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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}
Results obtained in previous benchmarks of wavefunction (and BSE) approaches. We report the tested method, the year of publication, the set used (both number of excited states
and number and nature of the molecules), the selected benchmark, the obtained MAE (in eV), and the reference. S ans T stands for singlet and triplet respectively, and are specified
only when the separated statistics are given  in the original corks. Further details can be found in these works. We do not intend to list all previous benchmarks, nor all results obtained
in all works, but to illustrate the of results that have been reached.}
\\
\hline
\hline
Method			&	Year		& No.~of ES	& No.~of molecules		& Benchmark & 		MAE	(eV) &	Ref. \\
\hline
\endfirsthead
\hline
\hline
Method			&	Year		& No.~of ES	& No.~of molecules		& Benchmark & 		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}

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\end{document} 







