From f25ec7747cdf79b455718e598576d92ebee6db58 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Tue, 19 Jan 2021 16:22:58 +0100 Subject: [PATCH] SI --- Manuscript/{sfBSE.rty => sfBSE-SI.tex} | 49 +++++++ Manuscript/sfBSE.tex | 174 +++++++++++++++++++++++++ 2 files changed, 223 insertions(+) rename Manuscript/{sfBSE.rty => sfBSE-SI.tex} (75%) diff --git a/Manuscript/sfBSE.rty b/Manuscript/sfBSE-SI.tex similarity index 75% rename from Manuscript/sfBSE.rty rename to Manuscript/sfBSE-SI.tex index 6db1d31..64c5005 100644 --- a/Manuscript/sfBSE.rty +++ b/Manuscript/sfBSE-SI.tex @@ -1,3 +1,18 @@ +\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}} @@ -172,4 +187,38 @@ % 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} diff --git a/Manuscript/sfBSE.tex b/Manuscript/sfBSE.tex index 3ff1b2d..347b57d 100644 --- a/Manuscript/sfBSE.tex +++ b/Manuscript/sfBSE.tex @@ -13,6 +13,180 @@ ]{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{Spin-Conserved and Spin-Flip Optical Excitations From the Bethe-Salpeter Equation Formalism}