answer to reviewer 2 and to one easy comment of reviewer 1

Manuscript/SRGGW.tex

@@ -207,7 +207,7 @@ with
 \end{subequations}
 and where
 \begin{equation}
-	\braket{pq}{rs} = \iint \frac{\SO{p}(\bx_1) \SO{q}(\bx_2)\SO{r}(\bx_1) \SO{s}(\bx_2)  }{\abs{\br_1 - \br_2}} d\bx_1 d\bx_2
+	\braket{pq}{rs} = \iint \frac{\textcolor{red}{\SO{p}^*(\bx_1) \SO{q}^*(\bx_2)}\SO{r}(\bx_1) \SO{s}(\bx_2)  }{\abs{\br_1 - \br_2}} d\bx_1 d\bx_2
 \end{equation}
 are bare two-electron integrals in the spin-orbital basis.
 
@@ -312,7 +312,7 @@ In this work, we consider Wegner's canonical generator \cite{Wegner_1994}
 which satisfies the following condition \cite{Kehrein_2006}
 \begin{equation}
   \label{eq:derivative_trace}
-  \dv{s}\text{Tr}\left[ \bH^\text{od}(s)^2 \right] \leq 0.
+  \textcolor{red}{\dv{s}\text{Tr}\left[  \bH^\text{od}(s)^\dagger \bH^\text{od}(s) \right] \leq 0.}
 \end{equation}
 This implies that the matrix elements of the off-diagonal part decrease in a monotonic way throughout the transformation.
 Moreover, the coupling coefficients associated with the highest-energy determinants are removed first as we shall evidence in the perturbative analysis below.

Response_Letter/Response_Letter.tex

@@ -51,7 +51,7 @@ We look forward to hearing from you.
 \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 $H^{\text{od}}(s)^2$.}
 \\
-\alert{}
+\alert{Indeed, the expression suggested by the reviewer would be more precise and 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.}
@@ -73,19 +73,27 @@ We look forward to hearing from you.
 
 \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.}
 \\
-\alert{}
+\alert{Indeed, this is not consistent so we changed the definition in Eq. (8) in order to allow for complex-valued spin-orbitals. We thank the reviewer for pointing this out.}
 
 \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.}
 \\
-\alert{}
+\alert{We think that it is already discussed at the very end of Section VI, see the following paragraph:}
+  
+  \textcolor{red}{\textit{''Note that a positive EA indicates a bounded anion state, which can be accurately described by the methods considered in this study. However, a negative EA suggests a resonance state, which is beyond the scope of the methods used in this study, including the $\Delta$CCSD(T) reference. As such, it is not advisable to assign a physical interpretation to these values. Nonetheless, it is possible to compare $GW$-based and $\Delta$CCSD(T) values in such cases, provided that the comparison is limited to a given basis set.''}}
+
 
 \end{itemize}
 
 %%%  %%%
 \noindent \textbf{\large Additional minor changes}
 
+\begin{itemize}
+\item References suggested by Arn\"o.
+\end{itemize}
+
 \end{letter}
 \end{document}