Manu: done with my revisions. T2, you neeed to check some of my responses.

Response_Letter/Response_Letter.tex

@@ -82,10 +82,10 @@ relevance of these
 expansions by considering weak deviations from the uniform density
 regime. Indeed, in this case, eLDA is a reasonable approximation and the
 difference in density between the ensemble and the individual states is
-weak. Let us finally stress that our embedding strategy does not rely on these
+small. Let us finally stress that our embedding strategy does not rely on these
 Taylor expansions. They are exclusively used for analysis purposes in
-this work. As written explicitly in the revised manuscript, it just
-gives more insight into eLDA.}
+this work. As written explicitly in the revised manuscript, they just
+give more insight into eLDA.}
 
 	\item 
 	{Page 5: Though the ringium model is developed elsewhere in the literature in great detail, a diagram for readers not as familiar with it would be a kindness. }
@@ -138,7 +138,16 @@ gives more insight into eLDA.}
 	{Page 7: Does strong correlation always result in non-linear ghosts uncorrected by the GIC-eLDA, or is it particularly difficult or changed by the embedding scheme somehow? 
 	Is this result influenced by the state mixing shown by FCI in Figure 3's discussion? }
 	\\
-	\alert{According to our observation, yes.}
+	\alert{As now discussed in more detail in the revised manuscript,
+the remaining non-linear ghosts originate from the weight dependence
+(i.e. the dependence on the state mixing) of
+the individual correlation energies, which is itself connected to the eLDA correlation
+functional. This can be understood from the general ensemble correlation
+energy per particle expression in Eq. (41) and the above-mentioned
+Taylor expansions, without referring to our
+embedding approach. In summary, the deviation from linearity of the
+ensemble GIC-eLDA energy is a
+general feature of ensemble LDA-type functionals.}
 
 	\item 
 	{Page 7: In the penultimate paragraph on this page, the discussion of Eqns 47 and 49 and the variation in the ensemble weights touches on one of the more subtle results of the GIC-eLDA, in my opinion, so it would be best to more explicitly describe this and its tie to the aforementioned equations.}
@@ -190,13 +199,24 @@ you agree?}
 	\item 
 	{Page 8: If the authors have evidence of behavior between $w=(0,0)$ and the equiensemble, instead of just these endpoints, that would be interesting to mention for the eDFT crowd. }
 	\\
-	\alert{Nothing to mention here.}
+	\alert{Actually, we were probably not clear enough about what we
+plotted in Figs. 1 and 2 of the original manuscript, but it was exactly
+the continuous variation of (individual or ensemble) energies from
+$w=(0,0)$ up to the equiensemble case $w=(1/3,1/3)$. For convenience,
+the path was just split in two parts: a first one where $w_2=0$ and
+$0\leq w_1\leq 1/3$, and a second one where $w_1=1/3$ and $0\leq w_2\leq
+1/3$. For clarity, this is now mentioned explicitly in the revised
+manuscrit before commenting on the plots.}\manu{OK?}
 
 	\item 
 	{Are there similar issues with combining HF exchange with LDA C as seen in the ground-state? 
 	If not, why not? }
 	\\
-	\alert{Yes, similar issues appear for excited states.}
+	\alert{Yes, as readily seen from the data provided in the
+supplemental material, similar issues appear for excited states.
+Interestingly, increasing the ensemble weights (which of course cannot
+be done in conventional ground-state DFT) seems to reduce
+errors}\manu{We need to check the tables in the SI}
 
 	\item 
 	{Figure 3 discussion: Will eLDA always overestimate double excitations? 
@@ -218,7 +238,12 @@ you agree?}
 	\alert{As mentioned in the original manuscript (see Results and Discussion section), we believe that it might be a consequence of how we constructed the eLDA functional, as the weight dependence of the eLDA functional is based on a two-electron uniform electron gas.
 	We do not think this is due to the uniformity of its density, though.
 	Incorporating a $N$-dependence in the functional through the curvature of the Fermi hole might be valuable in this respect. 
-	This is left for future work.}
+	This is left for future work.}\manu{Could we argue that the
+difference in density between the ground and the excited states is
+not that substantial? Or the deviations cancel out after integration? The
+question does not seem to be focused on the functional itself but more
+on the evaluation of this term for a system (boxium) that is not
+uniform. What do you think?}
 
 	\item 
 	{Figure 6: Do the ground-state and equiensemble results for doubles converge as $N$ goes to infinity?}