CO added to SI

Manuscript/Ex-srDFT.tex

@@ -678,7 +678,8 @@ However, these results also clearly evidence that special care has to be taken f
 It is interesting to study the behavior of $\rsmu{}{\Bas}(\br{})$ for different states as the basis set incompleteness error is obviously state specific.
 To do so, we consider the ground state (${}^{1}\Sigma^+$) of carbon monoxide as well as its lowest singlet excited state (${}^{1}\Pi$). 
 The values of the vertical excitation energies obtained for various methods and basis sets are reported in Table \ref{tab:Mol}.
-Figure \ref{fig:CO} represents $\rsmu{}{}(\br{})$ for these two electronic states computed with the AVDZ, AVTZ and AVQZ basis sets.
+Figure \ref{fig:CO} represents $\rsmu{}{}(z)$ along the nuclear axis ($z$) for these two electronic states computed with the AVDZ, AVTZ and AVQZ basis sets.
+\titou{Add description about the graphs here.}
 
 %%% FIG 4 %%%
 \begin{figure}
@@ -693,13 +694,13 @@ Figure \ref{fig:CO} represents $\rsmu{}{}(\br{})$ for these two electronic state
 \subsection{Doubly-Excited States of the Carbon Dimer}
 \label{sec:C2}
 %=======================
-In order to have a miscellaneous test set of excitations, in a third time, we propose to study some doubly-excited states of the carbon dimer \ce{C2}, a prototype system for strongly correlated and multireference systems. \cite{AbrShe-JCP-04, AbrShe-CPL-05, Var-JCP-08, PurZhaKra-JCP-09, AngCimPas-MP-12, BooCleThoAla-JCP-11, Sha-JCP-15, SokCha-JCP-16, HolUmrSha-JCP-17, VarRoc-PTRSMPES-18}
+In order to have a miscellaneous test set of excitations, in a fourth time, we propose to study some doubly-excited states of the carbon dimer \ce{C2}, a prototype system for strongly correlated and multireference systems. \cite{AbrShe-JCP-04, AbrShe-CPL-05, Var-JCP-08, PurZhaKra-JCP-09, AngCimPas-MP-12, BooCleThoAla-JCP-11, Sha-JCP-15, SokCha-JCP-16, HolUmrSha-JCP-17, VarRoc-PTRSMPES-18}
 These two valence excitations --- $1\,^{1}\Sigma_g^+ \ra 1\,^{1}\Delta_g$ and $1\,^{1}\Sigma_g^+ \ra 2\,^{1}\Sigma_g^+$ --- are both of $(\pi,\pi) \ra (\si,\si)$ character.
 They have been recently studied with state-of-the-art methods, and have been shown to be ``pure'' doubly-excited states as they do not involve single excitations. \cite{LooBogSceCafJac-JCTC-19} 
 The vertical excitation energies associated with these transitions are reported in Table \ref{tab:Mol} and represented in Fig.~\ref{fig:C2}.
-An interesting point here is that one really needs the PBEot to get chemically-accurate absorption energies with the AVDZ atomic basis set.
+An interesting point here is that one really needs to consider the PBEot functional to get chemically-accurate absorption energies with the AVDZ atomic basis set.
 We believe that the present result is a direct consequence of the multireference character of the \ce{C2} molecule.
-In other words, the UEG on-top density used in the LDA and PBE functionals (see Sec.~\ref{sec:func}) is a particularly bad approximation of the true on-top density.
+In other words, the UEG on-top density used in the LDA and PBE functionals (see Sec.~\ref{sec:func}) is a particularly bad approximation of the true on-top density for the present system.
 
 %%% FIG 5 %%%
 \begin{figure}

Manuscript/SI/Ex-srDFT-SI.tex

@@ -450,14 +450,14 @@ Here, we report the absolute energetic corrections for each state of each molecu
 	\\
 	\\
 	Carbon monoxyde	&	$1\,^{1}\Sigma^+$		
-												&	 &  & 
-												&	 &  & 
-												&	 &  & 
+												&	-0.074\,328 & -0.031\,117	& -0.015\,510
+												&	-0.084\,655 & -0.035\,318	& -0.017\,142
+												&	-0.076\,668 & -0.077\,437	& -0.018\,768
 	\\
 					&	$1\,^{1}\Pi$		
-												&	 &  & 
-												&	 &  & 
-												&	 &  & 
+												&	-0.075\,790	& -0.031\,456	& -0.016\,083
+												&	-0.085\,494	& -0.035\,255	& -0.017\,182
+												&	-0.036\,301 & -0.036\,359	& -0.018\,855
 	\\
 	\\
 	Water		&	$1\,^{1}A_1$