CBD/Manuscript/CBD-SI.tex

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\usepackage{siunitx}
\DeclareSIUnit[number-unit-product = {\,}]
\cal{cal}
\DeclareSIUnit\kcal{\kilo\cal}
\newcommand{\kcalmol}{\si{\kcal\per\mole}}

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\newcommand{\QP}{\textsc{quantum package}}
\newcommand{\T}[1]{#1^{\intercal}}

%% bold in Table
\newcommand{\bb}[1]{\textbf{#1}}
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%geometries
\newcommand{\Dtwo}{$D_{2h}$}
\newcommand{\Dfour}{$D_{4h}$}

\sisetup{range-phrase=--}
\sisetup{range-units=single}

%states
%D2h states
\newcommand{\oneAg}{$1{}^1A_g$}
\newcommand{\tBoneg}{$1{}^3B_{1g}$}
\newcommand{\sBoneg}{$1{}^1B_{1g}$}
\newcommand{\twoAg}{$2{}^1A_g$}

%D4h states
%\newcommand{\oneBoneg}{$1{}^1B_{1g}$} same label as the D2h state
\newcommand{\Atwog}{$1{}^3A_{2g}$}
\newcommand{\Aoneg}{$1{}^1A_{1g}$}
\newcommand{\Btwog}{$1{}^1B_{2g}$}

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

\begin{document}	

\title{Supporting Information for ``Reference Energies for Cyclobutadiene: Autoisomerization and Excited States''}

\author{Enzo \surname{Monino}}
	\email{emonino@irsamc.ups-tlse.fr}
	\affiliation{\LCPQ}	 
\author{Martial \surname{Boggio-Pasqua}}
	\affiliation{\LCPQ}
\author{Anthony \surname{Scemama}}
	\affiliation{\LCPQ}
\author{Denis \surname{Jacquemin}}
	\affiliation{\CEISAM}
\author{Pierre-Fran\c{c}ois \surname{Loos}}
	\email{loos@irsamc.ups-tlse.fr}
	\affiliation{\LCPQ}

%\maketitle

%%%%%%%%%%%%%%%%%%%%%%%%
\section{Geometries}
%%%%%%%%%%%%%%%%%%%%%%%%
Below, we provide the cartesian coordinates (in \si{\angstrom}) of the geometries that we have employed in our study.

\begin{itemize}
\item {\Dtwo} rectangular equilibrium geometry of the {\oneAg} ground state computed at the CASPT2(12,12)/aug-cc-pVTZ level:
\begin{verbatim}
C          0.0000000000       -0.6769380253       -0.7827569236
C          0.0000000000       -0.6769380253        0.7827569236
C          0.0000000000        0.6769380253        0.7827569236
C          0.0000000000        0.6769380253       -0.7827569236
H          0.0000000000       -1.4379809006       -1.5441628360
H          0.0000000000       -1.4379809006        1.5441628360
H          0.0000000000        1.4379809006        1.5441628360
H          0.0000000000        1.4379809006       -1.5441628360
\end{verbatim}
%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%
\item {\Dfour} square planar equilibrium geometry of the {\sBoneg} ground state computed at the CASPT2(12,12)/aug-cc-pVTZ level:
\begin{verbatim}
C          1.0248323754        0.0000000000        0.0000000000
C          0.0000000000       -1.0248323754        0.0000000000
C         -1.0248323754        0.0000000000        0.0000000000
C          0.0000000000        1.0248323754        0.0000000000
H          2.1005277359        0.0000000000        0.0000000000
H          0.0000000000       -2.1005277359        0.0000000000
H         -2.1005277359        0.0000000000        0.0000000000
H          0.0000000000        2.1005277359        0.0000000000
\end{verbatim}
%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%
\item {\Dtwo} rectangular equilibrium geometry of the {\oneAg} ground state computed at the CC3/aug-cc-pVTZ level:
\begin{verbatim}
C            -0.78248546      -0.67208001       0.00000000
C             0.78248546      -0.67208001       0.00000000
C            -0.78248546       0.67208001       0.00000000
C             0.78248546       0.67208001       0.00000000
H            -1.54227765      -1.43404123      -0.00000000
H             1.54227765      -1.43404123       0.00000000
H            -1.54227765       1.43404123       0.00000000
H             1.54227765       1.43404123      -0.00000000
\end{verbatim}
%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%
\item {\Dfour} square planar equilibrium geometry of the {\Atwog} state computed at the (RO)-CCSD(T)/aug-cc-pVTZ level:
\begin{verbatim}
C             0.000000    1.017702    0.000000
C             1.017702   -0.000000    0.000000
C            -1.017702    0.000000    0.000000
C            -0.000000   -1.017702    0.000000
H             0.000000    2.092429    0.000000
H             2.092429   -0.000000    0.000000
H            -0.000000   -2.092429    0.000000
H            -2.092429    0.000000    0.000000
\end{verbatim}
%%%%%%%%%%%%%%%%%%%%%%%%
\end{itemize}

\begin{squeezetable}
\begin{table*}
	\caption{Energy differences between the various methods and the reference TBE values. 
	Note that AB stands for the automerization barrier and is reported in \si{\kcalmol}. 
	The numbers reported in parenthesis are the percentage of single excitations involved in the transition ($\%T_1$) calculated at the CC3/aug-cc-pVTZ level.
	The values between square brackets have been obtained by extrapolation via the procedure described in the corresponding footnote.}
	\label{tab:TBE}
	\begin{ruledtabular}
	\begin{tabular}{lrrrrrrr}
%\begin{tabular}{*{1}{*{8}{l}}}
& &\mc{3}{c}{{\Dtwo} excitation energies (eV)} & \mc{3}{c}{{\Dfour} excitation energies (eV)} \\
									\cline{3-5}  \cline{6-8}
Method		&	AB & {\tBoneg}(99\%) 	&	{\sBoneg}(95\%)&	 {\twoAg}(1\%) & 	{\Atwog}	&	 {\Aoneg}	&	{\Btwog} \\
	\hline
SF-TD-B3LYP & $10.41$ & $0.241$ & $-0.926$ & $-0.161$ & $-0.164$ & $-1.028$ & $-1.501$ \\
SF-TD-PBE0 & $8.95$ & $0.220$ & $-0.829$ & $-0.068$ & $-0.163$ & $-0.903$ & $-1.357$ \\
SF-TD-BH\&HLYP & $3.79$ & $0.078$ & $-0.393$ & $0.343$ & $-0.099$ & $-0.251$ & $-0.603$ \\
SF-TD-M06-2X & $1.42$ & $0.000$ & $-0.354$ & $0.208$ & $-0.066$ & $-0.097$ & $-0.432$ \\
SF-TD-CAM-B3LYP & $9.90$ & $0.280$ & $-0.807$ & $-0.011$ & $-0.134$ & $-0.920$ & $-1.370$ \\
SF-TD-$\omega $B97X-V &  $10.01$ & $0.335$ & $-0.774$ & $0.064$ & $-0.118$ & $-0.928$ & $-1.372$ \\
SF-TD-LC-$\omega $PBE08 & $10.81$ &  $0.435$ & $-0.710$ & $0.199$ & $-0.086$ & $-0.939$ & $-1.376$ \\
SF-TD-M11 & $2.29$ & $0.097$ & $-0.474$ & $0.151$ & $-0.063$ & $-0.312$ & $-0.675$ \\[0.1cm]
SF-ADC(2)-s & $-0.30$ & $0.069$ & $-0.026$ & $-0.018$ & $0.112$ & $0.112$ & $-0.190$ \\
SF-ADC(2)-x & $1.44$ &  $0.077$ & $-0.094$ & $-0.446$ & $0.068$ & $-0.409$ & $-0.303$ \\
SF-ADC(2.5) & $0.18$ & $0.013$ & $0.006$ & $0.029$ & $0.024$ & $0.094$ & $-0.185$ \\
SF-ADC(3) & $0.65$ &  $-0.043$ & $0.037$ & $0.075$ & $-0.065$ & $0.075$ & $-0.181$ \\[0.1cm]
CASSCF(4,4) & $-1.55$  & $0.208$ & $1.421$ & $0.292$ & $0.290$ & $0.734$ & $1.390$ \\
CASPT2(4,4) & $-1.16$ & $-0.050$ & $-0.202$ & $-0.077$ & $-0.016$ & $0.006$ & $-0.399$ \\
%XMS-CASPT2(4,4) &  &  &  & $-0.035$ &  &  &  \\
SC-NEVPT2(4,4) & $0.30$ & $-0.083$ & $-0.703$ & $-0.041$ & $-0.120$ & $-0.072$ & $-0.979$ \\
PC-NEVPT2(4,4) & $0.31$ & $-0.080$ & $-0.757$ & $-0.066$ & $-0.118$ & $-0.097$ & $-1.031$ \\
%MRCI(4,4) &  & $0.106$ & $0.553$ & $0.121$ & $0.127$ & $0.324$ & $0.381$ \\[0.1cm]
CASSCF(12,12) & $2.66$ &  $0.224$ & $0.719$ & $0.068$ & $0.226$ & $0.443$ & $0.600$ \\
CASPT2(12,12) & $-0.42$&  $0.018$ & $0.058$ & $-0.106$ & $0.039$ & $0.038$ & $-0.108$ \\
%XMS-CASPT2(12,12) & &   &  & $-0.090$ &  &  &  \\
SC-NEVPT2(12,12) & $-0.64$ &  $0.039$ & $0.063$ & $-0.063$ & $0.021$ & $0.046$ & $-0.142$ \\
PC-NEVPT2(12,12) & $-0.65$ & $0.000$ & $-0.062$ & $-0.093$ & $-0.013$ & $-0.024$ & $-0.278$ \\[0.1cm]
CCSD & $0.95$ &  &  &  & $-0.059$ & $0.100$ &  \\
CC3 & $-1.05$ &  $-0.060$  & $-0.006$   & $0.628$  &  & $0.162$ & $0.686$ \\
CCSDT & $-0.25$ & $-0.051$ & $0.014$ & $0.280$ & $0.005$ & $0.131$ & $0.503$ \\
CC4 & $-0.11$ &  & $0.003$ & $-0.006$ &  & $0.011$ & $-0.013$ \\
CCSDTQ & $0.00$ &   & $0.000$ & $0.000$ & $0.000$ & $0.000$ & $0.000$ \\[0.1cm]
%CIPSI &  & $-0.001\pm 0.030$ & $0.017\pm 0.035$ & $-0.120\pm 0.090$ & $0.025\pm 0.029$ & $0.130\pm 0.050$ &  \\
\bf{TBE} & $[\bf{8.93}]$\fnm[1] &  $[\bf{1.462}]$\fnm[2] & $[\bf{3.125}]$\fnm[3] & $[\bf{4.149}]$\fnm[3] & $[\bf{0.144}]$\fnm[4] & $[\bf{1.500}]$\fnm[3] & $[\bf{2.034}]$\fnm[3] \\[0.1cm]
Literature & $8.53$\fnm[5] & $1.573$\fnm[5] & $3.208$\fnm[5] & $4.247$\fnm[5] & $0.266$\fnm[5] & $1.664$\fnm[5] & $1.910$\fnm[5] \\
            & $10.35$\fnm[6] & $1.576$\fnm[6] & $3.141$\fnm[6] & $3.796$\fnm[6] & $0.217$\fnm[6] & $1.123$\fnm[6] & $1.799$\fnm[6]\\
            & $9.58$ \fnm[7]& $1.456$\fnm[7] & $3.285$\fnm[7] & $4.334$\fnm[7] & $0.083$\fnm[7] & $1.621$\fnm[7] & $1.930$\fnm[7]  \\
            & $7.48$\fnm[8]& $1.654$\fnm[8] & $3.416$\fnm[8] & $4.360$\fnm[8] & $0.369$\fnm[8] & $1.824$\fnm[8] & $2.143$\fnm[8] \\
\end{tabular}

	\end{ruledtabular}
	\fnt[1]{Value obtained using CCSDTQ/aug-cc-pVDZ corrected by the difference between CC4/aug-cc-pVTZ and CC4/aug-cc-pVDZ.}
	\fnt[2]{Value obtained using NEVPT2(12,12).}
	\fnt[3]{Value obtained using CCSDTQ/aug-cc-pVDZ corrected by the difference between CC4/aug-cc-pVTZ and CC4/aug-cc-pVDZ.}
	\fnt[4]{Value obtained using CCSDTQ/aug-cc-pVDZ corrected by the difference between CCSDT/aug-cc-pVTZ and CCSDT/aug-cc-pVDZ.}
	\fnt[5]{Value obtained from Ref.~\onlinecite{Lefrancois_2015} at the SF-ADC(2)-s/cc-pVTZ level with the geometry obtained at the CCSD(T)/cc-pVTZ level.}
	\fnt[6]{Value obtained from Ref.~\onlinecite{Lefrancois_2015} at the SF-ADC(2)-x/cc-pVTZ level with the geometry obtained at the CCSD(T)/cc-pVTZ level.}
	\fnt[7]{Value obtained from Ref.~\onlinecite{Lefrancois_2015} at the SF-ADC(3)/cc-pVTZ level with the geometry obtained at the CCSD(T)/cc-pVTZ level.}
	\fnt[8]{Value obtained from Ref.~\onlinecite{Manohar_2008} at the EOM-SF-CCSD/cc-pVTZ level with the geometry obtained at the CCSD(T)/cc-pVTZ level.}
\end{table*}
\end{squeezetable}


%%% %%% %%% %%%
\begin{table}
	\caption{}
%	\label{}
	\begin{ruledtabular}
		\begin{tabular}{lcr}
%									&	\mc{4}{c}{Basis sets}	\\
%										\cline{2-5}
			Level of theory			&	Automerization barrier	& Reference	\\
									&	(\kcalmol) 				& 	\\
			\hline
            CCSDTQ/aug-cc-pVTZ 		& $8.93$	&	This work	\\
            ic-MRCISD+Q/cc-pVTZ 	& $8.93$	&	Ref.~\onlinecite{Zhang_2019}\\
            Mk-MRCCSD/cc-pVTZ		& $10.09$	&	Ref.~\onlinecite{Zhang_2019}\\
            Mk-MRCCSD(T)/cc-pVTZ	& $8.56$	&	Ref.~\onlinecite{Zhang_2019}\\
            SUCCSD/cc-pVTZ 			& $8.7$		&	Ref.~\onlinecite{Li_2009}\\
            MkCCSD/cc-pVTZ			& $9.6$		&	Ref.~\onlinecite{Li_2009}\\
            RMRCCSD(T)/cc-pVTZ 		& $9.5$		&	Ref.~\onlinecite{Li_2009}\\
            MRCISD/cc-pVTZ 			& $8.4$		&	Ref.~\onlinecite{Eckert-Maksic_2006}\\
            MRCISD + Q/cc-pVTZ 		& $8.8$		&	Ref.~\onlinecite{Eckert-Maksic_2006}\\
            MRAQCC/cc-pVTZ 			& $8.9$		&	Ref.~\onlinecite{Eckert-Maksic_2006}\\
            CCSDt/cc-pVTZ 			& $9.5$		&	Ref.~\onlinecite{Shen_2012}\\
            CCSD(T)-h/cc-pVTZ 		& $6.8$		&	Ref.~\onlinecite{Shen_2012}\\
            CC(t;3)/cc-pVTZ			& $10.0$	&	Ref.~\onlinecite{Shen_2012}\\
		\end{tabular}
	\end{ruledtabular}
\end{table}
%%% %%% %%% %%%




%%%%%%%%%%%%%%%%%%%%%%%%
\begin{table}
	\caption{$\expval*{S^2}$ values for the different excited states computed at the SF-TD-DFT/aug-cc-pVTZ level for the {\Dtwo} and {\Dfour} structures.
	}
%	\label{tab:Ssquare}
	\begin{ruledtabular}
	\begin{tabular}{lrrrrrr}

 &\mc{2}{r}{$\expval*{S^2}$ ({\Dtwo})} & \mc{3}{r}{{$\expval*{S^2}$ (\Dfour})} \\
									\cline{2-4}  \cline{5-7}
Method		&	 {\tBoneg}	&	{\sBoneg} &	 {\twoAg} & 	{\Atwog}	&	 {\Aoneg}	&	{\Btwog} \\
	\hline
SF-TD-B3LYP 
 &  $1.989$ & $0.030$ & $0.017$ & $2.007$ & $0.014$ & $0.012$\\[0.1cm]
 
SF-TD-PBE0 
 & $2.001$ & $0.021$ & $0.019$ & $2.009$ & $0.018$ & $0.012$ \\[0.1cm]
 
SF-TD-BH\&HLYP 
&  $2.017$ & $0.026$ & $0.041$ & $2.020$ & $0.021$ & $0.018$\\[0.1cm]

 SF-TD-M06-2X 
& $2.014$ & $0.017$ & $0.040$ & $2.014$ & $0.015$ & $0.012$\\[0.1cm]

SF-TD-CAM-B3LYP 
 & $1.990$ & $0.033$ & $0.024$ & $2.008$ & $0.013$ & $0.012$\\[0.1cm]

 SF-TD-$\omega$B97X-V 
& $1.986$ & $0.035$ & $0.024$ & $2.008$ & $0.012$ & $0.010$\\[0.1cm]

 SF-TD-LC-$\omega $PBE08 
& $1.984$ & $0.044$ & $0.031$ & $2.012$ & $0.015$ & $0.012$\\[0.1cm]

SF-TD-M11 
& $2.011$ & $0.023$ & $0.045$ & $2.012$ & $0.016$ & $0.014$\\

		\end{tabular}
	\end{ruledtabular}
\end{table}
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\bibliography{CBD}
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\end{document}