117 lines
4.2 KiB
TeX
117 lines
4.2 KiB
TeX
\documentclass[aip,jcp,reprint,onecolumn,noshowkeys,superscriptaddress]{revtex4-1}
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\usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,longtable,wrapfig,txfonts,siunitx}
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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{siunitx}
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\usepackage{soul}
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\DeclareSIUnit[number-unit-product = {\,}]
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\cal{cal}
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\DeclareSIUnit\kcal{\kilo\cal}
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\newcommand{\kcalmol}{\si{\kcal\per\mole}}
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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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% methods
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\newcommand{\GW}{\text{$GW$}}
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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{\Hxc}{\text{Hxc}}
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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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\newcommand{\KS}{\text{KS}}
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\newcommand{\HF}{\text{HF}}
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\newcommand{\RPA}{\text{RPA}}
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% orbital energies
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\newcommand{\eps}[2]{\epsilon_{#1}^{#2}}
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\newcommand{\reps}[2]{\Tilde{\epsilon}_{#1}^{#2}}
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\newcommand{\Om}[2]{\Omega_{#1}^{#2}}
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\newcommand{\RHH}{R_{\ce{H-H}}}
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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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\begin{document}
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\title{Supporting Information for ``Unphysical Discontinuities, Intruder States and Regularization in $GW$ Methods''}
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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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\maketitle
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%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Energy differences}
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%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{$\eta$ shift}
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\begin{figure}
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\includegraphics[width=0.6\linewidth]{eta_0_1}
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\caption{Difference between non-regularized and regularized quasiparticle energies $\eps{p}{\GW}-\reps{p}{\GW}$ computed with $\eta = 0.1$ as functions of the internuclear distance $\RHH$ (in \si{\angstrom}) of \ce{H2} at the {\GOWO}@HF/6-31G level. }
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\end{figure}
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\begin{figure}
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\includegraphics[width=0.6\linewidth]{eta_1}
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\caption{Difference between non-regularized and regularized quasiparticle energies $\eps{p}{\GW}-\reps{p}{\GW}$ computed with $\eta = 1$ as functions of the internuclear distance $\RHH$ (in \si{\angstrom}) of \ce{H2} at the {\GOWO}@HF/6-31G level. }
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\end{figure}
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\begin{figure}
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\includegraphics[width=0.6\linewidth]{eta_10}
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\caption{Difference between non-regularized and regularized quasiparticle energies $\eps{p}{\GW}-\reps{p}{\GW}$ computed with $\eta = 10$ as functions of the internuclear distance $\RHH$ (in \si{\angstrom}) of \ce{H2} at the {\GOWO}@HF/6-31G level. }
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\end{figure}
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\subsection{$\kappa$ shift}
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\begin{figure}
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\includegraphics[width=0.6\linewidth]{kappa_0_1}
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\caption{Difference between non-regularized and regularized quasiparticle energies $\eps{p}{\GW}-\reps{p}{\GW}$ computed with $\kappa = 0.1$ as functions of the internuclear distance $\RHH$ (in \si{\angstrom}) of \ce{H2} at the {\GOWO}@HF/6-31G level. }
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\end{figure}
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\begin{figure}
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\includegraphics[width=0.6\linewidth]{kappa_10}
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\caption{Difference between non-regularized and regularized quasiparticle energies $\eps{p}{\GW}-\reps{p}{\GW}$ computed with $\kappa = 10$ as functions of the internuclear distance $\RHH$ (in \si{\angstrom}) of \ce{H2} at the {\GOWO}@HF/6-31G level. }
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\end{figure}
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%%%%%%%%%%%%%%%%%%%%%%%%
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\section{\ce{F2} ground state}
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%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{figure}
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\includegraphics[width=0.6\linewidth]{f2_eta_1}
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\caption{Ground-state potential energy surface of \ce{F2} around its equilibrium geometry obtained at various levels of theory with the cc-pVDZ basis set.}
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\end{figure}
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\begin{figure}
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\includegraphics[width=0.6\linewidth]{f2_kappa_1}
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\caption{Ground-state potential energy surface of \ce{F2} around its equilibrium geometry obtained at various levels of theory with the cc-pVDZ basis set.}
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\end{figure}
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\begin{figure}
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\includegraphics[width=0.6\linewidth]{f2_kappa_10}
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\caption{Ground-state potential energy surface of \ce{F2} around its equilibrium geometry obtained at various levels of theory with the cc-pVDZ basis set.}
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\end{figure}
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%%%%%%%%%%%%%%%%%%%%%%%%
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\bibliography{ufGW}
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%%%%%%%%%%%%%%%%%%%%%%%%
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\end{document} |