minor modifs

Response_Letter/Response_Letter.tex

@@ -33,18 +33,18 @@ We look forward to hearing from you.
 \begin{itemize}
 
 \item 
-{The article of Marie and Loos describes a regularized GW approach inspired by the similarity renormalization group second-order perturbative analysis to the linear GW eigenvalue equations. The article is well-organized and the presentation is clear. I think this article can be accepted as is. Nonetheless, I do have a few minor suggestions.}
+{The article of Marie and Loos describes a regularized $GW$ approach inspired by the similarity renormalization group second-order perturbative analysis to the linear $GW$ eigenvalue equations. The article is well-organized and the presentation is clear. I think this article can be accepted as is. Nonetheless, I do have a few minor suggestions.}
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 \alert{We thank the reviewer for supporting publication of the present manuscript.
 }
 
 \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 GW50 and compare to qsGW and SRG-qsGW?}
+{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{}
 
 \item 
-{I am a bit surprised that the SRG-qsGW 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?}
+{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?}
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 \alert{}
 
@@ -67,15 +67,15 @@ The corresponding expression in the manuscript has been updated.}
 \begin{itemize}
 
 \item 
-{This is an excellent manuscript, which I very much enjoyed reading. In particular, it includes a comprehensive overview of the literature in the field, which I find very valuable (ref. 119 should be updated). The final result is an expression with a slighly different regularization as before, but it works well, is well founded, and is easy to implement. I don't see arguments against it.}
+{This is an excellent manuscript, which I very much enjoyed reading. In particular, it includes a comprehensive overview of the literature in the field, which I find very valuable (ref. 119 should be updated). The final result is an expression with a slightly different regularization as before, but it works well, is well-founded, and is easy to implement. I don't see arguments against it.}
 \\
 \alert{We thank the reviewer for supporting publication of the present manuscript.
 }
 
 \item 
-{There are two issues that my be improved:
+{There are two issues that may be improved:
 
-The authors used the "dagger" symbol in eq. (21) and further, although they use real-valued spin-orbitals. In that case, also the matrices W are real. It seems more  consistent to either allow for complex-valued  spin-orbitals (e.g. in eq. (8)) or only use the matrix transpose.}
+The authors used the "dagger" symbol in eq. (21) and further, although they use real-valued spin-orbitals. In that case, also the matrices $W$ are real. It seems more consistent to either allow for complex-valued spin-orbitals (e.g. in eq. (8)) or only use the matrix transpose.}
 \\
 \alert{Indeed, this is inconsistent. Therefore, we have changed the definition in Eq.~(8) in order to allow for complex-valued spin-orbitals. We thank the reviewer for pointing this out.}