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Manuscript/sfBSE-SI.tex

@@ -507,6 +507,17 @@ $4.$ & $0 .3189$ & $0 .8867$ & $0 .3328$ & $0 .2172$ & $0 .9453$ & $0 \
 \end{figure}
 %%% %%% %%% 
 
+%%% FIG 3 %%%
+\begin{figure}
+	\includegraphics[width=0.5\linewidth]{H2_BSE_RHF}
+\caption{
+	Excitation energies with respect to the $\text{X}\,{}^1 \Sigma_g^+$ ground state of the $\text{B}\,{}^1\Sigma_u^+$ (red), $\text{E}\,{}^1\Sigma_g^+$ (black), and $\text{F}\,{}^1\Sigma_g^+$ (blue) states of \ce{H2} obtained with the cc-pVQZ basis at the (SF-)BSE level of theory.  
+	The reference EOM-CCSD excitation energies are represented as solid lines, while the results obtained with and without spin-flip are represented as dashed and dotted lines, respectively.
+	In this case, the spin-conserved calculations have been performed with a restricted reference while the spin-flip calculations have been performed with an unrestricted reference.
+	\label{fig:H2_RHF}}
+\end{figure}
+%%% %%% %%% 
+
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 \bibliography{sfBSE}
 %%%%%%%%%%%%%%%%%%%%%%%%

Manuscript/sfBSE.tex

@@ -890,7 +890,7 @@ A similar graph comparing (SF-)dBSE and EOM-CCSD excitation energies can be foun
 This unfortunate feature is due to the appearance of the symmetry-broken UHF solution and the lack of self-consistent in {\GOWO}.	
 Indeed, $R = 1.2~\AA$ corresponds to the location of the well-known Coulson-Fischer point. \cite{Coulson_1949}
 Note that, as mentioned earlier, all the calculations are performed with a UHF reference even the ones based on a closed-shell singlet reference.
-If one relies solely on the restricted HF solution, this kink disappears and one obtains smooth potential energy curves.} 
+If one relies solely on the restricted HF solution, this kink disappears and one obtains smooth potential energy curves (see {\SI}).} 
 	
 The right side of Fig.~\ref{fig:H2} shows the amount of spin contamination as a function of the bond length for SF-CIS (top), SF-TD-BH\&HLYP (center), and SF-BSE (bottom).
 Overall, one can see that $\expval{\hS^2}$ behaves similarly for SF-CIS and SF-BSE with a small spin contamination of the $\text{B}\,{}^1\Sigma_u^+$ at short bond length. In contrast, the $\text{B}$ state is much more spin contaminated at the SF-TD-BH\&HLYP level.

Response_Letter/Response_Letter.tex

@@ -66,7 +66,8 @@ I recommend this manuscript for publication after the minor points addressed:}
 	\alert{The kink in the SF-BSE@$G_0W_0$ and SF-dBSE/$G_0W_0$ curves for \ce{H2} are due to the appearance of the symmetry-broken UHF solution.
 	Indeed, $R = 1.2~\AA$ corresponds to the location of the well-known Coulson-Fischer point.
 	Note that, as mentioned in our manuscript, all the calculations are performed with a UHF reference (even the ones based on a closed-shell singlet reference).
-	Of course, if one relies solely on the RHF solution, this kink disappears (see figure below). it would be, nonetheless, inconsistent with the rest of the paper.
+	Of course, if one relies solely on the RHF solution, this kink disappears as illustrated by the figure below which has been also included in the Supporting Information. 
+	However, it would be inconsistent with the rest of the paper.
 	The appearance of this kink is now discussed in the revised version of the manuscript.
 	At the ev$GW$ level, this kink would certainly still exist as one does not self-consistently optimised the orbitals in this case.
 	However, it would likely disappear at the qs$GW$ level but it remains to be confirmed (work is currently being done in this direction).