fix prob

Response_Letter/Response_Letter.tex

@@ -26,14 +26,14 @@ We look forward to hearing from you.
 %%% REVIEWER 1 %%%
 \noindent \textbf{\large Authors' answer to Reviewer \#1}
 
-\begin{itemize}
-
-	\item
 	{The authors describe the ensemble formulation of DFT or the Gross-Oliveira-Kohn DFT (GOK-DFT) in its Kohn-Sham formulation as a viable method for excited state calculations. They provide a very clear summary of the theory, followed by the main work of the paper which is the investigation of weight-dependent LDA-type xc functionals for eDFT calculations. The provide important insights on small systems with 2 electrons and functionals that are tailored for double excitations in these systems. The manuscript makes an important contribution to the field of DFT and should be accepted for publication. However, I would be grateful if the authors modify the paper slightly to address the following minor points and corrections:}
 	\\
-	\alert{We thank the reviewer for his/her kind comments. 
+	\alert{We thank the reviewer for his/her support. 
 	His/her comments are addressed below.}
 
+
+\begin{enumerate}
+
 	\item 
 	{They should comment about what is needed (or even if it is possible) to develop a weight-dependent universal xc functional for eDFT calculations instead of application-specific functionals as presented in this paper.}
 	\\
@@ -45,9 +45,11 @@ We look forward to hearing from you.
 	\alert{This has been fixed.}
 
 	\item 
-	{The density $n(r)$ used in equation 21, 9, 10 and more doesn't represent any specific density. 
-	In the case of equation 21, we simply present the well-known Dirac-exchange density functional and, by definition of a density functional, we don't have to specify in its formulation to which density it is applied but only that it is a mathematical object applying to any density $n(r)$.
-Of course, when we will use this functional or any other one in our work we will surely apply it to the ensemble Density $n^w(r)$ and the notation will be carefully modified accordingly. }
+	{Not clear what density is used in equation 21: From the discussion that follows this appears to not be the ensemble density (which is weight dependent and I would expect it to be used here) but the density only for the ground state Slater determinant. The authors should explain why this is so. }
+	\\
+	\alert{The density $n$ used in Eq.~(21), (9), (10) can be any density and does not represent any specific density. 
+	In the case of Eq.~(21), we simply present the well-known Dirac-exchange density functional and, by definition of a density functional, does not need to specify in its formulation to which density it is applied but only that it is a mathematical object applying to any density $n(r)$.
+	Of course, when we will use this functional or any other one in our work we will surely apply it to the ensemble density $n^w(r)$ and the notation will be carefully modified accordingly. }
 	
 	\item 
 	{Change "Third, we add up correlation effects" to "Third, we include correlation effects"}	
@@ -65,7 +67,7 @@ Of course, when we will use this functional or any other one in our work we will
 	{They need to be a bit more consistent with their notation as in equation 9 and elsewhere "$n(r)$" should be the ensemble (weight-dependent) density "$n^w(r)$". 
 	I don?t believe they defined "$n(r)$" in the paper so I don?t know which density it represents. }	
 	\\
-	\alert{See our response to 6.}	
+	\alert{See our response to 4.}	
 		
 	\item 
 	{Even if it sounds trivial, they should explain why the exact xc functional should have linear dependence in the excitation energies as a function of the weight value.}	
@@ -85,7 +87,7 @@ Of course, when we will use this functional or any other one in our work we will
 	The use of an approximate weight-dependant xc-functional could reduce the ensemble energy curvature and give less weight-dependant excitation energies but it is reasonable to admit that it also could make things worse it the weight-dependency of the functional is poorly chosen.
 	That is why the construction of "good" weight-dependant xc-functionals is a really challenging matter in eDFT.}	
 	
-\end{itemize}
+\end{enumerate}
 
 \end{letter}
 \end{document}