\GW}$ computed with computed with $\kappa = 0.1$ (left), $\kappa = 1$ (center), and  $\kappa = 10$ (right) as functions of the internuclear distance $\RHH$ (in \si{\angstrom}) of \ce{H2} at the {\GOWO}@HF/6-31G level. }
 \end{figure}	
 
 \begin{figure}
-	\includegraphics[width=0.6\linewidth]{eta_1}
-	\caption{Difference between non-regularized and regularized quasiparticle energies $\eps{p}{\GW}-\reps{p}{\GW}$ computed with $\eta = 1$ as functions of the internuclear distance $\RHH$ (in \si{\angstrom}) of \ce{H2} at the {\GOWO}@HF/6-31G level. }
+	\includegraphics[width=0.45\linewidth]{f2_eta_1}
+	\hspace{0.05\textwidth}
+%	\includegraphics[width=0.45\linewidth]{f2_eta_1}
+	\caption{Ground-state potential energy surface of \ce{F2} around its equilibrium geometry obtained at various levels of theory with the cc-pVDZ basis set for $\eta = 1$.}
 \end{figure}	
 
 \begin{figure}
-	\includegraphics[width=0.6\linewidth]{eta_10}
-	\caption{Difference between non-regularized and regularized quasiparticle energies $\eps{p}{\GW}-\reps{p}{\GW}$ computed with $\eta = 10$ as functions of the internuclear distance $\RHH$ (in \si{\angstrom}) of \ce{H2} at the {\GOWO}@HF/6-31G level. }
+	\includegraphics[width=0.45\linewidth]{f2_kappa_1}
+	\hspace{0.05\textwidth}
+	\includegraphics[width=0.45\linewidth]{f2_kappa_10}
+	\caption{Ground-state potential energy surface of \ce{F2} around its equilibrium geometry obtained at various levels of theory with the cc-pVDZ basis set for $\kappa = 1$ (left) and $\kappa = 10$ (right).
+	For $\kappa = 10$, the black and gray curves are superposed.}
 \end{figure}	
 
-\subsection{$\kappa$ shift}
-
-\begin{figure}
-	\includegraphics[width=0.6\linewidth]{kappa_0_1}
-	\caption{Difference between non-regularized and regularized quasiparticle energies $\eps{p}{\GW}-\reps{p}{\GW}$ computed with $\kappa = 0.1$ as functions of the internuclear distance $\RHH$ (in \si{\angstrom}) of \ce{H2} at the {\GOWO}@HF/6-31G level. }
-\end{figure}	
-
-\begin{figure}
-	\includegraphics[width=0.6\linewidth]{kappa_10}
-	\caption{Difference between non-regularized and regularized quasiparticle energies $\eps{p}{\GW}-\reps{p}{\GW}$ computed with $\kappa = 10$ as functions of the internuclear distance $\RHH$ (in \si{\angstrom}) of \ce{H2} at the {\GOWO}@HF/6-31G level. }
-\end{figure}	
-
-%%%%%%%%%%%%%%%%%%%%%%%%
-\section{\ce{F2} ground state}
-%%%%%%%%%%%%%%%%%%%%%%%%
-
-\begin{figure}
-	\includegraphics[width=0.6\linewidth]{f2_eta_1}
-	\caption{Ground-state potential energy surface of \ce{F2} around its equilibrium geometry obtained at various levels of theory with the cc-pVDZ basis set.}
-\end{figure}	
-
-\begin{figure}
-	\includegraphics[width=0.6\linewidth]{f2_kappa_1}
-	\caption{Ground-state potential energy surface of \ce{F2} around its equilibrium geometry obtained at various levels of theory with the cc-pVDZ basis set.}
-\end{figure}	
-
-\begin{figure}
-	\includegraphics[width=0.6\linewidth]{f2_kappa_10}
-	\caption{Ground-state potential energy surface of \ce{F2} around its equilibrium geometry obtained at various levels of theory with the cc-pVDZ basis set.}
-\end{figure}	
 
 %%%%%%%%%%%%%%%%%%%%%%%%
 \bibliography{ufGW}

Manuscript/ufGW.tex

@@ -373,7 +373,7 @@ Therefore, one can conclude that this downfall of $GW$ is a key signature of str
 	\includegraphics[width=\linewidth]{fig4}
 	\caption{
 	\label{fig:H2reg}
-	Difference between regularized and non-regularized quasiparticle energies $\reps{p}{\GW} - \eps{p}{\GW}$ computed with $\eta = 1$ as functions of the internuclear distance $\RHH$ (in \si{\angstrom}) of \ce{H2} at the {\GOWO}@HF/6-31G level.
+	Difference between regularized and non-regularized quasiparticle energies $\reps{p}{\GW} - \eps{p}{\GW}$ computed with $\alert{\kappa} = 1$ as functions of the internuclear distance $\RHH$ (in \si{\angstrom}) of \ce{H2} at the {\GOWO}@HF/6-31G level.
 }
 \end{figure}	
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -430,7 +430,7 @@ Our investigations have shown that the following energy-dependent regularizer
 	f_\kappa(\Delta) = \frac{1-e^{-2\Delta^2/\kappa^2}}{\Delta}
 \end{equation}
 derived from the (second-order) perturbative analysis of the similarity renormalization group (SRG) equations \cite{Wegner_1994,Glazek_1994,White_2002} by Evangelista \cite{Evangelista_2014} is particularly convenient and effective for our purposes.
-Increasing $\kappa$ gradually integrates out states with denominators $\Delta$ larger than $\kappa$ while the states with $\Delta \ll \kappa$ are not decoupled from the reference space, hence avoiding intruder state problems. \cite{Li_2019a}
+Increasing $\alert{\kappa}$ gradually integrates out states with denominators $\Delta$ larger than $\alert{\kappa}$ while the states with $\Delta \ll \alert{\kappa}$ are not decoupled from the reference space, hence avoiding intruder state problems. \cite{Li_2019a}
 
 
 Figure \ref{fig:H2reg_zoom} compares the non-regularized and regularized quasiparticle energies in the two regions of interest for various $\eta$ values.