Manu: done with my revisions.

Response_Letter/Response_Letter.tex

@@ -186,12 +186,11 @@ that the deviation from linearity of the ensemble energy would be zero.}
 	\\
 	\alert{The legend of Fig.~2 was incorrect (the curves were mislabeled), but this has now been corrected.
 	In the corrected Fig.~2 (which is now Fig.~4 in the revised
-manuscript), the crossover point occurs for two different states that
-belong to two different ensembles. In other words, this point is not
+manuscript), the crossover point occurs for two different states in  
+two different ensembles. In other words, this point is not
 interesting anymore. The discussion of this Figure has become much more fluid:
 	when the weight of a state increases, this state is stabilized
-while the two others increase in energy (as it should). \manu{Well, the
-energy of the first excited state still decreases when $w_2$ increases}
+while the two others increase in energy (as it should). 
 	The discussion regarding this figure has been modified accordingly.}
 %	\alert{It is clear from our derivations that the individual
 %correlation energies should vary with both the density {\it
@@ -221,10 +220,20 @@ manuscrit before commenting on the plots.}
 	If not, why not? }
 	\\
 	\alert{Yes, as readily seen from the data provided in the
-supplemental material, similar issues appear for excited states.
+supplemental material, similar issues appear for excited states.\manu{I
+would remove your sentence and be more optimistic (see what follows). Do
+you agree?}\\
 Interestingly, increasing the ensemble weights (which of course cannot
-be done in conventional ground-state DFT) seems to reduce
-errors}
+be done in conventional ground-state DFT calculations) leads to a
+significant improvement of the ground-state energy while either
+improving or not deteriorating too much the excited-state energies, at
+least in the weak correlation regime. The main reason is the
+destabilization of the ground state that occurs when increasing the
+weights assigned to the excited states. This major difference between
+practical 
+conventional DFT (where the correlation energy would be overestimated)
+and GOK-DFT calculations is a promising result that is
+now highlighted in the revised manuscript.}
 %\manu{We need to check the tables in the SI}
 
 	\item