285 lines
9.8 KiB
TeX
285 lines
9.8 KiB
TeX
\documentclass[aip,jcp,reprint,noshowkeys,superscriptaddress]{revtex4-1}
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\usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,longtable,wrapfig,txfonts}
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\usepackage[version=4]{mhchem}
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\usepackage{natbib}
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\bibliographystyle{achemso}
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\usepackage[utf8]{inputenc}
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\usepackage[T1]{fontenc}
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\usepackage{txfonts}
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\usepackage[
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colorlinks=true,
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citecolor=blue,
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breaklinks=true
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]{hyperref}
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\urlstyle{same}
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\usepackage[normalem]{ulem}
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\newcommand{\QP}{\textsc{quantum package}}
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\newcommand{\T}[1]{#1^{\intercal}}
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% coordinates
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\newcommand{\br}{\mathbf{r}}
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\newcommand{\dbr}{d\br}
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% methods
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\newcommand{\evGW}{ev$GW$}
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\newcommand{\qsGW}{qs$GW$}
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\newcommand{\GOWO}{$G_0W_0$}
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\newcommand{\xc}{\text{xc}}
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\newcommand{\Ha}{\text{H}}
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\newcommand{\co}{\text{c}}
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\newcommand{\x}{\text{x}}
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%
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\newcommand{\Norb}{N_\text{orb}}
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\newcommand{\Nocc}{O}
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\newcommand{\Nvir}{V}
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% operators
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\newcommand{\hH}{\Hat{H}}
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\newcommand{\hS}{\Hat{S}}
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% methods
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\newcommand{\KS}{\text{KS}}
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\newcommand{\HF}{\text{HF}}
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\newcommand{\RPA}{\text{RPA}}
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\newcommand{\BSE}{\text{BSE}}
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\newcommand{\dBSE}{\text{dBSE}}
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\newcommand{\GW}{GW}
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\newcommand{\stat}{\text{stat}}
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\newcommand{\dyn}{\text{dyn}}
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\newcommand{\TDA}{\text{TDA}}
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% energies
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\newcommand{\Enuc}{E^\text{nuc}}
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\newcommand{\Ec}{E_\text{c}}
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\newcommand{\EHF}{E^\text{HF}}
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\newcommand{\EBSE}{E^\text{BSE}}
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\newcommand{\EcRPA}{E_\text{c}^\text{RPA}}
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\newcommand{\EcBSE}{E_\text{c}^\text{BSE}}
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% orbital energies
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\newcommand{\e}[1]{\eps_{#1}}
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\newcommand{\eHF}[1]{\eps^\text{HF}_{#1}}
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\newcommand{\eKS}[1]{\eps^\text{KS}_{#1}}
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\newcommand{\eQP}[1]{\eps^\text{QP}_{#1}}
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\newcommand{\eGOWO}[1]{\eps^\text{\GOWO}_{#1}}
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\newcommand{\eGW}[1]{\eps^{GW}_{#1}}
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\newcommand{\eevGW}[1]{\eps^\text{\evGW}_{#1}}
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\newcommand{\eGnWn}[2]{\eps^\text{\GnWn{#2}}_{#1}}
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\newcommand{\Om}[2]{\Omega_{#1}^{#2}}
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\newcommand{\tOm}[2]{\Tilde{\Omega}_{#1}^{#2}}
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\newcommand{\homu}{\frac{{\omega}_1}{2}}
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% Matrix elements
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\newcommand{\A}[2]{A_{#1}^{#2}}
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\newcommand{\tA}[2]{\Tilde{A}_{#1}^{#2}}
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\newcommand{\B}[2]{B_{#1}^{#2}}
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\renewcommand{\S}[1]{S_{#1}}
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\newcommand{\ABSE}[2]{A_{#1}^{#2,\text{BSE}}}
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\newcommand{\BBSE}[2]{B_{#1}^{#2,\text{BSE}}}
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\newcommand{\ARPA}[2]{A_{#1}^{#2,\text{RPA}}}
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\newcommand{\BRPA}[2]{B_{#1}^{#2,\text{RPA}}}
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\newcommand{\ARPAx}[2]{A_{#1}^{#2,\text{RPAx}}}
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\newcommand{\BRPAx}[2]{B_{#1}^{#2,\text{RPAx}}}
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\newcommand{\G}[1]{G_{#1}}
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\newcommand{\LBSE}[1]{L_{#1}}
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\newcommand{\XiBSE}[1]{\Xi_{#1}}
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\newcommand{\Po}[1]{P_{#1}}
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\newcommand{\W}[2]{W_{#1}^{#2}}
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\newcommand{\tW}[2]{\widetilde{W}_{#1}^{#2}}
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\newcommand{\Wc}[1]{W^\text{c}_{#1}}
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\newcommand{\vc}[1]{v_{#1}}
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\newcommand{\Sig}[2]{\Sigma_{#1}^{#2}}
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\newcommand{\SigC}[1]{\Sigma^\text{c}_{#1}}
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\newcommand{\SigX}[1]{\Sigma^\text{x}_{#1}}
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\newcommand{\SigXC}[1]{\Sigma^\text{xc}_{#1}}
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\newcommand{\Z}[1]{Z_{#1}}
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\newcommand{\MO}[1]{\phi_{#1}}
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\newcommand{\ERI}[2]{(#1|#2)}
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\newcommand{\rbra}[1]{(#1|}
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\newcommand{\rket}[1]{|#1)}
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\newcommand{\sERI}[2]{[#1|#2]}
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%% bold in Table
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\newcommand{\bb}[1]{\textbf{#1}}
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\newcommand{\rb}[1]{\textbf{\textcolor{red}{#1}}}
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\newcommand{\gb}[1]{\textbf{\textcolor{darkgreen}{#1}}}
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% excitation energies
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\newcommand{\OmRPA}[1]{\Omega_{#1}^{\text{RPA}}}
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\newcommand{\OmRPAx}[1]{\Omega_{#1}^{\text{RPAx}}}
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\newcommand{\OmBSE}[1]{\Omega_{#1}^{\text{BSE}}}
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% Matrices
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\newcommand{\bI}{\mathbf{1}}
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\newcommand{\bvc}{\mathbf{v}}
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\newcommand{\bSig}{\mathbf{\Sigma}}
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\newcommand{\bSigX}{\mathbf{\Sigma}^\text{x}}
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\newcommand{\bSigC}{\mathbf{\Sigma}^\text{c}}
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\newcommand{\bSigGW}{\mathbf{\Sigma}^{GW}}
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\newcommand{\be}{\mathbf{\epsilon}}
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\newcommand{\beGW}{\mathbf{\epsilon}^{GW}}
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\newcommand{\beGnWn}[1]{\mathbf{\epsilon}^\text{\GnWn{#1}}}
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\newcommand{\bde}{\mathbf{\Delta\epsilon}}
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\newcommand{\bdeHF}{\mathbf{\Delta\epsilon}^\text{HF}}
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\newcommand{\bdeGW}{\mathbf{\Delta\epsilon}^{GW}}
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\newcommand{\bOm}[1]{\mathbf{\Omega}^{#1}}
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\newcommand{\bA}[2]{\mathbf{A}_{#1}^{#2}}
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\newcommand{\bB}[2]{\mathbf{B}_{#1}^{#2}}
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\newcommand{\bX}[2]{\mathbf{X}_{#1}^{#2}}
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\newcommand{\bY}[2]{\mathbf{Y}_{#1}^{#2}}
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\newcommand{\bZ}[2]{\mathbf{Z}_{#1}^{#2}}
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\newcommand{\bK}{\mathbf{K}}
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\newcommand{\bP}[1]{\mathbf{P}^{#1}}
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% units
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\newcommand{\IneV}[1]{#1 eV}
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\newcommand{\InAU}[1]{#1 a.u.}
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\newcommand{\InAA}[1]{#1 \AA}
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\newcommand{\kcal}{kcal/mol}
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% orbitals, gaps, etc
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\newcommand{\eps}{\varepsilon}
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\newcommand{\IP}{I}
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\newcommand{\EA}{A}
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\newcommand{\HOMO}{\text{HOMO}}
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\newcommand{\LUMO}{\text{LUMO}}
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\newcommand{\Eg}{E_\text{g}}
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\newcommand{\EgFun}{\Eg^\text{fund}}
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\newcommand{\EgOpt}{\Eg^\text{opt}}
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\newcommand{\EB}{E_B}
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\newcommand{\sig}{\sigma}
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\newcommand{\bsig}{{\Bar{\sigma}}}
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\newcommand{\sigp}{{\sigma'}}
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\newcommand{\bsigp}{{\Bar{\sigma}'}}
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\newcommand{\taup}{{\tau'}}
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\newcommand{\up}{\uparrow}
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\newcommand{\dw}{\downarrow}
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\newcommand{\upup}{\uparrow\uparrow}
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\newcommand{\updw}{\uparrow\downarrow}
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\newcommand{\dwup}{\downarrow\uparrow}
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\newcommand{\dwdw}{\downarrow\downarrow}
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\newcommand{\spc}{\text{sc}}
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\newcommand{\spf}{\text{sf}}
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\begin{document}
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% addresses
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\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France}
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\newcommand{\CEISAM}{Universit\'e de Nantes, CNRS, CEISAM UMR 6230, F-44000 Nantes, France}
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\title{Reference energies for cyclobutadiene}
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\author{Enzo \surname{Monino}}
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\affiliation{\LCPQ}
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\author{Martial \surname{Boggio-Pasqua}}
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\affiliation{\LCPQ}
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\author{Anthony \surname{Scemama}}
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\affiliation{\LCPQ}
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\author{Denis \surname{Jacquemin}}
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\affiliation{\CEISAM}
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\author{Pierre-Fran\c{c}ois \surname{Loos}}
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\email{loos@irsamc.ups-tlse.fr}
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\affiliation{\LCPQ}
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\begin{abstract}
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Write an abstract
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\end{abstract}
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\maketitle
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Introduction}
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\label{sec:intro}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Despite the fact that excited states are involved in ubiquitious processes such as photochemistry, catalysis or in solar cell technology, none of the many methods existing is the reference in providing accurate excited states energies. Indeed, each method has its own flaws and there are so many chemical scenario that can occur, so it is still one of the biggest challenge in theoretical chemistry. Speaking of difficult task, cyclobutadiene (CBD) molecule has been a real challenge for experimental and theoretical chemists for many decades \cite{bally_cyclobutadiene_1980}. Due to his antiaromaticity \cite{noauthor_aromaticity_nodate} and his large angular strain \cite{baeyer_ueber_1885} the CBD molecule presents a high reactivity which made the synthesis of this molecule a particularly difficult task. Hückel molecular orbital theory gives a triplet state with square ($D_{4h}$) geometry for the ground state of the CBD,with the two singly occupied frontier orbitals that are degenerated by symmetry. This degeneracy is lifted by the Jahn-Teller effect, meaning by distortion of the molecule (lowering symmetry), and gives a singlet state with rectangular ($D_{2h}$) geometry for the ground state. Indeed, synthetic work from Pettis and co-workers \cite{reeves_further_1969} gives a rectangular geometry to the singlet ground state of CBD and then was confirmed by experimental works \cite{irngartinger_bonding_1983,ermer_three_1983,kreile_uv_1986}. At the ground state structrure ($D_{2h}$), the ${}^1A_g$ state has a weak multi-configurational character because of the well separated frontier orbitals and can be described by single-reference methods. But at the square ($D_{4h}$) geometry, the singlet state (${}^1B_{1g}$) has two singly occupied frontier orbitals that are degenerated so has a two-configurational character and single-reference methods are unreliable to describe it. The singlet ($D_{4h}$) is a transition state in the automerization reaction between the two rectangular structures.
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\begin{figure}
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\includegraphics[width=0.6\linewidth]{figure2.png}
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\caption{Here comes the caption of the figure.}
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\label{fig:CBD}
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\end{figure}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Computational methods}
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\label{sec:compdet}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{CIPSI}
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\label{sec:CIPSI}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Coupled-Cluster}
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\label{sec:CC}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{CASPT2/NEVPT2}
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\label{sec:CAS}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Spin-Flip}
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\label{sec:sf}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Results and discussion}
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\label{sec:res}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%================================================
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\subsection{Excited States}
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%================================================
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%================================================
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\subsection{Automerization}
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%================================================
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Conclusion}
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\label{sec:res}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%
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\acknowledgements{
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EM, AS, and PFL acknowledge funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant agreement No.~863481).}
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%%%%%%%%%%%%%%%%%%%%%%%%
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\bibliography{CBD}
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\end{document}
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