297 lines
16 KiB
TeX
297 lines
16 KiB
TeX
\documentclass[aip,jcp,reprint,onecolumn,noshowkeys]{revtex4-1}
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\usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,mhchem,longtable,xspace}
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colorlinks=true,
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linkcolor=blue,
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}
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\newcommand{\tabc}[1]{\multicolumn{1}{c}{#1}}
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\newcommand{\SI}{\textcolor{blue}{supporting information}}
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\newcommand{\QP}{\textsc{quantum package}}
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% second quantized operators
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\newcommand{\ai}[1]{\hat{a}_{#1}}
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\newcommand{\aic}[1]{\hat{a}^{\dagger}_{#1}}
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% units
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\newcommand{\IneV}[1]{#1 eV}
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\newcommand{\InAU}[1]{#1 a.u.}
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\newcommand{\InAA}[1]{#1 \AA}
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\newcommand{\kcal}{kcal/mol}
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% methods
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\newcommand{\D}{\text{D}}
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\newcommand{\T}{\text{T}}
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\newcommand{\Q}{\text{Q}}
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\newcommand{\X}{\text{X}}
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\newcommand{\UEG}{\text{UEG}}
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\newcommand{\HF}{\text{HF}}
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\newcommand{\LDA}{\text{LDA}}
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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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\newcommand{\lr}{\text{lr}}
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\newcommand{\sr}{\text{sr}}
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\newcommand{\Ng}{N_\text{grid}}
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\newcommand{\nocca}{n_{\text{occ}^{\alpha}}}
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\newcommand{\noccb}{n_{\text{occ}^{\beta}}}
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\newcommand{\n}[2]{n_{#1}^{#2}}
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\newcommand{\Ec}{E_\text{c}}
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\newcommand{\E}[2]{E_{#1}^{#2}}
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\newcommand{\bE}[2]{\Bar{E}_{#1}^{#2}}
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\newcommand{\bEc}[1]{\Bar{E}_\text{c}^{#1}}
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% basis sets
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% operators
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% coordinates
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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, Sorbonne Universit\'e, CNRS, Paris, France}
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\newcommand{\ISCD}{Institut des Sciences du Calcul et des Donn\'ees, Sorbonne Universit\'e, Paris, France}
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\begin{document}
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\title{Supplementary Information for ``A Density-Based Basis-Set Correction For Wave Function Theory''}
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\author{Pierre-Fran\c{c}ois Loos}
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\email{loos@irsamc.ups-tlse.fr}
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\affiliation{\LCPQ}
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\author{Bath\'elemy Pradines}
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\affiliation{\LCT}
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\affiliation{\ISCD}
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\author{Anthony Scemama}
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\affiliation{\LCPQ}
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\author{Julien Toulouse}
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\email{toulouse@lct.jussieu.fr}
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\affiliation{\LCT}
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\author{Emmanuel Giner}
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\email{emmanuel.giner@lct.jussieu.fr}
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\affiliation{\LCT}
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\begin{abstract}
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\end{abstract}
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\maketitle
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Local-density approximation}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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The local-density approximation (LDA) of the ECMD complementary functional is defined as
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\begin{equation}
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\label{eq:def_lda_tot}
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\bE{\LDA}{\Bas}[\n{}{},\rsmu{}{\Bas}] = \int \n{}{}(\br{}) \be{\text{c,md}}{\sr,\LDA}\qty(\n{}{}(\br{}),\zeta(\br{}),\rsmu{}{\Bas}(\br{})) \dbr{},
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\end{equation}
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where $\zeta = (\n{\uparrow}{} - \n{\downarrow}{})/\n{}{}$ is the spin polarization and $\be{\text{c,md}}{\sr,\LDA}(\n{}{},\zeta,\rsmu{}{})$ is the ECMD short-range correlation energy per electron of the uniform electron gas (UEG) \cite{LooGil-WIRES-16} parameterized in Ref.~\onlinecite{PazMorGorBac-PRB-06}.
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The short-range LDA correlation functional relies on the transferability of the physics of the UEG which is certainly valid for large $\mu$ but is known to over correlate for small $\mu$.
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The sensitivity with respect to the RS-DFT functional is quite large for the double- and triple-$\zeta$ basis sets, where clearly the PBE functional performs better.
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However, from the quadruple-$\zeta$ basis, the LDA and PBE functionals agree within a few tenths of a {\kcal}.
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Such weak sensitivity to the density-functional approximation when reaching large basis sets shows the robustness of the approach.
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%%% TABLE I %%%
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\begin{table*}
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\caption{
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\label{tab:diatomics}
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Frozen-core atomization energies (in {\kcal}) of \ce{C2}, \ce{O2}, \ce{N2} and \ce{F2} computed with various methods and basis sets.
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The deviations with respect to the corresponding CBS values are reported in parenthesis.
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See main text for more details.
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}
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\begin{ruledtabular}
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\begin{tabular}{llddddd}
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& & \mc{4}{c}{Dunning's basis set cc-pVXZ}
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\\
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\cline{3-6}
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Molecule & Method & \tabc{$\X = \D$} & \tabc{$\X = \T$} & \tabc{$\X = \Q$} & \tabc{$\X = 5$} & \tabc{CBS}
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\\
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\hline
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\ce{C2} & exFCI & 132.0 (-13.7 ) & 140.3 (-5.4 ) & 143.6 (-2.1 ) & 144.7 (-1.0 ) & 145.7 \\
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& exFCI+LDA & 141.3 (-4.4 ) & 145.1 (-0.6 ) & 146.4 (+0.7 ) & 146.3 (+0.6 ) & \\
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& exFCI+PBE & 145.7 (+0.0 ) & 145.7 (+0.0 ) & 146.3 (+0.6 ) & 146.2 (+0.5 ) & \\
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& CCSD(T) & 129.2 (-16.2 ) & 139.1 (-6.3 ) & 143.0 (-2.4 ) & 144.2 (-1.2 ) & 145.4 \\
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& CCSD(T)+LDA & 139.1 (-6.3 ) & 143.7 (-1.7 ) & 145.9 (+0.5 ) & 145.9 (+0.5 ) & \\
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& CCSD(T)+PBE & 142.8 (-2.6 ) & 144.2 (-1.2 ) & 145.9 (+0.5 ) & 145.8 (+0.4 ) & \\ \\
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% \ce{C2} & exFCI\fnm[2] & 131.0 (-16.1 ) & 141.5 (-5.6 ) & 145.1 (-2.0 ) & 146.1 (-1.0 ) & 147.1 \\
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% (cc-pCVXZ) & exFCI+LDA\fnm[2] & 141.4 (-5.7 ) & 146.7 (-0.4 ) & 147.8 (+0.7 ) & 147.6 (+0.5 ) & \\
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% & exFCI+PBE\fnm[2] & 145.1 (-2.0 ) & 147.0 (-0.1 ) & 147.7 (+0.6 ) & 147.5 (+0.4 ) & \\ \\
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\ce{N2} & exFCI & 201.1 (-26.7 ) & 217.1 (-10.7 ) & 223.5 (-4.3 ) & 225.7 (-2.1 ) & 227.8 \\
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& exFCI+LDA & 217.9 (-9.9 ) & 225.9 (-1.9 ) & 228.0 (+0.2 ) & 228.6 (+0.8 ) & \\
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& exFCI+PBE & 227.7 (-0.1 ) & 227.8 (+0.0 ) & 228.3 (+0.5 ) & 228.5 (+0.7 ) & \\
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& CCSD(T) & 199.9 (-27.3 ) & 216.3 (-10.9 ) & 222.8 (-4.4 ) & 225.0 (-2.2 ) & 227.2 \\
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& CCSD(T)+LDA & 216.3 (-10.9 ) & 224.8 (-2.4 ) & 227.2 (-0.0 ) & 227.8 (+0.6 ) & \\
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& CCSD(T)+PBE & 225.9 (-1.3 ) & 226.7 (-0.5 ) & 227.5 (+0.3 ) & 227.8 (+0.6 ) & \\ \\
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% \ce{N2} & exFCI\fnm[2] & 202.2 (-26.6 ) & 218.5 (-10.3 ) & 224.4 (-4.4 ) & 226.6 (-2.2 ) & 228.8 \\
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% (cc-pCVXZ) & exFCI+LDA\fnm[2] & 218.0 (-10.8 ) & 226.8 (-2.0 ) & 229.1 (+0.3 ) & 229.4 (+0.6 ) & \\
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% & exFCI+PBE\fnm[2] & 226.4 (-2.4 ) & 228.2 (-0.6 ) & 229.1 (+0.3 ) & 229.2 (+0.4 ) & \\ \\
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\ce{O2} & exFCI & 105.2 (-14.8 ) & 114.5 (-5.5 ) & 118.0 (-2.0 ) & 119.1 (-0.9 ) & 120.0 \\
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& exFCI+LDA & 112.4 (-7.6 ) & 118.4 (-1.6 ) & 120.2 (+0.2 ) & 120.4 (+0.4 ) & \\
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& exFCI+PBE & 117.2 (-2.8 ) & 119.4 (-0.6 ) & 120.3 (+0.3 ) & 120.4 (+0.4 ) & \\
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& CCSD(T) & 103.9 (-16.1 ) & 113.6 (-6.0 ) & 117.1 (-2.5 ) & 118.6 (-1.0 ) & 119.6 \\
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& CCSD(T)+LDA & 110.6 (-9.0 ) & 117.2 (-2.4 ) & 119.2 (-0.4 ) & 119.8 (+0.2 ) & \\
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& CCSD(T)+PBE & 115.1 (-4.5 ) & 118.0 (-1.6 ) & 119.3 (-0.3 ) & 119.8 (+0.2 ) & \\ \\
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\ce{F2} & exFCI & 26.7 (-12.3 ) & 35.1 (-3.9 ) & 37.1 (-1.9 ) & 38.0 (-1.0 ) & 39.0 \\
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& exFCI+LDA & 30.4 (-8.6 ) & 37.2 (-1.8 ) & 38.4 (-0.6 ) & 38.9 (-0.1 ) & \\
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& exFCI+PBE & 33.1 (-5.9 ) & 37.9 (-1.1 ) & 38.5 (-0.5 ) & 38.9 (-0.1 ) & \\
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& CCSD(T) & 25.7 (-12.5 ) & 34.4 (-3.8 ) & 36.5 (-1.7 ) & 37.4 (-0.8 ) & 38.2 \\
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& CCSD(T)+LDA & 29.2 (-9.0 ) & 36.5 (-1.7 ) & 37.2 (-1.0 ) & 38.2 (+0.0 ) & \\
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& CCSD(T)+PBE & 31.5 (-6.7 ) & 37.1 (-1.1 ) & 37.8 (-0.4 ) & 38.2 (+0.0 ) & \\
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\end{tabular}
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\end{ruledtabular}
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% \fnt[1]{ calculations. Only valence orbitals are taken into account in the basis set correction.}
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% \fnt[2]{``Full'' calculation, i.e., all electrons are correlated. All spinorbitals are taken into account in the basis set correction.}
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\end{table*}
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\begin{turnpage}
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\begin{squeezetable}
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\begin{table}
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\caption{
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\label{tab:AE}
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Deviation from the reference CCSD(T)/CBS atomization energies (in {\kcal}) for various methods and basis sets.
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See main text for more details.}
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\begin{ruledtabular}
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\begin{tabular}{lddddddddddd}
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&
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& \mc{10}{c}{Deviation from CBS atomization energies} \\
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\cline{3-12}
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& & \mc{4}{c}{CCSD(T)} & \mc{3}{c}{CCSD(T)+LDA} & \mc{3}{c}{CCSD(T)+PBE} \\
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\cline{3-6} \cline{7-9} \cline{10-12}
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Molecule & \tabc{CCSD(T)/CBS}
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& \tabc{cc-pVDZ} & \tabc{cc-pVTZ} & \tabc{cc-pVQZ} & \tabc{cc-pV5Z}
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& \tabc{cc-pVDZ} & \tabc{cc-pVTZ} & \tabc{cc-pVQZ}
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& \tabc{cc-pVDZ} & \tabc{cc-pVTZ} & \tabc{cc-pVQZ}
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\\
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\hline
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\ce{BeH} & 50.12 & -3.38 & -1.01 & -0.36 & -0.19 & -0.75 & -0.03 & 0.04 & -0.75 & -0.03 & 0.04 \\
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\ce{C2H2} & 403.00 & -22.99 & -8.69 & -3.43 & -1.76 & -5.12 & -1.08 & 0.37 & -5.12 & -1.08 & 0.37 \\
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\ce{C2H4} & 561.69 & -27.16 & -9.44 & -3.59 & -1.84 & -4.88 & -0.56 & 0.58 & -4.88 & -0.56 & 0.58 \\
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\ce{C2H6} & 710.81 & -32.62 & -10.65 & -3.97 & -2.03 & -5.28 & -0.20 & 0.76 & -5.28 & -0.20 & 0.76 \\
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\ce{CH} & 83.89 & -5.96 & -1.97 & -0.75 & -0.39 & -0.81 & -0.03 & 0.15 & -0.81 & -0.03 & 0.15 \\
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\ce{CH2 ^1A_1} & 180.61 & -10.99 & -3.57 & -1.34 & -0.68 & -1.55 & 0.00 & 0.29 & -1.55 & 0.00 & 0.29 \\
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\ce{CH2 ^3B_1} & 189.94 & -8.82 & -2.78 & -1.0 & -0.51 & -1.87 & -0.38 & 0.00 & -1.87 & -0.38 & -0.00 \\
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\ce{CH3} & 306.81 & -14.33 & -4.47 & -1.62 & -0.83 & -2.33 & -0.08 & 0.27 & -2.33 & -0.08 & 0.27 \\
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\ce{CH3Cl} & 395.02 & -20.77 & -8.34 & -3.35 & -1.72 & -4.38 & -1.60 & -0.16 & -4.38 & -1.60 & -0.16 \\
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\ce{CH4} & 419.19 & -18.35 & -5.64 & -2.01 & -1.03 & -2.55 & 0.18 & 0.51 & -2.55 & 0.18 & 0.51 \\
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\ce{CN} & 179.32 & -14.98 & -7.26 & -3.18 & -1.63 & -2.16 & -0.82 & 0.20 & -2.16 & -0.82 & 0.20 \\
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\ce{CO} & 258.64 & -11.01 & -5.94 & -2.60 & -1.33 & -0.93 & -0.61 & 0.44 & -0.93 & -0.61 & 0.44 \\
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\ce{CO2} & 388.29 & -20.79 & -10.95 & -4.67 & -2.39 & -3.19 & -1.69 & 0.60 & -3.19 & -1.69 & 0.60 \\
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\ce{CS} & 170.82 & -10.72 & -6.25 & -2.88 & -1.47 & -1.94 & -1.58 & -0.16 & -1.94 & -1.58 & -0.16 \\
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\ce{Cl2} & 59.33 & -8.26 & -5.23 & -2.49 & -1.28 & -3.63 & -2.46 & -0.90 & -3.63 & -2.46 & -0.90 \\
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\ce{ClF} & 62.43 & -8.51 & -4.83 & -2.33 & -1.19 & -4.02 & -2.23 & -0.81 & -4.02 & -2.23 & -0.81 \\
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\ce{ClO} & 64.35 & -11.86 & -6.35 & -3.16 & -1.62 & -5.99 & -3.08 & -1.25 & -5.99 & -3.08 & -1.25 \\
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\ce{F2} & 38.24 & -6.62 & -3.52 & -1.72 & -0.88 & -3.17 & -1.54 & -0.48 & -3.17 & -1.54 & -0.48 \\
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\ce{H2CO} & 373.18 & -19.31 & -8.07 & -3.31 & -1.70 & -2.84 & -0.70 & 0.50 & -2.84 & -0.70 & 0.50 \\
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\ce{H2O} & 232.78 & -15.21 & -5.83 & -2.37 & -1.21 & -4.03 & -1.07 & -0.14 & -4.03 & -1.07 & -0.14 \\
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\ce{H2O2} & 268.77 & -22.78 & -9.44 & -4.08 & -2.09 & -6.64 & -2.06 & -0.30 & -6.64 & -2.06 & -0.30 \\
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\ce{H2S} & 183.36 & -10.66 & -4.33 & -1.55 & -0.79 & -2.50 & -1.16 & -0.12 & -2.50 & -1.16 & -0.12 \\
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\ce{H3COH} & 512.25 & -28.32 & -10.40 & -4.10 & -2.10 & -5.95 & -1.17 & 0.31 & -5.95 & -1.17 & 0.31 \\
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\ce{H3CSH} & 473.92 & -25.84 & -10.02 & -3.88 & -1.98 & -5.49 & -1.79 & -0.01 & -5.49 & -1.79 & -0.01 \\
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\ce{HCN} & 311.54 & -20.86 & -9.06 & -3.80 & -1.95 & -3.59 & -0.85 & 0.37 & -3.59 & -0.85 & 0.37 \\
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\ce{HCO} & 277.92 & -15.04 & -6.87 & -2.84 & -1.46 & -2.38 & -0.89 & 0.37 & -2.38 & -0.89 & 0.37 \\
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\ce{HCl} & 107.31 & -5.64 & -2.46 & -0.93 & -0.48 & -1.37 & -0.81 & -0.22 & -1.37 & -0.81 & -0.22 \\
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\ce{HF} & 141.67 & -8.45 & -3.48 & -1.42 & -0.73 & -2.70 & -0.96 & -0.23 & -2.70 & -0.96 & -0.23 \\
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\ce{HOCl} & 165.85 & -15.82 & -7.34 & -3.28 & -1.68 & -5.39 & -2.29 & -0.62 & -5.39 & -2.29 & -0.62 \\
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\ce{Li2} & 24.10 & -0.78 & -0.30 & -0.07 & -0.04 & 0.39 & 0.13 & 0.1 & 0.39 & 0.13 & 0.1 \\
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\ce{LiF} & 138.33 & -10.78 & -4.56 & -1.95 & -1.0 & -3.30 & -0.91 & 0.02 & -3.30 & -0.91 & 0.02 \\
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\ce{LiH} & 57.70 & -4.15 & -1.05 & -0.38 & -0.20 & -0.71 & 0.12 & 0.11 & -0.71 & 0.12 & 0.11 \\
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\ce{N2} & 227.18 & -18.66 & -9.41 & -4.20 & -2.15 & -2.26 & -0.90 & 0.20 & -2.26 & -0.90 & 0.20 \\
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\ce{N2H4} & 437.39 & -36.95 & -14.25 & -5.83 & -2.99 & -8.13 & -1.60 & -0.01 & -8.13 & -1.60 & -0.01 \\
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\ce{NH} & 82.86 & -8.10 & -3.02 & -1.24 & -0.63 & -1.51 & -0.22 & -0.06 & -1.51 & -0.22 & -0.06 \\
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\ce{NH2} & 182.14 & -15.31 & -5.61 & -2.26 & -1.16 & -3.16 & -0.50 & -0.03 & -3.16 & -0.50 & -0.03 \\
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\ce{NH3} & 297.46 & -21.21 & -7.62 & -3.01 & -1.54 & -4.42 & -0.62 & 0.07 & -4.42 & -0.62 & 0.07 \\
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\ce{NO} & 151.73 & -13.87 & -7.26 & -3.25 & -1.66 & -2.20 & -1.10 & 0.08 & -2.20 & -1.10 & 0.08 \\
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\ce{Na2} & 16.44 & -0.71 & -0.14 & -0.06 & -0.03 & 0.20 & 0.15 & 0.08 & 0.20 & 0.15 & 0.08 \\
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\ce{NaCl} & 99.61 & -11.48 & -5.41 & -2.26 & -1.16 & -4.34 & -2.13 & -0.52 & -4.34 & -2.13 & -0.52 \\
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\ce{O2} & 119.64 & -9.86 & -5.34 & -2.40 & -1.23 & -3.08 & -1.72 & -0.30 & -3.08 & -1.72 & -0.30 \\
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\ce{OH} & 107.08 & -8.37 & -3.27 & -1.34 & -0.69 & -2.23 & -0.63 & -0.08 & -2.23 & -0.63 & -0.08 \\
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\ce{P2} & 115.68 & -18.05 & -9.34 & -4.00 & -2.05 & -3.96 & -1.89 & 0.26 & -3.96 & -1.89 & 0.26 \\
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\ce{PH2} & 153.91 & -11.50 & -4.32 & -1.51 & -0.77 & -2.56 & -0.82 & 0.16 & -2.56 & -0.82 & 0.16 \\
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\ce{PH3} & 241.49 & -15.43 & -5.80 & -2.03 & -1.04 & -3.12 & -1.03 & 0.20 & -3.12 & -1.03 & 0.20 \\
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\ce{S2} & 103.07 & -12.76 & -7.34 & -3.28 & -1.68 & -5.69 & -3.18 & -0.95 & -5.69 & -3.18 & -0.95 \\
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\ce{SO} & 125.12 & -10.77 & -6.14 & -2.94 & -1.51 & -3.33 & -2.10 & -0.59 & -3.33 & -2.10 & -0.59 \\
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\ce{SO2} & 258.09 & -22.35 & -13.90 & -6.75 & -3.46 & -5.16 & -4.67 & -1.32 & -5.16 & -4.67 & -1.32 \\
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\ce{Si2} & 75.74 & -10.01 & -4.47 & -1.82 & -0.93 & -4.19 & -1.49 & -0.17 & -4.19 & -1.49 & -0.17 \\
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\ce{Si2H6} & 535.58 & -27.32 & -10.13 & -3.46 & -1.77 & -5.59 & -1.86 & 0.30 & -5.59 & -1.86 & 0.30 \\
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\ce{SiH2 ^1A_1} & 153.66 & -8.72 & -2.98 & -0.98 & -0.50 & -3.51 & -1.46 & -0.34 & -3.51 & -1.46 & -0.34 \\
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\ce{SiH2 ^3B_1} & 133.17 & -6.68 & -2.40 & -0.73 & -0.37 & -3.02 & -1.57 & -0.49 & -3.02 & -1.57 & -0.49 \\
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\ce{SiH3} & 227.99 & -10.53 & -3.72 & -1.15 & -0.59 & -1.82 & -0.74 & 0.12 & -1.82 & -0.74 & 0.12 \\
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\ce{SiH4} & 324.59 & -14.10 & -4.88 & -1.52 & -0.78 & -1.91 & -0.58 & 0.33 & -1.91 & -0.58 & 0.33 \\
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\ce{SiO} & 191.48 & -11.34 & -6.72 & -3.15 & -1.61 & -0.76 & -1.18 & 0.12 & -0.76 & -1.18 & 0.12 \\
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\end{tabular}
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\end{ruledtabular}
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\end{table}
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\end{squeezetable}
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\end{turnpage}
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\bibliography{../G2_srDFT,../G2_srDFT-control}
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\end{document}
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