diff --git a/FarDFT.nb b/FarDFT.nb
index 7cabac4..321ed4e 100644
--- a/FarDFT.nb
+++ b/FarDFT.nb
@@ -10,10 +10,10 @@
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diff --git a/Manuscript/Cx_H2.pdf b/Manuscript/Cx_H2.pdf
index f3ccb0b..0b6b1b0 100644
Binary files a/Manuscript/Cx_H2.pdf and b/Manuscript/Cx_H2.pdf differ
diff --git a/Manuscript/Ew_H2.pdf b/Manuscript/Ew_H2.pdf
index 25b6255..62c8f10 100644
Binary files a/Manuscript/Ew_H2.pdf and b/Manuscript/Ew_H2.pdf differ
diff --git a/Manuscript/FarDFT.bib b/Manuscript/FarDFT.bib
index 92d5bab..ccd21bc 100644
--- a/Manuscript/FarDFT.bib
+++ b/Manuscript/FarDFT.bib
@@ -1,13 +1,76 @@
 %% This BibTeX bibliography file was created using BibDesk.
 %% http://bibdesk.sourceforge.net/
 
-%% Created for Pierre-Francois Loos at 2020-04-08 14:13:22 +0200 
+%% Created for Pierre-Francois Loos at 2020-04-09 10:05:15 +0200 
 
 
 %% Saved with string encoding Unicode (UTF-8) 
 
 
 
+@article{Woon_1994,
+	Author = {Woon, D. and Dunning, T. H.},
+	Date-Added = {2020-04-09 09:59:19 +0200},
+	Date-Modified = {2020-04-09 10:00:56 +0200},
+	Doi = {10.1063/1.466439},
+	Journal = {J. Chem. Phys.},
+	Pages = {2975--2988},
+	Title = {Gaussian basis sets for use in correlated molecular calculations. IV. Calculation of static electrical response properties},
+	Volume = {100},
+	Year = {1994},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.466439}}
+
+@article{Kendall_1992,
+	Author = {Kendall, R. A. and Dunning, T. H. and Harisson, R. J.},
+	Date-Added = {2020-04-09 09:58:17 +0200},
+	Date-Modified = {2020-04-09 10:01:10 +0200},
+	Doi = {10.1063/1.462569},
+	Journal = {J. Chem. Phys.},
+	Pages = {6796--6806},
+	Title = {Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions},
+	Volume = {96},
+	Year = {1992},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.462569}}
+
+@article{Dunning_1989,
+	Author = {T. H. {Dunning, Jr.}},
+	Date-Added = {2020-04-09 09:55:22 +0200},
+	Date-Modified = {2020-04-09 09:55:22 +0200},
+	Doi = {10.1063/1.456153},
+	Journal = {J. Chem. Phys.},
+	Pages = {1007},
+	Title = {Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen},
+	Volume = {90},
+	Year = {1989},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.456153}}
+
+@misc{numgrid,
+	Author = {R. Bast},
+	Date-Added = {2020-04-09 09:23:10 +0200},
+	Date-Modified = {2020-04-09 09:23:10 +0200},
+	Doi = {10.5281/zenodo.2659208},
+	Month = {May},
+	Note = {\url{https://github.com/dftlibs/numgrid}},
+	Publisher = {Zenodo},
+	Title = {numgrid: numerical integration grid for molecules},
+	Url = {https://github.com/dftlibs/numgrid},
+	Year = {2019},
+	Bdsk-Url-1 = {https://github.com/LCPQ/quantum_package},
+	Bdsk-Url-2 = {http://dx.doi.org/10.5281/zenodo.200970}}
+
+@misc{QuAcK,
+	Author = {P. F. Loos},
+	Date-Added = {2020-04-09 09:19:41 +0200},
+	Date-Modified = {2020-04-09 09:33:32 +0200},
+	Doi = {10.5281/zenodo.3745928},
+	Note = {\url{https://github.com/pfloos/QuAcK}},
+	Publisher = {Zenodo},
+	Title = {{{QuAcK: a software for emerging quantum electronic structure methods}}},
+	Url = {https://github.com/pfloos/QuAcK},
+	Year = {2019},
+	Bdsk-Url-1 = {https://github.com/LCPQ/quantum_package},
+	Bdsk-Url-2 = {http://dx.doi.org/10.5281/zenodo.200970}}
+
 @article{Fromager_2020,
 	Archiveprefix = {arXiv},
 	Author = {Emmanuel Fromager},
@@ -27,7 +90,8 @@
 	Pages = {L5},
 	Title = {Autoionizing States of the Hydrogen Molecule.},
 	Volume = {7},
-	Year = {1974}}
+	Year = {1974},
+	Bdsk-Url-1 = {https://doi.org/10.1088/0022-3700/7/1/002}}
 
 @article{Mielke_2005,
 	Author = {S. L. Mielke and D. W. Schwenke and K. A. Peterson},
@@ -91,13 +155,6 @@
 	Pages = {arXiv:2003.05553},
 	Title = {A weight-dependent local correlation density-functional approximation for ensembles},
 	Year = {submitted}}
-	
-@article{Fromager_2020,
-  title={Individual correlations in ensemble density-functional theory: State-driven/density-driven decomposition without additional Kohn-Sham systems},
-  author={Fromager, Emmanuel},
-  journal={arXiv:2001.08605},
-  year={submitted},
-  url={https://arxiv.org/abs/2001.08605}}
 
 @article{Lindh_2001,
 	Author = {R. Lindh and P.-A. Malmqvist and L. Gagliardi},
@@ -376,7 +433,8 @@
 @article{Perdew_1983,
 	Author = {J. P. Perdew and M. Levy},
 	Date-Added = {2019-09-05 12:04:19 +0200},
-	Date-Modified = {2019-09-05 12:13:34 +0200},
+	Date-Modified = {2020-04-09 10:05:15 +0200},
+	Doi = {10.1103/PhysRevLett.51.1884},
 	Journal = {Phys. Rev. Lett.},
 	Pages = {1884},
 	Title = {Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities},
diff --git a/Manuscript/FarDFT.tex b/Manuscript/FarDFT.tex
index 9e69b65..ca71a03 100644
--- a/Manuscript/FarDFT.tex
+++ b/Manuscript/FarDFT.tex
@@ -183,12 +183,12 @@ However, Loos and Gill have recently shown that there exists other UEGs which co
 Electrons restricted to remain on the surface of a $\cD$-sphere (where $\cD$ is the dimensionality of the surface of the sphere) are an example of finite UEGs (FUEGs). \cite{Loos_2011b}
 In particular, we combine these FUEGs with the usual infinite UEG (IUEG) to construct a weigh-dependent LDA correlation functional for ensembles, which is specifically designed to compute double excitations within GOK-DFT, and automatically incorporates the infamous derivative discontinuity contribution to the excitation energies through its explicit ensemble weight dependence. \cite{Levy_1995, Perdew_1983}
 
-%The paper is organised as follows.
-%In Sec.~\ref{sec:theo}, the theory behind GOK-DFT is presented.
-%Section \ref{sec:func} provides details about the construction of the weight-dependent xc LDA functional.
-%The results of our calculations for the prototypical \ce{H2} molecule are reported and discussed in Sec.~\ref{sec:resdis}. 
-%Finally, we draw our conclusions in Sec.~\ref{sec:ccl}. 
-%Unless otherwise stated, atomic units are used throughout.
+The paper is organised as follows.
+In Sec.~\ref{sec:theo}, the theory behind GOK-DFT is presented.
+Section \ref{sec:compdet} provides the computational details.
+The results of our calculations for two-electron systems are reported and discussed in Secs.~\ref{sec:res_H2} and \ref{sec:res_He}. 
+Finally, we draw our conclusions in Sec.~\ref{sec:ccl}. 
+Unless otherwise stated, atomic units are used throughout.
 
 %%%%%%%%%%%%%%%%%%%%
 %%% THEORY %%%
@@ -248,7 +248,7 @@ is the density matrix operator, $\lbrace \Det{I}{\bw} \rbrace_{0 \le I \le \nEns
 \end{split}
 \end{equation}
 is the ensemble Hartree-exchange-correlation (Hxc) functional.
-Note that the weight-independent Hartree functional $\E{\Ha}{}[\n{}{}]$ causes the infamous ghost-interaction error (GIE) \cite{Gidopoulos_2002, Pastorczak_2014, Alam_2016, Alam_2017, Gould_2017} in eDFT, which is supposed to be cancelled by the weight-dependent xc functional $\E{\xc}{\bw}[\n{}{}]$.
+Note that the weight-independent Hartree functional $\E{\Ha}{}[\n{}{}]$ causes the infamous ghost-interaction error \cite{Gidopoulos_2002, Pastorczak_2014, Alam_2016, Alam_2017, Gould_2017} in eDFT, which is supposed to be cancelled by the weight-dependent xc functional $\E{\xc}{\bw}[\n{}{}]$.
 
 From the GOK-DFT ensemble energy expression in Eq.~\eqref{eq:Ew-GOK}, we obtain \cite{Gross_1988b,Deur_2019}
 \begin{equation}
@@ -312,15 +312,15 @@ where $\e{\ex}{\ew{}}(\n{}{})$ and $\e{\co}{\ew{}}(\n{}{})$ are the weight-depen
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Computational details}
 \label{sec:compdet}
-The self-consistent GOK-DFT calculations have been performed with the \texttt{QuAcK} software, freely available on \texttt{github}, where the present functional has been implemented. 
+The self-consistent GOK-DFT calculations have been performed in a restricted formalism with the \texttt{QuAcK} software, \cite{QuAcK} which is freely available on \texttt{github}, and where the present weight-dependent functionals have been implemented. 
 For more details about the self-consistent implementation of GOK-DFT, we refer the interested reader to Ref.~\onlinecite{Loos_2020} where additional technical details can be found.
-For all calculations, we use a restricted formalism and the aug-cc-pVXZ (X = D, T, and Q) Dunning's family of atomic basis sets.
-Numerical quadratures are performed with the \texttt{numgrid} library using 194 angular points (Lebedev grid) and a radial precision of $10^{-6}$. \cite{Becke_1988,Lindh_2001}
+For all calculations, we use the aug-cc-pVXZ (X = D, T, Q, and 5) Dunning family of atomic basis sets. \cite{Dunning_1989,Kendall_1992,Woon_1994}
+Numerical quadratures are performed with the \texttt{numgrid} library \cite{numgrid} using 194 angular points (Lebedev grid) and a radial precision of $10^{-6}$. \cite{Becke_1988,Lindh_2001}
 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 two-state ensemble (\ie, $\nEns = 2$) where both the ground state ($I=0$ with weight $1 - \ew{}$) and the first doubly-excited state ($I=1$ with weight $\ew{}$) are considered. 
-Although we should have $0 \le \ew{} \le 1/2$ to ensure the GOK variational principle, we will sometimes ``violate'' this variational constraint.
+Although one should have $0 \le \ew{} \le 1/2$ to ensure the GOK variational principle, we will sometimes ``violate'' this variational constraint.
 Indeed, the limit $\ew{} = 1$ is of particular interest as it corresponds to a genuine saddle point of the KS equations, and match perfectly the results obtained with the maximum overlap method (MOM) developed by Gilbert, Gill and coworkers. \cite{Gilbert_2008,Barca_2018a,Barca_2018b}
-Moreover, the limits $\ew{} = 0$ and $\ew{} = 1$ are the only two weights for which there is no ghost-interaction error.
+\titou{Moreover, the limits $\ew{} = 0$ and $\ew{} = 1$ are the only two weights for which there is no ghost-interaction error.}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Hydrogen molecule}
@@ -340,9 +340,9 @@ First, we compute the ensemble energy of the \ce{H2} molecule (at equilibrium bo
 In the case of \ce{H2}, the ensemble is composed by the $1\sigma_g^2$ ground state and the lowest doubly-excited state of configuration $1\sigma_u^2$, which has an autoionising resonance nature. \cite{Bottcher_1974}
 The ensemble energy $\E{}{\ew{}}$ is depicted in Fig.~\ref{fig:Ew_H2} as a function of the weight $0 \le \ew{} \le 1$.
 Because this exchange functional does not depend on the ensemble weight, there is no contribution from the ensemble derivative term [last term in Eq.~\eqref{eq:dEdw}].
-As anticipated, $\E{}{\ew{}}$ is far from being linear, which means that the excitation energy obtained via the derivative of the local energy varies significantly with the weight of the double excitation (see Fig.~\ref{fig:Om_H2}).
+As anticipated, $\E{}{\ew{}}$ is far from being linear, which means that the excitation energy obtained via the derivative of the ensemble energy varies significantly with the weight of the double excitation (see Fig.~\ref{fig:Om_H2}).
 Taking as a reference the full configuration interaction (FCI) value of $28.75$ eV obtained with the aug-mcc-pV8Z basis set, \cite{Barca_2018a} one can see that the excitation energy varies by more than $8$ eV from $\ew{} = 0$ to $1/2$.
-Note that the exact xc correlation ensemble functional would yield a perfectly linear energy and, hence, the same value of the excitation energy independently of $\ew{}$.
+Note that the exact xc ensemble functional would yield a perfectly linear energy and, hence, the same value of the excitation energy independently of $\ew{}$.
 
 \begin{figure}
 	\includegraphics[width=\linewidth]{Ew_H2}
@@ -365,8 +365,8 @@ Note that the exact xc correlation ensemble functional would yield a perfectly l
 \subsection{Weight-dependent exchange functional}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-Second, in order to remove this spurious curvature of the ensemble energy (which is mostly due to the ghost-interaction error, but not only), one can easily reverse-engineer (for this particular system and basis set) a local exchange functional to make $\E{}{\ew{}}$ as linear as possible for $0 \le \ew{} \le 1$.
-Doing so, we have found that the present weight-dependent exchange functional (denoted as GIC-S in the following as its main purpose is to correct for the ghost-interaction error), represented in Fig.~\ref{fig:Cx_H2},
+Second, in order to remove this spurious curvature of the ensemble energy (which is mostly due to the ghost-interaction error, but not only), one can easily reverse-engineer (for this particular system, geometry, and basis set) a local exchange functional to make $\E{}{\ew{}}$ as linear as possible for $0 \le \ew{} \le 1$.
+Doing so, we have found that the present weight-dependent exchange functional (denoted as GIC-S in the following as its main purpose is to correct for the ghost-interaction error)
 \begin{equation}
 	\e{\ex}{\ew{},\text{GIC-S}}(\n{}{}) = \Cx{\ew{}} \n{}{1/3},
 \end{equation}
@@ -379,22 +379,23 @@ and
 \begin{subequations}
 \begin{align}
 	\alpha & = + 0.575\,178,
-	\\
+	&
 	\beta & = - 0.021\,108,
-	\\
+	&
 	\gamma & = - 0.367\,189,
 \end{align}
 \end{subequations}
 makes the ensemble almost perfectly linear (see Fig.~\ref{fig:Ew_H2}), and the excitation energy much more stable and closer to the FCI reference (see Fig.~\ref{fig:Om_H2}).
-As readily seen from Eq.~\eqref{eq:Cxw}, $\Cx{\ew{}}$ reduces to $\Cx{}$ for $\ew{} = 0$.
-Note that we are not only using data from $\ew{} = 0$ to $\ew{} = 1/2$, but we also consider ensemble energies for $1/2 < \ew{} \le 1$, which is strictly forbidden by the GOK variational principle. \cite{Gross_1988a} 
-However, it is important to ensure that the weight-dependent functional does not affect the two ghost-interaction-free limits at $\ew{} = 0$ and $\ew{} = 1$.
-Therefore, by construction, the weight-dependent correction vanishes for these two limiting weight values (see Fig.~\ref{fig:Cx_H2}).
+As readily seen from Eq.~\eqref{eq:Cxw} and graphically illustrated in Fig.~\ref{fig:Cx_H2}, the weight-dependent correction does not affect the two ghost-interaction-free limits at $\ew{} = 0$ and $\ew{} = 1$, as $\Cx{\ew{}}$ reduces to $\Cx{}$ in these two limits.
+Note that we are not only using data from $0 \le \ew{} \le 1/2$, but we also consider ensemble energies for $1/2 < \ew{} \le 1$, which is strictly forbidden by the GOK variational principle. \cite{Gross_1988a} 
+However, it is important to ensure that the weight-dependent functional does not alter the $\ew{} = 1$, which corresponds to a genuine saddle point of the KS equations, as mentioned above.
 Finally, let us mention that, around $\ew{} = 0$, the behaviour of Eq.~\eqref{eq:Cxw} is linear.
+
 \begin{figure}
 	\includegraphics[width=0.8\linewidth]{Cx_H2}
 	\caption{
-	$\Cx{\ew{}}/\Cx{\ew{}=0}$ as a function of $\ew{}$ [see Eq.~\eqref{eq:Cxw}].
+	$\Cx{\ew{}}/\Cx{\ew{}=0}$ as a function of $\ew{}$ [see Eq.~\eqref{eq:Cxw}] for the \ce{H2} molecule at equilibrium bond length and the aug-cc-pVTZ basis set.
+	\titou{T2: Add the same curve for He and stretch H2.}
 	\label{fig:Cx_H2}
 	}
 \end{figure}
@@ -733,8 +734,6 @@ Excitation energies (in eV) associated with the lowest double excitation of \ce{
 	HF			&	FCI				&	aug-cc-pV5Z		&					&					&		&		8.69	\\
 \end{tabular}
 \end{ruledtabular}
-\fnt[1]{Reference \onlinecite{Mielke_2005}.}
-\fnt[2]{Reference \onlinecite{Barca_2018a}.}
 \end{table*}
 %%% %%% %%% %%%
 
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