diff --git a/Manuscript/FarDFT.tex b/Manuscript/FarDFT.tex
index bbdde92..7650313 100644
--- a/Manuscript/FarDFT.tex
+++ b/Manuscript/FarDFT.tex
@@ -481,8 +481,7 @@ Numerical quadratures are performed with the \texttt{numgrid} library \cite{numg
 This study deals only with spin-unpolarised systems, \ie, $\n{\uparrow}{} = \n{\downarrow}{} = \n{}{}/2$ (where $\n{\uparrow}{}$ and $\n{\downarrow}{}$ are the spin-up and spin-down electron densities).
 Moreover, we restrict our study to the case of a three-state ensemble (\ie, $\nEns = 3$) where the ground state ($I=0$ with weight $1 - \ew{1} - \ew{2}$), a singly-excited state ($I=1$ with weight $\ew{1}$), as well as the lowest doubly-excited state ($I=2$ with weight $\ew{2}$) are considered.
 Assuming that the singly-excited state is lower in energy than the doubly-excited state, one should have $0 \le \ew{2} \le 1/3$ and $\ew{2} \le \ew{1} \le (1 - \ew{2})/2$ to ensure the GOK variational principle.
-If the doubly-excited state is lower in energy than the singly-excited one (which can be the case as one would notice later), then one has to swap $w_1$ and $w_2$ in the
-above inequalities.
+If the doubly-excited state is lower in energy than the singly-excited state (which can be the case as one would notice later), then one has to swap $\ew{1}$ and $\ew{2}$ in the above inequalities.
 Unless otherwise stated, we set the same weight to the two excited states (\ie, $\ew{} \equiv \ew{1} = \ew{2}$).
 In this case, the ensemble energy will be written as a single-weight quantity, $\E{}{\ew{}}$.
 The zero-weight limit (\ie, $\ew{} \equiv \ew{1} = \ew{2} = 0$), and the equiweight ensemble (\ie, $\ew{} \equiv \ew{1} = \ew{2} = 1/3$) are considered in the following.
@@ -750,16 +749,16 @@ a pragmatic way of getting weight-independent excitation energies, defined as
 	\Ex{\LIM}{(2)} & = 3 \qty[\E{}{\bw{}=(1/3,1/3)} - \E{}{\bw{}=(1/2,0)}] + \frac{1}{2} \Ex{\LIM}{(1)}, \label{eq:LIM2}
 \end{align}
 \end{subequations}
-\manu{
-$\frac{1}{2}\Ex{\LIM}{(1)}=\frac{1}{2}\left(E_1-E_0\right)$\\
-$\E{}{\bw{}=(1/3,1/3)}=\frac{1}{3}\left(E_0+E_1+E_2\right)$\\
-$\E{}{\bw{}=(1/2,0)}=\frac{1}{2}\left(E_0+E_1\right)$\\
-$3 \qty[\E{}{\bw{}=(1/3,1/3)} -
-\E{}{\bw{}=(1/2,0)}]=-\frac{1}{2}\left(E_0+E_1\right)+E_2$ 
-\\
-$3 \qty[\E{}{\bw{}=(1/3,1/3)} -
-\E{}{\bw{}=(1/2,0)}]+\frac{1}{2} \Ex{\LIM}{(1)}=E_2-E_0$
-}\\
+%\manu{
+%$\frac{1}{2}\Ex{\LIM}{(1)}=\frac{1}{2}\left(E_1-E_0\right)$\\
+%$\E{}{\bw{}=(1/3,1/3)}=\frac{1}{3}\left(E_0+E_1+E_2\right)$\\
+%$\E{}{\bw{}=(1/2,0)}=\frac{1}{2}\left(E_0+E_1\right)$\\
+%$3 \qty[\E{}{\bw{}=(1/3,1/3)} -
+%\E{}{\bw{}=(1/2,0)}]=-\frac{1}{2}\left(E_0+E_1\right)+E_2$ 
+%\\
+%$3 \qty[\E{}{\bw{}=(1/3,1/3)} -
+%\E{}{\bw{}=(1/2,0)}]+\frac{1}{2} \Ex{\LIM}{(1)}=E_2-E_0$
+%}\\
 which require three independent calculations, as well as the MOM excitation energies \cite{Gilbert_2008,Barca_2018a,Barca_2018b}
 \begin{subequations}
 \begin{align}
@@ -769,29 +768,26 @@ which require three independent calculations, as well as the MOM excitation ener
 \end{align}
 \end{subequations}
 which also require three separate calculations at a different set of ensemble weights.
-As readily seen in Eqs.~(\ref{eq:LIM1}) and (\ref{eq:LIM2}), LIM is a recursive strategy where the first excitation energy has to be determined
+For a general expression with multiple (and possibly degenerate) states, we refer the reader to Eq.~(106) of Ref.~\onlinecite{Senjean_2015}, where LIM is shown to interpolate linearly the ensemble energy between equi-ensembles.
+Note that two calculations are needed to get the first LIM excitation energy, but only one is required for each higher excitation. 
+
+As readily seen in Eqs.~\eqref{eq:LIM1} and \eqref{eq:LIM2}, LIM is a recursive strategy where the first excitation energy has to be determined
 in order to compute the second one.
 In the above equations, we
-assumed that the singly-excited state (with weight $w_1$) was lower
-in energy compared to the doubly-excited one (with weight $w_2$).
-If the ordering changes, then one should read $\E{}{\bw{}=(0,1/2)}$
-instead of $\E{}{\bw{}=(1/2,0)}$ in Eqs.~(\ref{eq:LIM1}) and (\ref{eq:LIM2}) which then correspond to the excitation energies of the
-doubly-excited state and the singly-excited one, respectively.
+assumed that the singly-excited state (with weight $\ew{1}$) is lower
+in energy than the doubly-excited state (with weight $\ew{2}$).
+If the ordering changes (like in the case of the stretched \ce{H2} molecule, see below), then one should substitute $\E{}{\bw{}=(0,1/2)}$
+by $\E{}{\bw{}=(1/2,0)}$ in Eqs.~\eqref{eq:LIM1} and \eqref{eq:LIM2} which then correspond to the excitation energies of the
+doubly-excited and singly-excited states, respectively.
 The same holds for the MOM excitation energies in 
-Eqs.~\ref{eq:MOM1} and \ref{eq:MOM2}.
-For a general expression with multiple (and possibly degenerate) 
-states, we
-refer the reader to Eq.~106 of Ref.~\onlinecite{Senjean_2015}, where
-LIM is shown to interpolate linearly the
-ensemble energy between equi-ensembles.
-Note that two calculations are needed for the first excitation energy 
-within LIM, but only one is required for each higher excitation 
-energies. By construction, for ensemble energies that are quadratic with 
-respect to the weight (which is almost always the case in this paper), the 
-first excitation energy within LIM 
-and MOM can actually be obtained in a single calculation at 
-$\ew{} = 1/4$ and 
-$\ew{} = 1/2$, respectively.
+Eqs.~\eqref{eq:MOM1} and \eqref{eq:MOM2}.
+
+%By construction, for ensemble energies that are quadratic with 
+%respect to the weight (which is almost always the case in this paper), the 
+%first excitation energy within LIM 
+%and MOM can actually be obtained in a single calculation at 
+%$\ew{} = 1/4$ and 
+%$\ew{} = 1/2$, respectively.
 
 The results gathered in Table \ref{tab:BigTab_H2} show that the GOK-DFT excitation energies obtained with the CC-SeVWN5 functional at zero weights are the most accurate with an improvement of $0.25$ eV as compared to CC-SVWN5, which is due to the ensemble derivative contribution of the eVWN5 functional.
 The CC-SeVWN5 excitation energies at equi-weights (\ie, $\ew{} = 1/3$) are less satisfactory, but still remain in good agreement with FCI.
@@ -854,7 +850,7 @@ Excitation energies (in eV) associated with the lowest double excitation of \ce{
 	\mc{6}{l}{Accurate\fnm[2]}														&		28.75	\\
 \end{tabular}
 \end{ruledtabular}
-\fnt[1]{Eqs.~(\ref{eq:LIM2}) and (\ref{eq:MOM2}) are used where the first weight corresponds to the singly-excited state.}
+\fnt[1]{Equations \eqref{eq:LIM2} and \eqref{eq:MOM2} are used where the first weight corresponds to the singly-excited state.}
 \fnt[2]{FCI/aug-mcc-pV8Z calculation from Ref.~\onlinecite{Barca_2018a}.}
 \end{table}
 %%% %%% %%% %%%
@@ -867,8 +863,7 @@ Excitation energies (in eV) associated with the lowest double excitation of \ce{
 To investigate the weight dependence of the xc functional in the strong correlation regime, we now consider the \ce{H2} molecule in a stretched geometry ($\RHH = 3.7$ bohr).
 Note that, for this particular geometry, the doubly-excited state becomes the lowest excited state with the same symmetry as the ground state.
 Although we could safely restrict ourselves to a biensemble composed by the ground state and the doubly-excited state, we eschew doing this and we still consider the same triensemble defined in Sec.~\ref{sec:H2}.
-One should just be careful when reading the equations, as they correspond to the case where the
-singly-excited state is lower in energy than the doubly-excited one.
+Nonetheless, one should just be careful when reading the equations reported above, as they correspond to the case where the singly-excited state is lower in energy than the doubly-excited state.
 We then follow the same protocol as in Sec.~\ref{sec:H2}, and considering again the aug-cc-pVTZ basis set, we design a CC-S functional for this system at $\RHH = 3.7$ bohr.
 It yields $\alpha = +0.019\,226$, $\beta = -0.017\,996$, and $\gamma = -0.022\,945$ [see Eq.~\eqref{eq:Cxw}].
 The weight dependence of $\Cx{\ew{}}$ is illustrated in Fig.~\ref{fig:Cxw} (green curve). 
@@ -927,7 +922,7 @@ Excitation energies (in eV) associated with the lowest double excitation of \ce{
 	\mc{5}{l}{Accurate\fnm[4]}															&	8.69	\\
 \end{tabular}
 \end{ruledtabular}
-\fnt[1]{Eqs.~(\ref{eq:LIM1}) and (\ref{eq:MOM1}) are used where the first weight corresponds to the doubly-excited state.}
+\fnt[1]{Equations \eqref{eq:LIM1} and \eqref{eq:MOM1} are used where the first weight corresponds to the doubly-excited state.}
 \fnt[2]{KS calculation does not converge.}
 \fnt[3]{Short-range multiconfigurational DFT/aug-cc-pVQZ calculations from Ref.~\onlinecite{Senjean_2015}.}
 \fnt[4]{FCI/aug-cc-pV5Z calculation performed with QUANTUM PACKAGE. \cite{QP2}}
@@ -990,7 +985,7 @@ Excitation energies (in hartree) associated with the lowest double excitation of
 	\mc{2}{l}{Accurate\fnm[2]}			&					&					&			&	2.126	\\
 \end{tabular}
 \end{ruledtabular}
-\fnt[1]{Eqs.~(\ref{eq:LIM2}) and (\ref{eq:MOM2}) are used where the first weight corresponds to the singly-excited state.}
+\fnt[1]{Equations \eqref{eq:LIM2} and \eqref{eq:MOM2} are used where the first weight corresponds to the singly-excited state.}
 \fnt[1]{Explicitly-correlated calculations from Ref.~\onlinecite{Burges_1995}.}
 \end{table}