From a2e50cd21e8e7986041c858ee3d5a7e3223fd566 Mon Sep 17 00:00:00 2001 From: EnzoMonino Date: Fri, 15 Apr 2022 16:26:11 +0200 Subject: [PATCH] SI --- Manuscript/eta_0_1.pdf | Bin 0 -> 75464 bytes Manuscript/eta_1.pdf | Bin 0 -> 88367 bytes Manuscript/eta_10.pdf | Bin 0 -> 87128 bytes Manuscript/kappa_0_1.pdf | Bin 0 -> 75549 bytes Manuscript/kappa_10.pdf | Bin 0 -> 86919 bytes Manuscript/ufGW-SI.tex | 98 ++++++++++++++++++++++++++++ Notebooks/GW_conundrum.nb | 28 ++++---- Response_Letter/Response_Letter.tex | 4 +- 8 files changed, 114 insertions(+), 16 deletions(-) create mode 100644 Manuscript/eta_0_1.pdf create mode 100644 Manuscript/eta_1.pdf create mode 100644 Manuscript/eta_10.pdf create mode 100644 Manuscript/kappa_0_1.pdf create mode 100644 Manuscript/kappa_10.pdf create mode 100644 Manuscript/ufGW-SI.tex diff --git a/Manuscript/eta_0_1.pdf b/Manuscript/eta_0_1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c0e7d6bb9513fc36950e455ab567324f70dfb75e GIT 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+\documentclass[aip,jcp,reprint,onecolumn,noshowkeys,superscriptaddress]{revtex4-1} +\usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,longtable,wrapfig,txfonts,siunitx} +\usepackage[version=4]{mhchem} + +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{txfonts} +\usepackage{siunitx} +\usepackage{soul} +\DeclareSIUnit[number-unit-product = {\,}] +\cal{cal} +\DeclareSIUnit\kcal{\kilo\cal} +\newcommand{\kcalmol}{\si{\kcal\per\mole}} + +\usepackage[ + colorlinks=true, + citecolor=blue, + breaklinks=true + ]{hyperref} +\urlstyle{same} + +\usepackage[normalem]{ulem} + +% methods +\newcommand{\GW}{\text{$GW$}} +\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{\KS}{\text{KS}} +\newcommand{\HF}{\text{HF}} +\newcommand{\RPA}{\text{RPA}} + + +% orbital energies +\newcommand{\eps}[2]{\epsilon_{#1}^{#2}} +\newcommand{\reps}[2]{\Tilde{\epsilon}_{#1}^{#2}} +\newcommand{\Om}[2]{\Omega_{#1}^{#2}} + +\newcommand{\RHH}{R_{\ce{H-H}}} + +% addresses +\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France} + +\begin{document} + +\title{Supporting Information for ``Unphysical Discontinuities, Intruder States and Regularization in $GW$ Methods''} + + +\author{Enzo \surname{Monino}} + \affiliation{\LCPQ} +\author{Pierre-Fran\c{c}ois \surname{Loos}} + \email{loos@irsamc.ups-tlse.fr} + \affiliation{\LCPQ} + +\maketitle + +%%%%%%%%%%%%%%%%%%%%%%%% +\section{Energy differences} +%%%%%%%%%%%%%%%%%%%%%%%% + +\subsection{$\eta$ shift} + +\begin{figure} + \includegraphics[width=0.6\linewidth]{eta_0_1} + \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. } +\end{figure} + +\begin{figure} + \includegraphics[width=0.6\linewidth]{eta_1} + \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. } +\end{figure} + +\begin{figure} + \includegraphics[width=0.6\linewidth]{eta_10} + \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. } +\end{figure} + +\subsection{$\kappa$ shift} + +\begin{figure} + \includegraphics[width=0.6\linewidth]{kappa_0_1} + \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. } +\end{figure} + +\begin{figure} + \includegraphics[width=0.6\linewidth]{kappa_10} + \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. } +\end{figure} + +%%%%%%%%%%%%%%%%%%%%%%%% +\bibliography{ufGW} +%%%%%%%%%%%%%%%%%%%%%%%% +\end{document} \ No newline at end of file diff --git a/Notebooks/GW_conundrum.nb b/Notebooks/GW_conundrum.nb index 44dd034..f4b7a2f 100644 --- a/Notebooks/GW_conundrum.nb +++ b/Notebooks/GW_conundrum.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 218174, 5054] +NotebookDataLength[ 218181, 5054] NotebookOptionsPosition[ 209419, 4919] -NotebookOutlinePosition[ 209943, 4939] 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b/Response_Letter/Response_Letter.tex @@ -95,7 +95,7 @@ Otherwise it all is a bit incomprehensible.} It seems to me that the difference between the values of qp energies before and post shifting are of the same order of magnitude for both regularizers. Could authors elaborate what they see differently and what my untrained eyes could not see?} \\ -\alert{ +\alert{We had additionnal graphs for different values of $\eta$, i.e., the traditional shift, and $\kappa$, i.e., the Evangelista shift. } \item @@ -204,7 +204,7 @@ So, why doesn't the curve with $\eta=0.01$ jump abruptly to the solutions comput \item {For all plots, the authors should include the units for $\eta$.} \\ -\alert{ +\alert{We specified the units for the $\eta$ and $\kappa$. } \item