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Pierre-Francois Loos 2019-05-19 17:56:07 +02:00
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Manuscript/Ex-srDFT.tex
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@ -221,109 +221,111 @@ In the present study, we rely on the recently proposed short-range density-funct
\begin{squeezetable}
\begin{table*}
\caption{
Vertical absorption energies $\Eabs$ (in eV) of excited states of water and ammonia for various methods and basis sets.}
Vertical absorption energies $\Eabs$ (in eV) of excited states of water, carbon dimer and ammonia for various methods and basis sets.}
\begin{ruledtabular}{}
\begin{tabular}{llddddddddddddd}
& & & \mc{12}{c}{Deviation with respect to TBE}
\begin{tabular}{lllddddddddddddd}
& & & & \mc{12}{c}{Deviation with respect to TBE}
\\
\cline{4-15}
& & & \mc{3}{c}{exFCI}
\cline{5-16}
& & & & \mc{3}{c}{exFCI}
& \mc{3}{c}{exFCI+PBEot}
& \mc{3}{c}{exFCI+PBE}
& \mc{3}{c}{exFCI+LDA}
\\
\cline{4-6} \cline{7-9} \cline{10-12} \cline{13-15}
Molecule & Transition & \tabc{TBE} & \tabc{AVDZ} & \tabc{AVTZ} & \tabc{AVQZ}
\cline{5-7} \cline{8-10} \cline{11-13} \cline{14-16}
Molecule & Transition & Nature & \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}
\\
\hline
Water & $1\,^{1}A_1 \ra 1\,^{1}B_1$ & 7.70 & -0.17 & -0.07 & -0.02
Water & $1\,^{1}A_1 \ra 1\,^{1}B_1$ & Ryd. & 7.70 & -0.17 & -0.07 & -0.02
& 0.01 & 0.00 & 0.02
& -0.02 & -0.01 & 0.00
& -0.04 & -0.01 & 0.01
\\
& $1\,^{1}A_1 \ra 1\,^{1}A_2$ & 9.47 & -0.15 & -0.06 & -0.01
& $1\,^{1}A_1 \ra 1\,^{1}A_2$ & Ryd. & 9.47 & -0.15 & -0.06 & -0.01
& 0.03 & 0.01 & 0.03
& 0.00 & 0.00 & 0.02
& -0.03 & 0.00 & 0.00
\\
& $1\,^{1}A_1 \ra 2\,^{1}A_1$ & 9.97 & -0.03 & 0.02 & 0.06
& $1\,^{1}A_1 \ra 2\,^{1}A_1$ & Ryd. & 9.97 & -0.03 & 0.02 & 0.06
& 0.13 & 0.08 & 0.09
& 0.10 & 0.07 & 0.08
& 0.09 & 0.07 & 0.03
\\
& $1\,^{1}A_1 \ra 1\,^{3}B_1$ & 7.33 & -0.19 & -0.08 & -0.03
& $1\,^{1}A_1 \ra 1\,^{3}B_1$ & Ryd. & 7.33 & -0.19 & -0.08 & -0.03
& 0.02 & 0.00 & 0.02
& 0.05 & 0.01 & 0.02
& 0.00 & 0.00 & 0.04
\\
& $1\,^{1}A_1 \ra 1\,^{3}A_2$ & 9.30 & -0.16 & -0.06 & -0.01
& $1\,^{1}A_1 \ra 1\,^{3}A_2$ & Ryd. & 9.30 & -0.16 & -0.06 & -0.01
& 0.04 & 0.02 & 0.04
& 0.07 & 0.03 & 0.04
& 0.03 & 0.03 & 0.04
\\
& $1\,^{1}A_1 \ra 1\,^{3}A_1$ & 9.59 & -0.11 & -0.05 & -0.01
& $1\,^{1}A_1 \ra 1\,^{3}A_1$ & Ryd. & 9.59 & -0.11 & -0.05 & -0.01
& 0.07 & 0.02 & 0.03
& 0.09 & 0.03 & 0.03
& 0.06 & 0.03 & 0.04
\\
\\
Carbon dimer & $1\,^{1}\Sigma_g^+ \ra 1\,^{1}\Delta_g$ & 2.06 & 0.15 & 0.03 & 0.00
Carbon dimer\fnm[1] & $1\,^{1}\Sigma_g^+ \ra 1\,^{1}\Delta_g$ & Val. & 2.06 & 0.15 & 0.03 & 0.00
& & &
& & &
& & &
\\
& $1\,^{1}\Sigma_g^+ \ra 2\,^{1}\Sigma_g^+$ & 2.40 & 0.10 & 0.02 & 0.00
& $1\,^{1}\Sigma_g^+ \ra 2\,^{1}\Sigma_g^+$ & Val. & 2.40 & 0.10 & 0.02 & 0.00
& & &
& & &
& & &
\\
\\
Hydrogen sulfide & $1\,^{1}A_1 \ra 1\,^{1}A_2$ & 6.10 & 0.19 & 0.08 & 0.05
Hydrogen sulfide & $1\,^{1}A_1 \ra 1\,^{1}A_2$ & Ryd. & 6.10 & 0.19 & 0.08 & 0.05
& 0.34 & 0.12 & 0.07
& 0.33 & 0.11 & 0.07
& 0.33 & 0.11 & 0.07
\\
& $1\,^{1}A_1 \ra 1\,^{1}B_1$ & 6.29 & -0.19 & -0.05 & 0.00
& $1\,^{1}A_1 \ra 1\,^{1}B_1$ & Ryd. & 6.29 & -0.19 & -0.05 & 0.00
& -0.12 & 0.01 & 0.03
& -0.14 & 0.00 & 0.03
& -0.14 & 0.01 & 0.03
\\
& $1\,^{1}A_1 \ra 1\,^{3}A_2$ & 5.74 & 0.16 & 0.07 & 0.05
& $1\,^{1}A_1 \ra 1\,^{3}A_2$ & Ryd. & 5.74 & 0.16 & 0.07 & 0.05
& 0.33 & 0.12 & 0.08
& 0.35 & 0.13 & 0.08
& 0.34 & 0.34 & 0.08
\\
& $1\,^{1}A_1 \ra 1\,^{3}B_1$ & 5.94 & -0.19 & -0.05 & -0.01
& $1\,^{1}A_1 \ra 1\,^{3}B_1$ & Ryd. & 5.94 & -0.19 & -0.05 & -0.01
& -0.08 & 0.02 & 0.03
& -0.06 & 0.03 & 0.03
& -0.08 & 0.04 & 0.04
\\
\\
Ammonia & $1\,^{1}A_{1} \ra 1\,^{1}A_{2}$ & 6.66 & -0.18 & -0.07 & -0.02
Ammonia & $1\,^{1}A_{1} \ra 1\,^{1}A_{2}$ & Ryd. & 6.66 & -0.18 & -0.07 & -0.02
& -0.04 & -0.02 & 0.00
& -0.07 & -0.03 & 0.00
& -0.07 & -0.03 & 0.00
\\
& $1\,^{1}A_{1} \ra 2\,^{1}A_{1}$ & 8.65 & 1.03 & 0.68 & 0.49
& $1\,^{1}A_{1} \ra 2\,^{1}A_{1}$ & Ryd. & 8.65 & 1.03 & 0.68 & 0.49
& 1.17 & 0.73 & 0.75
& 1.13 & 0.72 & 0.74
& 1.13 & 0.71 & 0.78
\\
& $1\,^{1}A_{1} \ra 1\,^{3}A_{2}$ & 6.37 & -0.18 & -0.06 & -0.02
& $1\,^{1}A_{1} \ra 1\,^{3}A_{2}$ & Ryd. & 6.37 & -0.18 & -0.06 & -0.02
& -0.03 & 0.00 & 0.03
& -0.07 & 0.02 & 0.00
& -0.07 & -0.01 & 0.00
\\
\\
Hydrogen chloride& ${}^1\Sigma \ra {}^1\Pi$ & 7.86 & -0.04 & -0.02 & 0.02
Hydrogen chloride& ${}^1\Sigma \ra {}^1\Pi$ & CT\fnm[2] & 7.86 & -0.04 & -0.02 & 0.02
& 0.13 & 0.06 & 0.06
& 0.11 & 0.04 & 0.05
& 0.10 & 0.05 & 0.06
\end{tabular}
\end{ruledtabular}
\fnt[1]{Doubly-excited states of $(\pi,\pi) \ra (\pis,\pis)$ character.}
\fnt[2]{CT stands for charge transfer.}
\end{table*}
\end{squeezetable}
%%% %%% %%%
@ -332,112 +334,112 @@ In the present study, we rely on the recently proposed short-range density-funct
\begin{squeezetable}
\begin{table*}
\caption{
Vertical absorption energies $\Eabs$ (in eV) of excited states of ethylene and formaldehyde for various methods and basis sets.}
Vertical absorption energies $\Eabs$ (in eV) of excited states of acetylene, ethylene and formaldehyde for various methods and basis sets.}
\begin{ruledtabular}{}
\begin{tabular}{llddddddddd}
& & & \mc{8}{c}{Deviation with respect to TBE}
\begin{tabular}{lllddddddddd}
& & & & \mc{8}{c}{Deviation with respect to TBE}
\\
\cline{4-11}
& & & \mc{2}{c}{exFCI}
\cline{5-12}
& & & & \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}
\cline{5-6} \cline{7-8} \cline{9-10} \cline{11-12}
Molecule & Transition & Nature & \tabc{TBE} & \tabc{AVDZ} & \tabc{AVTZ}
& \tabc{AVDZ} & \tabc{AVTZ}
& \tabc{AVDZ} & \tabc{AVTZ}
& \tabc{AVDZ} & \tabc{AVTZ}
\\
\hline
Acetylene & $1\,^{1}\Sigma_{g}^{+} \ra 1\,^{1}\Sigma_{u}^{-}$ & 7.10 & 0.10 & 0.00
Acetylene & $1\,^{1}\Sigma_{g}^{+} \ra 1\,^{1}\Sigma_{u}^{-}$ & Val. & 7.10 & 0.10 & 0.00
& 0.07 &
& 0.11 &
& 0.11 &
\\
& $1\,^{1}\Sigma_{g}^{+} \ra 1\,^{1}\Delta_{u}$ & Val. & 7.44 & 0.07 & 0.00
& 0.04 &
& 0.12 &
& 0.11 &
\\
& $1\,^{1}\Sigma_{g}^{+} \ra 1\,^{3}\Sigma_{u}^{+}$ & Val. & 5.56 & -0.06 & -0.03
& 0.07 &
& 0.04 &
& 0.02 &
\\
& $1\,^{1}\Sigma_{g}^{+} \ra 1\,^{3}\Delta_{u}$ & Val. & 6.40 & 0.06 & 0.00
& &
& &
& &
\\
& $1\,^{1}\Sigma_{g}^{+} \ra 1\,^{1}\Delta_{u}$ & 7.44 & 0.07 & 0.00
& &
& &
& &
\\
& $1\,^{1}\Sigma_{g}^{+} \ra 1\,^{3}\Sigma_{u}^{+}$ & 5.56 & -0.06 & -0.03
& &
& &
& &
\\
& $1\,^{1}\Sigma_{g}^{+} \ra 1\,^{3}\Delta_{u}$ & 6.40 & 0.06 & 0.00
& &
& &
& &
\\
& $1\,^{1}\Sigma_{g}^{+} \ra 1\,^{3}\Sigma_{u}^{-}$ & 7.09 & 0.05 & -0.01
& $1\,^{1}\Sigma_{g}^{+} \ra 1\,^{3}\Sigma_{u}^{-}$ & Val. & 7.09 & 0.05 & -0.01
& &
& &
& &
\\
\\
Ethylene & $1\,^{1}A_{1g} \ra 1\,^{1}B_{3u}$ & 7.43 & -0.12 & -0.04
Ethylene & $1\,^{1}A_{1g} \ra 1\,^{1}B_{3u}$ & Ryd. & 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
& $1\,^{1}A_{1g} \ra 1\,^{1}B_{1u}$ & Val. & 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
& $1\,^{1}A_{1g} \ra 1\,^{1}B_{1g}$ & Ryd. & 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
& $1\,^{1}A_{1g} \ra 1\,^{3}B_{1u}$ & Val. & 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
Formaldehyde& $1\,^{1}A_{1} \ra 1\,^{1}A_{2}$ & Val. & 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
& $1\,^{1}A_{1} \ra 1\,^{1}B_{2}$ & Ryd. & 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
& $1\,^{1}A_{1} \ra 2\,^{1}B_{2}$ & Ryd. & 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
& $1\,^{1}A_{1} \ra 2\,^{1}A_{1}$ & Ryd. & 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
& $1\,^{1}A_{1} \ra 1\,^{3}A_{2}$ & Val. & 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
& $1\,^{1}A_{1} \ra 1\,^{3}A_{1}$ & Val. & 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
& $1\,^{1}A_{1} \ra 1\,^{3}B_{2}$ & Ryd. & 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
& $1\,^{1}A_{1} \ra 2\,^{3}B_{2}$ & Ryd. & 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
& $1\,^{1}A_{1} \ra 1\,^{3}A_{1}$ & Ryd. & 8.15 & -0.14 & -0.05
& 0.07 & 0.05
& 0.07 & 0.04
& 0.04 & 0.04