diff --git a/Manuscript/CBD-SI.tex b/Manuscript/CBD-SI.tex
index e9d20c3..0c1a44b 100644
--- a/Manuscript/CBD-SI.tex
+++ b/Manuscript/CBD-SI.tex
@@ -160,7 +160,7 @@ Method		&	AB & {\tBoneg}(99\%) 	&	{\sBoneg}(95\%)&	 {\twoAg}(1\%) & 	{\Atwog}	&
 	\hline
 SF-TD-B3LYP & $10.41$ & $0.241$ & $-0.926$ & $-0.161$ & $-0.164$ & $-1.028$ & $-1.501$ \\
 SF-TD-PBE0 & $8.95$ & $0.220$ & $-0.829$ & $-0.068$ & $-0.163$ & $-0.903$ & $-1.357$ \\
-SF-TD-BHHLYP & $3.79$ & $0.078$ & $-0.393$ & $0.343$ & $-0.099$ & $-0.251$ & $-0.603$ \\
+SF-TD-BH\&HLYP & $3.79$ & $0.078$ & $-0.393$ & $0.343$ & $-0.099$ & $-0.251$ & $-0.603$ \\
 SF-TD-M06-2X & $1.42$ & $0.000$ & $-0.354$ & $0.208$ & $-0.066$ & $-0.097$ & $-0.432$ \\
 SF-TD-CAM-B3LYP & $9.90$ & $0.280$ & $-0.807$ & $-0.011$ & $-0.134$ & $-0.920$ & $-1.370$ \\
 SF-TD-$\omega $B97X-V &  $10.01$ & $0.335$ & $-0.774$ & $0.064$ & $-0.118$ & $-0.928$ & $-1.372$ \\
@@ -170,11 +170,6 @@ SF-ADC(2)-s & $-0.30$ & $0.069$ & $-0.026$ & $-0.018$ & $0.112$ & $0.112$ & $-0.
 SF-ADC(2)-x & $1.44$ &  $0.077$ & $-0.094$ & $-0.446$ & $0.068$ & $-0.409$ & $-0.303$ \\
 SF-ADC(2.5) & $0.18$ & $0.013$ & $0.006$ & $0.029$ & $0.024$ & $0.094$ & $-0.185$ \\
 SF-ADC(3) & $0.65$ &  $-0.043$ & $0.037$ & $0.075$ & $-0.065$ & $0.075$ & $-0.181$ \\[0.1cm]
-CCSD & $0.95$ &  &  &  & $-0.059$ & $0.100$ &  \\
-CC3 & $-1.05$ &  $-0.060$  & $-0.006$   & $0.628$  &  & $0.162$ & $0.686$ \\
-CCSDT & $-0.25$ & $-0.051$ & $0.014$ & $0.280$ & $0.005$ & $0.131$ & $0.503$ \\
-CC4 & $-0.11$ &  & $0.003$ & $-0.006$ &  & $0.011$ & $-0.013$ \\
-CCSDTQ & $0.00$ &   & $0.000$ & $0.000$ & $0.000$ & $0.000$ & $0.000$ \\[0.1cm]
 CASSCF(4,4) & $-1.55$  & $0.208$ & $1.421$ & $0.292$ & $0.290$ & $0.734$ & $1.390$ \\
 CASPT2(4,4) & $-1.16$ & $-0.050$ & $-0.202$ & $-0.077$ & $-0.016$ & $0.006$ & $-0.399$ \\
 %XMS-CASPT2(4,4) &  &  &  & $-0.035$ &  &  &  \\
@@ -186,6 +181,11 @@ CASPT2(12,12) & $-0.42$&  $0.018$ & $0.058$ & $-0.106$ & $0.039$ & $0.038$ & $-0
 %XMS-CASPT2(12,12) & &   &  & $-0.090$ &  &  &  \\
 SC-NEVPT2(12,12) & $-0.64$ &  $0.039$ & $0.063$ & $-0.063$ & $0.021$ & $0.046$ & $-0.142$ \\
 PC-NEVPT2(12,12) & $-0.65$ & $0.000$ & $-0.062$ & $-0.093$ & $-0.013$ & $-0.024$ & $-0.278$ \\[0.1cm]
+CCSD & $0.95$ &  &  &  & $-0.059$ & $0.100$ &  \\
+CC3 & $-1.05$ &  $-0.060$  & $-0.006$   & $0.628$  &  & $0.162$ & $0.686$ \\
+CCSDT & $-0.25$ & $-0.051$ & $0.014$ & $0.280$ & $0.005$ & $0.131$ & $0.503$ \\
+CC4 & $-0.11$ &  & $0.003$ & $-0.006$ &  & $0.011$ & $-0.013$ \\
+CCSDTQ & $0.00$ &   & $0.000$ & $0.000$ & $0.000$ & $0.000$ & $0.000$ \\[0.1cm]
 %CIPSI &  & $-0.001\pm 0.030$ & $0.017\pm 0.035$ & $-0.120\pm 0.090$ & $0.025\pm 0.029$ & $0.130\pm 0.050$ &  \\
 \bf{TBE} & $[\bf{8.93}]$\fnm[1] &  $[\bf{1.462}]$\fnm[2] & $[\bf{3.125}]$\fnm[3] & $[\bf{4.149}]$\fnm[3] & $[\bf{0.144}]$\fnm[4] & $[\bf{1.500}]$\fnm[3] & $[\bf{2.034}]$\fnm[3] \\[0.1cm]
 Literature & $8.53$\fnm[5] & $1.573$\fnm[5] & $3.208$\fnm[5] & $4.247$\fnm[5] & $0.266$\fnm[5] & $1.664$\fnm[5] & $1.910$\fnm[5] \\
@@ -196,7 +196,7 @@ Literature & $8.53$\fnm[5] & $1.573$\fnm[5] & $3.208$\fnm[5] & $4.247$\fnm[5] &
 
 	\end{ruledtabular}
 	\fnt[1]{Value obtained using CCSDTQ/aug-cc-pVDZ corrected by the difference between CC4/aug-cc-pVTZ and CC4/aug-cc-pVDZ.}
-	\fnt[2]{Value obtained using the NEVPT2(12,12) one.}
+	\fnt[2]{Value obtained using NEVPT2(12,12).}
 	\fnt[3]{Value obtained using CCSDTQ/aug-cc-pVDZ corrected by the difference between CC4/aug-cc-pVTZ and CC4/aug-cc-pVDZ.}
 	\fnt[4]{Value obtained using CCSDTQ/aug-cc-pVDZ corrected by the difference between CCSDT/aug-cc-pVTZ and CCSDT/aug-cc-pVDZ.}
 	\fnt[5]{Value obtained from Ref.~\onlinecite{Lefrancois_2015} at the SF-ADC(2)-s/cc-pVTZ level with the geometry obtained at the CCSD(T)/cc-pVTZ level.}
diff --git a/Manuscript/CBD.tex b/Manuscript/CBD.tex
index 2f9b3f0..da06ecd 100644
--- a/Manuscript/CBD.tex
+++ b/Manuscript/CBD.tex
@@ -324,7 +324,8 @@ Table \ref{tab:geometries} reports the key geometrical parameters obtained at th
 \begin{squeezetable}
 \begin{table}
 	\caption{Automerization barrier (in \kcalmol) of CBD computed with various computational methods and basis sets.
-	The values in square parenthesis have been obtained by extrapolation via the procedure described in the corresponding footnote.}
+	The values in square parenthesis have been obtained by extrapolation via the procedure described in the corresponding footnote.
+	The TBE/aug-cc-pVTZ value is highlighted in bold.}
 	\label{tab:auto_standard}
 	\begin{ruledtabular}
 		\begin{tabular}{lrrrr}
@@ -358,7 +359,7 @@ CCSD & $8.31$ & $8.80$ & $9.88$ & $10.10$ \\
 CC3 & $6.59$ & $6.89$ & $7.88$ & $8.06$ \\
 CCSDT & $7.26$ & $7.64$ & $8.68$ &$[ 8.86]$\fnm[1]  \\
 CC4 & $7.40$ & $7.78$ & $[ 8.82]$\fnm[2] &  $[ 9.00]$\fnm[3]\\
-CCSDTQ & $7.51$ & $[ 7.89]$\fnm[4]& $[ 8.93]$\fnm[5]& $[ 9.11]$\fnm[6]\\
+CCSDTQ & $7.51$ & $[ 7.89]$\fnm[4]& $[\bf  8.93]$\fnm[5]& $[ 9.11]$\fnm[6]\\
 %\alert{CIPSI} & $7.91\pm 0.21$ & $8.58\pm 0.14$ &  &  \\
 		\end{tabular}
 	\end{ruledtabular}
@@ -366,7 +367,7 @@ CCSDTQ & $7.51$ & $[ 7.89]$\fnm[4]& $[ 8.93]$\fnm[5]& $[ 9.11]$\fnm[6]\\
 	\fnt[2]{Value obtained using CC4/aug-cc-pVDZ corrected by the difference between CCSDT/aug-cc-pVTZ and CCSDT/aug-cc-pVDZ.}
 	\fnt[3]{Value obtained using CC4/aug-cc-pVTZ corrected by the difference between CCSDT/aug-cc-pVQZ and CCSDT/aug-cc-pVTZ.}
 	\fnt[4]{Value obtained using CCSDTQ/6-31+G(d) corrected by the difference between CC4/aug-cc-pVDZ basis and CC4/6-31+G(d).}
-	\fnt[5]{Value obtained using CCSDTQ/aug-cc-pVDZ corrected by the difference between CC4/aug-cc-pVTZ and CC4/aug-cc-pVDZ.}
+	\fnt[5]{TBE value obtained using CCSDTQ/aug-cc-pVDZ corrected by the difference between CC4/aug-cc-pVTZ and CC4/aug-cc-pVDZ.}
 	\fnt[6]{Value obtained using CCSDTQ/aug-cc-pVTZ corrected by the difference between CC4/aug-cc-pVQZ and CC4/aug-cc-pVTZ.}
 \end{table}
 \end{squeezetable}
@@ -410,11 +411,11 @@ Note that the introduction of the triple excitations is clearly mandatory to hav
 %================================================
 
 %================================================
-\subsection{Excited States}
+\subsection{Vertical excitation energies}
 \label{sec:states}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\subsubsection{{\Dtwo} symmetry}
+\subsubsection{{\Dtwo} rectangular geometry}
 \label{sec:D2h}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
@@ -499,7 +500,8 @@ SF-ADC(3) & 6-31+G(d) & $1.435$ & $3.352$ & $4.242$ \\
 \begin{table}
 	\caption{
 	Vertical excitation energies (with respect to the {\oneAg} ground state) of the {\tBoneg}, {\sBoneg}, and {\twoAg} states of CBD at the {\Dtwo} rectangular equilibrium geometry of the {\oneAg} ground state.	
-	The values in square parenthesis have been obtained by extrapolation via the procedure described in the corresponding footnote.}
+	The values in square parenthesis have been obtained by extrapolation via the procedure described in the corresponding footnote.
+	The TBE/aug-cc-pVTZ values are highlighted in bold.}
 	\label{tab:D2h}
 	\begin{ruledtabular}
 		\begin{tabular}{llrrr}
@@ -549,7 +551,7 @@ SC-NEVPT2(12,12) &6-31+G(d)& $1.522$ & $3.409$ & $4.130$ \\
 & aug-cc-pVQZ & $1.503$ & $3.167$ & $4.088$ \\[0.1cm]
 PC-NEVPT2(12,12) &6-31+G(d)& $1.487$ & $3.296$ & $4.103$ \\
 & aug-cc-pVDZ & $1.472$ & $3.141$ & $4.064$ \\
-& aug-cc-pVTZ & $1.462$ & $3.063$ & $4.056$ \\
+& aug-cc-pVTZ & $\bf 1.462$ & $3.063$ & $4.056$ \\
 & aug-cc-pVQZ & $1.464$ & $3.043$ & $4.059$ \\[0.1cm]
 %MRCI(12,12) &6-31+G(d)& & & $4.125$ \\[0.1cm]
 CC3 &6-31+G(d)& $1.420$ & $3.341$ & $4.658$ \\
@@ -561,10 +563,10 @@ CCSDT &6-31+G(d)& $1.442$ & $3.357$ & $4.311$ \\
  & aug-cc-pVTZ & $1.411$ & $3.139$ & $4.429$ \\[0.1cm]
 CC4 &6-31+G(d)&   & $3.343$ & $4.067$ \\
  & aug-cc-pVDZ &  & $3.164$ & $4.041$ \\
- & aug-cc-pVTZ &  & $\left[3.128\right]$\fnm[1] & $\left[4.143\right]$\fnm[1]\\[0.1cm]
+ & aug-cc-pVTZ &  & $[3.128]$\fnm[1] & $[4.143]$\fnm[1]\\[0.1cm]
 CCSDTQ &6-31+G(d)&  & $3.340$ & $4.073$ \\
-& aug-cc-pVDZ & & $\left[3.161\right]$\fnm[2]&  $\left[4.047\right]$\fnm[2] \\
-& aug-cc-pVTZ & & $\left[3.125\right]$\fnm[3]&  $\left[4.149\right]$\fnm[3]\\[0.1cm]
+& aug-cc-pVDZ & & $[3.161]$\fnm[2]&  $[4.047]$\fnm[2] \\
+& aug-cc-pVTZ & & $[\bf 3.125]$\fnm[3]&  $[\bf 4.149]$\fnm[3]\\[0.1cm]
 CIPSI &6-31+G(d)& $1.486\pm 0.005$ & $3.348\pm 0.024$ & $4.084\pm 0.012$ \\
 & aug-cc-pVDZ & $1.458\pm 0.009$ & $3.187\pm 0.035$ & $4.04\pm 0.04$ \\
 & aug-cc-pVTZ & $1.461\pm 0.030$ & $3.142\pm 0.035$ & $4.03\pm 0.09$ \\
@@ -572,7 +574,7 @@ CIPSI &6-31+G(d)& $1.486\pm 0.005$ & $3.348\pm 0.024$ & $4.084\pm 0.012$ \\
 	\end{ruledtabular}
 	\fnt[1]{Value obtained using CC4/aug-cc-pVDZ corrected by the difference between CCSDT/aug-cc-pVTZ and CCSDT/aug-cc-pVDZ.}
 	\fnt[2]{Value obtained using CCSDTQ/6-31+G(d) corrected by the difference between CC4/aug-cc-pVDZ and CC4/6-31+G(d).}
-	\fnt[3]{Value obtained using CCSDTQ/aug-cc-pVDZ corrected by the difference between CC4/aug-cc-pVTZ and CC4/aug-cc-pVDZ.}
+	\fnt[3]{TBE value obtained using CCSDTQ/aug-cc-pVDZ corrected by the difference between CC4/aug-cc-pVTZ and CC4/aug-cc-pVDZ.}
 \end{table}
 \end{squeezetable}
 %%% %%% %%% %%%
@@ -634,7 +636,7 @@ For the doubly-excited state, {\twoAg}, the convergence of the CC expansion is m
 The CCSDTQ excitation energies (which are used to define the TBEs) are systematically within the error bar of the CIPSI calculations, which confirms the outstanding performance of CC methods including quadruple excitations in the context of excited states.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\subsubsection{{\Dfour} symmetry}
+\subsubsection{{\Dfour} square-planar geometry}
 \label{sec:D4h}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
@@ -711,7 +713,8 @@ SF-ADC(3) & 6-31+G(d) & $0.123$ & $1.650$ & $2.078$ \\
 \begin{table}
 	\caption{
 	Vertical excitation energies (with respect to the {\sBoneg} ground state) of the {\Atwog}, {\Aoneg}, and {\Btwog} states of CBD at the {\Dfour} square-planar equilibrium geometry of the {\Atwog} state.
-	The values in square brackets have been obtained by extrapolation via the procedure described in the corresponding footnote.}
+	The values in square brackets have been obtained by extrapolation via the procedure described in the corresponding footnote.
+	The TBE/aug-cc-pVTZ values are highlighted in bold.}
 	\label{tab:D4h}
 	\begin{ruledtabular}
 		\begin{tabular}{llrrr}
@@ -767,10 +770,10 @@ CCSDT & 6-31+G(d) & $0.210$ & $1.751$ & $2.565$ \\
  & aug-cc-pVTZ & $0.149$ & $1.631$ & $2.537$ \\[0.1cm]
 CC4 & 6-31+G(d) &  & $1.604$ & $2.121$ \\
  & aug-cc-pVDZ &  & $1.539$ & $1.934$ \\
- & aug-cc-pVTZ &  & $\left[1.511 \right]$\fnm[1] &$\left[2.021 \right]$\fnm[1]  \\[0.1cm]
+ & aug-cc-pVTZ &  & $[1.511 ]$\fnm[1] &$[2.021 ]$\fnm[1]  \\[0.1cm]
 CCSDTQ & 6-31+G(d) & $0.205$ & $1.593$ & $2.134$ \\
-& aug-cc-pVDZ & $\left[0.160\right]$\fnm[2] & $\left[1.528 \right]$\fnm[4]&$\left[1.947\right]$\fnm[4] \\
-& aug-cc-pVTZ & $\left[0.144\right]$\fnm[3]  & $\left[1.500 \right]$\fnm[5]&$\left[2.034\right]$\fnm[5] \\	[0.1cm]
+& aug-cc-pVDZ & $[0.160]$\fnm[2] & $[1.528 ]$\fnm[4]&$[1.947]$\fnm[4] \\
+& aug-cc-pVTZ & $[\bf 0.144]$\fnm[3]  & $[\bf 1.500 ]$\fnm[5]&$[\bf 2.034]$\fnm[5] \\	[0.1cm]
 CIPSI & 6-31+G(d) & $0.201\pm 0.003$ & $1.602\pm 0.007$ & $2.13\pm 0.04$ \\
  & aug-cc-pVDZ & $0.157\pm 0.003$ & $1.587\pm 0.005$ & $2.102\pm 0.027$ \\
  & aug-cc-pVTZ & $0.169\pm 0.029$ & $1.63\pm 0.05$ &  \\
@@ -778,9 +781,9 @@ CIPSI & 6-31+G(d) & $0.201\pm 0.003$ & $1.602\pm 0.007$ & $2.13\pm 0.04$ \\
 	\end{ruledtabular}
 	\fnt[1]{Value obtained using CC4/aug-cc-pVDZ corrected by the difference between CCSDT/aug-cc-pVTZ and CCSDT/aug-cc-pVDZ.}
 	\fnt[2]{Value obtained using CCSDTQ/6-31+G(d) corrected by the difference between CCSDT/aug-cc-pVDZ and CCSDT/6-31+G(d).}
-	\fnt[3]{Value obtained using CCSDTQ/aug-cc-pVDZ corrected by the difference between CCSDT/aug-cc-pVTZ and CCSDT/aug-cc-pVDZ.}
+	\fnt[3]{TBE value obtained using CCSDTQ/aug-cc-pVDZ corrected by the difference between CCSDT/aug-cc-pVTZ and CCSDT/aug-cc-pVDZ.}
 	\fnt[4]{Value obtained using CCSDTQ/6-31+G(d) corrected by the difference between CC4/aug-cc-pVDZ and CC4/6-31+G(d).}
-	\fnt[5]{Value obtained using CCSDTQ/aug-cc-pVDZ corrected by the difference between CC4/aug-cc-pVTZ and CC4/aug-cc-pVDZ.}
+	\fnt[5]{TBE value obtained using CCSDTQ/aug-cc-pVDZ corrected by the difference between CC4/aug-cc-pVTZ and CC4/aug-cc-pVDZ.}
 	
 \end{table}
 \end{squeezetable}
@@ -799,24 +802,17 @@ CIPSI & 6-31+G(d) & $0.201\pm 0.003$ & $1.602\pm 0.007$ & $2.13\pm 0.04$ \\
 In Table \ref{tab:sf_D4h}, we report, at the {\Dfour} square planar equilibrium geometry of the {\Atwog} state, the vertical transition energies associated with the {\Atwog}, {\Aoneg}, and {\Btwog} states obtained using the spin-flip formalism, while Table \ref{tab:D4h} gathers the same quantities obtained with the multi-reference, CC, and CIPSI methods. 
 The vertical excitation energies computed at various levels of theory are depicted in Fig.~\ref{fig:D4h} for the aug-cc-pVTZ basis.
 Unfortunately, due to technical limitations, we could not compute $\%T_1$ values associated with the {\Atwog}, {\Aoneg}, and {\Btwog} excited states in the {\Dfour} symmetry.
-However, it is clear from the inspection of the wave function that, with respect to the \sBoneg ground state, {\Atwog} and {\Btwog} are dominated by single excitations, while {\Aoneg} is strongly dominated by double excitations.
+However, it is clear from the inspection of the wave function that, with respect to the {\sBoneg} ground state, {\Atwog} and {\Btwog} are dominated by single excitations, while {\Aoneg} is strongly dominated by double excitations.
+
+As for the previous geometry we start by discussing the SF-TD-DFT results, and in particular the singlet-triplet gap, \ie, the energy difference between {\sBoneg} and {\Atwog}.
+For all functionals, this gap is small (basically below \SI{0.1}{\eV} while the TBE value is \SI{0.144}{\eV}) but it is worth mentioning that B3LYP and PBE0 predict a negative singlet-triplet gap (hence a triplet ground state).
+Increasing the exact exchange in hybrids or relying on RSHs (even with a small amount of short-range exact exchange) allows to recover a positive gap and a singlet ground state.
+At the SF-TD-DFT level, the energy gap between the two singlet excited states, {\Aoneg} and {\Btwog}, is particularly small and grows moderately with the amount of short-range exact exchange.
+The influence of the exact exchange on the singlet energies is quite significant with an energy difference of the order of \SI{1}{\eV} between the functional with the smallest amount of exact exchange (B3LYP) and the functional with the largest amount (M06-2X).
+As for the excitation energies computed at the {\Dtwo} equilibrium structure and the automerization barrier, functionals with a large fraction of short-range exact exchange deliver much more accurate results.
+Yet, the transition energy to {\Btwog} is off by more than half an \si{\eV} compared to the TBE, while the doubly-excited state is much closer to the reference value (errors of \SI{-0.251}{}, \SI{-0.097}{}, and \SI{-0.312}{\eV} for BH\&HLYP, M06-2X, and M11, respectively)
+Again, for all the excited states, the basis set effects are extremely small at the SF-TD-DFT level.
 
-Table \ref{tab:sf_D4h} shows vertical energies obtained with spin-flip methods and Table \ref{tab:D4h} vertical energies obtained with standard methods. 
-As for the previous geometry we start with the SF-TD-DFT results with hybrid functionals. 
-We can first notice that for the B3LYP and the PBE0 functionals we have a wrong ordering of the first triplet state {\Atwog} and the ground state {\sBoneg}. 
-We retrieve the good ordering with the BH\&HLYP functional, so adding exact exchange to the functional allows us to have the right ordering between these two states. For the B3LYP and the PBE0 functionals we have that the energy differences for each states and for all bases are small with \SIrange{0.004}{0.007}{\eV} for the triplet state {\Atwog}. 
-We have \SIrange{0.015}{0.021}{\eV} of energy difference for the {\Aoneg} state through all bases, we can notice that this state is around \SI{0.13}{\eV} (considering all bases) higher with the PBE0 functional. 
-We can make the same observation for the {\Btwog} state for the B3LYP and the PBE0 functionals, indeed we have small energy differences for all bases and the state is around \SIrange{0.14}{0.15}{\eV} for the PBE0 functional. 
-For the BH\&HLYP functional the {\Aoneg} and {\Btwog} states are higher in energy than for the two other hybrid functionals with about \SIrange{0.65}{0.69}{\eV} higher for the {\Aoneg} state and \SIrange{0.75}{0.77}{\eV} for the {\Btwog} state compared to the PBE0 functional. 
-Then, we have the RSH functionals CAM-B3LYP, $\omega$B97X-V and LC-$\omega$PBE08. 
-For these functionals the vertical energies are similar for the {\Aoneg} and {\Btwog} states with a maximum energy difference of \SIrange{0.01}{0.02}{\eV} for the{\Aoneg} state and \SIrange{0.005}{0.009}{\eV} for the {\Btwog} state considering all bases. 
-The maximum energy difference for the triplet state is larger with \SIrange{0.047}{0.057}{\eV} for all bases. 
-Note that the vertical energies obtained with the RSH functionals are close to the PBE0 ones except that we have the right ordering between the triplet state {\Atwog} and the ground state {\sBoneg}. 
-The M06-2X results are closer to the BH\&HLYP ones but the M06-2X vertical energies are always higher than the BH\&HLYP ones. 
-We can notice that the M06-2X energies for the {\Aoneg} state are close to the BH\&HLYP energies for the {\Btwog} state. 
-For these two states, when we compared the results obtained with the M06-2X and the BH\&HLYP functionals, we have an energy difference of \SIrange{0.16}{0.17}{\eV} for the {\Aoneg} state and \SIrange{0.17}{0.18}{\eV} for the {\Btwog} state considering all bases. 
-For the triplet state {\Atwog} the energy differences are smaller with \SIrange{0.03}{0.04}{\eV} for all bases. 
-The M11 vertical energies are very close to the M06-2X ones for the triplet state with a maximum energy difference of \SI{0.003}{\eV} considering all bases, and are closer to the BH\&HLYP results for the two other states with \SIrange{0.06}{0.07}{\eV} and \SIrange{0.07}{0.08}{\eV} of energy difference for the {\Aoneg} and {\Btwog} states, respectively. 
 Then we discuss the various ADC scheme results, note that we were not able to obtain the vertical energies with the aug-cc-pVQZ basis due to computational resources. 
 For the ADC(2)-s scheme we can see that the energy difference for the triplet state are smaller than for the two other states, indeed we have an energy difference of \SI{0.09}{\eV} for the triplet state whereas we have \SI{0.15}{\eV} and \SI{0.25}{eV} for the {\Aoneg} and {\Btwog} states, again when considering all bases. 
 The energy difference for each state and through the bases are similar for the two other ADC schemes. 
@@ -865,6 +861,12 @@ In the present study, we have benchmarked a larger number of computational metho
 %When the CC4/aug-cc-pVTZ values were not obtained we corrected the CC4/aug-cc-pVDZ values by the difference between CCSDT/aug-cc-pVTZ and CCSDT/aug-cc-pVDZ to obtain them (Eq.~\eqref{eq:CC4_aug-cc-pVTZ}). 
 %If the CC4 values have not been obtained then we used the same scheme that we just described but by using the CCSDT values. 
 %If neither the CC4 and CCSDTQ values were not available then we used the NEVPT2(12,12)/aug-cc-pVTZ values. 
+
+\titou{Within the SF-TD-DFT framework, we advice the use of exchange-correlation (hybrids or range-separated hybrids) with a large fraction of short-range exact exchange. 
+This has been shown to be beneficial for the automerization barrier and the vertical excitation energies in the {\Dtwo} and {\Dfour} arrangements.}
+
+\titou{At the SF-ADC level, we have found that the extended scheme SF-ADC(2)-x is not good, while SF-ADC(2)-s and SF-ADC(3) have opposite behavior which means that SF-ADC(2.5) is really good.}
+
 In order to provide a benchmark of the automerization barrier and vertical energies we used coupled-cluster (CC) methods with doubles (CCSD), with triples (CCSDT and CC3) and with quadruples (CCSTQ and CC4). 
 Due to the presence of multi-configurational states we used multi-reference methods (CASSCF, CASPT2 and NEVPT2) with two active spaces ((4,4) and (12,12)). 
 We also used spin-flip (SF-) within two frameworks, in TD-DFT with various global and range-separated hybrids functionals, and in ADC with the ADC(2)-s, ADC(2)-x and ADC(3) schemes.