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Pierre-Francois Loos 2019-04-16 22:30:34 +02:00
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Manuscript/G2-srDFT.tex
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\affiliation{\LCT} \affiliation{\LCT}
\begin{abstract} \begin{abstract}
%\begin{wrapfigure}[12]{o}[-1.2cm]{0.4\linewidth}
% \centering
% \includegraphics[width=\linewidth]{TOC}
%\end{wrapfigure}
We report a universal density-based basis set incompleteness correction that can be applied to any wave function method. We report a universal density-based basis set incompleteness correction that can be applied to any wave function method.
The present correction, which appropriately vanishes in the complete basis set (CBS) limit, relies on short-range correlation density functionals (with multi-determinant reference) from range-separated density-functional theory (RS-DFT) to estimate the basis set incompleteness error. The present correction, which appropriately vanishes in the complete basis set (CBS) limit, relies on short-range correlation density functionals (with multi-determinant reference) from range-separated density-functional theory (RS-DFT) to estimate the basis set incompleteness error.
Contrary to conventional RS-DFT schemes which require an \textit{ad hoc} range-separation \textit{parameter} $\mu$, the key ingredient here is a range-separation \textit{function} $\mu(\bf{r})$ which automatically adapts to the spatial non-homogeneity of the basis set incompleteness error. Contrary to conventional RS-DFT schemes which require an \textit{ad hoc} range-separation \textit{parameter} $\mu$, the key ingredient here is a range-separation \textit{function} $\mu(\bf{r})$ which automatically adapts to the spatial non-homogeneity of the basis set incompleteness error.

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Manuscript/SI/G2_srDFT-SI.tex
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\label{tab:diatomics} \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. 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. The deviations with respect to the corresponding CBS values are reported in parenthesis.
See main text for more details.
} }
\begin{ruledtabular} \begin{ruledtabular}
\begin{tabular}{llddddd} \begin{tabular}{llddddd}
@ -194,7 +195,8 @@
\begin{table} \begin{table}
\caption{ \caption{
\label{tab:AE} \label{tab:AE}
Deviation from the reference CBS atomization energies (in {\kcal}) for various methods and basis sets.} 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{ruledtabular}
\begin{tabular}{lddddddddddd} \begin{tabular}{lddddddddddd}
& &
@ -208,61 +210,61 @@
& \tabc{cc-pVDZ} & \tabc{cc-pVTZ} & \tabc{cc-pVQZ} & \tabc{cc-pVDZ} & \tabc{cc-pVTZ} & \tabc{cc-pVQZ}
\\ \\
\hline \hline
\ce{BeH} & 50.12 & -4.87 & -1.52 & -0.40 & -0.19 & -2.24 & -0.54 & 0.\times 10^{-2} & -2.24 & -0.54 & 0.00 \\ \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 & -33.08 & -9.89 & -3.64 & -1.76 & -15.21 & -2.27 & 0.16 & -15.21 & -2.27 & 0.16 \\ \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 & -36.58 & -10.70 & -3.87 & -1.84 & -14.30 & -1.82 & 0.30 & -14.30 & -1.82 & 0.30 \\ \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 & -41.69 & -11.64 & -4.19 & -2.03 & -14.35 & -1.19 & 0.54 & -14.35 & -1.19 & 0.54 \\ \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 & -8.39 & -2.42 & -0.86 & -0.39 & -3.24 & -0.48 & 0.05 & -3.24 & -0.48 & 0.05 \\ \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 & -15.23 & -4.29 & -1.51 & -0.68 & -5.80 & -0.72 & 0.12 & -5.80 & -0.72 & 0.12 \\ \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 & -12.60 & -3.25 & -1.11 & -0.51 & -5.65 & -0.86 & -0.12 & -5.65 & -0.86 & -0.12 \\ \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 & -19.55 & -5.08 & -1.77 & -0.83 & -7.54 & -0.69 & 0.12 & -7.54 & -0.69 & 0.12 \\ \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 & -29.15 & -9.70 & -3.83 & -1.72 & -12.76 & -2.96 & -0.64 & -12.76 & -2.96 & -0.64 \\ \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 & -23.97 & -6.19 & -2.14 & -1.03 & -8.17 & -0.37 & 0.38 & -8.17 & -0.37 & 0.38 \\ \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 & -21.44 & -8.55 & -3.30 & -1.63 & -8.63 & -2.11 & 0.09 & -8.63 & -2.11 & 0.09 \\ \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 & -17.46 & -7.01 & -2.62 & -1.33 & -7.38 & -1.69 & 0.42 & -7.38 & -1.69 & 0.42 \\ \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 & -32.10 & -12.54 & -4.75 & -2.39 & -14.50 & -3.28 & 0.52 & -14.50 & -3.28 & 0.52 \\ \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 & -17.82 & -8.45 & -3.71 & -1.47 & -9.04 & -3.78 & -1.0 & -9.04 & -3.78 & -1.0 \\ \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 & -17.79 & -7.18 & -3.39 & -1.28 & -13.16 & -4.41 & -1.80 & -13.16 & -4.41 & -1.80 \\ \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 & -20.00 & -7.36 & -3.18 & -1.19 & -15.52 & -4.76 & -1.66 & -15.52 & -4.76 & -1.66 \\ \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 & -23.33 & -8.68 & -4.09 & -1.62 & -17.46 & -5.40 & -2.19 & -17.46 & -5.40 & -2.19 \\ \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 & -12.53 & -3.70 & -1.76 & -0.88 & -9.09 & -1.72 & -0.52 & -9.09 & -1.72 & -0.52 \\ \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 & -28.21 & -9.53 & -3.55 & -1.70 & -11.74 & -2.16 & 0.26 & -11.74 & -2.16 & 0.26 \\ \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 & -23.97 & -7.67 & -2.85 & -1.21 & -12.79 & -2.92 & -0.62 & -12.79 & -2.92 & -0.62 \\ \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 & -33.22 & -10.75 & -4.37 & -2.09 & -17.09 & -3.37 & -0.59 & -17.09 & -3.37 & -0.59 \\ \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 & -16.42 & -6.09 & -2.26 & -0.79 & -8.26 & -2.91 & -0.83 & -8.26 & -2.91 & -0.83 \\ \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 & -39.65 & -12.16 & -4.52 & -2.10 & -17.28 & -2.93 & -0.1 & -17.28 & -2.93 & -0.1 \\ \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 & -36.54 & -12.24 & -4.71 & -1.98 & -16.19 & -4.00 & -0.85 & -16.19 & -4.00 & -0.85 \\ \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 & -29.08 & -10.32 & -3.95 & -1.95 & -11.81 & -2.11 & 0.22 & -11.81 & -2.11 & 0.22 \\ \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 & -22.87 & -8.28 & -3.06 & -1.46 & -10.20 & -2.31 & 0.16 & -10.20 & -2.31 & 0.16 \\ \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 & -9.11 & -3.37 & -1.31 & -0.48 & -4.84 & -1.73 & -0.60 & -4.84 & -1.73 & -0.60 \\ \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 & -15.33 & -4.73 & -1.72 & -0.73 & -9.59 & -2.21 & -0.53 & -9.59 & -2.21 & -0.53 \\ \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 & -27.19 & -9.45 & -4.05 & -1.68 & -16.76 & -4.40 & -1.38 & -16.76 & -4.40 & -1.38 \\ \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 & -1.64 & -0.37 & -0.08 & -0.04 & -0.47 & 0.05 & 0.09 & -0.47 & 0.05 & 0.09 \\ \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 & -15.98 & -6.20 & -2.02 & -1.0 & -8.50 & -2.56 & -0.06 & -8.50 & -2.56 & -0.06 \\ \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 & -5.80 & -1.34 & -0.43 & -0.20 & -2.36 & -0.16 & 0.07 & -2.36 & -0.16 & 0.07 \\ \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 & -27.25 & -10.85 & -4.40 & -2.15 & -10.85 & -2.34 & -0.\times 10^{-2} & -10.85 & -2.34 & 0.00 \\ \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 & -50.52 & -16.80 & -6.47 & -2.99 & -21.69 & -4.16 & -0.66 & -21.69 & -4.16 & -0.66 \\ \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 & -11.49 & -3.67 & -1.40 & -0.63 & -4.91 & -0.87 & -0.23 & -4.91 & -0.87 & -0.23 \\ \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 & -21.58 & -6.83 & -2.59 & -1.16 & -9.43 & -1.72 & -0.36 & -9.43 & -1.72 & -0.36 \\ \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 & -30.02 & -9.32 & -3.49 & -1.54 & -13.23 & -2.33 & -0.41 & -13.23 & -2.33 & -0.41 \\ \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 & -20.13 & -8.33 & -3.40 & -1.66 & -8.46 & -2.18 & -0.07 & -8.46 & -2.18 & -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 & -1.14 & -0.21 & -0.11 & -0.03 & -0.22 & 0.08 & 0.02 & -0.22 & 0.08 & 0.02 \\ \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 & -13.83 & -6.33 & -2.63 & -1.16 & -6.70 & -3.05 & -0.88 & -6.70 & -3.05 & -0.88 \\ \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 & -15.78 & -6.09 & -2.52 & -1.23 & -9.00 & -2.47 & -0.41 & -9.00 & -2.47 & -0.41 \\ \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 & -12.86 & -4.17 & -1.57 & -0.69 & -6.71 & -1.54 & -0.30 & -6.71 & -1.54 & -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 & -26.99 & -12.04 & -5.02 & -2.05 & -12.90 & -4.59 & -0.77 & -12.90 & -4.59 & -0.77 \\ \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 & -16.69 & -5.87 & -2.08 & -0.77 & -7.75 & -2.37 & -0.42 & -7.75 & -2.37 & -0.42 \\ \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 & -22.83 & -8.02 & -2.88 & -1.04 & -10.51 & -3.25 & -0.65 & -10.51 & -3.25 & -0.65 \\ \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 & -21.55 & -9.78 & -4.44 & -1.68 & -14.48 & -5.62 & -2.11 & -14.48 & -5.62 & -2.11 \\ \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 & -29.67 & -10.55 & -4.65 & -1.51 & -22.23 & -6.51 & -2.30 & -22.23 & -6.51 & -2.30 \\ \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 & -72.08 & -25.99 & -11.66 & -3.46 & -54.88 & -16.77 & -6.22 & -54.88 & -16.77 & -6.22 \\ \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 & -14.79 & -5.51 & -2.25 & -0.93 & -8.98 & -2.52 & -0.60 & -8.98 & -2.52 & -0.60 \\ \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 & -42.77 & -14.82 & -5.05 & -1.77 & -21.04 & -6.55 & -1.29 & -21.04 & -6.55 & -1.29 \\ \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 & -13.20 & -4.29 & -1.47 & -0.50 & -7.98 & -2.76 & -0.83 & -7.98 & -2.76 & -0.83 \\ \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 & -11.32 & -3.83 & -1.15 & -0.37 & -7.66 & -3.01 & -0.91 & -7.66 & -3.01 & -0.91 \\ \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 & -17.54 & -5.85 & -1.82 & -0.59 & -8.83 & -2.88 & -0.56 & -8.83 & -2.88 & -0.56 \\ \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 & -23.03 & -7.65 & -2.44 & -0.78 & -10.85 & -3.35 & -0.58 & -10.85 & -3.35 & -0.58 \\ \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 & -31.12 & -10.81 & -4.45 & -1.61 & -20.54 & -5.27 & -1.19 & -20.54 & -5.27 & -1.19 \\ \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{tabular}
\end{ruledtabular} \end{ruledtabular}
\end{table} \end{table}
@ -271,4 +273,63 @@
\bibliography{../G2_srDFT} \bibliography{../G2_srDFT}
\end{document} \end{document}