\documentclass[aip,jcp,reprint,noshowkeys,superscriptaddress]{revtex4-1} \usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,longtable,wrapfig,txfonts} \usepackage[version=4]{mhchem} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{txfonts} \usepackage[ colorlinks=true, citecolor=blue, breaklinks=true ]{hyperref} \urlstyle{same} \newcommand{\ie}{\textit{i.e.}} \newcommand{\eg}{\textit{e.g.}} \newcommand{\alert}[1]{\textcolor{red}{#1}} \usepackage[normalem]{ulem} \newcommand{\titou}[1]{\textcolor{red}{#1}} \newcommand{\trashPFL}[1]{\textcolor{red}{\sout{#1}}} \newcommand{\trashXB}[1]{\textcolor{darkgreen}{\sout{#1}}} \newcommand{\PFL}[1]{\titou{(\underline{\bf PFL}: #1)}} \newcommand{\mc}{\multicolumn} \newcommand{\fnm}{\footnotemark} \newcommand{\fnt}{\footnotetext} \newcommand{\tabc}[1]{\multicolumn{1}{c}{#1}} \newcommand{\SI}{\textcolor{blue}{supporting information}} \newcommand{\QP}{\textsc{quantum package}} \newcommand{\T}[1]{#1^{\intercal}} % coordinates \newcommand{\br}{\mathbf{r}} \newcommand{\dbr}{d\br} % methods \newcommand{\evGW}{ev$GW$} \newcommand{\qsGW}{qs$GW$} \newcommand{\GOWO}{$G_0W_0$} \newcommand{\Hxc}{\text{Hxc}} \newcommand{\xc}{\text{xc}} \newcommand{\Ha}{\text{H}} \newcommand{\co}{\text{c}} \newcommand{\x}{\text{x}} % \newcommand{\Norb}{N_\text{orb}} \newcommand{\Nocc}{O} \newcommand{\Nvir}{V} % operators \newcommand{\hH}{\Hat{H}} \newcommand{\hS}{\Hat{S}} % methods \newcommand{\KS}{\text{KS}} \newcommand{\HF}{\text{HF}} \newcommand{\RPA}{\text{RPA}} \newcommand{\BSE}{\text{BSE}} \newcommand{\dBSE}{\text{dBSE}} \newcommand{\GW}{GW} \newcommand{\stat}{\text{stat}} \newcommand{\dyn}{\text{dyn}} \newcommand{\TDA}{\text{TDA}} % energies \newcommand{\Enuc}{E^\text{nuc}} \newcommand{\Ec}{E_\text{c}} \newcommand{\EHF}{E^\text{HF}} \newcommand{\EBSE}{E^\text{BSE}} \newcommand{\EcRPA}{E_\text{c}^\text{RPA}} \newcommand{\EcBSE}{E_\text{c}^\text{BSE}} % orbital energies \newcommand{\e}[1]{\eps_{#1}} \newcommand{\eHF}[1]{\eps^\text{HF}_{#1}} \newcommand{\eKS}[1]{\eps^\text{KS}_{#1}} \newcommand{\eQP}[1]{\eps^\text{QP}_{#1}} \newcommand{\eGOWO}[1]{\eps^\text{\GOWO}_{#1}} \newcommand{\eGW}[1]{\eps^{GW}_{#1}} \newcommand{\eevGW}[1]{\eps^\text{\evGW}_{#1}} \newcommand{\eGnWn}[2]{\eps^\text{\GnWn{#2}}_{#1}} \newcommand{\Om}[2]{\Omega_{#1}^{#2}} \newcommand{\tOm}[2]{\Tilde{\Omega}_{#1}^{#2}} \newcommand{\homu}{\frac{{\omega}_1}{2}} % Matrix elements \newcommand{\A}[2]{A_{#1}^{#2}} \newcommand{\tA}[2]{\Tilde{A}_{#1}^{#2}} \newcommand{\B}[2]{B_{#1}^{#2}} \renewcommand{\S}[1]{S_{#1}} \newcommand{\ABSE}[2]{A_{#1}^{#2,\text{BSE}}} \newcommand{\BBSE}[2]{B_{#1}^{#2,\text{BSE}}} \newcommand{\ARPA}[2]{A_{#1}^{#2,\text{RPA}}} \newcommand{\BRPA}[2]{B_{#1}^{#2,\text{RPA}}} \newcommand{\ARPAx}[2]{A_{#1}^{#2,\text{RPAx}}} \newcommand{\BRPAx}[2]{B_{#1}^{#2,\text{RPAx}}} \newcommand{\G}[1]{G_{#1}} \newcommand{\LBSE}[1]{L_{#1}} \newcommand{\XiBSE}[1]{\Xi_{#1}} \newcommand{\Po}[1]{P_{#1}} \newcommand{\W}[2]{W_{#1}^{#2}} \newcommand{\tW}[2]{\widetilde{W}_{#1}^{#2}} \newcommand{\Wc}[1]{W^\text{c}_{#1}} \newcommand{\vc}[1]{v_{#1}} \newcommand{\Sig}[2]{\Sigma_{#1}^{#2}} \newcommand{\SigC}[1]{\Sigma^\text{c}_{#1}} \newcommand{\SigX}[1]{\Sigma^\text{x}_{#1}} \newcommand{\SigXC}[1]{\Sigma^\text{xc}_{#1}} \newcommand{\Z}[1]{Z_{#1}} \newcommand{\MO}[1]{\phi_{#1}} \newcommand{\ERI}[2]{(#1|#2)} \newcommand{\rbra}[1]{(#1|} \newcommand{\rket}[1]{|#1)} \newcommand{\sERI}[2]{[#1|#2]} %% bold in Table \newcommand{\bb}[1]{\textbf{#1}} \newcommand{\rb}[1]{\textbf{\textcolor{red}{#1}}} \newcommand{\gb}[1]{\textbf{\textcolor{darkgreen}{#1}}} % excitation energies \newcommand{\OmRPA}[1]{\Omega_{#1}^{\text{RPA}}} \newcommand{\OmRPAx}[1]{\Omega_{#1}^{\text{RPAx}}} \newcommand{\OmBSE}[1]{\Omega_{#1}^{\text{BSE}}} % Matrices \newcommand{\bO}{\mathbf{0}} \newcommand{\bI}{\mathbf{1}} \newcommand{\bvc}{\mathbf{v}} \newcommand{\bSig}{\mathbf{\Sigma}} \newcommand{\bSigX}{\mathbf{\Sigma}^\text{x}} \newcommand{\bSigC}{\mathbf{\Sigma}^\text{c}} \newcommand{\bSigGW}{\mathbf{\Sigma}^{GW}} \newcommand{\be}{\mathbf{\epsilon}} \newcommand{\beGW}{\mathbf{\epsilon}^{GW}} \newcommand{\beGnWn}[1]{\mathbf{\epsilon}^\text{\GnWn{#1}}} \newcommand{\bde}{\mathbf{\Delta\epsilon}} \newcommand{\bdeHF}{\mathbf{\Delta\epsilon}^\text{HF}} \newcommand{\bdeGW}{\mathbf{\Delta\epsilon}^{GW}} \newcommand{\bOm}[1]{\mathbf{\Omega}^{#1}} \newcommand{\bA}[2]{\mathbf{A}_{#1}^{#2}} \newcommand{\bB}[2]{\mathbf{B}_{#1}^{#2}} \newcommand{\bX}[2]{\mathbf{X}_{#1}^{#2}} \newcommand{\bY}[2]{\mathbf{Y}_{#1}^{#2}} \newcommand{\bZ}[2]{\mathbf{Z}_{#1}^{#2}} \newcommand{\bK}{\mathbf{K}} \newcommand{\bP}[1]{\mathbf{P}^{#1}} % units \newcommand{\IneV}[1]{#1 eV} \newcommand{\InAU}[1]{#1 a.u.} \newcommand{\InAA}[1]{#1 \AA} \newcommand{\kcal}{kcal/mol} % orbitals, gaps, etc \newcommand{\eps}{\varepsilon} \newcommand{\IP}{I} \newcommand{\EA}{A} \newcommand{\HOMO}{\text{HOMO}} \newcommand{\LUMO}{\text{LUMO}} \newcommand{\Eg}{E_\text{g}} \newcommand{\EgFun}{\Eg^\text{fund}} \newcommand{\EgOpt}{\Eg^\text{opt}} \newcommand{\EB}{E_B} \newcommand{\sig}{\sigma} \newcommand{\bsig}{{\Bar{\sigma}}} \newcommand{\sigp}{{\sigma'}} \newcommand{\bsigp}{{\Bar{\sigma}'}} \newcommand{\taup}{{\tau'}} \newcommand{\up}{\uparrow} \newcommand{\dw}{\downarrow} \newcommand{\upup}{\uparrow\uparrow} \newcommand{\updw}{\uparrow\downarrow} \newcommand{\dwup}{\downarrow\uparrow} \newcommand{\dwdw}{\downarrow\downarrow} \newcommand{\spc}{\text{sc}} \newcommand{\spf}{\text{sf}} % addresses \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 %%% 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. The raw data are reported in the {\SI}. \label{fig:H2}} \end{figure} %%% %%% %%% %%%%%%%%%%%%%%%%%%%%%%%% \bibliography{sfBSE} %%%%%%%%%%%%%%%%%%%%%%%% \end{document}