288 lines
13 KiB
TeX
288 lines
13 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}
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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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\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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\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{\trashPFL}[1]{\textcolor{red}{\sout{#1}}}
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\newcommand{\trashXB}[1]{\textcolor{darkgreen}{\sout{#1}}}
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\newcommand{\PFL}[1]{\titou{(\underline{\bf PFL}: #1)}}
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\newcommand{\mc}{\multicolumn}
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\newcommand{\fnm}{\footnotemark}
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\newcommand{\fnt}{\footnotetext}
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\newcommand{\tabc}[1]{\multicolumn{1}{c}{#1}}
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\newcommand{\SupInf}{\textcolor{blue}{supporting information}}
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\newcommand{\QP}{\textsc{quantum package}}
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\newcommand{\T}[1]{#1^{\intercal}}
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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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%geometries
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\newcommand{\Dtwo}{$D_{2h}$}
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\newcommand{\Dfour}{$D_{4h}$}
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\sisetup{range-phrase=--}
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\sisetup{range-units=single}
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%states
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%D2h states
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\newcommand{\oneAg}{$1{}^1A_g$}
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\newcommand{\tBoneg}{$1{}^3B_{1g}$}
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\newcommand{\sBoneg}{$1{}^1B_{1g}$}
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\newcommand{\twoAg}{$2{}^1A_g$}
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%D4h states
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%\newcommand{\oneBoneg}{$1{}^1B_{1g}$} same label as the D2h state
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\newcommand{\Atwog}{$1{}^3A_{2g}$}
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\newcommand{\Aoneg}{$1{}^1A_{1g}$}
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\newcommand{\Btwog}{$1{}^1B_{2g}$}
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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 ``Reference Energies for Cyclobutadiene: Autoisomerization and Excited States''}
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\author{Enzo \surname{Monino}}
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\email{emonino@irsamc.ups-tlse.fr}
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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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%\maketitle
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%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Geometries}
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%%%%%%%%%%%%%%%%%%%%%%%%
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Below, we provide the cartesian coordinates (in \si{\angstrom}) of the geometries that we have employed in our study.
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\begin{itemize}
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\item {\Dtwo} rectangular equilibrium geometry of the {\oneAg} ground state computed at the CASPT2(12,12)/aug-cc-pVTZ level:
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\begin{verbatim}
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C 0.0000000000 -0.6769380253 -0.7827569236
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C 0.0000000000 -0.6769380253 0.7827569236
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C 0.0000000000 0.6769380253 0.7827569236
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C 0.0000000000 0.6769380253 -0.7827569236
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H 0.0000000000 -1.4379809006 -1.5441628360
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H 0.0000000000 -1.4379809006 1.5441628360
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H 0.0000000000 1.4379809006 1.5441628360
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H 0.0000000000 1.4379809006 -1.5441628360
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\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%
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\item {\Dfour} square planar equilibrium geometry of the {\sBoneg} ground state computed at the CASPT2(12,12)/aug-cc-pVTZ level:
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\begin{verbatim}
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C 1.0248323754 0.0000000000 0.0000000000
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C 0.0000000000 -1.0248323754 0.0000000000
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C -1.0248323754 0.0000000000 0.0000000000
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C 0.0000000000 1.0248323754 0.0000000000
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H 2.1005277359 0.0000000000 0.0000000000
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H 0.0000000000 -2.1005277359 0.0000000000
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H -2.1005277359 0.0000000000 0.0000000000
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H 0.0000000000 2.1005277359 0.0000000000
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\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%
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\item {\Dtwo} rectangular equilibrium geometry of the {\oneAg} ground state computed at the CC3/aug-cc-pVTZ level:
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\begin{verbatim}
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C -0.78248546 -0.67208001 0.00000000
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C 0.78248546 -0.67208001 0.00000000
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C -0.78248546 0.67208001 0.00000000
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C 0.78248546 0.67208001 0.00000000
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H -1.54227765 -1.43404123 -0.00000000
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H 1.54227765 -1.43404123 0.00000000
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H -1.54227765 1.43404123 0.00000000
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H 1.54227765 1.43404123 -0.00000000
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\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%
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\item {\Dfour} square planar equilibrium geometry of the {\Atwog} state computed at the (RO)-CCSD(T)/aug-cc-pVTZ level:
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\begin{verbatim}
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C 0.000000 1.017702 0.000000
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C 1.017702 -0.000000 0.000000
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C -1.017702 0.000000 0.000000
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C -0.000000 -1.017702 0.000000
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H 0.000000 2.092429 0.000000
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H 2.092429 -0.000000 0.000000
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H -0.000000 -2.092429 0.000000
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H -2.092429 0.000000 0.000000
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\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%%%
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\end{itemize}
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\begin{squeezetable}
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\begin{table*}
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\caption{Energy differences between the various methods and the reference TBE values.
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Note that AB stands for the automerization barrier and is reported in \si{\kcalmol}.
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The numbers reported in parenthesis are the percentage of single excitations involved in the transition ($\%T_1$) calculated at the CC3/aug-cc-pVTZ level.
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The values between square brackets have been obtained by extrapolation via the procedure described in the corresponding footnote.}
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\label{tab:TBE}
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\begin{ruledtabular}
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\begin{tabular}{lrrrrrrr}
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%\begin{tabular}{*{1}{*{8}{l}}}
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& &\mc{3}{c}{{\Dtwo} excitation energies (eV)} & \mc{3}{c}{{\Dfour} excitation energies (eV)} \\
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\cline{3-5} \cline{6-8}
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Method & AB & {\tBoneg}(99\%) & {\sBoneg}(95\%)& {\twoAg}(1\%) & {\Atwog} & {\Aoneg} & {\Btwog} \\
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\hline
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SF-TD-B3LYP & $10.41$ & $0.241$ & $-0.926$ & $-0.161$ & $-0.164$ & $-1.028$ & $-1.501$ \\
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SF-TD-PBE0 & $8.95$ & $0.220$ & $-0.829$ & $-0.068$ & $-0.163$ & $-0.903$ & $-1.357$ \\
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SF-TD-BHHLYP & $3.79$ & $0.078$ & $-0.393$ & $0.343$ & $-0.099$ & $-0.251$ & $-0.603$ \\
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SF-TD-M06-2X & $1.42$ & $0.000$ & $-0.354$ & $0.208$ & $-0.066$ & $-0.097$ & $-0.432$ \\
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SF-TD-CAM-B3LYP & $9.90$ & $0.280$ & $-0.807$ & $-0.011$ & $-0.134$ & $-0.920$ & $-1.370$ \\
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SF-TD-$\omega $B97X-V & $10.01$ & $0.335$ & $-0.774$ & $0.064$ & $-0.118$ & $-0.928$ & $-1.372$ \\
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SF-TD-LC-$\omega $PBE08 & $10.81$ & $0.435$ & $-0.710$ & $0.199$ & $-0.086$ & $-0.939$ & $-1.376$ \\
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SF-TD-M11 & $2.29$ & $0.097$ & $-0.474$ & $0.151$ & $-0.063$ & $-0.312$ & $-0.675$ \\[0.1cm]
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SF-ADC(2)-s & $-0.30$ & $0.069$ & $-0.026$ & $-0.018$ & $0.112$ & $0.112$ & $-0.190$ \\
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SF-ADC(2)-x & $1.44$ & $0.077$ & $-0.094$ & $-0.446$ & $0.068$ & $-0.409$ & $-0.303$ \\
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SF-ADC(2.5) & $0.18$ & $0.013$ & $0.006$ & $0.029$ & $0.024$ & $0.094$ & $-0.185$ \\
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SF-ADC(3) & $0.65$ & $-0.043$ & $0.037$ & $0.075$ & $-0.065$ & $0.075$ & $-0.181$ \\[0.1cm]
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CCSD & $0.95$ & & & & $-0.059$ & $0.100$ & \\
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CC3 & $-1.05$ & $-0.060$ & $-0.006$ & $0.628$ & & $0.162$ & $0.686$ \\
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CCSDT & $-0.25$ & $-0.051$ & $0.014$ & $0.280$ & $0.005$ & $0.131$ & $0.503$ \\
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CC4 & $-0.11$ & & $0.003$ & $-0.006$ & & $0.011$ & $-0.013$ \\
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CCSDTQ & $0.00$ & & $0.000$ & $0.000$ & $0.000$ & $0.000$ & $0.000$ \\[0.1cm]
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CASSCF(4,4) & $-1.55$ & $0.208$ & $1.421$ & $0.292$ & $0.290$ & $0.734$ & $1.390$ \\
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CASPT2(4,4) & $-1.16$ & $-0.050$ & $-0.202$ & $-0.077$ & $-0.016$ & $0.006$ & $-0.399$ \\
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%XMS-CASPT2(4,4) & & & & $-0.035$ & & & \\
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SC-NEVPT2(4,4) & $0.30$ & $-0.083$ & $-0.703$ & $-0.041$ & $-0.120$ & $-0.072$ & $-0.979$ \\
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PC-NEVPT2(4,4) & $0.31$ & $-0.080$ & $-0.757$ & $-0.066$ & $-0.118$ & $-0.097$ & $-1.031$ \\
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%MRCI(4,4) & & $0.106$ & $0.553$ & $0.121$ & $0.127$ & $0.324$ & $0.381$ \\[0.1cm]
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CASSCF(12,12) & $2.66$ & $0.224$ & $0.719$ & $0.068$ & $0.226$ & $0.443$ & $0.600$ \\
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CASPT2(12,12) & $-0.42$& $0.018$ & $0.058$ & $-0.106$ & $0.039$ & $0.038$ & $-0.108$ \\
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%XMS-CASPT2(12,12) & & & & $-0.090$ & & & \\
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SC-NEVPT2(12,12) & $-0.64$ & $0.039$ & $0.063$ & $-0.063$ & $0.021$ & $0.046$ & $-0.142$ \\
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PC-NEVPT2(12,12) & $-0.65$ & $0.000$ & $-0.062$ & $-0.093$ & $-0.013$ & $-0.024$ & $-0.278$ \\[0.1cm]
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%CIPSI & & $-0.001\pm 0.030$ & $0.017\pm 0.035$ & $-0.120\pm 0.090$ & $0.025\pm 0.029$ & $0.130\pm 0.050$ & \\
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\bf{TBE} & $[\bf{8.93}]$\fnm[1] & $[\bf{1.462}]$\fnm[2] & $[\bf{3.125}]$\fnm[3] & $[\bf{4.149}]$\fnm[3] & $[\bf{0.144}]$\fnm[4] & $[\bf{1.500}]$\fnm[3] & $[\bf{2.034}]$\fnm[3] \\[0.1cm]
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Literature & $8.53$\fnm[5] & $1.573$\fnm[5] & $3.208$\fnm[5] & $4.247$\fnm[5] & $0.266$\fnm[5] & $1.664$\fnm[5] & $1.910$\fnm[5] \\
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& $10.35$\fnm[6] & $1.576$\fnm[6] & $3.141$\fnm[6] & $3.796$\fnm[6] & $0.217$\fnm[6] & $1.123$\fnm[6] & $1.799$\fnm[6]\\
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& $9.58$ \fnm[7]& $1.456$\fnm[7] & $3.285$\fnm[7] & $4.334$\fnm[7] & $0.083$\fnm[7] & $1.621$\fnm[7] & $1.930$\fnm[7] \\
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& $7.48$\fnm[8]& $1.654$\fnm[8] & $3.416$\fnm[8] & $4.360$\fnm[8] & $0.369$\fnm[8] & $1.824$\fnm[8] & $2.143$\fnm[8] \\
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\end{tabular}
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\end{ruledtabular}
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\fnt[1]{Value obtained using CCSDTQ/aug-cc-pVDZ corrected by the difference between CC4/aug-cc-pVTZ and CC4/aug-cc-pVDZ.}
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\fnt[2]{Value obtained using the NEVPT2(12,12) one.}
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\fnt[3]{Value obtained using CCSDTQ/aug-cc-pVDZ corrected by the difference between CC4/aug-cc-pVTZ and CC4/aug-cc-pVDZ.}
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\fnt[4]{Value obtained using CCSDTQ/aug-cc-pVDZ corrected by the difference between CCSDT/aug-cc-pVTZ and CCSDT/aug-cc-pVDZ.}
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\fnt[5]{Value obtained from Ref.~\onlinecite{Lefrancois_2015} at the SF-ADC(2)-s/cc-pVTZ level with the geometry obtained at the CCSD(T)/cc-pVTZ level.}
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\fnt[6]{Value obtained from Ref.~\onlinecite{Lefrancois_2015} at the SF-ADC(2)-x/cc-pVTZ level with the geometry obtained at the CCSD(T)/cc-pVTZ level.}
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\fnt[7]{Value obtained from Ref.~\onlinecite{Lefrancois_2015} at the SF-ADC(3)/cc-pVTZ level with the geometry obtained at the CCSD(T)/cc-pVTZ level.}
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\fnt[8]{Value obtained from Ref.~\onlinecite{Manohar_2008} at the EOM-SF-CCSD/cc-pVTZ level with the geometry obtained at the CCSD(T)/cc-pVTZ level.}
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\end{table*}
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\end{squeezetable}
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%%% %%% %%% %%%
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\begin{table}
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\caption{}
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% \label{}
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\begin{ruledtabular}
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\begin{tabular}{lcr}
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% & \mc{4}{c}{Basis sets} \\
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% \cline{2-5}
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Level of theory & Automerization barrier & Reference \\
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& (\kcalmol) & \\
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\hline
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CCSDTQ/aug-cc-pVTZ & $8.93$ & This work \\
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ic-MRCISD+Q/cc-pVTZ & $8.93$ & Ref.~\onlinecite{Zhang_2019}\\
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Mk-MRCCSD/cc-pVTZ & $10.09$ & Ref.~\onlinecite{Zhang_2019}\\
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Mk-MRCCSD(T)/cc-pVTZ & $8.56$ & Ref.~\onlinecite{Zhang_2019}\\
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SUCCSD/cc-pVTZ & $8.7$ & Ref.~\onlinecite{Li_2009}\\
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MkCCSD/cc-pVTZ & $9.6$ & Ref.~\onlinecite{Li_2009}\\
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RMRCCSD(T)/cc-pVTZ & $9.5$ & Ref.~\onlinecite{Li_2009}\\
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MRCISD/cc-pVTZ & $8.4$ & Ref.~\onlinecite{Eckert-Maksic_2006}\\
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MRCISD + Q/cc-pVTZ & $8.8$ & Ref.~\onlinecite{Eckert-Maksic_2006}\\
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MRAQCC/cc-pVTZ & $8.9$ & Ref.~\onlinecite{Eckert-Maksic_2006}\\
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CCSDt/cc-pVTZ & $9.5$ & Ref.~\onlinecite{Shen_2012}\\
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CCSD(T)-h/cc-pVTZ & $6.8$ & Ref.~\onlinecite{Shen_2012}\\
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CC(t;3)/cc-pVTZ & $10.0$ & Ref.~\onlinecite{Shen_2012}\\
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\end{tabular}
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\end{ruledtabular}
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\end{table}
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%%% %%% %%% %%%
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%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{table}
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\caption{$\expval*{S^2}$ values for the different excited states computed at the SF-TD-DFT/aug-cc-pVTZ level for the {\Dtwo} and {\Dfour} structures.
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}
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% \label{tab:Ssquare}
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\begin{ruledtabular}
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\begin{tabular}{lrrrrrr}
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&\mc{2}{r}{$\expval*{S^2}$ ({\Dtwo})} & \mc{3}{r}{{$\expval*{S^2}$ (\Dfour})} \\
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\cline{2-4} \cline{5-7}
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Method & {\tBoneg} & {\sBoneg} & {\twoAg} & {\Atwog} & {\Aoneg} & {\Btwog} \\
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\hline
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SF-TD-B3LYP
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& $1.989$ & $0.030$ & $0.017$ & $2.007$ & $0.014$ & $0.012$\\[0.1cm]
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SF-TD-PBE0
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& $2.001$ & $0.021$ & $0.019$ & $2.009$ & $0.018$ & $0.012$ \\[0.1cm]
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SF-TD-BH\&HLYP
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& $2.017$ & $0.026$ & $0.041$ & $2.020$ & $0.021$ & $0.018$\\[0.1cm]
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SF-TD-M06-2X
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& $2.014$ & $0.017$ & $0.040$ & $2.014$ & $0.015$ & $0.012$\\[0.1cm]
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SF-TD-CAM-B3LYP
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& $1.990$ & $0.033$ & $0.024$ & $2.008$ & $0.013$ & $0.012$\\[0.1cm]
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SF-TD-$\omega$B97X-V
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& $1.986$ & $0.035$ & $0.024$ & $2.008$ & $0.012$ & $0.010$\\[0.1cm]
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SF-TD-LC-$\omega $PBE08
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& $1.984$ & $0.044$ & $0.031$ & $2.012$ & $0.015$ & $0.012$\\[0.1cm]
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SF-TD-M11
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& $2.011$ & $0.023$ & $0.045$ & $2.012$ & $0.016$ & $0.014$\\
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\end{tabular}
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\end{ruledtabular}
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\end{table}
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%%% %%% %%% %%%
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%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\bibliography{CBD}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\end{document}
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