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\begin{letter}%
{To the Editors of the Journal of Computational and Theoretical Chemistry,}

\opening{Dear Editors,}

\justifying
Please find attached a revised version of the manuscript entitled 
\begin{quote}
  \textit{``A similarity renormalization group approach to Green’s function methods''}.
\end{quote}
      
We thank the reviewers for their constructive comments.
Our detailed responses to their comments can be found below.
For convenience, changes are highlighted in red in the revised version of the manuscript. 

We look forward to hearing from you.

\closing{Sincerely, the authors.}

\newpage

%%% REVIEWER 1 %%%
\noindent \textbf{\large Authors' answer to Reviewer \#1}

\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.}
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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?}
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\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?}
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\alert{}

\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 $H^{\text{od}}(s)^2$.}
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\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.}
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\end{itemize}

%%% REVIEWER 2 %%%
\noindent \textbf{\large Authors' answer to Reviewer \#2}

\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.}
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\alert{We thank the reviewer for supporting publication of the present manuscript.
}

\item 
{There are two issues that my be improved:
1) 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.}
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\item 
{2) I find it somewhat disturbing to see positive and negative electron affinities. The authors may wish to comment briefly on the meaning of the sign.}
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\end{itemize}

%%%  %%%
\noindent \textbf{\large Additional minor changes}

\end{letter}
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