diff --git a/Manuscript/FarDFT.tex b/Manuscript/FarDFT.tex
index 3627f09..4686f5f 100644
--- a/Manuscript/FarDFT.tex
+++ b/Manuscript/FarDFT.tex
@@ -380,17 +380,16 @@ where
 \label{eq:KS-energy}
 	\Eps{I}{\bw} = \sum_{p}^{\nOrb} \ON{p}{(I)} \eps{p}{\bw}
 \end{equation}
-is the energy of the $I$th KS state.
-}%%%%%% end manuf
-
+is the energy of the $I$th KS state.\\
 Equation \eqref{eq:dEdw} is our working equation for computing excitation energies from a practical point of view.
 Note that the individual KS densities
 $\n{\Det{I}{\bw}\left[n^{\bw}\right]}{}(\br{})=\sum_{p}^{\nOrb}
 \ON{p}{(I)} [\MO{p}{\bw}(\br{})]^2$ do
-not necessarily match the \textit{exact} (interacting) individual-state densities as the non-interacting KS ensemble is expected to reproduce the true interacting ensemble density $\n{}{\bw}(\br{})$ defined in Eq.~\eqref{eq:nw}, and not each individual density. 
-Nevertheless, these densities can still be extracted in principle exactly from the KS ensemble as shown by Fromager. \cite{Fromager_2020}
-
-\manuf{
+not necessarily match the \textit{exact} (interacting) individual-state
+densities $n_{\Psi_I}(\br)$ as the non-interacting KS ensemble is expected to reproduce the true interacting ensemble density $\n{}{\bw}(\br{})$ defined in Eq.~\eqref{eq:nw}, and not each individual density. 
+Nevertheless, these densities can still be extracted in principle
+exactly from the KS ensemble as shown by Fromager.
+\cite{Fromager_2020}.\\
 In the following, we will work at the (weight-dependent) LDA
 level of approximation, \ie
 \beq
@@ -402,13 +401,18 @@ level of approximation, \ie
 &\overset{\rm LDA}{\approx}&
 \left. \pdv{\e{\xc}{\bw{}}(\n{}{})}{\n{}{}} \right|_{\n{}{} = \n{}{}(\br{})} \n{}{}(\br{}) + \e{\xc}{\bw{}}(\n{}{}(\br{})).
 \eeq
-In the following, we adopt the usual decomposition, and write down the weight-dependent xc functional as
+We will also adopt the usual decomposition, and write down the weight-dependent xc functional as
 \begin{equation}
-	\e{\xc}{\ew{}}(\n{}{}) = \e{\ex}{\ew{}}(\n{}{}) + \e{\co}{\ew{}}(\n{}{}),
+	\e{\xc}{\bw{}}(\n{}{}) = \e{\ex}{\bw{}}(\n{}{}) + \e{\co}{\bw{}}(\n{}{}),
 \end{equation}
-where $\e{\ex}{\ew{}}(\n{}{})$ and $\e{\co}{\ew{}}(\n{}{})$ are the weight-dependent exchange and correlation functionals, respectively.
-}
+where $\e{\ex}{\bw{}}(\n{}{})$ and $\e{\co}{\bw{}}(\n{}{})$ are the
+weight-dependent density-functional exchange and correlation energies
+per particle, respectively.
+}%%%%%% end manuf
 
+\manu{Maybe we should say a little bit more about how we will design
+such approximations, or just say the design of these functionals will be
+presented in the following...}
 %%%%%%%%%%%%%%%%
 %%%%%%% Manu: stuff that I removed from the first version %%%%%
 \iffalse%%%%