diff --git a/Manuscript/Ex-srDFT.tex b/Manuscript/Ex-srDFT.tex index 2b9b4df..0295480 100644 --- a/Manuscript/Ex-srDFT.tex +++ b/Manuscript/Ex-srDFT.tex @@ -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