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sfBSE.rty
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sfBSE.rty
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\newcommand{\ie}{\textit{i.e.}}
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\newcommand{\eg}{\textit{e.g.}}
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\newcommand{\alert}[1]{\textcolor{red}{#1}}
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\usepackage[normalem]{ulem}
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\newcommand{\titou}[1]{\textcolor{red}{#1}}
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\newcommand{\tabc}[1]{\multicolumn{1}{c}{#1}}
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\newcommand{\SI}{\textcolor{blue}{supplementary material}}
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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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%
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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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\newcommand{\IS}{\lambda}
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% operators
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\newcommand{\hH}{\Hat{H}}
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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{\RPAx}{\text{RPAx}}
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\newcommand{\TDHF}{\text{TDHF}}
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\newcommand{\dRPAx}{\text{dRPAx}}
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\newcommand{\BSE}{\text{BSE}}
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\newcommand{\TDABSE}{\text{BSE(TDA)}}
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\newcommand{\dBSE}{\text{dBSE}}
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\newcommand{\pBSE}{\text{pBSE}}
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\newcommand{\TDAdBSE}{\text{dBSE(TDA)}}
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\newcommand{\GW}{GW}
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\newcommand{\GF}{\text{GF2}}
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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}[2]{\eps_{#1}^{#2}}
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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{\eGW}[1]{\eps^{GW}_{#1}}
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\newcommand{\eGF}[1]{\eps^{\text{GF2}}_{#1}}
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\newcommand{\Om}[2]{\Omega_{#1}^{#2}}
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% Matrix elements
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\newcommand{\Z}[1]{Z_{#1}}
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\newcommand{\Sig}[1]{\Sigma_{#1}}
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\newcommand{\SigGW}[1]{\Sigma^{\GW}_{#1}}
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\newcommand{\SigGF}[1]{\Sigma^{\GF}_{#1}}
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\newcommand{\MO}[1]{\phi_{#1}}
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\newcommand{\ERI}[2]{(#1|#2)}
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\newcommand{\sERI}[2]{[#1|#2]}
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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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\newcommand{\spinup}{\downarrow}
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\newcommand{\spindw}{\uparrow}
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\newcommand{\singlet}{\uparrow\downarrow}
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\newcommand{\triplet}{\uparrow\uparrow}
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% Matrices
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\newcommand{\bO}{\mathbf{0}}
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\newcommand{\bH}{\mathbf{H}}
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\newcommand{\bR}{\mathbf{R}}
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\newcommand{\bX}{\mathbf{X}}
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\newcommand{\bY}{\mathbf{Y}}
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\newcommand{\bC}{\mathbf{C}}
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\newcommand{\bc}{\mathbf{c}}
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\newcommand{\bx}{\mathbf{x}}
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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{\updw}{\uparrow\downarrow}
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\newcommand{\upup}{\uparrow\uparrow}
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\newcommand{\eps}{\epsilon}
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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{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France}
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83
sfBSE.tex
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83
sfBSE.tex
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\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[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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\begin{document}
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\title{Spin-Conserved and Spin-Flip Optical Excitations From the Bethe-Salpeter Equation Formalism}
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\author{Enzo \surname{Monino}}
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\affiliation{\LCPQ}
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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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\alert{Here comes the abstract.}
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%\bigskip
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%\begin{center}
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% \boxed{\includegraphics[width=0.5\linewidth]{TOC}}
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%\end{center}
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%\bigskip
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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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\alert{Here comes the introduction.}
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Unless otherwise stated, atomic units are used, and we assume real quantities throughout this manuscript.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Unrestricted $GW$ formalism}
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\label{sec:UGW}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{The dynamical screening}
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\subsection{The $GW$ self-energy}
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The quasiparticle energies $\eGW{p}$ are obtained by solving the
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\begin{equation}
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\omega = \eHF{p} + \Z{p} \SigGW{p}(\omega)
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\end{equation}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Computational details}
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\label{sec:compdet}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Conclusion}
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\label{sec:ccl}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%
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\acknowledgements{
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We would like to thank Xavier Blase and Denis Jacquemin for insightful discussions.
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This project has received 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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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section*{Data availability statement}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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The data that supports the findings of this study are available within the article and its supplementary material.
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%%%%%%%%%%%%%%%%%%%%%%%%
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\bibliography{sf-BSE}
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%%%%%%%%%%%%%%%%%%%%%%%%
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\end{document}
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