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% second quantized operators
\newcommand{\ai}[1]{\hat{a}_{#1}}
\newcommand{\aic}[1]{\hat{a}^{\dagger}_{#1}}

% units
\newcommand{\IneV}[1]{#1 eV}
\newcommand{\InAU}[1]{#1 a.u.}
\newcommand{\InAA}[1]{#1 \AA}
\newcommand{\kcal}{kcal/mol}

% methods
\newcommand{\D}{\text{D}}
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% energies
\newcommand{\EHF}{E_\text{HF}}
\newcommand{\EPT}{E_\text{PT2}}
\newcommand{\EFCI}{E_\text{FCI}}
\newcommand{\EsCI}{E_\text{sCI}}
\newcommand{\EDMC}{E_\text{DMC}}
\newcommand{\EexFCI}{E_\text{exFCI}}
\newcommand{\EexDMC}{E_\text{exDMC}}
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\newcommand{\ex}[4]{$^{#1}#2_{#3}^{#4}$}

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\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France}
\newcommand{\LCT}{Laboratoire de Chimie Th\'eorique (UMR 7616), Sorbonne Universit\'e, CNRS, Paris, France}

\begin{document}	

\title{Supporting Information for ``Chemically Accurate Excitation Energies With Small Basis Sets''}

\author{Emmanuel Giner}
\email[Corresponding author: \jt{JTcomment: I propose to also put EG as a corresponding author}]{emmanuel.giner@lct.jussieu.fr}
\affiliation{\LCT}
\author{Anthony Scemama}
\affiliation{\LCPQ}
\author{Julien Toulouse}
\affiliation{\LCT}
\author{Pierre-Fran\c{c}ois Loos}
\email[Corresponding author: ]{loos@irsamc.ups-tlse.fr}
\affiliation{\LCPQ}

\begin{abstract}
\end{abstract}

\maketitle

%\tableofcontents

%%%%%%%%%%%%%%%%%%%%%%%%
\section{Geometries}
\label{sec:intro}
%%%%%%%%%%%%%%%%%%%%%%%%

Below are given the cartesian coordinates of the compounds investigated in this study. 
These are provided in Angstroms (\AA) and they have been obtained at the CC3(full)/aug-cc-pVTZ level of theory, \cite{LooSceBloGarCafJac-JCTC-18, LooBogSceCafJAc-JCTC-19} except for methylene where the FCI/TZVP geometries have been extracted from Ref.~\onlinecite{SheLeiVanSch-JCP-98}.

%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Ammonia}
%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{verbatim}
N                     0.067759     0.000000     0.000000
H                    -0.313823     0.468746    -0.811891
H                    -0.313823    -0.937491     0.000000
H                    -0.313823     0.468746     0.811891
\end{verbatim}

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

\begin{verbatim}
C                    0.000000     0.000000     0.624021
C                    0.000000     0.000000    -0.624021
\end{verbatim}

%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Carbon monoxyde}
%%%%%%%%%%%%%%%%%%%%%%%%%%%

%\begin{verbatim}
%C                    0.000000     0.000000    -1.249421
%0                    0.000000     0.000000     0.892667
%\end{verbatim}

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

\begin{verbatim}
C                    0.000000     0.666904     0.000000
C                    0.000000    -0.666904     0.000000
H                    0.000000     1.229522     0.922291
H                    0.000000    -1.229522     0.922291
H                    0.000000     1.229522    -0.922291
H                    0.000000    -1.229522    -0.922291
\end{verbatim}

%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Methylene}
%%%%%%%%%%%%%%%%%%%%%%%%%%%

%==============================
\subsubsection{$1\,{}^3 B_1$ state}
%==============================

\begin{verbatim}
C                     0.000000     0.000000     0.000000
H                     0.000000     0.000000     1.077500
H                    -0.784304     0.000000    -0.738832
\end{verbatim}

%==============================
\subsubsection{$1\,{}^1 A_1$ state}
%==============================

\begin{verbatim}
C                     0.000000     0.000000     0.000000
H                     0.000000     0.000000     1.108900
H                    -1.085109     0.000000    -0.228470
\end{verbatim}

%==============================
\subsubsection{$1\,{}^1 B _1$ state}
%==============================

\begin{verbatim}
C                     0.000000     0.000000     0.000000
H                     0.000000     0.000000     1.074800
H                    -0.668198     0.000000    -0.841847
\end{verbatim}

%==============================
\subsubsection{$2\,{}^1A_1$ state}
%==============================

\begin{verbatim}
C                     0.000000     0.000000     0.000000
H                     0.000000     0.000000     1.067800
H                    -0.183953     0.000000    -1.051836
\end{verbatim}

%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Water}
%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{verbatim}
O                    0.000000     0.000000    -0.069903
H                    0.000000     0.757532     0.518435
H                    0.000000    -0.757532     0.518435
\end{verbatim}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Total energies}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

The exFCI total energies can be found in the {\SI} of Refs.~\onlinecite{LooSceBloGarCafJac-JCTC-18, LooBogSceCafJAc-JCTC-19}.
Here, we report the absolute energetic corrections for each state of each molecule obtained with the three short-range correlation functionals considered in the present study (i.e., $\LDA$, $\PBEUEG$ and $\PBEot$).
 
 
%%% TABLE 1 %%%
	\begin{squeezetable}
	\begin{table*}[h]
	\caption{
	Total energies (in hartree) of excited states of methylene for various methods and basis sets.
	The value in parenthesis is an estimate on the last digit of the extrapolation error.}
	\label{tab:CH2}
	\begin{ruledtabular}
	\begin{tabular}{lldddd}
				&				&	\mc{4}{c}{States}	\\
				\cline{3-6}
	Method		&	Basis set	&	\tabc{$1\,^{3}B_1$}		
								&	\tabc{$1\,^{1}A_1$}		
								&	\tabc{$1\,^{1}B_1$}	
								&	\tabc{$2\,^{1}A_1$}		\\
	\hline
	exFCI		&	AVDZ		&	-39.04846(1)				
								&	-39.03225(1)	
								&	-38.99203(1)	
								&	-38.95076(1)	\\	
				&	AVTZ		&	-39.08064(3)	
								&	-39.06565(2)	
								&	-39.02833(1)	
								&	-38.98709(1)	\\	
				&	AVQZ		&	-39.08854(1)	
								&	-39.07402(2)	
								&	-39.03711(1)	
								&	-38.99607(1)	\\	
				&	AV5Z		&	-39.09079(1)	
								&	-39.07647(1)	
								&	-39.03964(3)	
								&	-38.99867(1)	\\	
				&	CBS			&	-39.09141		
								&	-39.07715		
								&	-39.04034		
								&	-38.99939		\\
								\\
	exFCI+$\PBEot$	&	AVDZ		&	-39.06924(1)				
								&	-39.05651(1)		
								&	-39.01777(1)		
								&	-38.97698(1)		\\	
				&	AVTZ		&	-39.08805(3)	
								&	-39.07430(2)		
								&	-39.03742(1)		
								&	-38.99652(1)		\\	
				&	AVQZ		&	-39.09189(1)	
								&	-39.07795(2)		
								&	-39.04124(1)		
								&	-39.00044(1)		\\	
								\\
	exFCI+$\PBE$	&	AVDZ		&	-39.07282(1)	
								&	-39.06150(1)		
								&	-39.02181(1)		
								&	-38.97873(1)		\\	
				&	AVTZ		&	-39.08948(3)	
								&	-39.07639(2)		
								&	-39.03911(1)		
								&	-38.99724(1)		\\	
				&	AVQZ		&	-39.09247(1)	
								&	-39.07885(2)	
								&	-39.04193(1)		
								&	-39.00066(1)		\\	
								\\
	exFCI+LDA	&	AVDZ		&	-39.07450(1)	
								&	-39.06213(1)		
								&	-39.02233(1)		
								&	-38.97946(1)		\\	
				&	AVTZ		&	-39.09099(3)	
								&	-39.07779(2)		
								&	-39.04051(1)		
								&	-38.99859(1)		\\	
				&	AVQZ		&	-39.09319(1)	
								&	-39.07959(2)		
								&	-39.04267(1)		
								&	-39.00135(1)		\\	
								\\
	SHCI\fnm[1]	&	AVQZ		&	-39.08849(1)				
								&	-39.07404(1)		
								&	-39.03711(1)		
								&	-38.99603(1)		\\
	CR-EOMCC (2,3)D\fnm[2]&	AVQZ&	-39.08817					
								&	-39.07303			
								&	-39.03450			
								&	-38.99457			\\
	FCI\fnm[3]		&	TZ2P	&	-39.066738					
								&	-39.048984			
								&	-39.010059			
								&	-38.968471			\\
	\end{tabular}
	\end{ruledtabular}
	\fnt[1]{Semistochastic heat-bath CI (SHCI) calculations from Ref.~\onlinecite{ChiHolAdaOttUmrShaZim-JPCA-18}.}
	\fnt[2]{Completely-renormalized equation-of-motion coupled cluster (CR-EOMCC) calculations from Refs.~\onlinecite{SheLeiVanSch-JCP-98, JenBun-JCP-88}.}
	\fnt[3]{Reference \onlinecite{SheLeiVanSch-JCP-98}.}
	\end{table*}
	\end{squeezetable}
%%% %%% %%% %%%	
	
%%% TABLE 2 %%%
	\begin{turnpage}
	\begin{squeezetable}
	\begin{table*}[h]
	\caption{
	Basis set energetic corrections (in hartree) on absorption energies for excited states of ammonia, carbon dimer, water, and ethylene for various methods and basis sets.}
	\begin{ruledtabular}{}
	\begin{tabular}{llddddddddd}
				&								&	\mc{9}{c}{Deviation with respect to TBE}		
	\\
	\cline{3-11}
				&								&	\mc{3}{c}{exFCI+$\PBEot$}	
												&	\mc{3}{c}{exFCI+$\PBE$}	
												&	\mc{3}{c}{exFCI+$\LDA$}
	\\
	\cline{3-5}	\cline{6-8}	\cline{9-11}
	Molecule	&	State						
												&	\tabc{AVDZ}	&	\tabc{AVTZ}	&	\tabc{AVQZ}	
												&	\tabc{AVDZ}	&	\tabc{AVTZ}	&	\tabc{AVQZ}	
												&	\tabc{AVDZ}	&	\tabc{AVTZ}	&	\tabc{AVQZ}	
	\\
	\hline
	Ammonia		&	$1\,^{1}A_{1}$				
												&	-0.044\,635 & -0.016\,982 & -0.008\,134 
												&	-0.051\,254 & -0.019\,468 & -0.008\,997
												&	-0.048\,544 & -0.020\,906 & -0.010\,081	
	\\
				&	$1\,^{1}A_{2}$					
												&	-0.039\,461 & -0.014\,997 & -0.007\,039	
												&	-0.047\,284 & -0.018\,061 & -0.008\,251
												&	-0.044\,515 & -0.019\,266 & -0.009\,218
	\\
				&	$1\,^{1}E$						
												&	-0.039\,392 & -0.014\,949 & -0.007\,017
												&	-0.047\,456 & -0.018\,077 & -0.008\,245	
												&	-0.044\,860 & -0.019\,344 & -0.009\,222
	\\
				&	$2\,^{1}A_{1}$					
												&	-0.040\,071 & -0.014\,995 & -0.006\,988 
												&	-0.047\,916 & -0.018\,163 & -0.008\,241	
												&	-0.045\,561 & -0.019\,651 & -0.009\,258 	
	\\
				&	$2\,^{1}A_{2}$					
												&	-0.039\,483 & -0.014\,904 & -0.006\,961
												&	-0.047\,307 & -0.018\,019 & -0.008\,211
												&	-0.045\,008 & -0.019\,252 & -0.009\,175 	
	\\
				&	$1\,^{3}A_{2}$					
												&	-0.038\,969 & -0.014\,725 & -0.006\,828
												&	-0.047\,144 & -0.018\,010 & -0.008\,221
												&	-0.044\,361 & -0.019\,216 & -0.009\,181	
	\\
	\\
	Carbon dimer	&	$1\,^{1}\Sigma_g^+$		
												&	-0.037\,716 & -0.014\,339 & -0.006\,758
												&	-0.050\,128 & -0.019\,217 & -0.008\,918
												&	-0.049\,570 & -0.021\,425 & -0.010\,307
	\\
					&	$1\,^{1}\Delta_g$		
												&	-0.042\,611 & -0.016\,313 & -0.007\,592
												&	-0.050\,686 & -0.019\,737 & -0.009\,079
												&	-0.049\,710 & -0.021\,590 & -0.010\,380
	\\
					&	$2\,^{1}\Sigma_g^+$		
												&	-0.042\,167 & -0.016\,136 & -0.00\,7567
												&	-0.050\,333 & -0.019\,473 & -0.00\,8978
												&	-0.049\,208 & -0.021\,292 & -0.01\,0257
	\\
	\\
%	Carbon monoxyde	&	$1\,^{1}\Sigma^+$		
%												&	-0.074\,328 & -0.031\,117	& -0.015\,510
%												&	-0.084\,655 & -0.035\,318	& -0.017\,142
%												&	-0.076\,668 & -0.077\,437	& -0.018\,768
%	\\
%					&	$1\,^{1}\Pi$		
%												&	-0.075\,790	& -0.031\,456	& -0.016\,083
%												&	-0.085\,494	& -0.035\,255	& -0.017\,182
%												&	-0.036\,301 & -0.036\,359	& -0.018\,855
%	\\
%	\\
	Water		&	$1\,^{1}A_1$				
												&	-0.058\,765 & -0.024\,014 & -0.011\,990
												&	-0.066\,603 & -0.027\,236 & -0.013\,127
												&	-0.059\,660 & -0.027\,777 & -0.014\,274
	\\		
				&	$1\,^{1}B_1$				
												&	-0.052\,137 & -0.021\,369 & -0.010\,611
												&	-0.061\,033 & -0.025\,180 & -0.012\,076	
												&	-0.054\,803 & -0.025\,596 & -0.013\,154
	\\		
				&	$1\,^{1}A_2$				
												&	-0.052\,102 & -0.021\,325 & -0.010\,591	
												&	-0.061\,406 & -0.025\,263 & -0.012\,114
												&	-0.055\,215 & -0.025\,776 & -0.013\,270
	\\		
				&	$2\,^{1}A_1$					
												&	-0.052\,995 & -0.021\,690 & -0.010\,852	
												&	-0.061\,959 & -0.025\,457 & -0.012\,258		
												&	-0.055\,301 & -0.025\,786 & -0.013\,304
	\\		
				&	$1\,^{3}B_1$					
												&	-0.051\,161 & -0.020\,974 & -0.010\,117
												&	-0.057\,882 & -0.023\,791 & -0.011\,280	
												&	-0.052\,744 & -0.024\,500 & -0.012\,358
	\\		
				&	$1\,^{3}A_2$				
												&	-0.051\,244 & -0.020\,982 & -0.010\,115
												&	-0.058\,090 & -0.023\,847 & -0.011\,302
												&	-0.052\,729 & -0.024\,611 & -0.012\,398 
	\\
				&	$1\,^{3}A_1$				
												&	-0.052\,193 & -0.021\,398 & -0.010\,401
												&	-0.059\,073 & -0.024\,272 & -0.011\,595
												&	-0.053\,409 & -0.024\,840 & -0.012\,699
	\\
	\\
	Ethylene	&	$1\,^{1}A_{1g}$				
												&	-0.057\,559 & -0.022\,007	&	
												&	-0.066\,251 & -0.024\,599	&	
												&	-0.065\,343 & -0.027\,274 	&	
	\\		
				&	$1\,^{1}B_{3u}$				
												&	-0.054\,862 & -0.020\,972	&	
												&	-0.063\,185 & -0.023\,501	&	
												&	-0.061\,786 & -0.025\,978	&	
	\\		
				&	$1\,^{1}B_{1u}$					
												&	-0.057\,591 & -0.022\,249	&	
												&	-0.064\,517 & -0.023\,971	&	
												&	-0.063\,619 & -0.026\,561	&	
	\\		
				&	$1\,^{1}B_{1g}$					
												&	-0.054\,995 & -0.020\,994	&	
												&	-0.063\,386 & -0.023\,564	&		
												&	-0.061\,978 & -0.026\,087	&	
	\\		
				&	$1\,^{3}B_{1u}$					
												&	-0.056\,056 & -0.020\,862	&	
												&	-0.063\,499 & -0.023\,241	&	
												&	-0.063\,304 & -0.025\,971	&	
	\\		
				&	$1\,^{3}B_{3u}$					
												&	-0.054\,752 & -0.020\,441	&	
												&	-0.062\,078 & -0.022\,891	&	
												&	-0.060\,894 & -0.025\,249	&	
	\\
				&	$1\,^{3}B_{1g}$					
												&	-0.054\,924 & -0.020\,480	&	
												&	-0.062\,306 & -0.022\,962	&	
												&	-0.061\,089 & -0.025\,334	&	
	\\
	\\
	\end{tabular}
	\end{ruledtabular}
	\end{table*}
	\end{squeezetable}
	\end{turnpage}
%%% %%% %%%

	
\bibliography{../Ex-srDFT,../Ex-srDFT-control}

\end{document}
