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

\begin{document}	

\title{Supporting Information for ``Spin-Conserved and Spin-Flip Optical Excitations From the Bethe-Salpeter Equation Formalism''}

\author{Enzo \surname{Monino}}
	\affiliation{\LCPQ}	 
\author{Pierre-Fran\c{c}ois \surname{Loos}}
	\email{loos@irsamc.ups-tlse.fr}
	\affiliation{\LCPQ}

\maketitle


\begin{table*}
\begin{ruledtabular}
		\begin{tabular}{lrrrrrrrr}
	&\mc{2}{c}{CIS} & \mc{2}{c}{BH\&HLYP} & \mc{2}{c}{BSE@{\GOWO}} & \mc{2}{c}{EOM-CCSD} \\
									&	\mc{2}{c}{$\Delta$ E \text{(eV)}} & \mc{2}{c}{$\Delta$ E \text{(eV)}} & \mc{2}{c}{$\Delta$ E \text{(eV)}} &\mc{2}{c}{$\Delta$ E \text{(eV)}}	\\
									\cline{2-3} \cline{4-5} \cline{6-7} \cline{8-9} 
			Distance (\AA)					&	$B ^1 \Sigma_u^+$&	$E ^1 \Sigma_g^+$	&	$B ^1 \Sigma_u^+$&	$E ^1 \Sigma_g^+$	&	$B ^1 \Sigma_u^+$&	$E ^1 \Sigma_g^+$ &	$B ^1 \Sigma_u^+$&	$E ^1 \Sigma_g^+$	\\
			\hline
				\\
				$0 .5$ & $15 .942$ & $17 .398$ & $15 .253$ & $16 .896$ & $15 .535$ & \
$16 .135$ & $15 .703$ & $16 .737$ \\
$0 .6$ & $14 .791$ & $16 .579$ & $14 .18$ & $16 .199$ & $14 .767$ & \
$15 .073$ & $14 .61$ & $16 .056$ \\
$0 .7$ & $13 .745$ & $15 .891$ & $13 .339$ & $15 .614$ & $14 .108$ & \
$14 .12$ & $13 .621$ & $15 .491$ \\
$0 .8$ & $12 .8$ & $15 .311$ & $12 .514$ & $15 .122$ & $13 .236$ & \
$13 .591$ & $12 .735$ & $15 .017$ \\
$0 .9$ & $11 .943$ & $14 .815$ & $11 .766$ & $14 .699$ & $12 .444$ & \
$13 .126$ & $11 .938$ & $14 .615$ \\
$1.$ & $11 .163$ & $14 .389$ & $11 .088$ & $14 .334$ & $11 .722$ & \
$12 .733$ & $11 .224$ & $14 .27$ \\
$1 .1$ & $10 .454$ & $14 .025$ & $10 .474$ & $14 .02$ & $11 .068$ & \
$12 .41$ & $10 .587$ & $13 .962$ \\
$1 .2$ & $9 .8096$ & $13 .712$ & $9 .919$ & $13 .75$ & $10 .477$ & \
$12 .132$ & $10 .023$ & $13 .648$ \\
$1 .3$ & $9 .3685$ & $13 .401$ & $9 .421$ & $13 .515$ & $9 .4696$ & \
$12 .139$ & $9 .5306$ & $13 .201$ \\
$1 .4$ & $9 .1278$ & $13 .262$ & $8 .9771$ & $13 .309$ & $8 .7427$ & \
$12 .211$ & $9 .1076$ & $14 .241$ \\
$1 .5$ & $8 .9859$ & $13 .18$ & $8 .5848$ & $13 .127$ & $8 .2988$ & \
$12 .3$ & $8 .7525$ & $13 .814$ \\
$1 .6$ & $8 .9106$ & $13 .125$ & $8 .2413$ & $12 .966$ & $8 .0543$ & \
$12 .395$ & $8 .4631$ & $13 .606$ \\
$1 .7$ & $8 .8839$ & $13 .085$ & $7 .9431$ & $12 .824$ & $7 .9457$ & \
$12 .482$ & $8 .2361$ & $13 .475$ \\
$1 .8$ & $8 .8936$ & $13 .058$ & $7 .6866$ & $12 .699$ & $7 .9282$ & \
$12 .563$ & $8 .0669$ & $13 .383$ \\
$1 .9$ & $8 .9307$ & $13 .041$ & $7 .4677$ & $12 .593$ & $7 .9697$ & \
$12 .641$ & $7 .9505$ & $13 .317$ \\
$2.$ & $8 .9888$ & $13 .033$ & $7 .2827$ & $12 .502$ & $8 .0486$ & \
$12 .714$ & $7 .881$ & $13 .272$ \\
$2 .1$ & $9 .0627$ & $13 .031$ & $7 .1279$ & $12 .421$ & $8 .1508$ & \
$12 .783$ & $7 .8523$ & $13 .239$ \\
$2 .2$ & $9 .1485$ & $13 .031$ & $6 .9996$ & $12 .343$ & $8 .2671$ & \
$12 .845$ & $7 .8581$ & $13 .212$ \\
$2 .3$ & $9 .2429$ & $13 .031$ & $6 .8947$ & $12 .265$ & $8 .3914$ & \
$12 .901$ & $7 .8923$ & $13 .187$ \\
$2 .4$ & $9 .3435$ & $13 .031$ & $6 .81$ & $12 .186$ & $8 .5197$ & \
$12 .951$ & $7 .9492$ & $13 .164$ \\
$2 .5$ & $9 .4484$ & $13 .032$ & $6 .7427$ & $12 .109$ & $8 .6495$ & \
$12 .997$ & $8 .0239$ & $13 .145$ \\
$2 .6$ & $9 .5561$ & $13 .037$ & $6 .6902$ & $12 .03$ & $8 .7792$ & \
$13 .042$ & $8 .1122$ & $13 .133$ \\
$2 .7$ & $9 .6657$ & $13 .043$ & $6 .6501$ & $11 .946$ & $8 .908$ & \
$13 .084$ & $8 .2105$ & $13 .125$ \\
$2 .8$ & $9 .7763$ & $13 .05$ & $6 .6205$ & $11 .851$ & $9 .0353$ & \
$13 .123$ & $8 .3162$ & $13 .12$ \\
$2 .9$ & $9 .8874$ & $13 .056$ & $6 .5996$ & $11 .744$ & $9 .1605$ & \
$13 .154$ & $8 .4269$ & $13 .115$ \\
$3.$ & $9 .9984$ & $13 .057$ & $6 .5857$ & $11 .627$ & $9 .283$ & $13 \
.174$ & $8 .5408$ & $13 .106$ \\
$3 .1$ & $10 .109$ & $13 .053$ & $6 .5778$ & $11 .505$ & $9 .4032$ & \
$13 .183$ & $8 .6564$ & $13 .091$ \\
$3 .2$ & $10 .219$ & $13 .043$ & $6 .5746$ & $11 .383$ & $9 .5211$ & \
$13 .181$ & $8 .7726$ & $13 .069$ \\
$3 .3$ & $10 .328$ & $13 .027$ & $6 .5754$ & $11 .266$ & $9 .6369$ & \
$13 .169$ & $8 .8884$ & $13 .041$ \\
$3 .4$ & $10 .435$ & $13 .006$ & $6 .5792$ & $11 .158$ & $9 .7506$ & \
$13 .15$ & $9 .003$ & $13 .008$ \\
$3 .5$ & $10 .541$ & $12 .983$ & $6 .5856$ & $11 .062$ & $9 .862$ & \
$13 .126$ & $9 .1159$ & $12 .972$ \\
$3 .6$ & $10 .645$ & $12 .958$ & $6 .5939$ & $10 .977$ & $9 .971$ & \
$13 .1$ & $9 .2265$ & $12 .935$ \\
$3 .7$ & $10 .748$ & $12 .933$ & $6 .6037$ & $10 .905$ & $10 .077$ & \
$13 .073$ & $9 .3347$ & $12 .899$ \\
$3 .8$ & $10 .848$ & $12 .908$ & $6 .6145$ & $10 .846$ & $10 .181$ & \
$13 .047$ & $9 .4401$ & $12 .863$ \\
$3 .9$ & $10 .947$ & $12 .884$ & $6 .626$ & $10 .798$ & $10 .282$ & \
$13 .023$ & $9 .5424$ & $12 .83$ \\
$4.$ & $11 .043$ & $12 .861$ & $6 .6381$ & $10 .761$ & $10 .38$ & \
$13.$ & $9 .6415$ & $12 .8$ \\
		\end{tabular}
\end{ruledtabular}
\end{table*}

%%% FIG 2 %%%
\begin{figure}
	\includegraphics[width=\linewidth]{H2_B3LYP}
	\hspace{0.05\linewidth}
	\\
	\includegraphics[width=\linewidth]{H2_BLYP}
	\vspace{0.025\linewidth}
	\\
	\includegraphics[width=\linewidth]{H2_dBSE}
\caption{
	Excitation energies with respect to the $\text{X}\,{}^1 \Sigma_g^+$ ground state of the $\text{B}\,{}^1\Sigma_u^+$ (red), $\text{E}\,{}^1\Sigma_g^+$ (black), and $\text{F}\,{}^1\Sigma_g^+$ (blue) states of \ce{H2} obtained with the cc-pVQZ basis at the (SF-)TD-B3LYP (top), (SF-) TD-BLYP (middle), and (SF-)dBSE (bottom) levels of theory.  
	The reference EOM-CCSD excitation energies are represented as solid lines, while the results obtained with and without spin-flip are represented as dashed and dotted lines, respectively.
	All the spin-conserved and spin-flip calculations have been performed with an unrestricted reference.
	\label{fig:H2}}
\end{figure}
%%% %%% %%% 

%%%%%%%%%%%%%%%%%%%%%%%%
\bibliography{sfBSE}
%%%%%%%%%%%%%%%%%%%%%%%%

\end{document}
