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Pierre-Francois Loos 2019-05-18 15:18:08 +02:00
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Manuscript/Ex-srDFT.tex
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@ -216,57 +216,167 @@ In the present study, we rely on the recently proposed short-range density-funct
%%% %%% %%% %%% %%% %%%
%%% TABLE 1 %%% %%% TABLE 2 %%%
\begin{squeezetable} \begin{squeezetable}
\begin{table*} \begin{table*}
\caption{ \caption{
Vertical absorption energies $\Ead$ (in eV) of excited states of water for various methods and basis sets.} Vertical absorption energies $\Ead$ (in eV) of excited states of water for various methods and basis sets.}
\begin{ruledtabular}{} \begin{ruledtabular}{}
\begin{tabular}{llddddddddddddd} \begin{tabular}{llddddddddddddd}
& & & \mc{12}{c}{Deviation with respect to TBE} & & & \mc{12}{c}{Deviation with respect to TBE}
\\ \\
\cline{4-15} \cline{4-15}
& & & \mc{3}{c}{exFCI} & & & \mc{3}{c}{exFCI}
& \mc{3}{c}{exFCI+PBEot} & \mc{3}{c}{exFCI+PBEot}
& \mc{3}{c}{exFCI+PBE} & \mc{3}{c}{exFCI+PBE}
& \mc{3}{c}{exFCI+LDA} & \mc{3}{c}{exFCI+LDA}
\\ \\
\cline{4-6} \cline{7-9} \cline{10-12} \cline{13-15} \cline{4-6} \cline{7-9} \cline{10-12} \cline{13-15}
Molecule & Transition & \tabc{TBE} & \tabc{AVDZ} & \tabc{AVTZ} & \tabc{AVQZ} Molecule & Transition & \tabc{TBE} & \tabc{AVDZ} & \tabc{AVTZ} & \tabc{AVQZ}
& \tabc{AVDZ} & \tabc{AVTZ} & \tabc{AVQZ} & \tabc{AVDZ} & \tabc{AVTZ} & \tabc{AVQZ}
& \tabc{AVDZ} & \tabc{AVTZ} & \tabc{AVQZ} & \tabc{AVDZ} & \tabc{AVTZ} & \tabc{AVQZ}
& \tabc{AVDZ} & \tabc{AVTZ} & \tabc{AVQZ} & \tabc{AVDZ} & \tabc{AVTZ} & \tabc{AVQZ}
\\ \\
\hline \hline
Water & \tabc{$1\,^{1}A_1 \ra 1\,^{1}B_1$} & 7.70 & -0.17 & -0.07 & Water & $1\,^{1}A_1 \ra 1\,^{1}B_1$ & 7.70 & -0.17 & -0.07 &
& -0.19 & +0.00 & & -0.19 & 0.00 &
& -0.02 & -0.01 & & -0.02 & -0.01 &
& -0.04 & -0.01 & & -0.04 & -0.01 &
\\ \\
& \tabc{$1\,^{1}A_1 \ra 1\,^{1}A_2$} & 9.47 & -0.15 & -0.06 & & $1\,^{1}A_1 \ra 1\,^{1}A_2$ & 9.47 & -0.15 & -0.06 &
& +0.03 & +0.01 & & 0.03 & 0.01 &
& +0.00 & +0.00 & & 0.00 & 0.00 &
& -0.03 & +0.00 & & -0.03 & 0.00 &
\\ \\
& \tabc{$1\,^{1}A_1 \ra 1\,^{1}A_1$} & 9.97 & -0.03 & +0.02 & & $1\,^{1}A_1 \ra 2\,^{1}A_1$ & 9.97 & -0.03 & 0.02 &
& +0.13 & +0.08 & & 0.13 & 0.08 &
& +0.10 & +0.07 & & 0.10 & 0.07 &
& +0.09 & 0.07 & & 0.09 & 0.07 &
\\ \\
& \tabc{$1\,^{1}A_1 \ra 3\,^{1}B_1$} & 7.33 & -0.19 & -0.08 & & $1\,^{1}A_1 \ra 1\,^{3}B_1$ & 7.33 & -0.19 & -0.08 &
& +0.02 & +0.00 & & 0.02 & 0.00 &
& +0.05 & +0.01 & & 0.05 & 0.01 &
& 0.00 & +0.00 & & 0.00 & 0.00 &
\\ \\
& \tabc{$1\,^{1}A_1 \ra 3\,^{1}A_2$} & 9.30 & -0.16 & -0.06 & & $1\,^{1}A_1 \ra 1\,^{3}A_2$ & 9.30 & -0.16 & -0.06 &
& +0.04 & +0.02 & & 0.04 & 0.02 &
& +0.07 & +0.03 & & 0.07 & 0.03 &
& +0.03 & 0.03 & & 0.03 & 0.03 &
\\ \\
& \tabc{$1\,^{1}A_1 \ra 3\,^{1}A_1$} & 9.59 & -0.11 & -0.05 & & $1\,^{1}A_1 \ra 1\,^{3}A_1$ & 9.59 & -0.11 & -0.05 &
& +0.07 & +0.02 & & 0.07 & 0.02 &
& +0.09 & +0.03 & & 0.09 & 0.03 &
& +0.06 & 0.03 & & 0.06 & 0.03 &
\\
\\
Ammonia & $1\,^{1}A_{1} \ra 1\,^{1}A_{2}$ & 6.66 & -0.18 & -0.07 &
& -0.04 & -0.02 &
& -0.07 & -0.03 &
& -0.07 & -0.03 &
\\
& $1\,^{1}A_{1} \ra 2\,^{1}A_{1}$ & 8.65 & 1.03 & 0.68 &
& 1.17 & 0.73 &
& 1.13 & 0.72 &
& 1.13 & 0.71 &
\\
& $1\,^{1}A_{1} \ra 1\,^{3}A_{2}$ & 6.37 & -0.18 & -0.06 &
& -0.03 & 0.00 &
& -0.07 & 0.02 &
& -0.07 & -0.01 &
\\
\end{tabular}
\end{ruledtabular}
\end{table*}
\end{squeezetable}
%%% %%% %%%
%%% TABLE 3 %%%
\begin{squeezetable}
\begin{table*}
\caption{
Vertical absorption energies $\Ead$ (in eV) of excited states of ethylene and formaldehyde for various methods and basis sets.}
\begin{ruledtabular}{}
\begin{tabular}{llddddddddd}
& & & \mc{8}{c}{Deviation with respect to TBE}
\\
\cline{4-11}
& & & \mc{2}{c}{exFCI}
& \mc{2}{c}{exFCI+PBEot}
& \mc{2}{c}{exFCI+PBE}
& \mc{2}{c}{exFCI+LDA}
\\
\cline{4-5} \cline{6-7} \cline{8-9} \cline{10-11}
Molecule & Transition & \tabc{TBE} & \tabc{AVDZ} & \tabc{AVTZ}
& \tabc{AVDZ} & \tabc{AVTZ}
& \tabc{AVDZ} & \tabc{AVTZ}
& \tabc{AVDZ} & \tabc{AVTZ}
\\
\hline
Ethylene & $1\,^{1}A_{1g} \ra 1\,^{1}B_{3u}$ & 7.43 & -0.12 & -0.04
& -0.05 & -0.01
& -0.04 & -0.01
& -0.02 & 0.00
\\
& $1\,^{1}A_{1g} \ra 1\,^{1}B_{1u}$ & 7.92 & 0.01 & 0.01
& 0.00 & 0.00
& 0.06 & 0.03
& 0.06 & 0.03
\\
& $1\,^{1}A_{1g} \ra 1\,^{1}B_{1g}$ & 8.10 & -0.1 & -0.02
& -0.03 & 0.00
& -0.02 & 0.00
& 0.00 & 0.01
\\
& $1\,^{1}A_{1g} \ra 1\,^{3}B_{1u}$ & 4.54 & 0.01 & 0.00
& 0.07 & 0.03
& 0.10 & 0.04
& 0.08 & 0.04
\\
\\
Formaldehyde& $1\,^{1}A_{1} \ra 1\,^{1}A_{2}$ & 3.97 & 0.02 & 0.01
& 0.05 & 0.02
& 0.03 & 0.02
& 0.02 & 0.01
\\
& $1\,^{1}A_{1} \ra 1\,^{1}B_{2}$ & 7.30 & -0.19 & -0.07
& 0.00 & 0.00
& -0.02 & 0.00
& -0.04 & 0.00
\\
& $1\,^{1}A_{1} \ra 2\,^{1}B_{2}$ & 8.14 & -0.10 & -0.01
& 0.09 & 0.07
& 0.08 & 0.06
& 0.05 & 0.06
\\
& $1\,^{1}A_{1} \ra 2\,^{1}A_{1}$ & 8.27 & -0.15 & -0.04
& 0.03 & 0.04
& 0.02 & 0.03
& 0.00 & 0.03
\\
& $1\,^{1}A_{1} \ra 1\,^{3}A_{2}$ & 3.58 & 0.00 & 0.00
& 0.09 & 0.05
& 0.11 & 0.06
& 0.07 & 0.04
\\
& $1\,^{1}A_{1} \ra 1\,^{3}A_{1}$ & 6.07 & 0.03 & 0.01
& 0.13 & 0.04
& 0.15 & 0.05
& 0.11 & 0.04
\\
& $1\,^{1}A_{1} \ra 1\,^{3}B_{2}$ & 7.14 & -0.19 & -0.08
& 0.01 & 0.01
& 0.02 & 0.01
& -0.01 & 0.00
\\
& $1\,^{1}A_{1} \ra 2\,^{3}B_{2}$ & 7.96 & -0.09 & -0.02
& 0.13 & 0.08
& 0.14 & 0.08
& 0.10 & 0.07
\\
& $1\,^{1}A_{1} \ra 1\,^{3}A_{1}$ & 8.15 & -0.14 & -0.05
& 0.07 & 0.05
& 0.07 & 0.04
& 0.04 & 0.04
\\ \\
\end{tabular} \end{tabular}
\end{ruledtabular} \end{ruledtabular}