diff --git a/Manuscript/eDFT.tex b/Manuscript/eDFT.tex
index 91ee865..524228d 100644
--- a/Manuscript/eDFT.tex
+++ b/Manuscript/eDFT.tex
@@ -4,6 +4,7 @@
 \usepackage[utf8]{inputenc}
 \usepackage[T1]{fontenc}
 \usepackage{txfonts}
+\usepackage{mathrsfs}
 
 \usepackage[
 	colorlinks=true,
@@ -769,7 +770,7 @@ What do you think?}
 Combining Eq.~\eqref{eq:exact_ind_ener_rdm} with Eq.~\eqref{eq:eLDA_corr_fun} leads to our final energy level expression within KS-eLDA: 
 \beq\label{eq:EI-eLDA}
 \begin{split}
-	\E{\titou{eLDA}}{(I)} 
+	\E{{eLDA}}{(I)} 
 	& = 
         \E{HF}{(I)}
 	\\
@@ -781,17 +782,31 @@ Combining Eq.~\eqref{eq:exact_ind_ener_rdm} with Eq.~\eqref{eq:eLDA_corr_fun} le
 	\left. \pdv{\e{c}{{\bw}}(\n{}{})}{\n{}{}} \right|_{\n{}{} = \n{\bGam{\bw}}{}(\br{})} d\br{}
 	\\
 	& + \int \sum_{K>0} \qty(\delta_{IK} - \ew{K} ) \n{\bGam{\bw}}{}(\br{})
-	\left. \pdv{\e{c}{\bw}(\n{}{})}{\ew{K}} \right|_{\n{}{}=\n{\bGam{\bw}}{}(\br{})} d\br{}.
+	\left. \pdv{\e{c}{\bw}(\n{}{})}{\ew{K}} \right|_{\n{}{}=\n{\bGam{\bw}}{}(\br{})} d\br{},
 \end{split}
 \eeq
-\titou{T2: I think we should specify what those terms are physically... Maybe earlier in the manuscript?}
 where
 \beq
 \E{HF}{(I)}=\Tr[\bGam{(I)} \bh] + \frac{1}{2} \Tr[\bGam{(I)} \bG \bGam{(I)}]
 \eeq   
-is the analog for ground {\it and} excited states of the HF energy. 
-Let us stress that, to the best of our knowledge, eLDA is the first
-density-functional approximation that incorporates weight
+is the analog for ground and excited states (within an ensemble) of the HF energy.  
+If, for analysis purposes, we Taylor expand the density-functional
+correlation contributions
+around the $I$th KS state density
+$\n{\bGam{(I)}}{}(\br{})$, the sum of 
+the second and third terms on the right-hand side
+of Eq.~\eqref{eq:EI-eLDA} can be simplified as follows through first order in
+$\n{\bGam{\bw}}{}(\br{})-\n{\bGam{(I)}}{}(\br{})$: 
+\beq
+\int \e{c}{\bw}(\n{\bGam{(I)}}{}(\br{})) \n{\bGam{(I)}}{}(\br{}) d\br{}
++\mathcal{O}\left([\n{\bGam{\bw}}{}-\n{\bGam{(I)}}{}]^2\right),
+\eeq
+and it can therefore be identified as 
+an individual-density-functional correlation energy where the density-functional
+correlation energy per particle is approximated by the ensemble one for
+all the states within the ensemble. 
+Let us finally stress that, to the best of our knowledge, eLDA is the first
+density-functional approximation that incorporates ensemble weight
 dependencies explicitly, thus allowing for the description of derivative
 discontinuities [see Eq.~\eqref{eq:excited_ener_level_gs_lim} and the
 comment that follows] {\it via} the last term on the right-hand side