response letter and manuscript updated, waiting for results to complete SI

Manuscript/SRGGW.tex

@@ -633,6 +633,9 @@ Performing a bijective transformation of the form,
   e^{- \Delta s} &= 1-e^{-\Delta t},
 \end{align}
 on the renormalized quasiparticle equation \eqref{eq:GW_renorm} reverses the situation and makes it possible to choose $t$ such that there is no intruder states in the dynamic part, hence removing discontinuities.
+
+\textcolor{red}{The intruder-state free dynamic part makes it possible to define a SRG-$G_0W_0$ and SRG-ev$GW$.
+The main manuscript focus on SRG-qs$GW$ but the performance of SRG-$G_0W_0$ and SRG-ev$GW$ are discussed in the {\SupInf} for the sake of completeness.}
 Note that, after this transformation, the form of the regularizer is actually closely related to the SRG-inspired regularizer introduced by Monino and Loos in Ref.~\onlinecite{Monino_2022}.
 
 %=================================================================%
@@ -658,8 +661,6 @@ The $\eta$ value has been set to \num{e-3} for the conventional $G_0W_0$ calcula
 The various $GW$-based sets of values are compared with a set of reference values computed at the $\Delta$CCSD(T) level with the same basis set.
 The $\Delta$CCSD(T) principal ionization potentials (IPs) and electron affinities (EAs) have been obtained using \textsc{gaussian 16} \cite{g16} (with default parameters) within the restricted and unrestricted formalism for the neutral and charged species, respectively.
 
-All the numerical data associated with this study are reported in the {\SupInf}.
-
 %=================================================================%
 \section{Results}
 \label{sec:results}

Response_Letter/Response_Letter.tex

@@ -41,12 +41,15 @@ We look forward to hearing from you.
 \item 
 {In Eq. (45), the authors mention a reverse approach where, if I understand correctly, the $\omega$-dependent self-energy is directly modified using the SRG regularizer. How does this approach perform on $GW$50 and compare to qs$GW$ and SRG-qs$GW$?}
 \\
-\alert{}
+\alert{This reversed approach allows one to remove the intruder states from the dynamic part rather than the static part.
+  Therefore, this should be used for SRG-$G_0W_0$ and SRG-ev$GW$ calculations.
+  Following the reviewer's suggestion and for the sake of completeness, the performance of these two methods are now discussed in addition to SRG-qs$GW$.
+Yet, we decided to include this discussion in the supporting information in order not to bring confusion to the take-home message of the manuscript which is the new SRG-qs$GW$ static form.}
 
 \item 
 {I am a bit surprised that the SRG-qs$GW$ converges all molecules for $s = 1000$ but not for $s = 5000$. The energy cutoff window is very narrow here: $0.032$-$0.014$ Ha. Moreover, from Figs. 3, 4, and 6, the IPs are roughly converged in the order of $s = 50$ to a few $100$. I think an analysis of the denominators $\Delta^{\nu}_{pr}$ for the typical molecules would be very informative. In particular, what are the several smallest denominators at the beginning and how do they change along the self-consistency procedure?}
 \\
-\alert{}
+\alert{We thank the reviewer for this suggestion. Unfortunately, we have not been able to extract useful information out of the enormous number of denominators. Indeed, the number of small denominators is large and their associated screened integrals can be very different as well, hence it is difficult to explain quantitatively why the convergence is not reached for a given value of the energy cutoff. Note that one could maybe converge the calculation for $s=5000$ by changing the DIIS parameters for example.}
 
 \item 
 {In Eq. (18), I think $H^{\text{od}}$ is generally not a square matrix and it is better to say  $H^{\text{od}}(s)^\dagger H^{\text{od}}(s)$ instead of $H^{\text{od}}(s)^2$.}
@@ -57,7 +60,7 @@ The corresponding expression in the manuscript has been updated.}
 \item 
 {I think the y axis (counts in each bin) should be presented in Figs. 5 and 7. Or at least the  limit of y axis should be fixed for all subplots in Fig. 5 or Fig. 7.}
 \\
-\alert{We added the scaling of the vertical axis of each panel of Fig.~5 and Fig.~7.}
+\alert{We added the scaling of the vertical axes on each panel of Fig.~5 and Fig.~7.}
 
 \end{itemize}