diff --git a/Manuscript/FarDFT.tex b/Manuscript/FarDFT.tex
index af19c0e..6d43bc5 100644
--- a/Manuscript/FarDFT.tex
+++ b/Manuscript/FarDFT.tex
@@ -49,6 +49,7 @@
 \newcommand{\F}[2]{F_{#1}^{#2}}
 \newcommand{\Ts}[1]{T_\text{s}^{#1}}
 \newcommand{\eps}[2]{\varepsilon_{#1}^{#2}}
+\newcommand{\Eps}[2]{\mathcal{E}_{#1}^{#2}}
 \newcommand{\e}[2]{\epsilon_{#1}^{#2}}
 \newcommand{\kin}[2]{t_\text{#1}^{#2}}
 \newcommand{\E}[2]{E_{#1}^{#2}}
@@ -91,11 +92,12 @@
 \newcommand{\hGamma}[2]{\Hat{\Gamma}_{#1}^{#2}}
 \newcommand{\eHc}[1]{h_{#1}}
 \newcommand{\eF}[2]{F_{#1}^{#2}}
+\newcommand{\ON}[2]{f_{#1}^{#2}}
 
 % Numbers
 \newcommand{\Nens}{M}
 \newcommand{\Nel}{N}
-\newcommand{\Nbas}{K}
+\newcommand{\Norb}{K}
 
 % Ao and MO basis
 \newcommand{\MO}[2]{\phi_{#1}^{#2}}
@@ -228,13 +230,13 @@ From the GOK-DFT ensemble energy expression in Eq.~\eqref{eq:Ew-GOK}, we obtain
 	\label{eq:dEdw}
 	\pdv{\E{}{\bw}}{\ew{I}} 
 	= \E{}{(I)} - \E{}{(0)} 
-	= \eps{I}{\bw} - \eps{0}{\bw} + \left. \pdv{\E{\xc}{\bw}[\n{}{}]}{\ew{I}} \right|_{\n{}{} = \n{}{\bw}},
+	= \Eps{I}{\bw} - \Eps{0}{\bw} + \left. \pdv{\E{\xc}{\bw}[\n{}{}]}{\ew{I}} \right|_{\n{}{} = \n{}{\bw}},
 \end{equation}
-\titou{where $\eps{I}{\bw}$ is the $I$th KS orbital energy (T2: wrong!)} given by the ensemble KS equation
+where $\Eps{I}{\bw} = \sum_{p}^{\Norb} \ON{p}{(I)} \eps{p}{\bw}$, $\eps{p}{\bw}$ is the $p$th KS orbital energy given by the ensemble KS equation
 \begin{equation}
 	\qty( -\frac{\nabla^2}{2}  + \vext(\br{}) + \fdv{\E{\Hxc}{\bw}[\n{}{}]}{\n{}{}(\br{})}) \MO{p}{\bw}(\br{}) = \eps{p}{\bw} \MO{p}{\bw}(\br{}),
 \end{equation}
-(where $\MO{p}{\bw}(\br{})$ is a KS orbital) and $\n{}{\bw} = \sum_{I=0}^{\Nens-1} \ew{I} \n{}{(I)}$ is the ensemble density.
+(where $\MO{p}{\bw}(\br{})$ is a KS orbital), $\ON{p}{(I)}$ its occupancy for the state $I$, and $\n{}{\bw} = \sum_{I=0}^{\Nens-1} \ew{I} \n{}{(I)}$ is the ensemble density.
 Equation \eqref{eq:dEdw} is our working equation for computing excitation energies.
 
 %%%%%%%%%%%%%%%%%%
@@ -476,8 +478,8 @@ As concluding remarks, we would like to say that, what we have done is awesome.
 %%% ACKNOWLEDGEMENTS %%%
 %%%%%%%%%%%%%%%%%%%%%%%%
 \begin{acknowledgements}
-PFL acknowledges funding from the \textit{Centre National de la Recherche Scientifique}.
 CM thanks the \textit{Universit\'e Paul Sabatier} (Toulouse, France) for a PhD scholarship.
+PFL acknowledges funding from the \textit{Centre National de la Recherche Scientifique}.
 \end{acknowledgements}
 
 %%%%%%%%%%%%%%%%%%%%