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\author{Pierre-Fran\c{c}ois Loos}
	\email{loos@irsamc.ups-tlse.fr}
	\affiliation[LCPQ, Toulouse]{Laboratoire de Chimie et Physique Quantiques, Universit\'e de Toulouse, CNRS, UPS, France}
\author{Anthony Scemama}
	\affiliation[LCPQ, Toulouse]{Laboratoire de Chimie et Physique Quantiques, Universit\'e de Toulouse, CNRS, UPS, France}
\author{Denis Jacquemin}
	\email{Denis.Jacquemin@univ-nantes.fr}
	\affiliation[CEISAM, Nantes]{Universit\'e de Nantes, CNRS,  CEISAM UMR 6230, F-44000 Nantes, France}


\let\oldmaketitle\maketitle
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	\title{The Quest For Highly Accurate Excitation Energies: A Computational Perspective: SI}
\date{\today}


\begin{document}
\clearpage

%
% Table-1
% 
\begin{scriptsize}
\renewcommand{\arraystretch}{0.7}
\begin{longtable}{lccllcc}
\caption{
\label{Table-1}
Non-exhaustive list of previous benchmark studies of wavefunction (and BSE) methods. 
We report the method, the year of publication, the characteristics of the set (both number of excited states and nature of the molecules), the benchmark set, the MAE (in eV), and the reference values. 
S ans T stands for singlet and triplet respectively, and are specified only when the separated statistics are provided in the original work. 
Further details can be found in the corresponding studies (references provided).}
\\
\hline
\hline
Method			&	Year		& No.~of ES	& No.~of molecules		& Benchmark set & 		MAE	(eV) &	Ref. \\
\hline
\endfirsthead
\hline
\hline
Method			&	Year		& No.~of ES	& No.~of molecules		& Benchmark set & 		MAE		(eV)	&	Ref. \\
\hline
\endhead
\hline \multicolumn{7}{l}{Continued on next page} \\
\endfoot
\hline
\hline
 \multicolumn{7}{l}{$^a$Depending on the selected solvent model: LR/cLR.}\\
 \multicolumn{7}{l}{$^b$With the largest considered basis set, 6-311G, using (or not) various IPEA, see the original work.}\\
\endlastfoot
BSE@ev$GW$		&	2015		&	91 		&28 (medium-size organic)& Th. $\Ea$ (Thiel's TBE-2)			& 0.25			&\citenum{Jac15a} \\
				&	2015		&	80		& 80 (organic dyes)		& Exp. $\EOO$ (solvated)				& 0.19/0.15$^a$	&\citenum{Jac15b} \\
				&	2017		&	23		&18	 (various)			& 	 Exp. excitation energies			& 0.18			&\citenum{Jac17b} \\
				&	2017		&	62	(T)	&20 (medium-size organic)& Th. $\Ea$ (CC3)					& 0.58			& \citenum{Jac17a} \\
				&	2018		&	104	(S)	&28 (medium-size organic	)& Th. $\Ea$ (CC3)					& 0.26			&\citenum{Gui18} \\	
				&	2018		&	63	(T)	&20 (medium-size organic)& Th. $\Ea$ (CC3)					& 0.84			&\citenum{Gui18} \\	
CIS				&	1995		&	6		&6 (diatomics)			& Exp. $\Ead$						& 0.73			& \citenum{Sta95}	\\
				&	2002		&	34		&28 (mostly di/triatomics)	& Exp. $\Ead$ 	and 	$\EOO$			& 0.63			& \citenum{Fur02} 	\\
				&	2005		&	19		& 4 (diatomics)			& Exp. $\Ead$ 						& 0.57			& \citenum{Hat05c}	\\
				&	2007		& 	32		& 22	(diverse)			&Exp. $\EOO$						& 0.71			&\citenum{Rhe07}	\\
				&	2009		&	20		& 29 (mostly di/triatomics)	&Exp. $\Ead$ and 	$\EOO$			& 0.58			& \citenum{Rhe09}	\\
				&	2010		&	69		&11 (medium-size organic)	&Exp. excitation energies			& 1.07			& \citenum{Car10} \\
				&	2010		&	12		&12 (organic dyes)		& Exp. $\EOO$ (solvated)				& 0.77			&\citenum{Goe10a} \\
				&	2011		&	91		& 109 (diverse)			&Exp. $\EOO$						& 0.98			& \citenum{Sen11b} \\
				&	2013		&	7		& 7 (organic dyes)		& Exp. $\EOO$ (solvated)				& 0.75			&\citenum{Cha13c}	\\
				&	2014		&	79		& 96 (various)			&Exp. $\EOO$						& 0.88			& \citenum{Fan14b} \\
				&	2014		& 	29		& 15 (small radicals)		&Exp. $\EOO$						& 1.75			&\citenum{Bar14b} \\
				&	2017		&	66		& 46 (aromatics)		&Exp. $\EOO$						& 1.08			& \citenum{Oru16}	\\
CIS(D)			&	1995		&	6		&6 (diatomics)			& Exp. $\Ead$ 						& 0.27			& \citenum{Sta95}	\\
				&	2004		&	32		& 22	(diverse)			& Exp. $\EOO$						& 0.19			& \citenum{Gri04b}	\\
				&	2005		&	19		& 4 (diatomics)			& Exp. $\Ead$ 						& 0.26			& \citenum{Hat05c}	\\
				&	2007		& 	32		& 22	(diverse)			&Exp. $\EOO$						& 0.22			&\citenum{Rhe07}	\\
				&	2010		&	69		&11 (medium-size organic)	&Exp. excitation energies			& 0.49			& \citenum{Car10} \\
				&	2010		&	12		&12 (organic dyes)		& Exp. $\EOO$ (solvated)				& 0.25			&\citenum{Goe10a} \\
				&	2015		&	80		& 80 (organic dyes)		& Exp. $\EOO$ (solvated)				& 0.18/0.26$^a$	&\citenum{Jac15b} \\
				&	2018		&	106		& 18 (small compounds)	& Th.  $\Ea$ (FCI)					& 0.25			& \citenum{Loo18a}\\
				&	2020		&	221		& 27 (medium-size organic)& Th.  $\Ea$ (FCI, CCSDTQ, CCSDT)	& 0.23			& \citenum{Loo20a} \\
ADC(2)			&	2002		&	43		& 4 (small)			& Th.   $\Ea$ (FCI)					& 0.64			& \citenum{Tro02} \\
				&	2005		&	19		& 4 (diatomics)			& Exp. $\Ead$ 						& 0.21			& \citenum{Hat05c}	\\
				&	2013		&	66		& 46 (aromatics)		& Exp. $\EOO$						& 0.08			& \citenum{Win13}	\\
				&	2014		&	104		& 28 (medium-size organic)&Th. $\Ea$ (Thiel's TBE)				& 0.29			& \citenum{Har14} \\	
				&	2015		&	80		& 80 (organic dyes)		& Exp. $\EOO$ (solvated)				& 0.22/0.14$^a$	&\citenum{Jac15b} \\
				&	2018		&	106		& 18 (small compounds)	& Th.  $\Ea$ (FCI)					& 0.21			& \citenum{Loo18a}\\
				&	2020		&	101		& 94 (medium-size organic)& Exp. $\EOO$					& 0.16			&\citenum{Loo20b} \\
				&	2020		&	328		& 45 (1--6 non-H atoms)	& Th.  $\Ea$ (FCI, CCSDTQ, CCSDT)	& 0.16			&\citenum{Loo20b} \\
				&	2020		&	218		& 27 (medium-size organic)& Th.  $\Ea$ (FCI, CCSDTQ, CCSDT)	& 0.14			& \citenum{Loo20a} \\
ADC(3)			&	2002		&	43		& 4 (small)			& Th.   $\Ea$ (FCI)					& 0.17			& \citenum{Tro02} \\
				&	2014		&	104		& 28 (medium-size organic)&Th. $\Ea$ (Thiel's TBE)				& 0.24			& \citenum{Har14} \\	
				&	2018		&	106		& 18 (small compounds)	& Th.  $\Ea$ (FCI)					& 0.23			& \citenum{Loo18a}\\
				&	2020		&	101		& 94 (medium-size organic)& Exp. $\EOO$					& 0.18			&\citenum{Loo20b} \\
				&	2020		&	328		& 45 (1--6 non-H atoms)	& Th. $\Ea$ (FCI, CCSDTQ, CCSDT) 	& 0.21			&\citenum{Loo20b} \\
CC2				&	2002		&	43		& 4 (small)			& Th.   $\Ea$ (FCI)					& 0.53			& \citenum{Tro02} \\
				&	2003		& 	20		& 29  (mostly di/triatomics)& Exp. $\Ead$ 	and 	$\EOO$			& 0.17			& \citenum{Koh03}	\\
				&	2005		&	19		& 4 (diatomics)			& Exp. $\Ead$ 						& 0.16			& \citenum{Hat05c}	\\
				&	2008		&	26		&	19 (di/triatomics)	& Exp. $\Ead$ and 	$\EOO$			& 0.17			& \citenum{Hel08}	\\
				&	2008		&	32		& 22	(diverse)			& Exp. $\EOO$ 					& 0.14			& \citenum{Hel08}	\\
				&	2008		&	152 (S)	& 28 (medium-size organic)&Th. $\Ea$ (CASPT2)				& 0.32			& \citenum{Sch08} \\
				&	2008		&	71 (T)	& 20 (medium-size organic)&Th. $\Ea$ (CASPT2)				& 0.19			& \citenum{Sch08} \\
				&	2009		&	20		& 29 (mostly di/triatomics)	&Exp. $\Ead$ and 	$\EOO$			& 0.18			& \citenum{Rhe09}	\\
				&	2011		&	15		& 15 (diverse)			&Exp. $\EOO$						& 0.17			& \citenum{Sen11b} \\
				&	2013		&	66		& 46 (aromatics)		&Exp. $\EOO$						& 0.07			& \citenum{Win13}	\\
				&	2014		&	79		& 96 (various)			&Exp. $\EOO$						& 0.19			& \citenum{Fan14b} \\
				&	2015		&	80		& 80 (organic dyes)		& Exp. $\EOO$ (solvated)				& 0.16/0.13$^a$	&\citenum{Jac15b} \\
				&	2016		&	132		& 25 (medium-size organic)& Th. $\Ea$ (CC3)					& 0.22			&  \citenum{Taj16} \\
				&	2017		&	66		& 46 (aromatics)		&Exp. $\EOO$						& 0.11			& \citenum{Oru16}	\\
				&	2018		&	106		& 18 (small compounds)	& Th.  $\Ea$ (FCI)					& 0.22			& \citenum{Loo18a}\\
				&	2018		&	35		& 31 (medium-size organic)&Exp. $\EOO$					& 0.08			& \citenum{Loo18b} \\
				&	2020		&	101		& 94 (medium-size organic)& Exp. $\EOO$					& 0.10			&\citenum{Loo20b} \\
				&	2020		&	328		& 45 (1--6 non-H atoms)	& Th. $\Ea$ (FCI, CCSDTQ, CCSDT) 	& 0.17			&\citenum{Loo20b} \\
				&	2020		&	223		& 27 (medium-size organic)& Th.  $\Ea$ (FCI, CCSDTQ, CCSDT)	& 0.15			& \citenum{Loo20a} \\
CCSD			&	1995		&	6		&6 (diatomics)			& Exp. $\Ead$ 						& 0.19			& \citenum{Sta95}	\\
				&	2002		&	43		& 4 (small)			& Th.   $\Ea$ (FCI)					& 0.15			& \citenum{Tro02} \\
				&	2005		&	19		& 4 (diatomics)			& Exp. $\Ead$ 						& 0.20			& \citenum{Hat05c}	\\
				&	2008		&	152 (S)	& 28 (medium-size organic)&Th. $\Ea$ (CASPT2)				& 0.50			& \citenum{Sch08} \\
				&	2008		&	71 (T)	& 20 (medium-size organic)&Th. $\Ea$ (CASPT2)				& 0.16			& \citenum{Sch08} \\
				&	2010		&	69		&11 (medium-size organic)	&Exp. excitation energies			& 0.27			& \citenum{Car10} \\
				&	2016		&	132		& 25 (medium-size organic)& Th. $\Ea$ (CC3)					& 0.15			&  \citenum{Taj16} \\
				&	2017		&	23		&18	 (various)			& 	 Exp. excitation energies			& 0.31			&\citenum{Jac17b} \\
				&	2018		&	106		& 18 (small compounds)	& Th.  $\Ea$ (FCI)					& 0.08			& \citenum{Loo18a}\\
				&	2018		&	35		& 31 (medium-size organic)&Exp. $\EOO$					& 0.21			& \citenum{Loo18b} \\
				&	2020		&	223		& 27 (medium-size organic)& Th.  $\Ea$ (FCI, CCSDTQ, CCSDT)	& 0.13			& \citenum{Loo20a} \\
CC3				&	2002		&	43		& 4 (small)			& Th.   $\Ea$ (FCI)					& 0.02			& \citenum{Tro02} \\
				&	2005		&	19		& 4 (diatomics)			& Exp. $\Ead$ 						& 0.04			& \citenum{Hat05c}	\\
				&	2008		&	121 (S)	& 28 (medium-size organic)&Th. $\Ea$ (CASPT2)				& 0.20			& \citenum{Sch08} \\
				&	2008		&	71 (T)	& 20 (medium-size organic)&Th. $\Ea$ (CASPT2)				& 0.08			& \citenum{Sch08} \\
				&	2018		&	35		& 31 (medium-size organic)&Exp. $\EOO$					& 0.02			& \citenum{Loo18b} \\
				&	2018		&	106		& 18 (small compounds)	& Th.  $\Ea$ (FCI)					& 0.04			& \citenum{Loo18a}\\
				&	2019		&	119		& 109 (diverse)			&Exp. $\EOO$						& 0.03			& \citenum{Loo19a} \\
				&	2020		&	101		& 94 (medium-size organic)& Exp. $\EOO$					& 0.04			&\citenum{Loo20b} \\
				&	2020		&	328		& 45 (1--6 non-H atoms)	& Th. $\Ea$ (FCI, CCSDTQ, CCSDT) 	& 0.02			&\citenum{Loo20b} \\
				&	2020		&	223		& 27 (medium-size organic)& Th.  $\Ea$ (FCI, CCSDTQ, CCSDT)	& 0.01			& \citenum{Loo20a} \\
CCSDT			&	2018		&	104		& 18 (small compounds)	& Th.  $\Ea$ (FCI)					& 0.03			& \citenum{Loo18a}\\
CCSDTQ			&	2018		&	73		& 18 (small compounds)	& Th.  $\Ea$ (FCI)					& 0.01			& \citenum{Loo18a}\\
CASPT2			&	2013		&	121		&28 (medium-size organic) & Th. $\Ea$ (CC3)					& 0.21			& \citenum{Sch13b} \\	
				&	2014		& 	29		& 15 (small radicals)		&Exp. $\EOO$						& 0.12			&\citenum{Bar14b} \\
				&	2016		&	23		&18	 (various)			& 	 Exp. excitation energies			& 0.21			&\citenum{Hoy16} \\
				&	2017		&	124		& 13 (di and triatomics)	& Th.  $\Ea$ (FCI)					& 0.10/0.11$^b$	&\citenum{Zob17} \\
				&	2017		&	130		&  28 (medium-size organic) & Exp. excitation energies			& 0.25--0.33$^b$	&\citenum{Zob17} \\
(PC-)NEVPT2		&	2013		&	121		&28 (medium-size organic) & Th. $\Ea$ (CC3)					& 0.28			& \citenum{Sch13b} \\	
				&	2020		&	223		& 27 (medium-size organic)& Th.  $\Ea$ (FCI, CCSDTQ, CCSDT)	& 0.13			& \citenum{Loo20a} \\
\end{longtable}
\end{scriptsize}


%%% FIG 1 %%%
\begin{figure*}
	\includegraphics[width=\linewidth]{MAX}
	\caption{Maximum positive and maximum negative errors (in eV) for the {\SetA} and {\SetC} sets of excitation energies with respect to the TBE/\textit{aug}-cc-pVTZ reference values (as described in Refs.~\citenum{Loo18a,Loo20a}) for various methods. 
	}
	\label{fig:Set1}
\end{figure*}
%%% %%% %%%

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\end{document} 







