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\newcommand { \LCPQ } { Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\' e de Toulouse, CNRS, UPS, France}
\newcommand { \LCT } { Laboratoire de Chimie Th\' eorique, Sorbonne Universit\' e, CNRS, Paris, France}
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\begin { document}
\title { Supplementary Information for ``A Density-Based Basis-Set Correction For Wave Function Theory''}
\author { Pierre-Fran\c { c} ois Loos}
\email { loos@irsamc.ups-tlse.fr}
\affiliation { \LCPQ }
\author { Bath\' elemy Pradines}
\affiliation { \LCT }
\affiliation { \ISCD }
\author { Anthony Scemama}
\affiliation { \LCPQ }
\author { Julien Toulouse}
\email { toulouse@lct.jussieu.fr}
\affiliation { \LCT }
\author { Emmanuel Giner}
\email { emmanuel.giner@lct.jussieu.fr}
\affiliation { \LCT }
\begin { abstract}
\end { abstract}
\maketitle
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section { Local-density approximation}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The local-density approximation (LDA) of the ECMD complementary functional is defined as
\begin { equation}
\label { eq:def_ lda_ tot}
\bE { \LDA } { \Bas } [\n { } { } ,\rsmu { } { \Bas } ] = \int \n { } { } (\br { } ) \be { \text { c,md} } { \sr ,\LDA } \qty (\n { } { } (\br { } ),\zeta (\br { } ),\rsmu { } { \Bas } (\br { } )) \dbr { } ,
\end { equation}
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} .
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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%%% TABLE I %%%
\begin { table*}
\caption {
\label { tab:diatomics}
Frozen-core atomization energies (in { \kcal } ) of \ce { C2} , \ce { O2} , \ce { N2} and \ce { F2} computed with various methods and basis sets.
The deviations with respect to the corresponding CBS values are reported in parenthesis.
See main text for more details.
}
\begin { ruledtabular}
\begin { tabular} { llddddd}
& & \mc { 4} { c} { Dunning's basis set cc-pVXZ}
\\
\cline { 3-6}
Molecule & Method & \tabc { $ \X = \D $ } & \tabc { $ \X = \T $ } & \tabc { $ \X = \Q $ } & \tabc { $ \X = 5 $ } & \tabc { CBS}
\\
\hline
\ce { C2} & exFCI & 132.0 (-13.7 ) & 140.3 (-5.4 ) & 143.6 (-2.1 ) & 144.7 (-1.0 ) & 145.7 \\
& exFCI+LDA & 141.3 (-4.4 ) & 145.1 (-0.6 ) & 146.4 (+0.7 ) & 146.3 (+0.6 ) & \\
& exFCI+PBE & 145.7 (+0.0 ) & 145.7 (+0.0 ) & 146.3 (+0.6 ) & 146.2 (+0.5 ) & \\
& CCSD(T) & 129.2 (-16.2 ) & 139.1 (-6.3 ) & 143.0 (-2.4 ) & 144.2 (-1.2 ) & 145.4 \\
& CCSD(T)+LDA & 139.1 (-6.3 ) & 143.7 (-1.7 ) & 145.9 (+0.5 ) & 145.9 (+0.5 ) & \\
& CCSD(T)+PBE & 142.8 (-2.6 ) & 144.2 (-1.2 ) & 145.9 (+0.5 ) & 145.8 (+0.4 ) & \\ \\
% \ce{C2} & exFCI\fnm[2] & 131.0 (-16.1 ) & 141.5 (-5.6 ) & 145.1 (-2.0 ) & 146.1 (-1.0 ) & 147.1 \\
% (cc-pCVXZ) & exFCI+LDA\fnm[2] & 141.4 (-5.7 ) & 146.7 (-0.4 ) & 147.8 (+0.7 ) & 147.6 (+0.5 ) & \\
% & exFCI+PBE\fnm[2] & 145.1 (-2.0 ) & 147.0 (-0.1 ) & 147.7 (+0.6 ) & 147.5 (+0.4 ) & \\ \\
\ce { N2} & exFCI & 201.1 (-26.7 ) & 217.1 (-10.7 ) & 223.5 (-4.3 ) & 225.7 (-2.1 ) & 227.8 \\
& exFCI+LDA & 217.9 (-9.9 ) & 225.9 (-1.9 ) & 228.0 (+0.2 ) & 228.6 (+0.8 ) & \\
& exFCI+PBE & 227.7 (-0.1 ) & 227.8 (+0.0 ) & 228.3 (+0.5 ) & 228.5 (+0.7 ) & \\
& CCSD(T) & 199.9 (-27.3 ) & 216.3 (-10.9 ) & 222.8 (-4.4 ) & 225.0 (-2.2 ) & 227.2 \\
& CCSD(T)+LDA & 216.3 (-10.9 ) & 224.8 (-2.4 ) & 227.2 (-0.0 ) & 227.8 (+0.6 ) & \\
& CCSD(T)+PBE & 225.9 (-1.3 ) & 226.7 (-0.5 ) & 227.5 (+0.3 ) & 227.8 (+0.6 ) & \\ \\
% \ce{N2} & exFCI\fnm[2] & 202.2 (-26.6 ) & 218.5 (-10.3 ) & 224.4 (-4.4 ) & 226.6 (-2.2 ) & 228.8 \\
% (cc-pCVXZ) & exFCI+LDA\fnm[2] & 218.0 (-10.8 ) & 226.8 (-2.0 ) & 229.1 (+0.3 ) & 229.4 (+0.6 ) & \\
% & exFCI+PBE\fnm[2] & 226.4 (-2.4 ) & 228.2 (-0.6 ) & 229.1 (+0.3 ) & 229.2 (+0.4 ) & \\ \\
\ce { O2} & exFCI & 105.2 (-14.8 ) & 114.5 (-5.5 ) & 118.0 (-2.0 ) & 119.1 (-0.9 ) & 120.0 \\
& exFCI+LDA & 112.4 (-7.6 ) & 118.4 (-1.6 ) & 120.2 (+0.2 ) & 120.4 (+0.4 ) & \\
& exFCI+PBE & 117.2 (-2.8 ) & 119.4 (-0.6 ) & 120.3 (+0.3 ) & 120.4 (+0.4 ) & \\
& CCSD(T) & 103.9 (-16.1 ) & 113.6 (-6.0 ) & 117.1 (-2.5 ) & 118.6 (-1.0 ) & 119.6 \\
& CCSD(T)+LDA & 110.6 (-9.0 ) & 117.2 (-2.4 ) & 119.2 (-0.4 ) & 119.8 (+0.2 ) & \\
& CCSD(T)+PBE & 115.1 (-4.5 ) & 118.0 (-1.6 ) & 119.3 (-0.3 ) & 119.8 (+0.2 ) & \\ \\
\ce { F2} & exFCI & 26.7 (-12.3 ) & 35.1 (-3.9 ) & 37.1 (-1.9 ) & 38.0 (-1.0 ) & 39.0 \\
& exFCI+LDA & 30.4 (-8.6 ) & 37.2 (-1.8 ) & 38.4 (-0.6 ) & 38.9 (-0.1 ) & \\
& exFCI+PBE & 33.1 (-5.9 ) & 37.9 (-1.1 ) & 38.5 (-0.5 ) & 38.9 (-0.1 ) & \\
& CCSD(T) & 25.7 (-12.5 ) & 34.4 (-3.8 ) & 36.5 (-1.7 ) & 37.4 (-0.8 ) & 38.2 \\
& CCSD(T)+LDA & 29.2 (-9.0 ) & 36.5 (-1.7 ) & 37.2 (-1.0 ) & 38.2 (+0.0 ) & \\
& CCSD(T)+PBE & 31.5 (-6.7 ) & 37.1 (-1.1 ) & 37.8 (-0.4 ) & 38.2 (+0.0 ) & \\
\end { tabular}
\end { ruledtabular}
% \fnt[1]{ calculations. Only valence orbitals are taken into account in the basis set correction.}
% \fnt[2]{``Full'' calculation, i.e., all electrons are correlated. All spinorbitals are taken into account in the basis set correction.}
\end { table*}
\begin { turnpage}
\begin { squeezetable}
\begin { table}
\caption {
\label { tab:AE}
Deviation from the reference CCSD(T)/CBS atomization energies (in { \kcal } ) for various methods and basis sets.
See main text for more details.}
\begin { ruledtabular}
\begin { tabular} { lddddddddddd}
&
& \mc { 10} { c} { Deviation from CBS atomization energies} \\
\cline { 3-12}
& & \mc { 4} { c} { CCSD(T)} & \mc { 3} { c} { CCSD(T)+LDA} & \mc { 3} { c} { CCSD(T)+PBE} \\
\cline { 3-6} \cline { 7-9} \cline { 10-12}
Molecule & \tabc { CCSD(T)/CBS}
& \tabc { cc-pVDZ} & \tabc { cc-pVTZ} & \tabc { cc-pVQZ} & \tabc { cc-pV5Z}
& \tabc { cc-pVDZ} & \tabc { cc-pVTZ} & \tabc { cc-pVQZ}
& \tabc { cc-pVDZ} & \tabc { cc-pVTZ} & \tabc { cc-pVQZ}
\\
\hline
\ce { BeH} & 50.12 & -3.38 & -1.01 & -0.36 & -0.19 & -0.75 & -0.03 & 0.04 & -0.75 & -0.03 & 0.04 \\
\ce { C2H2} & 403.00 & -22.99 & -8.69 & -3.43 & -1.76 & -5.12 & -1.08 & 0.37 & -5.12 & -1.08 & 0.37 \\
\ce { C2H4} & 561.69 & -27.16 & -9.44 & -3.59 & -1.84 & -4.88 & -0.56 & 0.58 & -4.88 & -0.56 & 0.58 \\
\ce { C2H6} & 710.81 & -32.62 & -10.65 & -3.97 & -2.03 & -5.28 & -0.20 & 0.76 & -5.28 & -0.20 & 0.76 \\
\ce { CH} & 83.89 & -5.96 & -1.97 & -0.75 & -0.39 & -0.81 & -0.03 & 0.15 & -0.81 & -0.03 & 0.15 \\
\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 \\
\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 \\
\ce { CH3} & 306.81 & -14.33 & -4.47 & -1.62 & -0.83 & -2.33 & -0.08 & 0.27 & -2.33 & -0.08 & 0.27 \\
\ce { CH3Cl} & 395.02 & -20.77 & -8.34 & -3.35 & -1.72 & -4.38 & -1.60 & -0.16 & -4.38 & -1.60 & -0.16 \\
\ce { CH4} & 419.19 & -18.35 & -5.64 & -2.01 & -1.03 & -2.55 & 0.18 & 0.51 & -2.55 & 0.18 & 0.51 \\
\ce { CN} & 179.32 & -14.98 & -7.26 & -3.18 & -1.63 & -2.16 & -0.82 & 0.20 & -2.16 & -0.82 & 0.20 \\
\ce { CO} & 258.64 & -11.01 & -5.94 & -2.60 & -1.33 & -0.93 & -0.61 & 0.44 & -0.93 & -0.61 & 0.44 \\
\ce { CO2} & 388.29 & -20.79 & -10.95 & -4.67 & -2.39 & -3.19 & -1.69 & 0.60 & -3.19 & -1.69 & 0.60 \\
\ce { CS} & 170.82 & -10.72 & -6.25 & -2.88 & -1.47 & -1.94 & -1.58 & -0.16 & -1.94 & -1.58 & -0.16 \\
\ce { Cl2} & 59.33 & -8.26 & -5.23 & -2.49 & -1.28 & -3.63 & -2.46 & -0.90 & -3.63 & -2.46 & -0.90 \\
\ce { ClF} & 62.43 & -8.51 & -4.83 & -2.33 & -1.19 & -4.02 & -2.23 & -0.81 & -4.02 & -2.23 & -0.81 \\
\ce { ClO} & 64.35 & -11.86 & -6.35 & -3.16 & -1.62 & -5.99 & -3.08 & -1.25 & -5.99 & -3.08 & -1.25 \\
\ce { F2} & 38.24 & -6.62 & -3.52 & -1.72 & -0.88 & -3.17 & -1.54 & -0.48 & -3.17 & -1.54 & -0.48 \\
\ce { H2CO} & 373.18 & -19.31 & -8.07 & -3.31 & -1.70 & -2.84 & -0.70 & 0.50 & -2.84 & -0.70 & 0.50 \\
\ce { H2O} & 232.78 & -15.21 & -5.83 & -2.37 & -1.21 & -4.03 & -1.07 & -0.14 & -4.03 & -1.07 & -0.14 \\
\ce { H2O2} & 268.77 & -22.78 & -9.44 & -4.08 & -2.09 & -6.64 & -2.06 & -0.30 & -6.64 & -2.06 & -0.30 \\
\ce { H2S} & 183.36 & -10.66 & -4.33 & -1.55 & -0.79 & -2.50 & -1.16 & -0.12 & -2.50 & -1.16 & -0.12 \\
\ce { H3COH} & 512.25 & -28.32 & -10.40 & -4.10 & -2.10 & -5.95 & -1.17 & 0.31 & -5.95 & -1.17 & 0.31 \\
\ce { H3CSH} & 473.92 & -25.84 & -10.02 & -3.88 & -1.98 & -5.49 & -1.79 & -0.01 & -5.49 & -1.79 & -0.01 \\
\ce { HCN} & 311.54 & -20.86 & -9.06 & -3.80 & -1.95 & -3.59 & -0.85 & 0.37 & -3.59 & -0.85 & 0.37 \\
\ce { HCO} & 277.92 & -15.04 & -6.87 & -2.84 & -1.46 & -2.38 & -0.89 & 0.37 & -2.38 & -0.89 & 0.37 \\
\ce { HCl} & 107.31 & -5.64 & -2.46 & -0.93 & -0.48 & -1.37 & -0.81 & -0.22 & -1.37 & -0.81 & -0.22 \\
\ce { HF} & 141.67 & -8.45 & -3.48 & -1.42 & -0.73 & -2.70 & -0.96 & -0.23 & -2.70 & -0.96 & -0.23 \\
\ce { HOCl} & 165.85 & -15.82 & -7.34 & -3.28 & -1.68 & -5.39 & -2.29 & -0.62 & -5.39 & -2.29 & -0.62 \\
\ce { Li2} & 24.10 & -0.78 & -0.30 & -0.07 & -0.04 & 0.39 & 0.13 & 0.1 & 0.39 & 0.13 & 0.1 \\
\ce { LiF} & 138.33 & -10.78 & -4.56 & -1.95 & -1.0 & -3.30 & -0.91 & 0.02 & -3.30 & -0.91 & 0.02 \\
\ce { LiH} & 57.70 & -4.15 & -1.05 & -0.38 & -0.20 & -0.71 & 0.12 & 0.11 & -0.71 & 0.12 & 0.11 \\
\ce { N2} & 227.18 & -18.66 & -9.41 & -4.20 & -2.15 & -2.26 & -0.90 & 0.20 & -2.26 & -0.90 & 0.20 \\
\ce { N2H4} & 437.39 & -36.95 & -14.25 & -5.83 & -2.99 & -8.13 & -1.60 & -0.01 & -8.13 & -1.60 & -0.01 \\
\ce { NH} & 82.86 & -8.10 & -3.02 & -1.24 & -0.63 & -1.51 & -0.22 & -0.06 & -1.51 & -0.22 & -0.06 \\
\ce { NH2} & 182.14 & -15.31 & -5.61 & -2.26 & -1.16 & -3.16 & -0.50 & -0.03 & -3.16 & -0.50 & -0.03 \\
\ce { NH3} & 297.46 & -21.21 & -7.62 & -3.01 & -1.54 & -4.42 & -0.62 & 0.07 & -4.42 & -0.62 & 0.07 \\
\ce { NO} & 151.73 & -13.87 & -7.26 & -3.25 & -1.66 & -2.20 & -1.10 & 0.08 & -2.20 & -1.10 & 0.08 \\
\ce { Na2} & 16.44 & -0.71 & -0.14 & -0.06 & -0.03 & 0.20 & 0.15 & 0.08 & 0.20 & 0.15 & 0.08 \\
\ce { NaCl} & 99.61 & -11.48 & -5.41 & -2.26 & -1.16 & -4.34 & -2.13 & -0.52 & -4.34 & -2.13 & -0.52 \\
\ce { O2} & 119.64 & -9.86 & -5.34 & -2.40 & -1.23 & -3.08 & -1.72 & -0.30 & -3.08 & -1.72 & -0.30 \\
\ce { OH} & 107.08 & -8.37 & -3.27 & -1.34 & -0.69 & -2.23 & -0.63 & -0.08 & -2.23 & -0.63 & -0.08 \\
\ce { P2} & 115.68 & -18.05 & -9.34 & -4.00 & -2.05 & -3.96 & -1.89 & 0.26 & -3.96 & -1.89 & 0.26 \\
\ce { PH2} & 153.91 & -11.50 & -4.32 & -1.51 & -0.77 & -2.56 & -0.82 & 0.16 & -2.56 & -0.82 & 0.16 \\
\ce { PH3} & 241.49 & -15.43 & -5.80 & -2.03 & -1.04 & -3.12 & -1.03 & 0.20 & -3.12 & -1.03 & 0.20 \\
\ce { S2} & 103.07 & -12.76 & -7.34 & -3.28 & -1.68 & -5.69 & -3.18 & -0.95 & -5.69 & -3.18 & -0.95 \\
\ce { SO} & 125.12 & -10.77 & -6.14 & -2.94 & -1.51 & -3.33 & -2.10 & -0.59 & -3.33 & -2.10 & -0.59 \\
\ce { SO2} & 258.09 & -22.35 & -13.90 & -6.75 & -3.46 & -5.16 & -4.67 & -1.32 & -5.16 & -4.67 & -1.32 \\
\ce { Si2} & 75.74 & -10.01 & -4.47 & -1.82 & -0.93 & -4.19 & -1.49 & -0.17 & -4.19 & -1.49 & -0.17 \\
\ce { Si2H6} & 535.58 & -27.32 & -10.13 & -3.46 & -1.77 & -5.59 & -1.86 & 0.30 & -5.59 & -1.86 & 0.30 \\
\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 \\
\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 \\
\ce { SiH3} & 227.99 & -10.53 & -3.72 & -1.15 & -0.59 & -1.82 & -0.74 & 0.12 & -1.82 & -0.74 & 0.12 \\
\ce { SiH4} & 324.59 & -14.10 & -4.88 & -1.52 & -0.78 & -1.91 & -0.58 & 0.33 & -1.91 & -0.58 & 0.33 \\
\ce { SiO} & 191.48 & -11.34 & -6.72 & -3.15 & -1.61 & -0.76 & -1.18 & 0.12 & -0.76 & -1.18 & 0.12 \\
\end { tabular}
\end { ruledtabular}
\end { table}
\end { squeezetable}
\end { turnpage}
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\bibliography { ../G2_ srDFT,../G2_ srDFT-control}
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\end { document}
