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\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France}
\newcommand{\CEISAM}{Laboratoire CEISAM (UMR 6230), CNRS, Universit\'e de Nantes, Nantes, France}

\begin{document}	

\title{Supplementary Material for ``Reference Energies for Double Excitations''}

\author{Pierre-Fran{\c c}ois Loos}
\email[Corresponding author: ]{loos@irsamc.ups-tlse.fr}
\affiliation{\LCPQ}
\author{Martial Boggio-Pasqua}
\affiliation{\LCPQ}
\author{Anthony Scemama}
\affiliation{\LCPQ}
\author{Michel Caffarel}
\affiliation{\LCPQ}
\author{Denis Jacquemin}
\affiliation{\CEISAM}     

\begin{abstract}
\end{abstract}

\maketitle

\tableofcontents

%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Geometries}
%%%%%%%%%%%%%%%%%%%%%%%%%%%

Below are given the cartesian coordinates of the compounds investigated in this study. 
These are provided in atomic units (bohr) and they have been obtained at the CC3(full)/aug-cc-pVTZ level of theory, except for hexatriene where the geometry has been optimized at the CCSD(T)/aug-cc-pVTZ level.

%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Acrolein}
%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{verbatim}
C   -1.11645072   -0.68348783    0.00000000
C    1.20647847    0.83714564    0.00000000
C    3.46831059   -0.28872636    0.00000000
O   -3.23666415    0.19187203    0.00000000
H   -0.80613858   -2.74747338    0.00000000
H    0.98699813    2.86613511    0.00000000
H    5.20930864    0.77443560    0.00000000
H    3.60951559   -2.33000749    0.00000000
\end{verbatim}

%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Benzene}
%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{verbatim}
C    0.00000000    2.63144965    0.00000000
C   -2.27890225    1.31572483    0.00000000
C   -2.27890225   -1.31572483    0.00000000
C    0.00000000   -2.63144965    0.00000000
C    2.27890225   -1.31572483    0.00000000
C    2.27890225    1.31572483    0.00000000
H   -4.04725813    2.33668557    0.00000000
H   -4.04725813   -2.33668557    0.00000000
H    0.00000000   -4.67337115    0.00000000
H    4.04725813   -2.33668557    0.00000000
H    4.04725813    2.33668557    0.00000000
H    0.00000000    4.67337115    0.00000000
\end{verbatim}

%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Butadiene}
%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{verbatim}
C    1.14656244    0.00000000    0.75468820
C   -1.14656244    0.00000000   -0.75468820
C    3.48132647    0.00000000   -0.22482805
C   -3.48132647    0.00000000    0.22482805
H    0.90770978    0.00000000    2.78883925
H   -0.90770978    0.00000000   -2.78883925
H    3.77525814    0.00000000   -2.24895470
H   -3.77525814    0.00000000    2.24895470
H    5.13664967    0.00000000    0.96861890
H   -5.13664967    0.00000000   -0.96861890
\end{verbatim}

%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Carbon dimer}
%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{verbatim}
C    0.00000000    0.00000000    1.17922927
C    0.00000000    0.00000000   -1.17922927
\end{verbatim}

%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Carbon trimer}
%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{verbatim}
C    0.00000000    0.00000000    0.00000000
C    0.00000000    0.00000000    2.45345613
C    0.00000000    0.00000000   -2.45345613
\end{verbatim}


%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Ethylene}
%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{verbatim}
C    0.00000000    1.26026583     0.00000000
C    0.00000000   -1.26026583     0.00000000
H    0.00000000    2.32345976     1.74287672
H    0.00000000   -2.32345976     1.74287672
H    0.00000000    2.32345976    -1.74287672
H    0.00000000   -2.32345976    -1.74287672
\end{verbatim}

%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Formaldehyde}
%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{verbatim}
C    0.00000000    0.00000000   -1.13947666
O    0.00000000    0.00000000    1.14402883
H    0.00000000    1.76627623   -2.23398653
H    0.00000000   -1.76627623   -2.23398653
\end{verbatim}

%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Glyoxal}
%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{verbatim}
C    1.21360282    0.75840215    0.00000000
C   -1.21360282   -0.75840215    0.00000000
O    3.25581408   -0.26453186    0.00000000
O   -3.25581408    0.26453186    0.00000000
H    0.96135276    2.81883243    0.00000000
H   -0.96135276   -2.81883243    0.00000000
\end{verbatim}

%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Hexatriene}
%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{verbatim}
C   -0.0002476    1.2717818   0.0000000
C    0.0002476   -1.2717818   0.0000000
C    2.2709215    2.7978697   0.0000000
C   -2.2709215   -2.7978697   0.0000000
C    2.2709215    5.3313687   0.0000000
C   -2.2709215   -5.3313687   0.0000000
H   -1.7938035    2.2677902   0.0000000
H    1.7938035   -2.2677902   0.0000000
H    4.0548550    1.7921594   0.0000000
H   -4.0548550   -1.7921594   0.0000000
H    0.5178662    6.3842559   0.0000000
H   -0.5178662   -6.3842559   0.0000000
H    4.0110587    6.3968755   0.0000000
H   -4.0110587   -6.3968755   0.0000000
\end{verbatim}

%%%%%%%%%%%%%%%%%%%%%%
\subsection{Nitrosomethane}
%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{verbatim}
C   -1.78426612    0.00000000   -1.07224050
N   -0.00541753    0.00000000    1.08060391
O    2.18814985    0.00000000    0.43452135
H   -0.77343975    0.00000000   -2.86415606
H   -2.97471478    1.66801808   -0.86424584
H   -2.97471478   -1.66801808   -0.86424584
\end{verbatim}

%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Nitroxyl}
%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{verbatim}
O    0.21099695    0.00000000    2.15462460
N   -0.44776863    0.00000000   -0.03589263
H    1.18163475    0.00000000   -1.17386890
\end{verbatim}

%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Pyrazine}
%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{verbatim}
N   -2.66620111    0.00000000    0.00000000
N    2.66620111    0.00000000    0.00000000
C   -1.31510863    2.13188686    0.00000000
C   -1.31510863   -2.13188686    0.00000000
C    1.31510863    2.13188686    0.00000000
C    1.31510863   -2.13188686    0.00000000
H   -2.35234226    3.88751412    0.00000000
H   -2.35234226   -3.88751412    0.00000000
H    2.35234226    3.88751412    0.00000000
H    2.35234226   -3.88751412    0.00000000
\end{verbatim}

%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Tetrazine}
%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{verbatim}
C  0.00000000  0.00000000   1.26054332
C  0.00000000  0.00000000  -1.26054332
N  0.00000000  1.19421138   0.66133002
N  0.00000000 -1.19421138   0.66133002
N  0.00000000  1.19421138  -0.66133002
N  0.00000000 -1.19421138  -0.66133002
H  0.00000000  0.00000000   2.33817427
H  0.00000000  0.00000000  -2.33817427
\end{verbatim}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Energetics of EOM-CC calculations}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%------------------------------
\subsection{Acrolein}
%------------------------------
%%% ACROLEIN %%%
\begin{table}[H]
	\caption{
	\label{tab:acrolein_CC}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of acrolein for various methods and basis sets.
	}
	\begin{ruledtabular}
	\begin{tabular}{llldddddd}
	Molecule	&	Method		&	Basis		&	\mc{3}{c}{1\,\ex{1}{A}{}{'} $\ra$ 2\,\ex{1}{A}{}{'}: \tr{\pi}{\pis}}	
												&	\mc{3}{c}{1\,\ex{1}{A}{}{'} $\ra$ 3\,\ex{1}{A}{}{'}: \tr{\pi,\pi}{\pis,\pis}}			\\
													\cline{4-6}	\cline{7-9}
				&				&				&	\mcc{1\,\ex{1}{A}{}{'}}	&	\mcc{2\,\ex{1}{A}{}{'}}	&	\mcc{$\Delta E$}	
												&	\mcc{1\,\ex{1}{A}{}{'}}	&	\mcc{3\,\ex{1}{A}{}{'}}	&	\mcc{$\Delta E$}	\\
	\hline
	Acrolein	&	CC3			&	6-31+G*		&	-191.370\,506 	&	-191.119\,437  	&	6.83	
												&	-191.370\,506 	&	-191.068\,953	&	8.21		\\
				&				&	AVDZ		&	-191.445\,933	&	-191.200\,748	&	6.67				
												&	-191.445\,933	&	-191.148\,026	&	8.11		\\
				&				&	AVTZ		&	-191.613\,332	&	-191.368\,842	&	6.65		
												&	-191.613\,332	&	-191.316\,467	&	8.08		\\
%				&	EOM-CCSDT	&	6-31+G*		&		&		&	\\
%				&				&	AVDZ		&		&		&	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}
%------------------------------
\subsection{Benzene}
%------------------------------

%%% BENZENE %%%
\begin{table}[H]
	\caption{
	\label{tab:benzene_CC}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of benzene for various methods and basis sets.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllddd}
	Molecule	&	Method		&	Basis	&	\mc{3}{c}{1\,\ex{1}{A}{1g}{} $\ra$ 1\,\ex{1}{E}{2g}{}: \tr{\pi,\pi}{\pis,\pis}}	\\
												\cline{4-6}	
				&				&			&	\mcc{1\,\ex{1}{A}{1g}{}}	&	\mcc{1\,\ex{1}{E}{2g}{}}	&	\mcc{$\Delta E$}	\\
	\hline
	Benzene		&	CC3				&	6-31+G*	&	-231.537\,359	&	-231.224\,840	&	8.50		\\
				&					&	AVDZ	&	-231.615\,828	&	-231.305\,692	&	8.44		\\
				&					&	AVTZ	&	-231.823\,303	&	-231.515\,298	&	8.38		\\
				&	EOM-CCSDT		&	6-31+G*	&	-231.544\,019	&	-231.234\,416	&	8.42  		\\
%				&					&	AVDZ	&		&		&			\\
	\end{tabular}
	\end{ruledtabular}
\end{table}

%------------------------------
\subsection{Beryllium}
%------------------------------

%%% BERYLLIUM
\begin{table}[H]
	\caption{
	\label{tab:Be_CC}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of beryllium for various methods and basis sets.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllddd}
	Molecule	&	Method				&	Basis		&	\mc{3}{c}{1\,\ex{1}{S}{}{} $\ra$ 1\,\ex{1}{D}{}{}: \tr{2s^2}{2p^2}}	\\
															\cline{4-6}
				&						&				&	\mcc{1\,\ex{1}{S}{}{}}	&	\mcc{1\,\ex{1}{D}{}{}}	&	\mcc{$\Delta E$}	\\
	\hline
	Beryllium	&	CC3					&	6-31+G*		&	-14.615\,618		&	-14.320\,113	&	8.04	\\
				&						&	AVDZ		&	-14.617\,469		&	-14.617\,469	&	7.23	\\
				&						&	AVTZ		&	-14.624\,384		&	-14.361\,336	&	7.16	\\
				&						&	AVQZ		&	-14.640\,094		&	-14.378\,479	&	7.12	\\
				&	EOM-CCSDT			&	6-31+G*		&	-14.615\,628		&	-14.320\,223	&	8.04	\\
				&						&	AVDZ		&	-14.617\,474		&	-14.351\,962	&	7.22	\\
				&						&	AVTZ		&	-14.624\,415		&	-14.361\,571	&	7.15	\\
				&						&	AVQZ		&	-14.640\,163		&	-14.378\,990	&	7.11	\\
				&	EOM-CCSDTQ			&	6-31+G*		&	-14.615\,630		&	-14.320\,232	&	8.04	\\
				&						&	AVDZ		&	-14.617\,476		&	-14.351\,972	&	7.23	\\
				&						&	AVTZ		&	-14.624\,424		&	-14.361\,624	&	7.15	\\
				&						&	AVQZ		&	-14.640\,171		&	-14.379\,038	&	7.11	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}


%------------------------------
\subsection{Butadiene}
%------------------------------

%%% BUTADIENE %%%
\begin{table}[H]
	\caption{
	\label{tab:butadiene_CC}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of butadiene for various methods and basis sets.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllddd}
	Molecule	&	Method		&	Basis	&	\mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{\pi,\pi}{\pis,\pis}}	\\
												\cline{4-6}
				&				&			&	\mcc{1\,\ex{1}{A}{g}{}}	&	\mcc{2\,\ex{1}{A}{g}{}}	&	\mcc{$\Delta E$}	\\
	\hline
	Butadiene	&	CC3				&	6-31+G*	&	-155.492\,606		&	-155.245\,263		&	6.73	\\
				&					&	AVDZ	&	-155.563\,604		&	-155.318\,201		&	6.68	\\
				&					&	AVTZ	&	-155.707\,377		&	-155.462\,232		&	6.67	\\
				&					&	AVQZ	&	-155.746\,249		&	-155.501\,078		&	6.67	\\
				&	EOM-CCSDT		&	6-31+G*	&	-155.498\,045		&	-155.254\,297		&	6.63	\\
				&					&	AVDZ	&	-155.563\,681		&	-155.321\,535		&	6.59	\\
				&					&	AVTZ	&	-155.706\,231		&			&		\\
	\end{tabular}
	\end{ruledtabular}
\end{table}

%------------------------------
\subsection{Carbon dimer}
%------------------------------

%%% CARBON DIMER %%%
\begin{table}[H]
	\caption{
	\label{tab:C2_CC}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of the carbon dimer for various methods and basis sets.
	}
	\begin{ruledtabular}
	\begin{tabular}{llldddddd}
	Molecule	&	Method		&	Basis	&	\mc{3}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 2\,\ex{1}{\Sigma}{g}{+}}	
											&	\mc{3}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 1\,\ex{1}{\Delta}{g}{}}		\\
												\cline{4-6}		\cline{7-9}
				&				&			&	\mcc{1\,\ex{1}{\Sigma}{g}{+}}	&	\mcc{2\,\ex{1}{\Sigma}{g}{+}}	&	\mcc{$\Delta E$}	
											&	\mcc{1\,\ex{1}{\Sigma}{g}{+}}	&	\mcc{1\,\ex{1}{\Delta}{g}{}}	&	\mcc{$\Delta E$}	\\
	\hline
	Carbon dimer&	CC3			&	6-31+G*	&	-75.726\,283	&	-75.612\,374	&	3.10		&	-75.726\,283	&	-75.607\,558	&	3.23	\\
				&				&	AVDZ	&	-75.734\,267	&	-75.620\,083	&	3.11		&	-75.734\,267	&	-75.613\,622	&	3.28	\\
				&				&	AVTZ	&	-75.787\,555	&	-75.675\,376	&	3.05		&	-75.787\,555	&	-75.667\,882	&	3.25	\\
				&				&	AVQZ	&	-75.803\,550	&	-75.692\,215	&	3.03		&	-75.803\,550	&	-75.684\,510	&	3.24	\\
				&	EOM-CCSDT	&	6-31+G*	&	-75.724\,387	&	-75.625\,387	&	2.69		&	-75.724\,387	&	-75.619\,114	&	2.86  	\\
				&				&	AVDZ	&	-75.732\,355	&	-75.635\,647	&	2.63		&	-75.732\,355	&	-75.626\,726	&	2.87	\\
				&				&	AVTZ	&	-75.784\,146	&	-75.689\,819	&	2.57		&	-75.784\,146	&	-75.678\,992	&	2.86	\\
				&				&	AVQZ	&	-75.799\,645	&	-75.705\,297	&	2.57		&	-75.799\,645	&	-75.694\,314	&	2.87	\\
				&	EOM-CCSDTQ	&	6-31+G*	&	-75.727\,010	&	-75.641\,912	&	2.32		&	-75.727\,010	&	-75.634\,258	&	2.52  	\\
				&				&	AVDZ	&	-75.735\,284	&	-75.652\,947	&	2.24		&	-75.735\,284	&	-75.642\,656	&	2.52	\\
				&				&	AVTZ	&	-75.787\,747	&	-75.709\,576	&	2.13		&	-75.787\,747	&	-75.697\,804	&	2.45	\\
				&	EOM-CCSDTQP	&	6-31+G*	&	-75.727\,492	&	-75.643\,261	&	2.29		&	-75.727\,492	&	-75.727\,492	&	2.51  	\\
				&				&	AVDZ	&	-75.735\,840	&	-75.654\,491	&	2.21		&	-75.735\,840	&	-75.643\,803	&	2.50	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}

%------------------------------
\subsection{Carbon trimer}
%------------------------------

%%% CARBON TRIMER %%%
\begin{table}[H]
	\caption{
	\label{tab:C3_CC}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of the carbon trimer for various methods and basis sets.
	}
	\begin{ruledtabular}
	\begin{tabular}{llldddddd}
	Molecule	&	Method		&	Basis	&	\mc{3}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 2\,\ex{1}{\Sigma}{g}{+}}	
											&	\mc{3}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 1\,\ex{1}{\Delta}{g}{}}		\\
												\cline{4-6}		\cline{7-9}
				&				&			&	\mcc{1\,\ex{1}{\Sigma}{g}{+}}	&	\mcc{2\,\ex{1}{\Sigma}{g}{+}}	&	\mcc{$\Delta E$}	
											&	\mcc{1\,\ex{1}{\Sigma}{g}{+}}	&	\mcc{1\,\ex{1}{\Delta}{g}{}}	&	\mcc{$\Delta E$}	\\
	\hline
	Carbon trimer	&	CC3			&	6-31+G*	&	-113.745\,261	&	-113.500\,779		&	6.65		&	-113.745\,261		&	-113.480\,808  	&	7.20	\\
					&				&	AVDZ	&	-113.759\,083	&	-113.514\,829		&	6.65		&	-113.759\,083		&	-113.494\,687 	&	7.20	\\
					&				&	AVTZ	&	-113.844\,068	&	-113.598\,548	 	&	6.68		&	-113.844\,068		&	-113.578\,066	&	7.24	\\
					&				&	AVQZ	&	-113.868\,492	&	-113.623\,578	 	&	6.66		&	-113.868\,492		&	-113.603\,104  	&	7.22	\\
					&	EOM-CCSDT	&	6-31+G*	&	-113.741\,023	&	-113.525\,900		&	5.85		&	-113.741\,023		&	-113.501\,431  	&	6.52  	\\
					&				&	AVDZ	&	-113.755\,069	&	-113.541\,328		&	5.82		&	-113.755\,069		&	-113.516\,450	&	6.49	\\
					&				&	AVTZ	&	-113.838\,608	&	-113.621\,830		&	5.90		&	-113.838\,608		&	-113.597\,120 	&	6.57	\\
					&				&	AVQZ	&	-113.862\,469	&	-113.645\,020		&	5.92		&	-113.862\,469		&	-113.620\,516	&	6.58	\\
					&	EOM-CCSDTQ	&	6-31+G*	&	-113.743\,343	&	-113.546\,630		&	5.35		&	-113.743\,343		&	-113.522\,060	&	6.02  	\\
					&				&	AVDZ	&	-113.757\,672   &	-113.562\,458		&	5.31		&	-113.757\,672		&	-113.537\,320	&	6.00	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}

%------------------------------
\subsection{Ethylene}
%------------------------------

%%% ETHYLENE %%%
\begin{table}[H]
	\caption{
	\label{tab:ethylene_CC}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of ethylene for various methods and basis sets.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllddd}
	Molecule	&	Method		&	Basis	&	\mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{\pi,\pi}{\pis,\pis}}	\\
														\cline{4-6}
				&				&			&	\mcc{1\,\ex{1}{A}{g}{}}	&	\mcc{2\,\ex{1}{A}{g}{}}	&	\mcc{$\Delta E$}	\\
	\hline
	Ethylene	&	CC3			&	6-31+G*	&	-78.325\,158	&	-77.817\,291	&	13.82		\\
				&				&	AVDZ	&	-78.368\,712	&	-77.870\,066  	&	13.57	\\
				&				&	AVTZ	&	-78.444\,299	&	-77.951\,137   	&	13.42	\\
				&				&	AVQZ	&	-78.464\,260	&	-77.984\,451	&	13.06\\
				&	EOM-CCSDT	&	6-31+G*	&	-78.325\,466  	&	-77.829\,347  	&	13.50 	\\
				&				&	AVDZ	&	-78.369\,061  	&	-77.883\,840 	&	13.20	\\
%				&				&	AVTZ	&	-78.444\,096	&		&		\\
				&	EOM-CCSDTQ	&	6-31+G*	&	-78.325\,913 	&	-77.833\,839	&	13.39	\\
				&				&	AVDZ	&	-78.369\,710   	&	-77.889\,453	&	13.07	\\
				&	EOM-CCSDTQP	&	6-31+G*	&	-78.325\,962 	&	-77.834\,035	&	13.39	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}

%------------------------------
\subsection{Formaldehyde}
%------------------------------

%%% FORMALDEHYDE %%%
\begin{table}[H]
	\caption{
	\label{tab:formaldehyde_CC}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of ethylene for various methods and basis sets.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllddd}
	Molecule	&	Method		&	Basis	&	\mc{3}{c}{1\,\ex{1}{A}{1}{} $\ra$ 3\,\ex{1}{A}{g}{}: \tr{n,n}{\pis,\pis}}	\\
														\cline{4-6}
				&				&			&	\mcc{1\,\ex{1}{A}{1}{}}	&	\mcc{3\,\ex{1}{A}{1}{}}	&	\mcc{$\Delta E$}	\\
	\hline
	Formaldehyde&	CC3			&	6-31+G*	&	-114.196\,244	&	-113.773\,939	&	11.49		\\
				&				&	AVDZ	&	-114.245\,501	&	-113.833\,222  	&	11.22	\\
				&				&	AVTZ	&	-114.344\,118	&	-113.932\,524 	&	11.20	\\
				&				&	AVQZ	&	-114.373\,678	&	-113.962\,323	&	11.19	\\
				&	EOM-CCSDT	&	6-31+G*	&	-114.195\,911  	&	-113.787\,932 	&	11.10 	\\
				&				&	AVDZ	&	-114.245\,054 	&	-113.848\,759	&	10.78	\\
				&				&	AVTZ	&	-114.343\,049	&	-113.946\,700	&	10.79	\\
				&				&	AVQZ	&	-114.372\,366	&	-113.975\,394	&	10.80	\\
				&	EOM-CCSDTQ	&	6-31+G*	&	-114.196\,803	&	-113.797\,250	&	10.87	\\
				&				&	AVDZ	&	-114.246\,007  	&	-113.862\,524	&	10.44	\\
				&	EOM-CCSDTQP	&	6-31+G*	&	-114.196\,855 	&	-113.797\,764	&	10.86	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}

%------------------------------
\subsection{Glyoxal}
%------------------------------

%%% GLYOXAL %%%
\begin{table}[H]
	\caption{
	\label{tab:glyoxal_CC}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of glyoxal for various methods and basis sets.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllddd}
	Molecule	&	Method				&	Basis		&	\mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{n,n}{\pis,\pis}}	\\
															\cline{4-6}
				&						&				&	\mcc{1\,\ex{1}{A}{g}{}}	&	\mcc{2\,\ex{1}{A}{g}{}}	&	\mcc{$\Delta E$}	\\
	\hline
	Glyoxal	&	CC3					&	6-31+G*		&	-227.236\,455		&	-226.988\,947		&	6.74	\\
			&						&	AVDZ		&	-227.317\,437		&	-227.070\,979		&	6.71	\\
			&						&	AVTZ		&	-227.507\,912		&	-227.259\,369		&	6.76	\\
			&						&	AVQZ		&	-227.566\,052		&	-227.317\,664		&	6.76	\\
			&	EOM-CCSDT			&	6-31+G*		&	-227.235\,215		&	-227.005\,775		&	6.24	\\
			&						&	AVDZ		&	-227.315\,943		&	-227.087\,288		&	6.22	\\
			&						&	AVTZ		&	-227.505\,065		&	-227.271\,579		&	6.35	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}

%------------------------------
\subsection{Hexatriene}
%------------------------------

%%% HEXATRIENE %%%
\begin{table}[H]
	\caption{
	\label{tab:hexatriene_CC}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of hexatriene for various methods and basis sets.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllddd}
	Molecule	&	Method				&	Basis		&	\mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{\pi,\pi}{\pis,\pis}}	\\
															\cline{4-6}
				&						&				&	\mcc{1\,\ex{1}{A}{g}{}}	&	\mcc{2\,\ex{1}{A}{g}{}}	&	\mcc{$\Delta E$}	\\
	\hline
	Hexatriene	&	CC3					&	6-31+G*		&	-232.661\,482		&	-232.449\,077	&	5.78	\\
				&						&	AVDZ		&	-232.759\,871		&	-232.547\,649	&	5.77	\\
				&						&	AVTZ		&	-232.971\,955		&	-232.760\,024	&	5.77	\\
				&	EOM-CCSDT			&	6-31+G*		&	-232.669\,310		&	-232.462\,052	&	5.64	\\
				&						&	AVDZ		&	-232.759\,513		&	-232.551\,992	&	5.65	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}

%------------------------------
\subsection{Nitrosomethane}
%------------------------------

%%% NITROSOMETHANE %%%
\begin{table}[H]
	\caption{
	\label{tab:nitrosomethane_CC}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of nitrosomethane for various methods and basis sets.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllddd}
	Molecule	&	Method				&	Basis		&	\mc{3}{c}{1\,\ex{1}{A}{}{'} $\ra$ 2\,\ex{1}{A}{}{'}: \tr{n,n}{\pis,\pis}}	\\
												\cline{4-6}
				&						&				&	\mcc{1\,\ex{1}{A}{}{'}}	&	\mcc{2\,\ex{1}{A}{}{'}}	&	\mcc{$\Delta E$}	\\
	\hline
	Nitrosomethane	&	CC3			&	6-31+G*		&	-169.342\,484	&	-169.131\,944	&	5.73	\\
					&				&	AVDZ		&	-169.414\,755	&	-169.203\,473	&	5.75	\\
					&				&	AVTZ		&	-169.559\,567	&	-169.347\,997	&	5.76	\\
					&				&	AVQZ		&	-169.602\,537	&	-169.391\,634	&	5.74	\\
					&	EOM-CCSDT	&	6-31+G*		&	-169.342\,012	&	-169.148\,711	&	5.26	\\
					&				&	AVDZ		&	-169.414\,096	&	-169.220\,885	&	5.26	\\
					&				&	AVTZ		&	-169.557\,831	&	-169.363\,318	&	5.29	\\
		\end{tabular}
	\end{ruledtabular}
\end{table}

%------------------------------
\subsection{Nitroxyl}
%------------------------------

%%% NITRSOXYL %%%
\begin{table}[H]
	\caption{
	\label{tab:nitroxyl_CC}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of nitroxyl for various methods and basis sets.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllddd}
	Molecule	&	Method		&	Basis		&	\mc{3}{c}{1\,\ex{1}{A}{}{'} $\ra$ 2\,\ex{1}{A}{}{'}: \tr{n,n}{\pis,\pis}}	\\
															\cline{4-6}
				&				&				&	\mcc{1\,\ex{1}{A}{}{'}}	&	\mcc{2\,\ex{1}{A}{}{'}}	&	\mcc{$\Delta E$}	\\
	\hline
	Nitroxyl&	CC3				&	6-31+G*		&	-130.151\,876	&	-129.957\,929	&	5.28	\\
			&					&	AVDZ		&	-130.204\,169	&	-130.011\,360	&	5.25	\\
			&					&	AVTZ		&	-130.310\,876	&	-130.117\,680	&	5.26	\\
			&					&	AVQZ		&	-130.343\,921	&	-130.151\,556	&	5.23	\\
			&	EOM-CCSDT		&	6-31+G*		&	-130.151\,628	&	-129.974\,547	&	4.82	\\
			&					&	AVDZ		&	-130.203\,765	&	-130.028\,985	&	4.76	\\
			&					&	AVTZ		&	-130.309\,652	&	-130.133\,807	&	4.79	\\
			&					&	AVQZ		&	-130.342\,420	&	-130.166\,137	&	4.80	\\
			&	EOM-CCSDTQ		&	6-31+G*		&	-130.153\,185	&	-129.986\,516	&	4.54	\\
			&					&	AVDZ		&	-130.205\,384	&	-130.042\,787	&	4.42	\\
			&	EOM-CCSDTQP		&	6-31+G*		&	-130.153\,329	&	-129.987\,473	&	4.51\\
	\end{tabular}
	\end{ruledtabular}
\end{table}

%------------------------------
\subsection{Pyrazine}
%------------------------------

%%% PYRAZINE %%%
\begin{table}[H]
	\caption{
	\label{tab:pyrazine_CC}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of pyrazine for various methods and basis sets.
	Note the inversion of the two transitions compared to multiconfigurational calculations (see Table \ref{tab:pyrazine_CAS}).
	}
	\begin{ruledtabular}
	\begin{tabular}{llldddddd}
	Molecule	&	Method				&	Basis		&	\mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{n,n}{\pis,\pis}}	
														&	\mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 3\,\ex{1}{A}{g}{}: \tr{\pi,\pi}{\pis,\pis}}	\\
															\cline{4-6} \cline{7-9}
				&						&				&	\mcc{1\,\ex{1}{A}{g}{}}	&	\mcc{2\,\ex{1}{A}{g}{}}	&	\mcc{$\Delta E$}	
														&	\mcc{1\,\ex{1}{A}{g}{}}	&	\mcc{3\,\ex{1}{A}{g}{}}	&	\mcc{$\Delta E$}	\\
	\hline
	Pyrazine	&	CC3					&	6-31+G*		&	-263.574\,080	&	-263.247\,798	&	8.88	&	-263.574\,080	&	-263.233\,284	&	9.27	\\
				&						&	AVDZ		&	-263.651\,711	&	-263.329\,377	&	8.77	&	-263.651\,711	&	-263.314\,640	&	9.17	\\
				&						&	AVTZ		&	-263.876\,837	&	-263.557\,246	&	8.69	&	-263.876\,837	&	-263.539\,937	&	9.17	\\
%				&						&	AVQZ		&		&		&	\\
%				&	EOM-CCSDT			&	6-31+G*		&		&		&	\\
%				&						&	AVDZ		&		&		&	\\
%				&						&	AVTZ		&		&		&	\\
%				&						&	AVQZ		&		&		&	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}


%------------------------------
\subsection{Tetrazine}
%------------------------------

%%% TETRAZINE %%%
\begin{squeezetable}
\begin{table}[H]
	\caption{
	\label{tab:tetrazine_CC}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of tetrazine for various methods and basis sets.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllddddddddd}
	Molecule	&	Method		&	Basis		&	\mc{3}{c}{1\,\ex{1}{A}{1g}{} $\ra$ 2\,\ex{1}{A}{1g}{}: \tr{n,n}{\pis,\pis}}
												&	\mc{3}{c}{1\,\ex{1}{A}{1g}{} $\ra$ 1\,\ex{1}{B}{3g}{}: \tr{n,n}{\pis_1,\pis_2}}	
												&	\mc{3}{c}{1\,\ex{1}{A}{1g}{} $\ra$ 1\,\ex{3}{B}{3g}{}: \tr{n,n}{\pis_1,\pis_2}}	\\
													\cline{4-6}	\cline{7-9} \cline{10-12}
				&				&				&	\mcc{1\,\ex{1}{A}{1g}{}}	&	\mcc{2\,\ex{1}{A}{1g}{}}	&	\mcc{$\Delta E$}
												&	\mcc{1\,\ex{1}{A}{1g}{}}	&	\mcc{1\,\ex{1}{B}{3g}{}}	&	\mcc{$\Delta E$}
												&	\mcc{1\,\ex{1}{A}{1g}{}}	&	\mcc{1\,\ex{3}{B}{3g}{}}	&	\mcc{$\Delta E$}	\\
	\hline
	Tetrazine	&	CC3			&	6-31+G*		&	295.547\,380	&	295.318\,726	&	6.22
												&	295.547\,380	&	295.266\,625	&	7.64
												&	295.547\,380	&	295.277\,104	&	7.35	\\
				&				&	AVDZ		&	295.628\,264	&	295.399\,771	&	6.22
												&	295.628\,264	&	295.348\,321	&	7.62
												&	295.628\,264	&	295.358\,861	&	7.33	\\
				&				&	AVTZ		&	295.870\,425	&	295.642\,258	&	6.21
												&	295.870\,425	&	295.590\,509	&	7.62
												&	295.870\,425	&	295.600\,445	&	7.35	\\
				&				&	AVQZ		&	295.943\,553	&	295.716\,082	&	6.19
												&	295.943\,553	&	295.664\,184	&	7.60
												&	295.943\,553	&	295.673\,917	&	7.34	\\
				&	EOM-CCSDT	&	6-31+G*		&	295.543\,914	&	295.328\,716	&	5.86
%												&		&		&	
%												&		&		&	\\
				&				&	AVDZ		&	295.624\,243	&	295.408\,977	&	5.86
%												&		&		&	
%												&		&		&	\\
%				&				&	AVTZ		&		&		&	
%												&		&		&	
%												&		&		&	\\
%				&				&	AVQZ		&		&		&	
%												&		&		&	
%												&		&		&	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}
\end{squeezetable}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Energetics of multiconfigurational calculations}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%------------------------------
\subsection{Acrolein}
%------------------------------

%%% ACROLEIN %%%
\begin{table}[H]
	\caption{
	\label{tab:acrolein_CAS}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of acrolein for various methods and basis sets.
	The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
	The $(4,4)$ active space contains the $\piCC$, $\piCO$, $\pisCC$ and $\pisCO$ orbitals. 
	The $(10,10)$ active space adds up the $\siCC$, $\siCO$, $\sisCC$ and $\sisCO$ orbitals.
	The state-averaged (SA) CASSCF calculation is performed with $3$ states.
	}
	\begin{ruledtabular}
	\begin{tabular}{llldddddd}
	Molecule	&	Method				&	Basis		&	\mc{3}{c}{1\,\ex{1}{A}{}{'} $\ra$ 2\,\ex{1}{A}{}{'}: \tr{\pi}{\pis}}	
														&	\mc{3}{c}{1\,\ex{1}{A}{}{'} $\ra$ 3\,\ex{1}{A}{}{'}: \tr{\pi,\pi}{\pis,\pis}}			\\
															\cline{4-6}\cline{7-9}
				&						&				&	\mcc{1\,\ex{1}{A}{}{'}}	&	\mcc{2\,\ex{1}{A}{}{'}}	&	\mcc{$\Delta E$}	
														&	\mcc{1\,\ex{1}{A}{}{'}}	&	\mcc{3\,\ex{1}{A}{}{'}}	&	\mcc{$\Delta E$}	\\
	\hline
	Acrolein	&	SA-CASSCF(4,4)		&	6-31+G*		&	-190.816\,793	&	-190.494\,611	&	8.77	&	-190.816\,793	&	-190.527\,136	&	7.88	\\
				&						&	AVDZ		&	-190.836\,891	&	-190.519\,307	&	8.64	&	-190.836\,891	&	-190.547\,121	&	7.89	\\
				&						&	AVTZ		&	-190.882\,696	&	-190.565\,771	&	8.62	&	-190.882\,696	&	-190.593\,513	&	7.87	\\
				&						&	AVQZ		&	-190.894\,452	&	-190.577\,536	&	8.62	&	-190.894\,452	&	-190.605\,403	&	7.87	\\
				&	CASPT2(4,4)			&	6-31+G*		&	-191.324\,307	&	-191.047\,227	&	7.28	&	-191.324\,307	&	-191.020\,060	&	8.02	\\
				&						&	AVDZ		&	-191.394\,637	&	-191.121\,911	&	7.13	&	-191.394\,637	&	-191.092\,243	&	7.94	\\
				&						&	AVTZ		&	-191.561\,092	&	-191.291\,491	&	7.03	&	-191.561\,092	&	-191.258\,865	&	7.92	\\
				&						&	AVQZ		&	-191.614\,759	&	-191.345\,798	&	7.01	&	-191.614\,759	&	-191.311\,943	&	7.93	\\
				&	MS-CASPT2(4,4)		&	6-31+G*		&	-191.315\,591	&	-191.061\,210	&	6.92	&	-191.315\,591	&	-191.005\,163	&	8.45	\\
				&						&	AVDZ		&	-191.385\,082	&	-191.137\,241	&	6.74	&	-191.385\,082	&	-191.075\,842	&	8.41	\\
				&						&	AVTZ		&	-191.551\,275	&	-191.306\,016	&	6.67	&	-191.551\,275	&	-191.243\,026	&	8.39	\\
				&						&	AVQZ		&	-191.604\,948	&	-191.360\,303	&	6.66	&	-191.604\,948	&	-191.296\,011	&	8.41	\\
				&	XMS-CASPT2(4,4)		&	6-31+G*		&	-191.314\,712	&	-191.055\,201	&	7.06	&	-191.314\,712	&	-191.009\,976	&	8.29	\\	
				&						&	AVDZ		&	-191.384\,070	&	-191.130\,132	&	6.91	&	-191.384\,070	&	-191.081\,589	&	8.23	\\	
				&						&	AVTZ		&	-191.550\,097	&	-191.299\,092	&	6.83	&	-191.550\,097	&	-191.248\,936	&	8.20	\\	
				&						&	AVQZ		&	-191.603\,706	&	-191.353\,389	&	6.81	&	-191.603\,706	&	-191.301\,988	&	8.21	\\	
				&	PC-NEVPT2(4,4)		&	6-31+G*		&	-191.324\,250	&	-191.076\,946	&	6.73	&	-191.324\,250	&	-191.024\,801	&	8.15	\\
				&						&	AVDZ		&	-191.393\,648	&	-191.151\,487	&	6.59	&	-191.393\,648	&	-191.096\,983	&	8.07	\\
				&						&	AVTZ		&	-191.559\,225	&	-191.321\,416	&	6.47	&	-191.559\,225	&	-191.263\,015	&	8.06	\\
				&						&	AVQZ		&	-191.612\,658	&	-191.375\,778	&	6.45	&	-191.612\,658	&	-191.315\,961	&	8.07	\\
				&	SC-NEVPT2(4,4)		&	6-31+G*		&	-191.323\,420	&	-191.068\,805	&	6.93	&	-191.323\,420	&	-191.022\,315	&	8.19	\\
				&						&	AVDZ		&	-191.392\,720	&	-191.143\,095	&	6.79	&	-191.392\,720	&	-191.094\,153	&	8.12	\\
				&						&	AVTZ		&	-191.558\,276	&	-191.312\,963	&	6.68	&	-191.558\,276	&	-191.260\,162	&	8.11	\\
				&						&	AVQZ		&	-191.611\,699	&	-191.367\,369	&	6.65	&	-191.611\,699	&	-191.313\,100	&	8.13	\\
				&	SA-CASSCF(10,10)	&	6-31+G*		&	-190.901\,844	&	-190.604\,891	&	8.52	&	-190.901\,844	&	-190.588\,596	&	8.08	\\
				&						&	AVDZ		&	-190.922\,572	&	-190.627\,675	&	8.48	&	-190.922\,572	&	-190.610\,975	&	8.02	\\
				&						&	AVTZ		&	-190.969\,088	&	-190.674\,144	&	8.45	&	-190.969\,088	&	-190.658\,408	&	8.03	\\
				&						&	AVQZ		&	-190.981\,013	&	-190.686\,066	&	8.45	&	-190.981\,013	&	-190.670\,433	&	8.03	\\
				&	CASPT2(10,10)		&	6-31+G*		&	-191.317\,112	&	-191.048\,898	&	7.30	&	-191.317\,112	&	-191.025\,543	&	7.93	\\
				&						&	AVDZ		&	-191.386\,586	&	-191.125\,107	&	7.12	&	-191.386\,586	&	-191.095\,164	&	7.93	\\
				&						&	AVTZ		&	-191.550\,979	&	-191.292\,124	&	7.04	&	-191.550\,979	&	-191.262\,481	&	7.85	\\
				&						&	AVQZ		&	-191.603\,845	&	-191.345\,407	&	7.03	&	-191.603\,845	&	-191.315\,601	&	7.84	\\
				&	MS-CASPT2(10,10)	&	6-31+G*		&	-191.317\,379	&	-191.064\,112	&	6.89	&	-191.317\,379	&	-191.010\,063	&	8.36	\\
				&						&	AVDZ		&	-191.386\,909	&	-191.138\,090	&	6.77	&	-191.386\,909	&	-191.081\,858	&	8.30	\\
				&						&	AVTZ		&	-191.551\,428	&	-191.307\,080	&	6.65	&	-191.551\,428	&	-191.247\,076	&	8.28	\\
				&						&	AVQZ		&	-191.604\,360	&	-191.361\,127	&	6.62	&	-191.604\,360	&	-191.299\,366	&	8.30	\\
				&	XMS-CASPT2(10,10)	&	6-31+G*		&	-191.317\,068	&	-191.054\,948	&	7.13	&	-191.317\,068	&	-191.016\,423	&	8.18	\\	
				&						&	AVDZ		&	-191.386\,545	&	-191.129\,376	&	7.00	&	-191.386\,545	&	-191.088\,046	&	8.12	\\	
				&						&	AVTZ		&	-191.550\,964	&	-191.297\,066	&	6.91	&	-191.550\,964	&	-191.254\,533	&	8.07	\\	
				&						&	AVQZ		&	-191.603\,851	&	-191.350\,762	&	6.89	&	-191.603\,851	&	-191.307\,168	&	8.07	\\	
				&	PC-NEVPT2(10,10)	&	6-31+G*		&	-191.306\,884	&	-191.042\,313	&	7.20	&	-191.306\,884	&	-191.016\,252	&	7.91	\\
				&						&	AVDZ		&	-191.373\,865	&	-191.117\,154	&	6.99	&	-191.373\,865	&	-191.082\,430	&	7.93	\\
				&						&	AVTZ		&	-191.535\,396	&	-191.281\,326	&	6.91	&	-191.535\,396	&	-191.247\,069	&	7.85	\\
				&						&	AVQZ		&	-191.587\,434	&	-191.333\,787	&	6.90	&	-191.587\,434	&	-191.299\,435	&	7.84	\\
				&	SC-NEVPT2(10,10)	&	6-31+G*		&	-191.301\,553	&	-191.029\,383	&	7.41	&	-191.301\,553	&	-191.004\,556	&	8.08	\\
				&						&	AVDZ		&	-191.368\,122	&	-191.102\,474	&	7.23	&	-191.368\,122	&	-191.070\,989	&	8.09	\\
				&						&	AVTZ		&	-191.529\,364	&	-191.266\,222	&	7.16	&	-191.529\,364	&	-191.235\,143	&	8.01	\\
				&						&	AVQZ		&	-191.581\,316	&	-191.318\,611	&	7.15	&	-191.581\,316	&	-191.287\,313	&	8.00	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}
		
%------------------------------
\subsection{Benzene}
%------------------------------

%%% BENZENE %%%
\begin{table}[H]
	\caption{
	\label{tab:benzene_CAS}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of benzene for various methods and basis sets.
	The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
	The $(6,6)$ active space contains the $\piCC$ and $\pisCC$ orbitals.
	The state-averaged (SA) CASSCF calculations for the 1\,\ex{1}{A}{1g}{} $\ra$ 1\,\ex{1}{E}{2g}{} and 1\,\ex{1}{A}{1g}{} $\ra$ 2\,\ex{1}{A}{1g}{} transition are performed with $3$ and $4$ states, respectively.
	}
	\begin{ruledtabular}
	\begin{tabular}{llldddddd}
	Molecule	&	Method		&	Basis	&	\mc{3}{c}{1\,\ex{1}{A}{1g}{} $\ra$ 1\,\ex{1}{E}{2g}{}: \tr{\pi,\pi}{\pis,\pis}}	
											&	\mc{3}{c}{1\,\ex{1}{A}{1g}{} $\ra$ 2\,\ex{1}{A}{1g}{}: \tr{\pi,\pi}{\pis,\pis}}	\\
												\cline{4-6}	\cline{7-9}
				&				&			&	\mcc{1\,\ex{1}{A}{1g}{}}	&	\mcc{1\,\ex{1}{E}{2g}{}}	&	\mcc{$\Delta E$}	
											&	\mcc{1\,\ex{1}{A}{1g}{}}	&	\mcc{2\,\ex{1}{A}{1g}{}}	&	\mcc{$\Delta E$}	\\
	\hline
	Benzene		&	SA-CASSCF(6,6)	&	6-31+G*	&	-230.777\,109	&	-230.478\,032	&	8.14	&	-230.775\,595	&	-230.352\,550	&	11.51	\\
				&					&	AVDZ	&	-230.794\,127	&	-230.495\,900	&	8.12	&	-230.792\,529	&	-230.371\,597	&	11.45	\\
				&					&	AVTZ	&	-230.847\,275	&	-230.549\,481	&	8.10	&	-230.845\,668	&	-230.425\,112	&	11.44	\\
				&					&	AVQZ	&	-230.860\,443	&	-230.562\,744	&	8.10	&	-230.858\,833	&	-230.438\,347	&	11.44	\\
				&	CASPT2(6,6)		&	6-31+G*	&	-231.454\,277	&	-231.144\,541	&	8.43	&	-231.454\,825	&	-231.067\,472	&	10.54	\\
				&					&	AVDZ	&	-231.526\,608	&	-231.218\,048	&	8.40	&	-231.527\,187	&	-231.145\,592	&	10.38	\\
				&					&	AVTZ	&	-231.732\,461	&	-231.426\,037	&	8.34	&	-231.733\,152	&	-231.355\,298	&	10.28	\\
				&					&	AVQZ	&	-231.797\,381	&	-231.490\,833	&	8.34	&	-231.798\,119	&	-231.420\,880	&	10.27	\\
				&	MS-CASPT2(6,6)	&	6-31+G*	&	-231.454\,293	&	-231.144\,525	&	8.43	&	-231.464\,691	&	-231.057\,606	&	11.08	\\
				&					&	AVDZ	&	-231.526\,628	&	-231.218\,028	&	8.40	&	-231.538\,479	&	-231.134\,299	&	11.00	\\
				&					&	AVTZ	&	-231.732\,486	&	-231.426\,013	&	8.34	&	-231.745\,669	&	-231.342\,781	&	10.96	\\
				&					&	AVQZ	&	-231.797\,406	&	-231.490\,808	&	8.34	&	-231.811\,068	&	-231.407\,931	&	10.97	\\
				&	XMS-CASPT2(6,6)	&	6-31+G*	&	-231.454\,271	&	-231.144\,528	&	8.43	&	-231.454\,496	&	-231.058\,586	&	10.77	\\
				&					&	AVDZ	&	-231.526\,602	&	-231.218\,033	&	8.40	&	-231.526\,893	&	-231.135\,964	&	10.64	\\
				&					&	AVTZ	&	-231.732\,455	&	-231.426\,021	&	8.34	&	-231.733\,000	&	-231.345\,434	&	10.55	\\
				&					&	AVQZ	&	-231.797\,374	&	-231.490\,817	&	8.34	&	-231.798\,070	&	-231.410\,862	&	10.54	\\
				&	PC-NEVPT2(6,6)	&	6-31+G*	&	-231.469\,185	&	-231.153\,743	&	8.58	&	-231.469\,458	&	-231.089\,140	&	10.35	\\
				&					&	AVDZ	&	-231.541\,157	&	-231.226\,445	&	8.56	&	-231.541\,534	&	-231.167\,452	&	10.18	\\
				&					&	AVTZ	&	-231.746\,700	&	-231.433\,880	&	8.51	&	-231.747\,162	&	-231.379\,842	&	10.00	\\
				&					&	AVQZ	&	-231.811\,494	&	-231.498\,524	&	8.52	&					&					&			\\
				&	SC-NEVPT2(6,6)	&	6-31+G*	&	-231.468\,398	&	-231.151\,496	&	8.62	&	-231.468\,632	&	-231.077\,860	&	10.63	\\
				&					&	AVDZ	&	-231.468\,398	&	-231.224\,034	&	8.61	&	-231.540\,646	&	-231.155\,560	&	10.48	\\
				&					&	AVTZ	&	-231.745\,845	&	-231.431\,454	&	8.56	&	-231.746\,267	&	-231.364\,760	&	10.38	\\
				&					&	AVQZ	&	-231.810\,639	&	-231.496\,111	&	8.56	&	-231.811\,095	&	-231.430\,238	&	10.36	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}

%------------------------------
\subsection{Beryllium}
%------------------------------

%%% BERYLLIUM
\begin{table}[H]
	\caption{
	\label{tab:Be_CAS}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of beryllium for various methods and basis sets.
	In this case, CASPT2, MS-CASPT2 and XMS-CASPT2 yield undistinguishable results.
	The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
	Similarly, PC-NEVPT2 and SC-NEVPT2 yield undistinguishable results.
	The $(2,12)$ active space contains the two valence electrons and the $2s$, $2p$, $3p$ and $3d$ orbitals.
	The state-averaged (SA) CASSCF calculation is performed with $3$ states.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllddd}
	Molecule	&	Method			&	Basis		&	\mc{3}{c}{1\,\ex{1}{S}{}{} $\ra$ 1\,\ex{1}{D}{}{}: \tr{2s^2}{2p^2}}	\\
															\cline{4-6}
				&					&				&	\mcc{1\,\ex{1}{S}{}{}}	&	\mcc{1\,\ex{1}{D}{}{}}	&	\mcc{$\Delta E$}	\\
	\hline
	Beryllium	&	SA-CASSCF(2,12)	&	6-31+G*		&	-14.612\,854	&	-14.318\,502	&	8.01	\\
				&					&	AVDZ		&	-14.615\,325	&	-14.350\,722	&	7.20	\\
				&					&	AVTZ		&	-14.615\,469	&	-14.354\,014	&	7.11	\\
				&					&	AVQZ		&	-14.615\,734	&	-14.354\,812	&	7.10	\\
				&	CASPT2(2,12)	&	6-31+G*		&	-14.614\,869	&	-14.320\,023	&	8.02	\\
				&					&	AVDZ		&	-14.616\,802	&	-14.351\,933	&	7.21	\\
				&					&	AVTZ		&	-14.622\,901	&	-14.361\,341	&	7.12	\\
				&					&	AVQZ		&	-14.637\,040	&	-14.375\,999	&	7.10	\\
				&	NEVPT2(2,12)	&	6-31+G*		&	-14.614\,901	&	-14.320\,403	&	8.01	\\
				&					&	AVDZ		&	-14.616\,757	&	-14.352\,020	&	7.20	\\
				&					&	AVTZ		&	-14.623\,028	&	-14.361\,559	&	7.11	\\
				&					&	AVQZ		&	-14.637\,151	&	-14.376\,228	&	7.10	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}


%------------------------------
\subsection{Butadiene}
%------------------------------

%%% BUTADIENE %%%
\begin{table}[H]
	\caption{
	\label{tab:butadiene_CAS}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of butadiene for various methods and basis sets.
	The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
	The $(4,4)$ active space includes the $\piCC$ and $\pisCC$ orbitals while the $(10,10)$ active space adds the $\siCC$ and $\sisCC$ orbitals.}
	The state-averaged (SA) CASSCF calculation is performed with $2$ states.
	\begin{ruledtabular}
	\begin{tabular}{lllddd}
	Molecule	&	Method		&	Basis	&	\mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{\pi,\pi}{\pis,\pis}}	\\
												\cline{4-6}
				&				&			&	\mcc{1\,\ex{1}{A}{g}{}}	&	\mcc{2\,\ex{1}{A}{g}{}}	&	\mcc{$\Delta E$}	\\
	\hline
	Butadiene	&	SA-CASSCF(4,4)	&	6-31+G*	&	-154.973\,885	&	-154.729\,068	&	6.66	\\
				&					&	AVDZ	&	-154.987\,684	&	-154.743\,317	&	6.65	\\
				&					&	AVTZ	&	-155.026\,077	&	-154.782\,092	&	6.64	\\
				&					&	AVQZ	&	-155.035\,161	&	-154.791\,236	&	6.64	\\
				&	CASPT2(4,4)		&	6-31+G*	&	-155.429\,138	&	-155.178\,472	&	6.82  	\\
				&					&	AVDZ	&	-155.493\,427	&	-155.243\,990	&	6.79	\\
				&					&	AVTZ	&	-155.637\,204	&	-155.388\,901	&	6.76	\\
				&					&	AVQZ	&	-155.681\,619	&	-155.433\,024	&	6.76	\\
				&	MS-CASPT2(4,4)	&	6-31+G*	&	-155.429\,142	&	-155.178\,468	&	6.82	\\
				&					&	AVDZ	&	-155.493\,429	&	-155.243\,989	&	6.79	\\
				&					&	AVTZ	&	-155.637\,207	&	-155.388\,898	&	6.76	\\
				&					&	AVQZ	&	-155.681\,624	&	-155.433\,019	&	6.76	\\
				&	XMS-CASPT2(4,4)	&	6-31+G*	&	-155.429\,147	&	-155.178\,464	&	6.82	\\
				&					&	AVDZ	&	-155.493\,431	&	-155.243\,985	&	6.79	\\
				&					&	AVTZ	&	-155.637\,212	&	-155.388\,892	&	6.76	\\
				&					&	AVQZ	&	-155.681\,629	&	-155.433\,013	&	6.77	\\
				&	PC-NEVPT2(4,4)	&	6-31+G*	&	-155.437\,512	&	-155.183\,695	&	6.91	\\
				&					&	AVDZ	&	-155.501\,541	&	-155.248\,495	&	6.89	\\
				&					&	AVTZ	&	-155.645\,027	&	-155.393\,039	&	6.86	\\
				&					&	AVQZ	&	-155.689\,335	&	-155.437\,062	&	6.86	\\
				&	SC-NEVPT2(4,4)	&	6-31+G*	&	-155.437\,070	&	-155.182\,225	&	6.93	\\
				&					&	AVDZ	&	-155.501\,076	&	-155.246\,822	&	6.92	\\
				&					&	AVTZ	&	-155.644\,552	&	-155.391\,318	&	6.89	\\
				&					&	AVQZ	&	-155.688\,858	&	-155.435\,387	&	6.90	\\
				&	SA-CASSCF(10,10)&	6-31+G*	&	-155.046\,301	&	-154.789\,097	&	7.00	\\
				&					&	AVDZ	&	-155.060\,856	&	-154.803\,483	&	7.00	\\
				&					&	AVTZ	&	-155.100\,013	&	-154.843\,143	&	6.99	\\
				&					&	AVQZ	&	-155.109\,236	&	-154.852\,461	&	6.99	\\
				&	CASPT2(10,10)	&	6-31+G*	&	-155.433\,830	&	-155.184\,024	&	6.80 	\\
				&					&	AVDZ	&	-155.498\,365	&	-155.249\,091	&	6.78	\\
				&					&	AVTZ	&	-155.640\,528	&	-155.392\,682	&	6.74	\\
				&					&	AVQZ	&	-155.684\,195	&	-155.436\,216	&	6.75	\\
				&	MS-CASPT2(10,10)&	6-31+G*	&	-155.433\,839	&	-155.184\,016	&	6.80	\\
				&					&	AVDZ	&	-155.498\,370	&	-155.249\,086	&	6.78	\\
				&					&	AVTZ	&	-155.640\,537	&	-155.392\,673	&	6.74	\\
				&					&	AVQZ	&	-155.684\,206	&	-155.436\,205	&	6.75	\\
				&	XMS-CASPT2(10,10)&	6-31+G*	&	-155.433\,843	&	-155.184\,013	&	6.80	\\
				&					&	AVDZ	&	-155.498\,372	&	-155.249\,085	&	6.78	\\
				&					&	AVTZ	&	-155.640\,541	&	-155.392\,670	&	6.74	\\
				&					&	AVQZ	&	-155.684\,210	&	-155.436\,202	&	6.75	\\
				&	PC-NEVPT2(10,10)&	6-31+G*	&	-155.423\,461	&	-155.175\,243	&	6.75	\\
				&					&	AVDZ	&	-155.485\,031	&	-155.237\,429	&	6.74	\\
				&					&	AVTZ	&	-155.623\,947	&	-155.377\,725	&	6.70	\\
				&					&	AVQZ	&	-155.666\,748	&	-155.420\,408	&	6.70	\\
				&	SC-NEVPT2(10,10)&	6-31+G*	&	-155.418\,966	&	-155.167\,964	&	6.83	\\
				&					&	AVDZ	&	-155.480\,099	&	-155.229\,526	&	6.82	\\
				&					&	AVTZ	&	-155.618\,701	&	-155.369\,542	&	6.78	\\
				&					&	AVQZ	&	-155.661\,442	&	-155.412\,153	&	6.78	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}


%------------------------------
\subsection{Carbon dimer}
%------------------------------

%%% CARBON DIMER %%%
\begin{table}[H]
	\caption{
	\label{tab:C2_CAS}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of the carbon dimer for various methods and basis sets.
	The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
	The $(8,8)$ active space contains all the valence electrons and orbitals.
	The state-averaged (SA) CASSCF calculations for the 1\,\ex{1}{\Sigma}{g}{+} $\ra$ 2\,\ex{1}{\Sigma}{g}{+} and 1\,\ex{1}{\Sigma}{g}{+} $\ra$ 1\,\ex{1}{\Delta}{g}{} transitions are performed with $2$ and $3$ states, respectively.
	}
	\begin{ruledtabular}
	\begin{tabular}{llldddddd}
	Molecule	&	Method		&	Basis	&	\mc{3}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 2\,\ex{1}{\Sigma}{g}{+}}	
											&	\mc{3}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 1\,\ex{1}{\Delta}{g}{}}		\\
												\cline{4-6}		\cline{7-9}
				&				&			&	\mcc{1\,\ex{1}{\Sigma}{g}{+}}	&	\mcc{2\,\ex{1}{\Sigma}{g}{+}}	&	\mcc{$\Delta E$}	
											&	\mcc{1\,\ex{1}{\Sigma}{g}{+}}	&	\mcc{1\,\ex{1}{\Delta}{g}{}}	&	\mcc{$\Delta E$}	\\
	\hline
	Carbon dimer&	SA-CASSCF(8,8)	&	6-31+G*	&	-75.611\,462	&	-75.505\,844	&	2.87	&	-75.606\,326	&	-75.511\,554	&	2.58	\\
				&					&	AVDZ	&	-75.615\,948	&	-75.510\,158	&	2.88	&	-75.610\,186	&	-75.516\,995	&	2.54	\\
				&					&	AVTZ	&	-75.629\,954	&	-75.525\,529	&	2.84	&	-75.623\,869	&	-75.532\,462	&	2.49	\\
				&					&	AVQZ	&	-75.634\,302	&	-75.529\,926	&	2.84	&	-75.628\,160	&	-75.536\,889	&	2.48	\\
				&	CASPT2(8,8)		&	6-31+G*	&	-75.712\,841	&	-75.616\,625	&	2.62  	&	-75.712\,081	&	-75.624\,016	&	2.40	\\
				&					&	AVDZ	&	-75.720\,037	&	-75.622\,541	&	2.65	&	-75.718\,980	&	-75.632\,150	&	2.36	\\
				&					&	AVTZ	&	-75.771\,020	&	-75.677\,915	&	2.53	&	-75.770\,442	&	-75.688\,258	&	2.24	\\
				&					&	AVQZ	&	-75.788\,081	&	-75.696\,113	&	2.50	&	-75.787\,711	&	-75.706\,614	&	2.21	\\
				&	MS-CASPT2(8,8)	&	6-31+G*	&	-75.713\,015	&	-75.616\,451	&	2.63	&	-75.712\,081	&	-75.624\,016	&	2.40	\\
				&					&	AVDZ	&	-75.720\,227	&	-75.622\,351	&	2.66	&	-75.718\,980	&	-75.632\,150	&	2.36	\\
				&					&	AVTZ	&	-75.771\,335	&	-75.677\,601	&	2.55	&	-75.770\,442	&	-75.688\,258	&	2.24	\\
				&					&	AVQZ	&	-75.788\,434	&	-75.695\,760	&	2.52	&	-75.787\,711	&	-75.706\,614	&	2.21	\\
				&	XMS-CASPT2(8,8)	&	6-31+G*	&	-75.712\,895	&	-75.616\,452	&	2.62	&	-75.712\,081	&	-75.624\,016	&	2.40	\\
				&					&	AVDZ	&	-75.720\,084	&	-75.622\,349	&	2.66	&	-75.718\,980	&	-75.632\,150	&	2.36	\\
				&					&	AVTZ	&	-75.771\,145	&	-75.677\,625	&	2.54	&	-75.770\,442	&	-75.688\,258	&	2.24	\\
				&					&	AVQZ	&	-75.788\,231	&	-75.695\,795	&	2.52	&	-75.787\,711	&	-75.706\,614	&	2.21	\\
				&	PC-NEVPT2(8,8)	&	6-31+G*	&	-75.705\,939	&	-75.612\,560	&	2.54	&	-75.705\,885	&	-75.620\,265	&	2.33	\\
				&					&	AVDZ	&	-75.711\,503	&	-75.618\,073	&	2.54	&	-75.711\,303	&	-75.628\,447	&	2.25	\\
				&					&	AVTZ	&	-75.759\,612	&	-75.670\,557	&	2.42	&	-75.759\,837	&	-75.681\,954	&	2.12	\\
				&					&	AVQZ	&	-75.775\,832	&	-75.688\,105	&	2.39	&	-75.776\,239	&	-75.699\,658	&	2.08	\\
				&	SC-NEVPT2(8,8)	&	6-31+G*	&	-75.703\,755	&	-75.608\,773	&	2.58	&	-75.703\,208	&	-75.616\,965	&	2.35	\\
				&					&	AVDZ	&	-75.709\,115	&	-75.613\,713	&	2.60	&	-75.708\,307	&	-75.624\,464	&	2.28	\\
				&					&	AVTZ	&	-75.757\,077	&	-75.666\,007	&	2.48	&	-75.756\,627	&	-75.677\,825	&	2.14	\\
				&					&	AVQZ	&	-75.773\,268	&	-75.683\,471	&	2.44	&	-75.772\,982	&	-75.695\,459	&	2.11	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}


%------------------------------
\subsection{Carbon trimer}
%------------------------------

%%% CARBON TRIMER %%%
\begin{table}[H]
	\caption{
	\label{tab:C3_CAS}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of the carbon trimer for various methods and basis sets.
	The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
	The $(12,12)$ active space contains all the valence electrons and orbitals.
	The state-averaged (SA) CASSCF calculations for the 1\,\ex{1}{\Sigma}{g}{+} $\ra$ 2\,\ex{1}{\Sigma}{g}{+} and 1\,\ex{1}{\Sigma}{g}{+} $\ra$ 1\,\ex{1}{\Delta}{g}{} transitions are performed with $2$ and $3$ states, respectively.
	}
	\begin{ruledtabular}
	\begin{tabular}{llldddddd}
	Molecule	&	Method		&	Basis	&	\mc{3}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 2\,\ex{1}{\Sigma}{g}{+}}	
											&	\mc{3}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 1\,\ex{1}{\Delta}{g}{}}		\\
												\cline{4-6}		\cline{7-9}
				&				&			&	\mcc{1\,\ex{1}{\Sigma}{g}{+}}	&	\mcc{2\,\ex{1}{\Sigma}{g}{+}}	&	\mcc{$\Delta E$}	
											&	\mcc{1\,\ex{1}{\Sigma}{g}{+}}	&	\mcc{1\,\ex{1}{\Delta}{g}{}}	&	\mcc{$\Delta E$}	\\
	\hline
	Carbon trimer&	SA-CASSCF(12,12)	&	6-31+G*	&	-113.547\,179	&	-113.332\,694	&	5.84	&	-113.543\,499	&	-113.360\,079	&	4.99		\\
				&						&	AVDZ	&	-113.554\,346	&	-113.340\,290	&	5.82	&	-113.550\,471	&	-113.367\,517	&	4.98		\\
				&						&	AVTZ	&	-113.576\,466	&	-113.361\,965	&	5.84	&	-113.572\,398	&	-113.389\,220	&	4.98		\\
				&						&	AVQZ	&	-113.582\,463	&	-113.368\,153	&	5.83	&	-113.578\,357	&	-113.395\,436	&	4.98		\\
				&	CASPT2(12,12)		&	6-31+G*	&	-113.716\,995	&	-113.501\,672	&	5.86	&	-113.715\,833	&	-113.527\,402	&	5.13	 	\\
				&						&	AVDZ	&	-113.728\,453	&	-113.514\,880	&	5.81	&	-113.727\,030	&	-113.540\,997	&	5.06		\\
				&						&	AVTZ	&	-113.810\,722	&	-113.596\,829	&	5.82	&	-113.809\,454	&	-113.622\,903	&	5.08		\\
				&						&	AVQZ	&	-113.837\,431	&	-113.623\,512	&	5.82	&	-113.836\,208	&	-113.649\,414	&	5.08		\\
				&	MS-CASPT2(12,12)	&	6-31+G*	&	-113.716\,996	&	-113.501\,671	&	5.86	&	-113.715\,833	&	-113.527\,402	&	5.13		\\
				&						&	AVDZ	&	-113.728\,454	&	-113.514\,879	&	5.81	&	-113.727\,030	&	-113.540\,997	&	5.06		\\
				&						&	AVTZ	&	-113.810\,722	&	-113.596\,828	&	5.82	&	-113.809\,454	&	-113.622\,903	&	5.08		\\
				&						&	AVQZ	&	-113.837\,431	&	-113.623\,511	&	5.82	&	-113.836\,208	&	-113.649\,414	&	5.08		\\
				&	XMS-CASPT2(12,12)	&	6-31+G*	&	-113.716\,997	&	-113.501\,671	&	5.86	&	-113.715\,833	&	-113.527\,402	&	5.13		\\
				&						&	AVDZ	&	-113.728\,456	&	-113.514\,879	&	5.81	&	-113.727\,030	&	-113.540\,997	&	5.06		\\
				&						&	AVTZ	&	-113.810\,725	&	-113.596\,828	&	5.82	&	-113.809\,454	&	-113.622\,903	&	5.08		\\
				&						&	AVQZ	&	-113.837\,433	&	-113.623\,511	&	5.82	&	-113.836\,208	&	-113.649\,414	&	5.08		\\
				&	PC-NEVPT2(12,12)	&	6-31+G*	&	-113.711\,719	&	-113.492\,466	&	5.97	&	-113.711\,402	&	-113.518\,270	&	5.26		\\
				&						&	AVDZ	&	-113.722\,348	&	-113.502\,996	&	5.97	&	-113.721\,864	&	-113.529\,435	&	5.24		\\
				&						&	AVTZ	&	-113.800\,831	&	-113.580\,845	&	5.99	&	-113.800\,484	&	-113.607\,374	&	5.25		\\
				&						&	AVQZ	&	-113.826\,452	&	-113.606\,310	&	5.99	&	-113.826\,144	&	-113.632\,678	&	5.26		\\
				&	SC-NEVPT2(12,12)	&	6-31+G*	&	-113.705\,615	&	-113.485\,949	&	5.98	&	-113.704\,595	&	-113.513\,036	&	5.21		\\
				&						&	AVDZ	&	-113.715\,356	&	-113.495\,802	&	5.97	&	-113.714\,109	&	-113.523\,345	&	5.19		\\
				&						&	AVTZ	&	-113.793\,489	&	-113.573\,267	&	5.99	&	-113.792\,375	&	-113.600\,931	&	5.21		\\
				&						&	AVQZ	&	-113.819\,136	&	-113.598\,720	&	6.00	&	-113.818\,079	&	-113.626\,223	&	5.22		\\
	\end{tabular}
	\end{ruledtabular}
\end{table}

%------------------------------
\subsection{Ethylene}
%------------------------------

%%% ETHYLENE %%%
\begin{table}[H]
	\caption{
	\label{tab:ethylene_CAS}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of ethylene for various methods and basis sets.
	The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
	The $(2,2)$ active space includes the $\piCC$ and $\pisCC$ orbitals while the $(4,4)$ active space adds the $\siCC$ and $\sisCC$ orbitals.}
	The state-averaged (SA) CASSCF calculation is performed with $2$ states.
	\begin{ruledtabular}
	\begin{tabular}{lllddd}
	Molecule	&	Method			&	Basis	&	\mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{\pi,\pi}{\pis,\pis}}	\\
											\cline{4-6}
				&					&			&	\mcc{1\,\ex{1}{A}{g}{}}	&	\mcc{2\,\ex{1}{A}{g}{}}	&	\mcc{$\Delta E$}	\\
	\hline
	Ethylene	&	SA-CASSCF(2,2)	&	6-31+G*	&	-78.050\,262	&	-77.512\,725	&	14.63		\\
				&					&	AVDZ	&	-78.057\,788	&	-77.523\,386	&	14.54	\\
				&					&	AVTZ	&	-78.078\,753	&	-77.544\,816	&	14.53	\\
				&					&	AVQZ	&	-78.083\,447	&	-77.549\,521	&	14.53	\\
				&	CASPT2(2,2)		&	6-31+G*	&	-78.288\,566	&	-77.793\,374	&	13.47  	\\
				&					&	AVDZ	&	-78.327\,262	&	-77.842\,617	&	13.19	\\
				&					&	AVTZ	&	-78.403\,843	&	-77.921\,305	&	13.13	\\
				&					&	AVQZ	&	-78.427\,094	&	-77.944\,614	&	13.13	\\
				&	MS-CASPT2(2,2)	&	6-31+G*	&	-78.290\,306	&	-77.791\,633	&	13.57	\\
				&					&	AVDZ	&	-78.329\,197	&	-77.840\,682	&	13.29	\\
				&					&	AVTZ	&	-78.406\,016	&	-77.919\,132	&	13.25	\\
				&					&	AVQZ	&	-78.429\,366	&	-77.942\,342	&	13.25	\\
				&	PC-NEVPT2(2,2)	&	6-31+G*	&	-78.292\,578	&	-77.793\,016	&	13.59	\\
				&					&	AVDZ	&	-78.331\,562	&	-77.851\,953	&	13.05	\\
				&					&	AVTZ	&	-78.407\,808	&	-77.937\,524	&	12.80	\\
				&					&	AVQZ	&	-78.430\,942	&	-77.964\,042	&	12.70	\\
				&	SC-NEVPT2(2,2)	&	6-31+G*	&	-78.292\,491	&	-77.792\,730	&	13.60	\\
				&					&	AVDZ	&	-78.331\,469	&	-77.851\,664	&	13.06	\\
				&					&	AVTZ	&	-78.407\,725	&	-77.937\,244	&	12.80	\\
				&					&	AVQZ	&	-78.430\,856	&	-77.963\,758	&	12.71	\\
				&	SA-CASSCF(4,4)	&	6-31+G*	&	-78.074\,309	&	-77.552\,058	&	14.21	\\
				&					&	AVDZ	&	-78.082\,060	&	-77.562\,851	&	14.13	\\
				&					&	AVTZ	&	-78.103\,340	&	-77.584\,460	&	14.12	\\
				&					&	AVQZ	&	-78.108\,098	&	-77.589\,227	&	14.12	\\
				&	CASPT2(4,4)		&	6-31+G*	&	-78.290\,576	&	-77.794\,942	&	13.49 	\\
				&					&	AVDZ	&	-78.329\,298	&	-77.843\,094	&	13.23	\\
				&					&	AVTZ	&	-78.405\,586	&	-77.921\,465	&	13.17	\\
				&					&	AVQZ	&	-78.428\,668	&	-77.944\,571	&	13.17	\\
				&	MS-CASPT2(4,4)	&	6-31+G*	&	-78.291\,055	&	-77.794\,463	&	13.51	\\
				&					&	AVDZ	&	-78.329\,856	&	-77.842\,536	&	13.26	\\
				&					&	AVTZ	&	-78.406\,272	&	-77.920\,779	&	13.21	\\
				&					&	AVQZ	&	-78.429\,409	&	-77.943\,830	&	13.21	\\
				&	XMS-CASPT(4,4)	&	6-31+G*	&	-78.290\,264	&	-77.794\,002	&	13.50	\\
				&					&	AVDZ	&	-78.328\,964	&	-77.842\,084	&	13.25	\\
				&					&	AVTZ	&	-78.405\,304	&	-77.920\,370	&	13.20	\\
				&					&	AVQZ	&	-78.428\,415	&	-77.943\,434	&	13.20	\\
				&	PC-NEVPT2(4,4)	&	6-31+G*	&	-78.289\,445	&	-77.761\,980	&	14.35	\\
				&					&	AVDZ	&	-78.327\,336	&	-77.834\,250	&	13.42	\\
				&					&	AVTZ	&	-78.402\,555	&	-77.920\,807	&	13.11	\\
				&					&	AVQZ	&	-78.425\,291	&	-77.946\,194	&	13.04	\\
				&	SC-NEVPT2(4,4)	&	6-31+G*	&	-78.287\,620	&	-77.788\,941	&	13.57	\\
				&					&	AVDZ	&	-78.325\,393	&	-77.835\,389	&	13.33	\\
				&					&	AVTZ	&	-78.400\,680	&	-77.913\,304	&	13.26	\\
				&					&	AVQZ	&	-78.423\,404	&	-77.936\,130	&	13.26	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}


%------------------------------
\subsection{Formaldehyde}
%------------------------------

%%% FORMALDEHYDE %%%
\begin{table}[H]
	\caption{
	\label{tab:formaldehyde_CAS}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of formaldehyde for various methods and basis sets.
	The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
	The $(4,3)$ active space contains the $\piCO$, $\pisCO$ orbitals and the lone pair on the oxygen atom $\nO$, while the $(6,5)$ active space adds up the $\siCO$ and $\sisCO$ orbitals.
	The state-averaged (SA) CASSCF calculation is performed with $3$ states.
	}
	\begin{ruledtabular}
	\begin{tabular}{llldddddd}
	Molecule	&	Method				&	Basis		&	\mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{\pi}{\pis}}	
														&	\mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 3\,\ex{1}{A}{g}{}: \tr{n,n}{\pis,\pis}}	\\
															\cline{4-6}\cline{7-9}
				&						&				&	\mcc{1\,\ex{1}{A}{g}{}}	&	\mcc{2\,\ex{1}{A}{g}{}}	&	\mcc{$\Delta E$}	&	\mcc{1\,\ex{1}{A}{g}{}}	&	\mcc{3\,\ex{1}{A}{g}{}}	&	\mcc{$\Delta E$}	\\
	\hline
	Formaldehyde&	SA-CASSCF(4,3)		&	6-31+G*		&	-113.888\,047	&	-113.459\,444	&	11.66	&	-113.888\,047	&	-113.434\,017	&	12.35	\\
				&						&	AVDZ		&	-113.901\,336	&	-113.480\,975	&	11.44	&	-113.901\,336	&	-113.458\,501	&	12.05	\\
				&						&	AVTZ		&	-113.929\,392	&	-113.510\,948	&	11.39	&	-113.929\,392	&	-113.486\,477	&	12.05	\\
				&						&	AVQZ		&	-113.936\,772	&	-113.518\,386	&	11.38	&	-113.936\,772	&	-113.493\,946	&	12.05	\\
				&	CASPT2(4,3)			&	6-31+G*		&	-114.173\,092	&	-113.809\,464	&	9.89	&	-114.173\,092	&	-113.780\,818	&	10.67	\\
				&						&	AVDZ		&	-114.219\,234	&	-113.862\,472	&	9.71	&	-114.219\,234	&	-113.842\,350	&	10.26	\\
				&						&	AVTZ		&	-114.317\,115	&	-113.964\,834	&	9.59	&	-114.317\,115	&	-113.943\,362	&	10.17	\\
				&						&	AVQZ		&	-114.349\,288	&	-113.997\,944	&	9.56	&	-114.349\,288	&	-113.975\,898	&	10.16	\\
				&	MS-CASPT2(4,3)		&	6-31+G*		&	-114.174\,654	&	-113.808\,721	&	9.96	&	-114.174\,654	&	-113.779\,999	&	10.74	\\
				&						&	AVDZ		&	-114.221\,059	&	-113.861\,959	&	9.77	&	-114.221\,059	&	-113.841\,038	&	10.34	\\
				&						&	AVTZ		&	-114.319\,457	&	-113.963\,748	&	9.68	&	-114.319\,457	&	-113.942\,106	&	10.27	\\
				&						&	AVQZ		&	-114.351\,896	&	-113.996\,538	&	9.67	&	-114.351\,896	&	-113.974\,697	&	10.26	\\
				&	XMS-CASPT2(4,3)		&	6-31+G*		&	-114.172\,660	&	-113.809\,912	&	9.87	&	-114.172\,660	&	-113.779\,080	&	10.71	\\
				&						&	AVDZ		&	-114.218\,915	&	-113.863\,463	&	9.67	&	-114.218\,915	&	-113.839\,985	&	10.31	\\
				&						&	AVTZ		&	-114.317\,029	&	-113.965\,465	&	9.57	&	-114.317\,029	&	-113.941\,143	&	10.23	\\
				&						&	AVQZ		&	-114.349\,335	&	-113.998\,350	&	9.55	&	-114.349\,335	&	-113.973\,756	&	10.22	\\
				&	PC-NEVPT2(4,3)		&	6-31+G*		&	-114.173\,095	&	-113.831\,834	&	9.29	&	-114.173\,095	&	-113.774\,873	&	10.84	\\
				&						&	AVDZ		&	-114.219\,119	&	-113.885\,309	&	9.08	&	-114.219\,119	&	-113.837\,756	&	10.38	\\
				&						&	AVTZ		&	-114.316\,536	&	-113.987\,365	&	8.96	&	-114.316\,536	&	-113.938\,195	&	10.30	\\
				&						&	AVQZ		&	-114.348\,498	&	-114.020\,453	&	8.93	&	-114.348\,498	&	-113.970\,486	&	10.29	\\
				&	SC-NEVPT2(4,3)		&	6-31+G*		&	-114.172\,451	&	-113.819\,698	&	9.60	&	-114.172\,451	&	-113.773\,374	&	10.86	\\
				&						&	AVDZ		&	-114.218\,408	&	-113.872\,839	&	9.40	&	-114.218\,408	&	-113.835\,975	&	10.41	\\
				&						&	AVTZ		&	-114.315\,807	&	-113.974\,856	&	9.28	&	-114.315\,807	&	-113.936\,333	&	10.33	\\
				&						&	AVQZ		&	-114.347\,768	&	-114.007\,835	&	9.25	&	-114.347\,768	&	-113.968\,621	&	10.32	\\
				&	SA-CASSCF(6,5)		&	6-31+G*		&	-113.923\,326	&	-113.516\,669	&	11.07	&	-113.923\,326	&	-113.463\,675	&	12.51	\\
				&						&	AVDZ		&	-113.936\,789	&	-113.535\,947	&	10.91	&	-113.936\,789	&	-113.487\,565	&	12.22	\\
				&						&	AVTZ		&	-113.965\,022	&	-113.565\,649	&	10.87	&	-113.965\,022	&	-113.515\,771	&	12.22	\\
				&						&	AVQZ		&	-113.972\,475	&	-113.573\,112	&	10.87	&	-113.972\,475	&	-113.523\,326	&	12.22	\\
				&	CASPT2(6,5)			&	6-31+G*		&	-114.168\,576	&	-113.797\,541	&	10.10	&	-114.168\,576	&	-113.771\,544	&	10.80	\\
				&						&	AVDZ		&	-114.214\,497	&	-113.850\,396	&	9.91	&	-114.214\,497	&	-113.833\,160	&	10.38	\\
				&						&	AVTZ		&	-114.312\,046	&	-113.952\,410	&	9.79	&	-114.312\,046	&	-113.934\,618	&	10.27	\\
				&						&	AVQZ		&	-114.344\,054	&	-113.985\,267	&	9.76	&	-114.344\,054	&	-113.967\,170	&	10.26	\\
				&	MS-CASPT2(6,5)		&	6-31+G*		&	-114.169\,130	&	-113.798\,631	&	10.08	&	-114.169\,130	&	-113.769\,900	&	10.86	\\
				&						&	AVDZ		&	-114.215\,151	&	-113.851\,965	&	9.88	&	-114.215\,151	&	-113.830\,937	&	10.45	\\
				&						&	AVTZ		&	-114.312\,919	&	-113.953\,623	&	9.78	&	-114.312\,919	&	-113.932\,532	&	10.35	\\
				&						&	AVQZ		&	-114.345\,057	&	-113.986\,272	&	9.76	&	-114.345\,057	&	-113.965\,161	&	10.34	\\
				&	XMS-CASPT2(6,5)		&	6-31+G*		&	-114.168\,274	&	-113.799\,663	&	10.03	&	-114.168\,274	&	-113.768\,890	&	10.87	\\
				&						&	AVDZ		&	-114.214\,224	&	-113.853\,375	&	9.82	&	-114.214\,224	&	-113.829\,632	&	10.47	\\
				&						&	AVTZ		&	-114.311\,859	&	-113.955\,167	&	9.71	&	-114.311\,859	&	-113.931\,240	&	10.36	\\
				&						&	AVQZ		&	-114.343\,925	&	-113.987\,863	&	9.69	&	-114.343\,925	&	-113.963\,884	&	10.34	\\
				&	PC-NEVPT2(6,5)		&	6-31+G*		&	-114.164\,041	&	-113.797\,582	&	9.97	&	-114.164\,041	&	-113.765\,688	&	10.84	\\
				&						&	AVDZ		&	-114.208\,870	&	-113.849\,954	&	9.77	&	-114.208\,870	&	-113.827\,797	&	10.37	\\
				&						&	AVTZ		&	-114.305\,480	&	-113.951\,302	&	9.64	&	-114.305\,480	&	-113.928\,261	&	10.26	\\
				&						&	AVQZ		&	-114.337\,071	&	-113.983\,857	&	9.61	&	-114.337\,071	&	-113.960\,344	&	10.25	\\
				&	SC-NEVPT2(6,5)		&	6-31+G*		&	-114.160\,723	&	-113.782\,789	&	10.28	&	-114.160\,723	&	-113.761\,439	&	10.87	\\
				&						&	AVDZ		&	-114.205\,182	&	-113.833\,995	&	10.10	&	-114.205\,182	&	-113.823\,061	&	10.40	\\
				&						&	AVTZ		&	-114.301\,651	&	-113.935\,028	&	9.98	&	-114.301\,651	&	-113.923\,273	&	10.30	\\
				&						&	AVQZ		&	-114.333\,299	&	-113.967\,528	&	9.95	&	-114.333\,299	&	-113.955\,272	&	10.29	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}


%------------------------------
\subsection{Glyoxal}
%------------------------------

%%% GLYOXAL %%%
\begin{table}[H]
	\caption{
	\label{tab:glyoxal_CAS}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of glyoxal for various methods and basis sets.
	The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
	In this case, CASPT2, MS-CASPT2 and XMS-CASPT2 yield undistinguishable results.
	The $(8,6)$ active space contains the $\piCC$, $\piCO$, $\pisCC$ and $\pisCO$ orbitals as well as the two lone pairs $\nO$ on the oxygen atoms. 
	The $(14,12)$ active space adds up the $\siCC$, $\siCO$, $\sisCC$ and $\sisCO$ orbitals.
	The state-averaged (SA) CASSCF calculation is performed with $2$ states.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllddd}
	Molecule	&	Method				&	Basis		&	\mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{n,n}{\pis,\pis}}	\\
															\cline{4-6}
				&						&				&	\mcc{1\,\ex{1}{A}{g}{}}	&	\mcc{2\,\ex{1}{A}{g}{}}	&	\mcc{$\Delta E$}	\\
	\hline
	Glyoxal	&	SA-CASSCF(8,6)		&	6-31+G*		&	-226.657\,931	&	-226.442\,282	&	5.87	\\
			&						&	AVDZ		&	-226.685\,161	&	-226.471\,894	&	5.80	\\
			&						&	AVTZ		&	-226.737\,720	&	-226.525\,322	&	5.78	\\
			&						&	AVQZ		&	-226.752\,190	&	-226.540\,026	&	5.77	\\
			&	CASPT2(8,6)			&	6-31+G*		&	-227.186\,625	&	-226.978\,713	&	5.66	\\
			&						&	AVDZ		&	-227.263\,032	&	-227.059\,166	&	5.55	\\
			&						&	AVTZ		&	-227.451\,133	&	-227.248\,454	&	5.52	\\
			&						&	AVQZ		&	-227.513\,827	&	-227.310\,931	&	5.52	\\
			&	PC-NEVPT2(8,6)		&	6-31+G*		&	-227.187\,115	&	-226.975\,789	&	5.75	\\
			&						&	AVDZ		&	-227.262\,427	&	-227.055\,140	&	5.64	\\
			&						&	AVTZ		&	-227.449\,337	&	-227.242\,966	&	5.62	\\
			&						&	AVQZ		&	-227.511\,566	&	-227.304\,962	&	5.62	\\
			&	SC-NEVPT2(8,6)		&	6-31+G*		&	-227.184\,722	&	-226.973\,382	&	5.75	\\
			&						&	AVDZ		&	-227.259\,926	&	-227.052\,509	&	5.64	\\
			&						&	AVTZ		&	-227.446\,780	&	-227.240\,281	&	5.62	\\
			&						&	AVQZ		&	-227.508\,996	&	-227.302\,250	&	5.63	\\
			&	SA-CASSCF(14,12)	&	6-31+G*		&	-226.766\,881	&	-226.545\,762	&	6.02	\\
			&						&	AVDZ		&	-226.794\,485	&	-226.576\,274	&	5.94	\\
			&						&	AVTZ		&	-226.847\,573	&	-226.629\,865	&	5.92	\\
			&						&	AVQZ		&	-226.862\,224	&	-226.644\,714	&	5.92	\\
			&	CASPT2(14,12)		&	6-31+G*		&	-227.188\,569	&	-226.983\,415	&	5.58	\\
			&						&	AVDZ		&	-227.264\,637	&	-227.063\,793	&	5.47	\\
			&						&	AVTZ		&	-227.451\,181	&	-227.251\,897	&	5.42	\\
			&						&	AVQZ		&	-227.513\,332	&	-227.313\,900	&	5.43	\\
			&	PC-NEVPT2(14,12)	&	6-31+G*		&	-227.172\,385	&	-226.964\,396	&	5.66	\\
			&						&	AVDZ		&	-227.245\,339	&	-227.041\,117	&	5.56	\\
			&						&	AVTZ		&	-227.428\,412	&	-227.225\,630	&	5.52	\\
			&						&	AVQZ		&	-227.489\,355	&	-227.286\,451	&	5.52	\\
			&	SC-NEVPT2(14,12)	&	6-31+G*		&	-227.163\,921	&	-226.955\,257	&	5.68	\\
			&						&	AVDZ		&	-227.236\,400	&	-227.031\,296	&	5.58	\\
			&						&	AVTZ		&	-227.419\,144	&	-227.215\,337	&	5.55	\\
			&						&	AVQZ		&	-227.479\,947	&	-227.276\,034	&	5.55	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}




%------------------------------
\subsection{Hexatriene}
%------------------------------

%%% HEXATRIENE %%%
\begin{table}[H]
	\caption{
	\label{tab:hexatriene_CAS}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of hexatriene for various methods and basis sets.
	The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
	In this case, CASPT2, MS-CASPT2 and XMS-CASPT2 yield undistinguishable results.
	The $(6,6)$ active space contains the $\piCC$ and $\pisCC$ orbitals.
	The state-averaged (SA) CASSCF calculation is performed with $2$ states.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllddd}
	Molecule	&	Method				&	Basis		&	\mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{\pi,\pi}{\pis,\pis}}	\\
															\cline{4-6}
				&						&				&	\mcc{1\,\ex{1}{A}{g}{}}	&	\mcc{2\,\ex{1}{A}{g}{}}	&	\mcc{$\Delta E$}	\\
	\hline
	Hexatriene	&	SA-CASSCF(6,6)		&	6-31+G*		&	-231.892\,206	&	-231.685\,636	&	5.62	\\
				&						&	AVDZ		&	-231.912\,669	&	-231.705\,976	&	5.62	\\
				&						&	AVTZ		&	-231.968\,514	&	-231.762\,041	&	5.62	\\
				&						&	AVQZ		&	-231.981\,952	&	-231.775\,526	&	5.62	\\
				&	CASPT2(6,6)			&	6-31+G*		&	-232.569\,064	&	-232.362\,351	&	5.62	\\
				&						&	AVDZ		&	-232.658\,877	&	-232.452\,721	&	5.61	\\
				&						&	AVTZ		&	-232.870\,299	&	-232.665\,237	&	5.58	\\
				&						&	AVQZ		&	-232.935\,889	&	-232.730\,678	&	5.58	\\
				&	PC-NEVPT2(6,6)		&	6-31+G*		&	-232.581\,395	&	-232.372\,911	&	5.67	\\
				&						&	AVDZ		&	-232.670\,452	&	-232.462\,312	&	5.66	\\
				&						&	AVTZ		&	-232.881\,425	&	-232.674\,317	&	5.64	\\
				&						&	AVQZ		&	-232.946\,879	&	-232.739\,625	&	5.64	\\
				&	SC-NEVPT2(6,6)		&	6-31+G*		&	-232.580\,549	&	-232.371\,009	&	5.70	\\
				&						&	AVDZ		&	-232.669\,518	&	-232.460\,234	&	5.69	\\
				&						&	AVTZ		&	-232.880\,451	&	-232.672\,201	&	5.67	\\
				&						&	AVQZ		&	-232.945\,903	&	-232.737\,479	&	5.67	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}	

%------------------------------
\subsection{Nitrosomethane}
%------------------------------

%%% NITROSOMETHANE %%%
\begin{table}[H]
	\caption{
	\label{tab:nitrosomethane_CAS}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of nitrosomethane for various methods and basis sets.
	The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
	In this case, CASPT2, MS-CASPT2 and XMS-CASPT2 yield undistinguishable results.
	The $(12,9)$ active space contains all the valence orbitals of the \ce{NO} fragment and the $\si_{\ce{CN}}$ and  $\sis_{\ce{CN}}$ orbitals.
	The state-averaged (SA) CASSCF calculation is performed with $2$ states.
	}
	\begin{ruledtabular}
	\begin{tabular}{llcddd}
	Molecule	&	Method				&	Basis		&	\mc{3}{c}{1\,\ex{1}{A}{}{'} $\ra$ 2\,\ex{1}{A}{}{'}: \tr{n,n}{\pis,\pis}}	\\
												\cline{4-6}
				&						&				&	\mcc{1\,\ex{1}{A}{}{'}}	&	\mcc{2\,\ex{1}{A}{}{'}}	&	\mcc{$\Delta E$}	\\
	\hline
	Nitrosomethane	&	SA-CASSCF(12,9)	&	6-31+G*		&	-168.951\,279	&	-168.766\,809	&	5.02	\\
					&					&	AVDZ		&	-168.974\,372	&	-168.790\,139	&	5.01	\\
					&					&	AVTZ		&	-169.012\,519	&	-168.830\,006	&	4.97	\\
					&					&	AVQZ		&	-169.023\,256	&	-168.840\,918	&	4.96	\\
					&	CASPT2(12,9)	&	6-31+G*		&	-169.303\,499	&	-169.122\,262	&	4.93	\\
					&					&	AVDZ		&	-169.370\,350	&	-169.190\,998	&	4.88	\\
					&					&	AVTZ		&	-169.513\,053	&	-169.336\,897	&	4.79	\\
					&					&	AVQZ		&	-169.559\,726	&	-169.384\,048	&	4.78	\\
					&	PC-NEVPT2(12,9)	&	6-31+G*		&	-169.289\,373	&	-169.108\,467	&	4.92	\\
					&					&	AVDZ		&	-169.354\,372	&	-169.174\,985	&	4.88	\\
					&					&	AVTZ		&	-169.492\,645	&	-169.316\,471	&	4.79	\\
					&					&	AVQZ		&	-169.537\,983	&	-169.362\,288	&	4.78	\\
					&	SC-NEVPT2(12,9)	&	6-31+G*		&	-169.282\,438	&	-169.100\,953	&	4.94	\\
					&					&	AVDZ		&	-169.346\,856	&	-169.166\,729	&	4.90	\\
					&					&	AVTZ		&	-169.484\,718	&	-169.307\,777	&	4.81	\\
					&					&	AVQZ		&	-169.529\,935	&	-169.353\,475	&	4.80	\\	
		\end{tabular}
	\end{ruledtabular}
\end{table}

%------------------------------
\subsection{Nitroxyl}
%------------------------------

%%% NITRSOXYL %%%
\begin{table}[H]
	\caption{
	\label{tab:nitroxyl_CAS}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of nitroxyl for various methods and basis sets.
	The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
	In this case, CASPT2, MS-CASPT2 and XMS-CASPT2 yield undistinguishable results.
	The $(12,9)$ active space contains all the valence orbitals (including  the $\si_{\ce{CH}}$ and $\sis_{\ce{CH}}$ orbitals).
	The state-averaged (SA) CASSCF calculation is performed with $2$ states.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllddd}
	Molecule	&	Method				&	Basis			&	\mc{3}{c}{1\,\ex{1}{A}{}{'} $\ra$ 2\,\ex{1}{A}{}{'}: \tr{n,n}{\pis,\pis}}	\\
															\cline{4-6}
				&						&					&	\mcc{1\,\ex{1}{A}{}{'}}	&	\mcc{2\,\ex{1}{A}{}{'}}	&	\mcc{$\Delta E$}	\\
	\hline
	Nitroxyl&	SA-CASSCF(12,9)		&	6-31+G*		&	-129.911\,884	&	-129.735\,534	&	4.80	\\
			&						&	AVDZ		&	-129.932\,723	&	-129.760\,088	&	4.70	\\
			&						&	AVTZ		&	-129.960\,749	&	-129.789\,113	&	4.67	\\
			&						&	AVQZ		&	-129.969\,310	&	-129.797\,750	&	4.67	\\
			&	CASPT2(12,9)		&	6-31+G*		&	-130.133\,397	&	-129.966\,066	&	4.55	\\
			&						&	AVDZ		&	-130.182\,652	&	-130.018\,908	&	4.46	\\
			&						&	AVTZ		&	-130.286\,304	&	-130.125\,988	&	4.36	\\
			&						&	AVQZ		&	-130.321\,398	&	-130.161\,843	&	4.34	\\
			&	PC-NEVPT2(12,9)		&	6-31+G*		&	-130.119\,401	&	-129.951\,698	&	4.56	\\
			&						&	AVDZ		&	-130.166\,359	&	-130.002\,551	&	4.46	\\
			&						&	AVTZ		&	-130.265\,882	&	-130.105\,240	&	4.37	\\
			&						&	AVQZ		&	-130.299\,672	&	-130.139\,724	&	4.35	\\
			&	SC-NEVPT2(12,9)		&	6-31+G*		&	-130.113\,407	&	-129.944\,930	&	4.58	\\
			&						&	AVDZ		&	-130.159\,685	&	-129.994\,868	&	4.48	\\
			&						&	AVTZ		&	-130.258\,778	&	-130.097\,150	&	4.40	\\
			&						&	AVQZ		&	-130.292\,532	&	-130.131\,589	&	4.38	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}


%------------------------------
\subsection{Pyrazine}
%------------------------------

%%% PYRAZINE %%%
\begin{squeezetable}
\begin{table}[H]
	\caption{
	\label{tab:pyrazine_CAS}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of pyrazine for various methods and basis sets.
	The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
	Note the inversion of the two transitions compared to coupled cluster calculations (see Table \ref{tab:pyrazine_CC}).
	The $(10,8)$ active space corresponds to the valence $\pi$ space and the two lone pairs $\nN$ on the nitrogen atoms.
	The state-averaged (SA) CASSCF calculation for both transitions is performed with $3$ states.
	}
	\begin{ruledtabular}
	\begin{tabular}{llldddddd}
	Molecule	&	Method				&	Basis		&	\mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{n,n}{\pis,\pis}} 	
														&	\mc{3}{c}{1\,\ex{1}{A}{g}{} $\ra$ 3\,\ex{1}{A}{g}{}: \tr{\pi,\pi}{\pis,\pis}}	\\
															\cline{4-6} \cline{7-9}
				&						&				&	\mcc{1\,\ex{1}{A}{g}{}}	&	\mcc{2\,\ex{1}{A}{g}{}}	&	\mcc{$\Delta E$}	&	\mcc{1\,\ex{1}{A}{g}{}}	&	\mcc{3\,\ex{1}{A}{g}{}}	&	\mcc{$\Delta E$}	\\
	\hline
	Pyrazine	&	SA-CASSCF(10,8)		&	6-31+G*		&	-262.766\,608	&	-262.466\,222	&	8.17	&	-262.766\,608	&	-262.455\,042	&	8.48		\\
				&						&	AVDZ		&	-262.792\,310	&	-262.492\,573	&	8.16	&	-262.792\,310	&	-262.481\,386	&	8.46	\\
				&						&	AVTZ		&	-262.848\,167	&	-262.550\,711	&	8.09	&	-262.848\,167	&	-262.538\,133	&	8.44	\\
				&						&	AVQZ		&	-262.863\,329	&	-262.566\,129	&	8.09	&	-262.863\,329	&	-262.553\,469	&	8.43	\\
				&	CASPT2(10,8)		&	6-31+G*		&	-263.497\,967	&	-263.201\,845	&	8.06	&	-263.497\,967	&	-263.170\,469	&	8.91		\\
				&						&	AVDZ		&	-263.570\,062	&	-263.279\,499	&	7.91	&	-263.570\,062	&	-263.244\,814	&	8.85	\\
				&						&	AVTZ		&	-263.792\,911	&	-263.505\,970	&	7.81	&	-263.792\,911	&	-263.470\,505	&	8.77	\\
				&						&	AVQZ		&	-263.865\,083	&	-263.578\,276	&	7.80	&	-263.865\,083	&	-263.542\,729	&	8.77	\\
				&	MS-CASPT2(10,8)		&	6-31+G*		&	-263.498\,163	&	-263.201\,849	&	8.06	&	-263.498\,163	&	-263.170\,269	&	8.92		\\
				&						&	AVDZ		&	-263.570\,282	&	-263.279\,508	&	7.91	&	-263.570\,282	&	-263.244\,585	&	8.86	\\
				&						&	AVTZ		&	-263.793\,167	&	-263.505\,971	&	7.81	&	-263.793\,167	&	-263.470\,248	&	8.79	\\
				&						&	AVQZ		&	-263.865\,351	&	-263.578\,276	&	7.81	&	-263.865\,351	&	-263.542\,460	&	8.79	\\
				&	XMS-CASPT2(10,8)	&	6-31+G*		&	-263.498\,193	&	-263.201\,862	&	8.06	&	-263.498\,193	&	-263.170\,207	&	8.92		\\
				&						&	AVDZ		&	-263.570\,300	&	-263.279\,528	&	7.91	&	-263.570\,300	&	-263.244\,520	&	8.86	\\
				&						&	AVTZ		&	-263.793\,179	&	-263.505\,986	&	7.81	&	-263.793\,179	&	-263.470\,190	&	8.79	\\
				&						&	AVQZ		&	-263.865\,363	&	-263.578\,291	&	7.81	&	-263.865\,363	&	-263.542\,403	&	8.79	\\
				&	PC-NEVPT2(10,8)		&	6-31+G*		&	-263.504\,412	&	-263.201\,181	&	8.25	&	-263.504\,412	&	-263.169\,289	&	9.12		\\
				&						&	AVDZ		&	-263.575\,850	&	-263.277\,429	&	8.12	&	-263.575\,850	&	-263.242\,663	&	9.07	\\
				&						&	AVTZ		&	-263.797\,309	&	-263.501\,963	&	8.04	&	-263.797\,309	&	-263.466\,615	&	9.00	\\
				&						&	AVQZ		&	-263.869\,053	&	-263.573\,733	&	8.04	&	-263.869\,053	&	-263.538\,356	&	9.00	\\
				&	SC-NEVPT2(10,8)		&	6-31+G*		&	-263.502\,262	&	-263.198\,175	&	8.27	&	-263.502\,262	&	-263.165\,513	&	9.16		\\
				&						&	AVDZ		&	-263.573\,569	&	-263.274\,044	&	8.15	&	-263.573\,569	&	-263.238\,492	&	9.12	\\
				&						&	AVTZ		&	-263.794\,986	&	-263.498\,517	&	8.07	&	-263.794\,986	&	-263.462\,364	&	9.05	\\
				&						&	AVQZ		&	-263.866\,723	&	-263.570\,259	&	8.07	&	-263.866\,723	&	-263.534\,098	&	9.05	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}
\end{squeezetable}



%------------------------------
\subsection{Tetrazine}
%------------------------------

%%% TETRAZINE %%%
\begin{squeezetable}
\begin{table}[H]
	\caption{
	\label{tab:tetrazine_CAS}
	Energies (in hartree) and transition energies $\Delta E$ (in eV) of tetrazine for various methods and basis sets.
	The level shift and IPEA parameters are set to $0.3$ and \InAU{$0.25$}, respectively.
	The $(14,10)$ active space corresponds to the valence $\pi$ space and the four lone pairs $\nN$ on the nitrogen atoms.
	The state-averaged (SA) CASSCF calculations for the 1\,\ex{1}{A}{1g}{} $\ra$ 2\,\ex{1}{A}{1g}{},  1\,\ex{1}{A}{1g}{} $\ra$ 1\,\ex{1}{B}{3g}{} and 1\,\ex{1}{A}{1g}{} $\ra$ 1\,\ex{3}{B}{3g}{}: \tr{n,n}{\pis_1,\pis_2} transitions are performed separately with $2$ states.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllddddddddd}
	Molecule	&	Method		&	Basis		&	\mc{3}{c}{1\,\ex{1}{A}{1g}{} $\ra$ 2\,\ex{1}{A}{1g}{}: \tr{n,n}{\pis,\pis}}
												&	\mc{3}{c}{1\,\ex{1}{A}{1g}{} $\ra$ 1\,\ex{1}{B}{3g}{}: \tr{n,n}{\pis_1,\pis_2}}	
												&	\mc{3}{c}{1\,\ex{1}{A}{1g}{} $\ra$ 1\,\ex{3}{B}{3g}{}: \tr{n,n}{\pis_1,\pis_2}}	\\
															\cline{4-6}	\cline{7-9} \cline{10-12}
				&						&				&	\mcc{1\,\ex{1}{A}{1g}{}}	&	\mcc{2\,\ex{1}{A}{g}{}}		&	\mcc{$\Delta E$}
														&	\mcc{1\,\ex{1}{A}{1g}{}}	&	\mcc{1\,\ex{1}{B}{3g}{}}	&	\mcc{$\Delta E$}	
														&	\mcc{1\,\ex{1}{A}{1g}{}}	&	\mcc{1\,\ex{3}{B}{3g}{}}	&	\mcc{$\Delta E$}	\\
	\hline
	Tetrazine	&	SA-CASSCF(14,10)	&	6-31+G*		&	-294.690\,221	&	-294.490\,365	&	5.44	&	-294.690\,155	&	-294.448\,416	&	6.58	&	-294.690\,183	&	-294.449\,273	&	6.56\\
			&				&	AVDZ		&	-294.727\,767	&	-294.526\,292	&	5.48	&	-294.727\,650	&	-294.483\,506	&	6.64	&	-294.727\,698	&	-294.484\,773	&	6.61\\
			&				&	AVTZ		&	-294.786\,064	&	-294.586\,910	&	5.42	&	-294.785\,943	&	-294.543\,776	&	6.59	&	-294.786\,000	&	-294.544\,836	&	6.56\\
			&				&	AVQZ		&	-294.803\,516	&	-294.604\,540	&	5.41	&	-294.803\,391	&	-294.561\,405	&	6.58	&	-294.803\,451	&	-294.562\,445	&	6.56\\
			&	CASPT2(14,10)		&	6-31+G*		&	-295.477\,304	&	-295.298\,713	&	4.86	&	-295.471\,597	&	-295.251\,195	&	6.00	&	-295.471\,629	&	-295.267\,973	&	5.54\\
			&				&	AVDZ		&	-295.553\,748	&	-295.377\,640	&	4.79	&	-295.548\,053	&	-295.329\,564	&	5.95	&	-295.548\,168	&	-295.347\,101	&	5.47\\
			&				&	AVTZ		&	-295.792\,600	&	-295.620\,128	&	4.69	&	-295.786\,792	&	-295.571\,688	&	5.85	&	-295.786\,920	&	-295.588\,928	&	5.39\\
			&				&	AVQZ		&	-295.872\,580	&	-295.700\,460	&	4.68	&	-295.866\,703	&	-295.651\,866	&	5.85	&	-295.866\,836	&	-295.668\,899	&	5.39\\
			&	PC-NEVPT2(14,10)	&	6-31+G*		&	-295.472\,765	&	-295.298\,260	&	4.75	&	-295.471\,378	&	-295.241\,519	&	6.25	&	-295.472\,493	&	-295.265\,525	&	5.63\\
			&				&	AVDZ		&	-295.548\,353	&	-295.375\,655	&	4.70	&	-295.547\,076	&	-295.318\,367	&	6.22	&	-295.548\,211	&	-295.343\,195	&	5.58\\
			&				&	AVTZ		&	-295.784\,554	&	-295.615\,226	&	4.61	&	-295.783\,476	&	-295.557\,518	&	6.15	&	-295.784\,648	&	-295.582\,320	&	5.51\\
			&				&	AVQZ		&	-295.863\,782	&	-295.694\,805	&	4.60	&	-295.862\,719	&	-295.636\,896	&	6.14	&	-295.863\,910	&	-295.661\,564	&	5.51\\
			&	SC-NEVPT2(14,10)	&	6-31+G*		&	-295.469\,393	&	-295.292\,159	&	4.82	&	-295.467\,983	&	-295.236\,511	&	6.30	&	-295.468\,997	&	-295.259\,950	&	5.69\\
			&				&	AVDZ		&	-295.544\,750	&	-295.369\,146	&	4.78	&	-295.543\,436	&	-295.312\,892	&	6.27	&	-295.544\,465	&	-295.337\,135	&	5.64\\
			&				&	AVTZ		&	-295.780\,889	&	-295.608\,612	&	4.69	&	-295.779\,775	&	-295.551\,944	&	6.20	&	-295.780\,838	&	-295.576\,130	&	5.57\\
			&				&	AVQZ		&	-295.860\,099	&	-295.688\,149	&	4.68	&	-295.859\,007	&	-295.631\,295	&	6.20	&	-295.860\,088	&	-295.655\,345	&	5.57\\
	\end{tabular}
	\end{ruledtabular}
\end{table}
\end{squeezetable}


%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Energetics of selected CI calculations}
%%%%%%%%%%%%%%%%%%%%%%%%%%%

%------------------------------
\subsection{Acrolein}
%------------------------------

%%% ACROLEIN %%%
\begin{table}[H]
	\caption{
	\label{tab:acrolein_sCI}
	sCI+PT2 and exFCI energies (in hartree) transition energies $\Delta E$ (in eV) and its corresponding error estimate (in eV) of acrolein for various methods and basis sets.
	The number of determinants ($\Ndet$) in the largest sCI wave function is also reported.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllrdddddddd}
	Molecule&	Method	&	Basis	&	\mcc{$\Ndet$}	&	\mc{4}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{\pi}{\pis}}	
														&	\mc{4}{c}{1\,\ex{1}{A}{g}{} $\ra$ 3\,\ex{1}{A}{g}{}: \tr{\pi,\pi}{\pis,\pis}}	\\
															\cline{5-8}	\cline{9-12}
			&			&			&					&	\mcc{1\,\ex{1}{A}{g}{}}	&	\mcc{2\,\ex{1}{A}{g}{}}	&	\mcc{$\Delta E$}	&	\mcc{Error}
														&	\mcc{1\,\ex{1}{A}{g}{}}	&	\mcc{3\,\ex{1}{A}{g}{}}	&	\mcc{$\Delta E$}	&	\mcc{Error}\\
	\hline
	Acrolein	&	sCI+PT2	&	6-31+G*	&	$228\,482\,893$	&	-191.3674		&	-191.1124		&	6.94	&			
															&	-191.3674		&	-191.0708		&	8.07				\\
%				&			&	AVDZ	&	$128\,777\,969$	&					&			&					\\
				&	exFCI	&	6-31+G*	&					&	-191.3720		&	-191.1190		&	6.89		&	0.02	
															&	-191.3720		&	-191.0782		&	8.00		&	0.03	\\
%				&			&	AVDZ	&					&			&			&			&		\\
	\end{tabular}
	\end{ruledtabular}
\end{table}

%------------------------------
\subsection{Benzene}
%------------------------------

%%% BENZENE %%%
\begin{table}[H]
	\caption{
	\label{tab:benzene_sCI}
	sCI+PT2 and exFCI energies (in hartree) transition energies $\Delta E$ (in eV) and its corresponding error estimate (in eV) of benzene for various methods and basis sets.
	The number of determinants ($\Ndet$) in the largest sCI wave function is also reported.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllrdddd}
	Molecule&	Method	&	Basis	&	\mcc{$\Ndet$}	&	\mc{4}{c}{1\,\ex{1}{A}{1g}{} $\ra$ 1\,\ex{1}{E}{2g}{}: \tr{\pi,\pi}{\pis,\pis}}	\\
															\cline{5-8}
			&			&			&					&	\mcc{1\,\ex{1}{S}{}{}}	&	\mcc{1\,\ex{1}{D}{}{'}}	&	\mcc{$\Delta E$}	&	\mcc{Error}\\
	\hline
	Benzene		&	sCI+PT2	&	6-31+G*	&	$128\,138\,453$		&	-231.5185	&	-231.2089		&		8.43				\\
				&			&	AVDZ	&	$$		&		&			&						\\
				&	exFCI	&	6-31+G*	&			&	-231.5384	&	-231.2299		&	8.40		&	0.03	\\
				&			&	AVDZ	&			&		&			&			&		\\
	\end{tabular}
	\end{ruledtabular}
\end{table}

%------------------------------
\subsection{Beryllium}
%------------------------------

%%% BERYLLIUM %%%
\begin{table}[H]
	\caption{
	\label{tab:Be_sCI}
	sCI+PT2 and exFCI energies (in hartree) transition energies $\Delta E$ (in eV) and its corresponding error estimate (in eV) of beryllium for various methods and basis sets.
	The number of determinants ($\Ndet$) in the largest sCI wave function is also reported.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllrdddd}
	Molecule&	Method	&	Basis	&	\mcc{$\Ndet$}	&	\mc{4}{c}{1\,\ex{1}{S}{}{} $\ra$ 1\,\ex{1}{D}{}{}: \tr{2s^2}{2p^2}}	\\
															\cline{5-8}
			&			&			&					&	\mcc{1\,\ex{1}{S}{}{}}	&	\mcc{1\,\ex{1}{D}{}{'}}	&	\mcc{$\Delta E$}	&	\mcc{Error}\\
	\hline
	Beryllium	&	sCI+PT2	&	6-31+G*	&	$6\,061$		&	-14.6156	&	-14.3202		&	8.04					\\
				&			&	AVDZ	&	$4\,515$		&	-14.6175	&	-14.3520		&	7.22					\\
				&			&	AVTZ	&	$259\,196$		&	-14.6244	&	-14.3616		&	7.15					\\
				&			&	AVQZ	&	$1\,266\,592$	&	-14.6403	&	-14.3790		&	7.11					\\
				&	exFCI	&	6-31+G*	&					&	-14.6156	&	-14.3202		&	8.04		&	0.00	\\
				&			&	AVDZ	&					&	-14.6175	&	-14.3520		&	7.22		&	0.00	\\
				&			&	AVTZ	&					&	-14.6244	&	-14.3616		&	7.15		&	0.00	\\
				&			&	AVQZ	&					&	-14.6403	&	-14.3790		&	7.11		&	0.00	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}

%------------------------------
\subsection{Butadiene}
%------------------------------

%%% BUTADIENE %%%
\begin{table}[H]
	\caption{
	\label{tab:butadiene_sCI}
	sCI+PT2 and exFCI energies (in hartree) transition energies $\Delta E$ (in eV) and its corresponding error estimate (in eV) of butadiene for various methods and basis sets.
	The number of determinants ($\Ndet$) in the largest sCI wave function is also reported.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllrdddd}
	Molecule&	Method	&	Basis	&	\mcc{$\Ndet$}	&	\mc{4}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{\pi,\pi}{\pis,\pis}}	\\
															\cline{5-8}
			&			&			&					&	\mcc{1\,\ex{1}{A}{g}{}}	&	\mcc{2\,\ex{1}{A}{g}{}}	&	\mcc{$\Delta E$}	&	\mcc{Error}\\
	\hline
	Butadiene	&	sCI+PT2	&	6-31+G*	&	$92\,506\,300$	&	-155.4884		&	-155.2463		&	6.59			\\
				&			&	AVDZ	&	$59\,594\,588$	&	-155.5559		&	-155.3142		&	6.58			\\
				&	exFCI	&	6-31+G*	&					&	-155.4942		&	-155.2537		&	6.55		&	0.03	\\
				&			&	AVDZ	&					&	-155.5652		&	-155.3259		&	6.51		&	0.12	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}

%------------------------------
\subsection{Carbon dimer}
%------------------------------

%%% CARBON DIMER %%%
\begin{table}[H]
	\caption{
	\label{tab:C2_sCI}
	sCI+PT2 and exFCI energies (in hartree) transition energies $\Delta E$ (in eV) and its corresponding error estimate (in eV) of the carbon dimer for various methods and basis sets.
	The number of determinants ($\Ndet$) in the largest sCI wave function is also reported.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllldddddddd}
	Molecule	&	Method		&	Basis	&	\mcc{$\Ndet$}	&	\mc{4}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 1\,\ex{1}{\Delta}{g}{}}	
														&	\mc{4}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 2\,\ex{1}{\Sigma}{g}{+}}		\\
												\cline{5-8}		\cline{9-12}
				&				&			&				&	\mcc{1\,\ex{1}{\Sigma}{g}{+}}	&	\mcc{2\,\ex{1}{\Sigma}{g}{+}}	&	\mcc{$\Delta E$}	&	\mcc{Error}	
														&	\mcc{1\,\ex{1}{\Sigma}{g}{+}}	&	\mcc{1\,\ex{1}{\Delta}{g}{}}	&	\mcc{$\Delta E$}	&	\mcc{Error}\\
	\hline
	Carbon dimer&	sCI+PT2		&	6-31+G*	&	$4\,859\,181$	&	-75.7276	&	-75.6434	&	2.29	&			&	-75.7276	&	-75.6354	&	2.51	&		\\
				&				&	AVDZ	&	$9\,012\,864$	&	-75.7360	&	-75.6546	&	2.21	&			&	-75.7360	&	-75.6440	&	2.50	&		\\
				&				&	AVTZ	&	$7\,403\,397$	&	-75.7885	&	-75.7117	&	2.09	&			&	-75.7885	&	-75.6995	&	2.42	&		\\
				&				&	AVQZ	&	$4\,996\,718$	&	-75.8040	&	-75.7283	&	2.06	&			&	-75.8040	&	-75.7144	&	2.39	&		\\
				&	exFCI		&	6-31+G*	&					&	-75.7276	&	-75.6434	&	2.29	&	0.00	&	-75.7276	&	-75.6354	&	2.51	&	0.00	\\
				&				&	AVDZ	&					&	-75.7360	&	-75.6546	&	2.21	&	0.00	&	-75.7360	&	-75.6440	&	2.51	&	0.00	\\
				&				&	AVTZ	&					&	-75.7884	&	-75.7116	&	2.09	&	0.00	&	-75.7884	&	-75.6995	&	2.42	&	0.00	\\
				&				&	AVQZ	&					&	-75.8038	&	-75.7281	&	2.06	&	0.00	&	-75.8038	&	-75.7158	&	2.40	&	0.01	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}

%------------------------------
\subsection{Carbon trimer}
%------------------------------

%%% CARBON TRIMER %%%
\begin{table}[H]
	\caption{
	\label{tab:C3_sCI}
	sCI+PT2 and exFCI energies (in hartree) transition energies $\Delta E$ (in eV) and its corresponding error estimate (in eV) of the carbon trimer for various methods and basis sets.
	The number of determinants ($\Ndet$) in the largest sCI wave function is also reported.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllrdddddddd}
	Molecule	&	Method		&	Basis	&	\mcc{$\Ndet$}	&	\mc{4}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 1\,\ex{1}{\Delta}{g}{}}	
														&	\mc{4}{c}{1\,\ex{1}{\Sigma}{g}{+} $\ra$ 2\,\ex{1}{\Sigma}{g}{+}}		\\
												\cline{5-8}		\cline{9-12}
				&				&			&				&	\mcc{1\,\ex{1}{\Sigma}{g}{+}}	&	\mcc{2\,\ex{1}{\Sigma}{g}{+}}	&	\mcc{$\Delta E$}	&	\mcc{Error}	
														&	\mcc{1\,\ex{1}{\Sigma}{g}{+}}	&	\mcc{1\,\ex{1}{\Delta}{g}{}}	&	\mcc{$\Delta E$}	&	\mcc{Error}\\
	\hline
	Carbon trimer&	sCI+PT2		&	6-31+G*	&	$11\,618\,295$	&	-113.7435	&	-113.5500	&	5.26	&		&	-113.7435	&	-113.5256	&	5.93	&		\\
				&				&	AVDZ	&	$12\,016\,205$	&	-113.7570	&	-113.5655	&	5.21	&		&	-113.7570	&	-113.5408	&	5.88	&		\\
				&				&	AVTZ	&	$21\,185\,136$	&	-113.8422	&	-113.6501	&	5.23	&		&	-113.8422	&	-113.6253	&	5.90	&		\\
				&				&	AVQZ	&	$1\,819\,523$	&	-113.8687	&	-113.6753	&	5.26	&		&	-113.8687	&	-113.6509	&	5.92	&		\\
				&	exFCI		&	6-31+G*	&					&	-113.7438	&	-113.5502	&	5.27	&	0.01&	-113.7438	&	-113.5258	&	5.93	&	0.01\\
				&				&	AVDZ	&					&	-113.7573	&	-113.5660	&	5.21	&	0.00&	-113.7573	&	-113.5413	&	5.88	&	0.00\\
				&				&	AVTZ	&					&	-113.8427	&	-113.6510	&	5.22	&	0.04&	-113.8427	&	-113.6256	&	5.91	&	0.02\\
				&				&	AVQZ	&					&	-113.8636	&	-113.6714	&	5.23	&	0.05&	-113.8636	&	-113.6483	&	5.86	&	0.01\\
	\end{tabular}
	\end{ruledtabular}
\end{table}

%------------------------------
\subsection{Ethylene}
%------------------------------

%%% ETHYLENE %%%
\begin{table}[H]
	\caption{
	\label{tab:ethylene_sCI}
	sCI+PT2 and exFCI energies (in hartree) transition energies $\Delta E$ (in eV) and its corresponding error estimate (in eV) of ethylene for various methods and basis sets.
	The number of determinants ($\Ndet$) in the largest sCI wave function is also reported.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllrdddd}
	Molecule&	Method	&	Basis	&	\mcc{$\Ndet$}	&	\mc{4}{c}{1\,\ex{1}{A}{g}{} $\ra$ 2\,\ex{1}{A}{g}{}: \tr{\pi,\pi}{\pis,\pis}}	\\
															\cline{5-8}
			&			&			&					&	\mcc{1\,\ex{1}{A}{g}{}}	&	\mcc{2\,\ex{1}{A}{g}{}}	&	\mcc{$\Delta E$}	&	\mcc{Error}\\
	\hline
	Ethylene	&	sCI+PT2	&	6-31+G*	&	$6\,533\,117$	&	-78.3261	&	-77.8338	&	13.39				\\
				&			&	AVDZ	&	$8\,143\,431$	&	-78.3701	&	-77.8893	&	13.08		\\
				&			&	AVTZ	&	$6\,116\,916$	&	-78.4460	&	-77.9709	&	12.93				\\
				&	exFCI	&	6-31+G*	&					&	-78.3260	&	-77.8341	&	13.38	&	0.06	\\
				&			&	AVDZ	&					&	-78.3700	&	-77.8896	&	13.07	&	0.01	\\
				&			&	AVTZ	&					&	-78.4460	&	-77.9712	&	12.92	&	0.06	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}

%------------------------------
\subsection{Formaldehyde}
%------------------------------

%%% FORMALDEHYDE %%%
\begin{table}[H]
	\caption{
	\label{tab:formaldehyde_sCI}
	sCI+PT2 and exFCI energies (in hartree) transition energies $\Delta E$ (in eV) and its corresponding error estimate (in eV) of formaldehyde for various methods and basis sets.
	The number of determinants ($\Ndet$) in the largest sCI wave function is also reported.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllrdddd}
	Molecule&	Method	&	Basis	&	\mcc{$\Ndet$}	&	\mc{4}{c}{1\,\ex{1}{A}{}{} $\ra$ 3\,\ex{1}{A}{}{}: \tr{n,n}{\pis,\pis}}	\\
															\cline{5-8}
			&			&			&					&	\mcc{1\,\ex{1}{A}{}{}}	&	\mcc{3\,\ex{1}{A}{}{}}	&	\mcc{$\Delta E$}	&	\mcc{Error}\\
	\hline
	Formaldehyde&	sCI+PT2	&	6-31+G*	&	$7\,388\,887$	&	-114.1970			&	-113.7979		&	10.86				\\
				&			&	AVDZ	&	$3\,645\,058$	&	-114.2466			&	-113.8621		&	10.46				\\
				&			&	AVTZ	&	$4\,858\,133$	&	-114.3463			&	-113.9643		&	10.40				\\
				&	exFCI	&	6-31+G*	&					&	-114.1968			&	-113.7976		&	10.86		&	0.01	\\
				&			&	AVDZ	&					&	-114.2458			&	-113.8616		&	10.45		&	0.01	\\
				&			&	AVTZ	&					&	-114.3438			&	-113.9636		&	10.35		&	0.03	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}

%------------------------------
\subsection{Glyoxal}
%------------------------------

%%% GLYOXAL %%%
\begin{table}[H]
	\caption{
	\label{tab:glyoxal_sCI}
	sCI+PT2 and exFCI energies (in hartree) transition energies $\Delta E$ (in eV) and its corresponding error estimate (in eV) of glyoxal for various methods and basis sets.
	The number of determinants ($\Ndet$) in the largest sCI wave function is also reported.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllrdddd}
	Molecule&	Method	&	Basis	&	\mcc{$\Ndet$}	&	\mc{4}{c}{1\,\ex{1}{A}{}{} $\ra$ 2\,\ex{1}{A}{}{}: \tr{n,n}{\pis,\pis}}	\\
															\cline{5-8}
			&			&			&					&	\mcc{1\,\ex{1}{A}{}{}}	&	\mcc{2\,\ex{1}{A}{}{}}	&	\mcc{$\Delta E$}	&	\mcc{Error}\\
	\hline
	Glyoxal		&	sCI+PT2	&	6-31+G*	&	$118\,275\,835$	&	-227.2342		&	-227.0252		&	5.69			\\
				&			&	AVDZ	&	$35\,354\,892$	&	-227.3121		&	-227.1065		&	5.59				\\
				&	exFCI	&	6-31+G*	&					&	-227.2376		&	-227.0319		&	5.60		&	0.01	\\
				&			&	AVDZ	&					&	-227.3173		&	-227.1161		&	5.48		&	0.00	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}

%------------------------------
\subsection{Nitrosomethane}
%------------------------------

%%% NITRSOMETHANE %%%
\begin{table}[H]
	\caption{
	\label{tab:nitromethane_sCI}
	sCI+PT2 and exFCI energies (in hartree) transition energies $\Delta E$ (in eV) and its corresponding error estimate (in eV) of nitrosomethane for various methods and basis sets.
	The number of determinants ($\Ndet$) in the largest sCI wave function is also reported.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllrdddd}
	Molecule&	Method	&	Basis	&	\mcc{$\Ndet$}	&	\mc{4}{c}{1\,\ex{1}{A}{}{'} $\ra$ 2\,\ex{1}{A}{}{'}: \tr{n,n}{\pis,\pis}}	\\
															\cline{5-8}
			&			&			&					&	\mcc{1\,\ex{1}{A}{}{'}}	&	\mcc{2\,\ex{1}{A}{}{'}}	&	\mcc{$\Delta E$}	&	\mcc{Error}\\
	\hline
	Nitrosomethane	&	sCI+PT2	&	6-31+G*	&	$17\,390\,237$	&	-169.3418			&	-169.1629		&	4.87		\\
					&			&	AVDZ	&	$3\,256\,229$	&	-169.4117			&	-169.2333		&	4.85		\\
					&			&	AVTZ	&	$17\,833\,307$	&	-169.5599			&	-169.3834		&	4.80		\\
					&	exFCI	&	6-31+G*	&					&	-169.3438			&	-169.1650		&	4.86		&	0.01	\\
					&			&	AVDZ	&					&	-169.4144			&	-169.2380		&	4.80		&	0.02	\\
					&			&	AVTZ	&					&	-169.5647			&	-169.3897		&	4.76		&	0.04	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}

%------------------------------
\subsection{Nitroxyl}
%------------------------------

%%% NITROXYL %%%
\begin{table}[H]
	\caption{
	\label{tab:nitroxyl_sCI}
	sCI+PT2 and exFCI energies (in hartree) transition energies $\Delta E$ (in eV) and its corresponding error estimate (in eV) of nitroxyl for various methods and basis sets.
	The number of determinants ($\Ndet$) in the largest sCI wave function is also reported.
	}
	\begin{ruledtabular}
	\begin{tabular}{lllrdddd}
	Molecule&	Method	&	Basis	&	\mcc{$\Ndet$}	&	\mc{4}{c}{1\,\ex{1}{A}{}{'} $\ra$ 2\,\ex{1}{A}{}{'}: \tr{n,n}{\pis,\pis}}	\\
															\cline{5-8}
			&			&			&					&	\mcc{1\,\ex{1}{A}{}{'}}	&	\mcc{2\,\ex{1}{A}{}{'}}	&	\mcc{$\Delta E$}	&	\mcc{Error}\\
	\hline
	Nitroxyl&	sCI+PT2	&	6-31+G*	&	$19\,924\,902$	&	-130.1534				&	-129.9876				&	4.51					\\
			&			&	AVDZ	&	$3\,502\,014$	&	-130.2056				&	-130.0440				&	4.40					\\
			&			&	AVTZ	&	$8\,185\,333$	&	-130.3125				&	-130.1529				&	4.34					\\
			&			&	AVQZ	&	$3\,723\,478$	&	-130.3479				&	-130.1888				&	4.33					\\
			&	exFCI	&	6-31+G*	&					&	-130.1534				&	-129.9876				&	4.51					&	0.00	\\
			&			&	AVDZ	&					&	-130.2056				&	-130.0440				&	4.40					&	0.01	\\
			&			&	AVTZ	&					&	-130.3113				&	-130.1522				&	4.33					&	0.00	\\
			&			&	AVQZ	&					&	-130.3450				&	-130.1864				&	4.32					&	0.00	\\
	\end{tabular}
	\end{ruledtabular}
\end{table}


\bibliography{../QUEST2}

\end{document}
