546 lines
17 KiB
TeX
546 lines
17 KiB
TeX
\documentclass[aip,jcp,reprint,onecolumn,noshowkeys]{revtex4-1}
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% units
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\newcommand{\PBE}{\text{PBE}}
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\newcommand{\FCI}{\text{FCI}}
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\newcommand{\CBS}{\text{CBS}}
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\newcommand{\exFCI}{\text{exFCI}}
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\newcommand{\CCSDT}{\text{CCSD(T)}}
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% energies
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\newcommand{\EexDMC}{E_\text{exDMC}}
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\newcommand{\Ead}{\Delta E_\text{ad}}
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\newcommand{\Eabs}{\Delta E_\text{abs}}
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\newcommand{\ex}[4]{$^{#1}#2_{#3}^{#4}$}
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\newcommand{\si}{\sigma}
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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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\newcommand{\LCT}{Laboratoire de Chimie Th\'eorique (UMR 7616), Universit\'e Pierre et Marie Curie, Sorbonne Universit\'e, CNRS, Paris, France}
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\begin{document}
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\title{Supporting Information for ``Chemically-Accurate Excitation Energies With Small Basis Sets''}
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\author{Emmanuel Giner}
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\affiliation{\LCT}
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\author{Anthony Scemama}
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\affiliation{\LCPQ}
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\author{Julien Toulouse}
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\affiliation{\LCT}
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\author{Pierre-Fran\c{c}ois Loos}
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\email[Corresponding author: ]{loos@irsamc.ups-tlse.fr}
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\affiliation{\LCPQ}
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\begin{abstract}
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\end{abstract}
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\maketitle
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%\tableofcontents
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%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Geometries}
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\label{sec:intro}
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%%%%%%%%%%%%%%%%%%%%%%%%
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Below are given the cartesian coordinates of the compounds investigated in this study.
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These are provided in Angstroms (\AA) and they have been obtained at the CC3(full)/aug-cc-pVTZ level of theory, \cite{LooSceBloGarCafJac-JCTC-18, LooBogSceCafJAc-JCTC-19} except for methylene where the FCI/TZVP geometries have been extracted from Ref.~\onlinecite{SheLeiVanSch-JCP-98}.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Ammonia}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{verbatim}
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N 0.067759 0.000000 0.000000
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H -0.313823 0.468746 -0.811891
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H -0.313823 -0.937491 0.000000
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H -0.313823 0.468746 0.811891
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\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Carbon dimer}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{verbatim}
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C 0.000000 0.000000 0.624021
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C 0.000000 0.000000 -0.624021
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\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Carbon monoxyde}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{verbatim}
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C 0.000000 0.000000 -1.249421
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0 0.000000 0.000000 0.892667
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\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Ethylene}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{verbatim}
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C 0.000000 0.666904 0.000000
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C 0.000000 -0.666904 0.000000
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H 0.000000 1.229522 0.922291
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H 0.000000 -1.229522 0.922291
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H 0.000000 1.229522 -0.922291
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H 0.000000 -1.229522 -0.922291
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\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Methylene}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%==============================
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\subsubsection{$1\,{}^3 B_1$ state}
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%==============================
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\begin{verbatim}
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C 0.000000 0.000000 0.000000
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H 0.000000 0.000000 1.077500
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H -0.784304 0.000000 -0.738832
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\end{verbatim}
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%==============================
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\subsubsection{$1\,{}^1 A_1$ state}
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%==============================
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\begin{verbatim}
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C 0.000000 0.000000 0.000000
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H 0.000000 0.000000 1.108900
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H -1.085109 0.000000 -0.228470
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\end{verbatim}
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%==============================
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\subsubsection{$1\,{}^1 B _1$ state}
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%==============================
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\begin{verbatim}
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C 0.000000 0.000000 0.000000
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H 0.000000 0.000000 1.074800
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H -0.668198 0.000000 -0.841847
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\end{verbatim}
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%==============================
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\subsubsection{$2\,{}^1A_1$ state}
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%==============================
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\begin{verbatim}
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C 0.000000 0.000000 0.000000
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H 0.000000 0.000000 1.067800
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H -0.183953 0.000000 -1.051836
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\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Water}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{verbatim}
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O 0.000000 0.000000 -0.069903
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H 0.000000 0.757532 0.518435
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H 0.000000 -0.757532 0.518435
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\end{verbatim}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Total energies}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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The exFCI total energies can be found in the {\SI} of Refs.~\onlinecite{LooSceBloGarCafJac-JCTC-18, LooBogSceCafJAc-JCTC-19}.
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Here, we report the absolute energetic corrections for each state of each molecule obtained with the three short-range correlation functionals considered in the present study (i.e., LDA, PBE and PBEot).
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%%% TABLE 1 %%%
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\begin{squeezetable}
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\begin{table*}[h]
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\caption{
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Total energies (in hartree) of excited states of methylene for various methods and basis sets.
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The value in parenthesis is an estimate on the last digit of the extrapolation error.}
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\label{tab:CH2}
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\begin{ruledtabular}
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\begin{tabular}{lldddd}
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& & \mc{4}{c}{States} \\
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\cline{3-6}
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Method & Basis set & \tabc{$1\,^{3}B_1$}
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& \tabc{$1\,^{1}A_1$}
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& \tabc{$1\,^{1}B_1$}
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& \tabc{$2\,^{1}A_1$} \\
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\hline
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exFCI & AVDZ & -39.04846(1)
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& -39.03225(1)
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& -38.99203(1)
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& -38.95076(1) \\
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& AVTZ & -39.08064(3)
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& -39.06565(2)
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& -39.02833(1)
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& -38.98709(1) \\
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& AVQZ & -39.08854(1)
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& -39.07402(2)
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& -39.03711(1)
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& -38.99607(1) \\
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& AV5Z & -39.09079(1)
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& -39.07647(1)
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& -39.03964(3)
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& -38.99867(1) \\
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& CBS & -39.09141
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& -39.07715
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& -39.04034
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& -38.99939 \\
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\\
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exFCI+PBEot & AVDZ & -39.06924(1)
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& -39.05651(1)
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& -39.01777(1)
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& -38.97698(1) \\
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& AVTZ & -39.08805(3)
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& -39.07430(2)
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& -39.03742(1)
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& -38.99652(1) \\
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& AVQZ & -39.09189(1)
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& -39.07795(2)
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& -39.04124(1)
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& -39.00044(1) \\
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\\
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exFCI+PBE & AVDZ & -39.07282(1)
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& -39.06150(1)
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& -39.02181(1)
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& -38.97873(1) \\
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& AVTZ & -39.08948(3)
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& -39.07639(2)
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& -39.03911(1)
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& -38.99724(1) \\
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& AVQZ & -39.09247(1)
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& -39.07885(2)
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& -39.04193(1)
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& -39.00066(1) \\
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\\
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exFCI+LDA & AVDZ & -39.07450(1)
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& -39.06213(1)
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& -39.02233(1)
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& -38.97946(1) \\
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& AVTZ & -39.09099(3)
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& -39.07779(2)
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& -39.04051(1)
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& -38.99859(1) \\
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& AVQZ & -39.09319(1)
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& -39.07959(2)
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& -39.04267(1)
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& -39.00135(1) \\
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\\
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SHCI\fnm[1] & AVQZ & -39.08849(1)
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& -39.07404(1)
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& -39.03711(1)
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& -38.99603(1) \\
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CR-EOMCC (2,3)D\fnm[2]& AVQZ& -39.08817
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& -39.07303
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& -39.03450
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& -38.99457 \\
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FCI\fnm[3] & TZ2P & -39.066738
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& -39.048984
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& -39.010059
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& -38.968471 \\
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\end{tabular}
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\end{ruledtabular}
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\fnt[1]{Semistochastic heat-bath CI (SHCI) calculations from Ref.~\onlinecite{ChiHolAdaOttUmrShaZim-JPCA-18}.}
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\fnt[2]{Completely-renormalized equation-of-motion coupled cluster (CR-EOMCC) calculations from Refs.~\onlinecite{SheLeiVanSch-JCP-98, JenBun-JCP-88}.}
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\fnt[3]{Reference \onlinecite{SheLeiVanSch-JCP-98}.}
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\end{table*}
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\end{squeezetable}
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%%% %%% %%% %%%
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%%% TABLE 2 %%%
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\begin{turnpage}
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\begin{squeezetable}
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\begin{table*}[h]
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\caption{
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Basis set energetic corrections (in hartree) on absorption energies for excited states of ammonia, carbon dimer, water and ethylene for various methods and basis sets.}
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\begin{ruledtabular}{}
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\begin{tabular}{llddddddddd}
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& & \mc{9}{c}{Deviation with respect to TBE}
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\\
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\cline{3-11}
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& & \mc{3}{c}{exFCI+PBEot}
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& \mc{3}{c}{exFCI+PBE}
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& \mc{3}{c}{exFCI+LDA}
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\\
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\cline{3-5} \cline{6-8} \cline{9-11}
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Molecule & State
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& \tabc{AVDZ} & \tabc{AVTZ} & \tabc{AVQZ}
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& \tabc{AVDZ} & \tabc{AVTZ} & \tabc{AVQZ}
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& \tabc{AVDZ} & \tabc{AVTZ} & \tabc{AVQZ}
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\\
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\hline
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Ammonia & $1\,^{1}A_{1}$
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& -0.044\,635 & -0.016\,982 & -0.008\,134
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& -0.051\,254 & -0.019\,468 & -0.008\,997
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& -0.048\,544 & -0.020\,906 & -0.010\,081
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\\
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& $1\,^{1}A_{2}$
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& -0.039\,461 & -0.014\,997 & -0.007\,039
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& -0.047\,284 & -0.018\,061 & -0.008\,251
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& -0.044\,515 & -0.019\,266 & -0.009\,218
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\\
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& $1\,^{1}E$
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& -0.039\,392 & -0.014\,949 & -0.007\,017
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& -0.047\,456 & -0.018\,077 & -0.008\,245
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& -0.044\,860 & -0.019\,344 & -0.009\,222
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\\
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& $2\,^{1}A_{1}$
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& -0.040\,071 & -0.014\,995 & -0.006\,988
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& -0.047\,916 & -0.018\,163 & -0.008\,241
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& -0.045\,561 & -0.019\,651 & -0.009\,258
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\\
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& $2\,^{1}A_{2}$
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& -0.039\,483 & -0.014\,904 & -0.006\,961
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& -0.047\,307 & -0.018\,019 & -0.008\,211
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& -0.045\,008 & -0.019\,252 & -0.009\,175
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\\
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& $1\,^{3}A_{2}$
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& -0.038\,969 & -0.014\,725 & -0.006\,828
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& -0.047\,144 & -0.018\,010 & -0.008\,221
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& -0.044\,361 & -0.019\,216 & -0.009\,181
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\\
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\\
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Carbon dimer & $1\,^{1}\Sigma_g^+$
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& -0.037\,716 & -0.014\,339 & -0.006\,758
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& -0.050\,128 & -0.019\,217 & -0.008\,918
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& -0.049\,570 & -0.021\,425 & -0.010\,307
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\\
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& $1\,^{1}\Delta_g$
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& -0.042\,611 & -0.016\,313 & -0.007\,592
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& -0.050\,686 & -0.019\,737 & -0.009\,079
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& -0.049\,710 & -0.021\,590 & -0.010\,380
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\\
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& $2\,^{1}\Sigma_g^+$
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& -0.042\,167 & -0.016\,136 & -0.00\,7567
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& -0.050\,333 & -0.019\,473 & -0.00\,8978
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& -0.049\,208 & -0.021\,292 & -0.01\,0257
|
|
\\
|
|
\\
|
|
Carbon monoxyde & $1\,^{1}\Sigma^+$
|
|
& -0.074\,328 & -0.031\,117 & -0.015\,510
|
|
& -0.084\,655 & -0.035\,318 & -0.017\,142
|
|
& -0.076\,668 & -0.077\,437 & -0.018\,768
|
|
\\
|
|
& $1\,^{1}\Pi$
|
|
& -0.075\,790 & -0.031\,456 & -0.016\,083
|
|
& -0.085\,494 & -0.035\,255 & -0.017\,182
|
|
& -0.036\,301 & -0.036\,359 & -0.018\,855
|
|
\\
|
|
\\
|
|
Water & $1\,^{1}A_1$
|
|
& -0.058\,765 & -0.024\,014 & -0.011\,990
|
|
& -0.066\,603 & -0.027\,236 & -0.013\,127
|
|
& -0.059\,660 & -0.027\,777 & -0.014\,274
|
|
\\
|
|
& $1\,^{1}B_1$
|
|
& -0.052\,137 & -0.021\,369 & -0.010\,611
|
|
& -0.061\,033 & -0.025\,180 & -0.012\,076
|
|
& -0.054\,803 & -0.025\,596 & -0.013\,154
|
|
\\
|
|
& $1\,^{1}A_2$
|
|
& -0.052\,102 & -0.021\,325 & -0.010\,591
|
|
& -0.061\,406 & -0.025\,263 & -0.012\,114
|
|
& -0.055\,215 & -0.025\,776 & -0.013\,270
|
|
\\
|
|
& $2\,^{1}A_1$
|
|
& -0.052\,995 & -0.021\,690 & -0.010\,852
|
|
& -0.061\,959 & -0.025\,457 & -0.012\,258
|
|
& -0.055\,301 & -0.025\,786 & -0.013\,304
|
|
\\
|
|
& $1\,^{3}B_1$
|
|
& -0.051\,161 & -0.020\,974 & -0.010\,117
|
|
& -0.057\,882 & -0.023\,791 & -0.011\,280
|
|
& -0.052\,744 & -0.024\,500 & -0.012\,358
|
|
\\
|
|
& $1\,^{3}A_2$
|
|
& -0.051\,244 & -0.020\,982 & -0.010\,115
|
|
& -0.058\,090 & -0.023\,847 & -0.011\,302
|
|
& -0.052\,729 & -0.024\,611 & -0.012\,398
|
|
\\
|
|
& $1\,^{3}A_1$
|
|
& -0.052\,193 & -0.021\,398 & -0.010\,401
|
|
& -0.059\,073 & -0.024\,272 & -0.011\,595
|
|
& -0.053\,409 & -0.024\,840 & -0.012\,699
|
|
\\
|
|
\\
|
|
Ethylene & $1\,^{1}A_{1g}$
|
|
& -0.057\,559 & -0.022\,007 &
|
|
& -0.066\,251 & -0.024\,599 &
|
|
& -0.065\,343 & -0.027\,274 &
|
|
\\
|
|
& $1\,^{1}B_{3u}$
|
|
& -0.054\,862 & -0.020\,972 &
|
|
& -0.063\,185 & -0.023\,501 &
|
|
& -0.061\,786 & -0.025\,978 &
|
|
\\
|
|
& $1\,^{1}B_{1u}$
|
|
& -0.057\,591 & -0.022\,249 &
|
|
& -0.064\,517 & -0.023\,971 &
|
|
& -0.063\,619 & -0.026\,561 &
|
|
\\
|
|
& $1\,^{1}B_{1g}$
|
|
& -0.054\,995 & -0.020\,994 &
|
|
& -0.063\,386 & -0.023\,564 &
|
|
& -0.061\,978 & -0.026\,087 &
|
|
\\
|
|
& $1\,^{3}B_{1u}$
|
|
& -0.056\,056 & -0.020\,862 &
|
|
& -0.063\,499 & -0.023\,241 &
|
|
& -0.063\,304 & -0.025\,971 &
|
|
\\
|
|
& $1\,^{3}B_{3u}$
|
|
& -0.054\,752 & -0.020\,441 &
|
|
& -0.062\,078 & -0.022\,891 &
|
|
& -0.060\,894 & -0.025\,249 &
|
|
\\
|
|
& $1\,^{3}B_{1g}$
|
|
& -0.054\,924 & -0.020\,480 &
|
|
& -0.062\,306 & -0.022\,962 &
|
|
& -0.061\,089 & -0.025\,334 &
|
|
\\
|
|
\\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table*}
|
|
\end{squeezetable}
|
|
\end{turnpage}
|
|
%%% %%% %%%
|
|
|
|
|
|
\bibliography{../Ex-srDFT,../Ex-srDFT-control}
|
|
|
|
\end{document}
|