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Pierre-Francois Loos 2020-06-08 10:59:36 +02:00
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BSEdyn.tex
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@ -725,38 +725,41 @@ All the static and dynamic BSE calculations have been performed with the softwar
%%%%%%%%%%%%%%%%%%%%%%%%
%%% TABLE I %%%
\begin{squeezetable}
\begin{table*}
\caption{
Singlet and triplet excitation energies (in eV) of \ce{N2} computed at the BSE@{\GOWO}@HF level for various basis sets.
\label{tab:N2}
}
\begin{ruledtabular}
\begin{tabular}{lddddddddd}
& \mc{3}{c}{aug-cc-pVDZ ($\Eg^{\GW} = 19.49$ eV)}
\begin{tabular}{llddddddddd}
& & \mc{3}{c}{aug-cc-pVDZ ($\Eg^{\GW} = 19.49$ eV)}
& \mc{3}{c}{aug-cc-pVTZ ($\Eg^{\GW} = 19.20$ eV)}
& \mc{3}{c}{aug-cc-pVQZ ($\Eg^{\GW} = 19.00$ eV)} \\
\cline{2-4} \cline{5-7} \cline{8-10}
State & \tabc{$\Om{s}{\stat}$} & \tabc{$\Delta\Om{s}{\dyn}$(dTDA)} & \tabc{$\Delta\Om{s}{\dyn}$}
\cline{3-5} \cline{6-8} \cline{9-11}
State & Nature & \tabc{$\Om{s}{\stat}$} & \tabc{$\Delta\Om{s}{\dyn}$(dTDA)} & \tabc{$\Delta\Om{s}{\dyn}$}
& \tabc{$\Om{s}{\stat}$} & \tabc{$\Delta\Om{s}{\dyn}$(dTDA)} & \tabc{$\Delta\Om{s}{\dyn}$}
& \tabc{$\Om{s}{\stat}$} & \tabc{$\Delta\Om{s}{\dyn}$(dTDA)} & \tabc{$\Delta\Om{s}{\dyn}$} \\
\hline
$^1\Pi_g(n \ra \pis)$ & 10.18 & -0.41 & -0.43 & 10.42 & -0.42 & -0.40 & 10.52 & -0.43 & -0.40 \\
$^1\Sigma_u^-(\pi \ra \pis)$ & 9.95 & -0.44 & -0.44 & 10.11 & -0.45 & -0.45 & 10.20 & -0.45 & -0.45 \\
$^1\Delta_u(\pi \ra \pis)$ & 10.57 & -0.41 & -0.40 & 10.75 & -0.42 & -0.41 & 10.85 & -0.42 & -0.42 \\
$^1\Sigma_g^+$(R) & 13.72 & -0.04 & -0.04 & 13.60 & -0.03 & -0.03 & 13.55 & -0.02 & -0.02 \\
$^1\Pi_u$(R) & 14.07 & -0.05 & -0.05 & 13.98 & -0.04 & -0.04 & 13.96 & -0.03 & -0.04 \\
$^1\Sigma_u^+$(R) & 13.80 & -0.08 & -0.08 & 13.98 & -0.07 & -0.08 & 14.08 & -0.06 & -0.06 \\
$^1\Pi_u$(R) & 14.22 & -0.04 & -0.03 & 14.24 & -0.03 & -0.03 & 14.26 & -0.03 & -0.02 \\
$^1\Pi_g(n \ra \pis)$ & Val. & 10.18 & -0.41 & -0.43 & 10.42 & -0.42 & -0.40 & 10.52 & -0.43 & -0.40 \\
$^1\Sigma_u^-(\pi \ra \pis)$ & Val. & 9.95 & -0.44 & -0.44 & 10.11 & -0.45 & -0.45 & 10.20 & -0.45 & -0.45 \\
$^1\Delta_u(\pi \ra \pis)$ & Val. & 10.57 & -0.41 & -0.40 & 10.75 & -0.42 & -0.41 & 10.85 & -0.42 & -0.42 \\
$^1\Sigma_g^+$ & Ryd. & 13.72 & -0.04 & -0.04 & 13.60 & -0.03 & -0.03 & 13.55 & -0.02 & -0.02 \\
$^1\Pi_u$ & Ryd. & 14.07 & -0.05 & -0.05 & 13.98 & -0.04 & -0.04 & 13.96 & -0.03 & -0.04 \\
$^1\Sigma_u^+$ & Ryd. & 13.80 & -0.08 & -0.08 & 13.98 & -0.07 & -0.08 & 14.08 & -0.06 & -0.06 \\
$^1\Pi_u$ & Ryd. & 14.22 & -0.04 & -0.03 & 14.24 & -0.03 & -0.03 & 14.26 & -0.03 & -0.02 \\
\\
$^3\Sigma_u^+(\pi \ra \pis)$ & 9.21 & -1.01 & -0.71 & 9.50 & -1.04 & -0.73 & 9.61 & -1.04 & -0.71 \\
$^3\Pi_g(n \ra \pis)$ & 9.58 & -0.57 & -0.34 & 9.85 & -0.58 & -0.33 & 9.96 & -0.57 & -0.23 \\
$^3\Delta_u(\pi \ra \pis)$ & 9.97 & -0.92 & -0.58 & 10.19 & -0.95 & -0.36 & 10.29 & -0.95 & -0.70 \\
$^3\Sigma_u^-(\pi \ra \pis)$ & 10.71 & -0.81 & -0.68 & 10.89 & -0.82 & -0.30 & 11.00 & -0.83 & -0.53 \\
$^3\Sigma_u^+(\pi \ra \pis)$ & Val. & 9.21 & -1.01 & -0.71 & 9.50 & -1.04 & -0.73 & 9.61 & -1.04 & -0.71 \\
$^3\Pi_g(n \ra \pis)$ & Val. & 9.58 & -0.57 & -0.34 & 9.85 & -0.58 & -0.33 & 9.96 & -0.57 & -0.23 \\
$^3\Delta_u(\pi \ra \pis)$ & Val. & 9.97 & -0.92 & -0.58 & 10.19 & -0.95 & -0.36 & 10.29 & -0.95 & -0.70 \\
$^3\Sigma_u^-(\pi \ra \pis)$ & Val. & 10.71 & -0.81 & -0.68 & 10.89 & -0.82 & -0.30 & 11.00 & -0.83 & -0.53 \\
\end{tabular}
\end{ruledtabular}
\end{table*}
\end{squeezetable}
%%%% TABLE I %%%
%\begin{squeezetable}
%\begin{table*}
% \caption{
% Singlet and triplet excitation energies (in eV) of \ce{N2} computed at the BSE@{\GOWO}@HF level for various basis sets.
@ -788,6 +791,7 @@ All the static and dynamic BSE calculations have been performed with the softwar
% \end{ruledtabular}
% \fnt[1]{Excitation energy larger than the fundamental gap.}
%\end{table*}
%\end{squeezetable}
First, we investigate the basis set dependency of the dynamical correction as well as the validity of the dTDA (which corresponds to neglecting the dynamical correction originating from the anti-resonant part of the BSE Hamiltonian).
Note that, in the present calculations, the zeroth-order Hamiltonian is always the ``full'' BSE static Hamiltonian, \ie, without TDA.
@ -803,95 +807,95 @@ This outcome is similar to the conclusions of several benchmark studies \cite{Ja
In accordance with the success of the dTDA, the remaining calculations of the present study are performed within this approximation.
%%% TABLE I %%%
%\begin{squeezetable}
\begin{squeezetable}
\begin{table*}
\caption{
Singlet excitation energies (in eV) for various molecules obtained with the aug-cc-pVTZ basis set computed at various levels of theory.
The dynamical correction is computed in the dTDA.
CT and R stand respectively for charge transfer and Rydberg.
CT stands for charge transfer.
\label{tab:BigTabSi}
}
\begin{ruledtabular}
\begin{tabular}{lldddddddddd}
& & \mc{5}{c}{BSE@{\GOWO}@HF} & \mc{5}{c}{Wave function-based methods} \\ %& \mc{5}{c}{Density-based methods} \\
\cline{3-7} \cline{8-12} %\cline{13-17}
Mol. & State & \tabc{$\Eg^{\GW}$} & \tabc{$\Om{s}{\stat}$} & \tabc{$\Om{s}{\dyn}$} & \tabc{$\Delta\Om{s}{\dyn}$} & \tabc{$Z_{s}$}
\begin{tabular}{llldddddddddd}
& & & \mc{5}{c}{BSE@{\GOWO}@HF} & \mc{5}{c}{Wave function-based methods} \\ %& \mc{5}{c}{Density-based methods} \\
\cline{4-8} \cline{9-13} %\cline{13-17}
Mol. & State & Nature & \tabc{$\Eg^{\GW}$} & \tabc{$\Om{s}{\stat}$} & \tabc{$\Om{s}{\dyn}$} & \tabc{$\Delta\Om{s}{\dyn}$} & \tabc{$Z_{s}$}
& \tabc{CIS(D)} & \tabc{ADC(2)} & \tabc{CCSD} & \tabc{CC2} & \tabc{TBE} \\
% & \tabc{B3LYP} & \tabc{PBE0} & \tabc{M06-2X} & \tabc{CAM-B3LYP} & \tabc{LC-$\omega$HPBE} \\
\hline
\ce{HCl} & $^1\Pi$(CT) & 13.43 & 8.30 & 8.19 & -0.11 & 1.009
\ce{HCl} & $^1\Pi$ & CT & 13.43 & 8.30 & 8.19 & -0.11 & 1.009
& 6.07 & 7.97 & 7.91 & 7.96 & 7.84 \\
% & 7.33 & 7.59 & 7.56 & 7.52 & 7.96 \\
\\
\ce{H2O} & $^1B_1(n \ra 3s)$ & 13.58 & 8.09 & 8.00 & -0.09 & 1.007
\ce{H2O} & $^1B_1(n \ra 3s)$ & Ryd. & 13.58 & 8.09 & 8.00 & -0.09 & 1.007
& 7.62 & 7.18 & 7.60 & 7.23 & 7.17 \\
% & 6.92 & 7.18 & 7.46 & 7.13 & 7.50 \\
& $^1A_2(n \ra 3p)$ & & 9.79 & 9.72 & -0.07 & 1.005
& $^1A_2(n \ra 3p)$ & Ryd. & & 9.79 & 9.72 & -0.07 & 1.005
& 9.41 & 8.84 & 9.36 & 8.89 & 8.92 \\
% & 8.33 & 8.61 & 8.93 & 8.69 & 9.11 \\
& $^1A_1(n \ra 3s)$ & & 10.42 & 10.35 & -0.07 & 1.006
& $^1A_1(n \ra 3s)$ & Ryd. & & 10.42 & 10.35 & -0.07 & 1.006
& 9.99 & 9.52 & 9.96 & 9.58 & 9.52 \\
% & 9.08 & 9.37 & 9.64 & 9.28 & 9.65 \\
\\
\ce{N2} & $^1\Pi_g(n \ra \pis)$ & 19.20 & 10.42 & 9.99 & -0.42 & 1.031
\ce{N2} & $^1\Pi_g(n \ra \pis)$ & Val. & 19.20 & 10.42 & 9.99 & -0.42 & 1.031
& 9.66 & 9.48 & 9.41 & 9.44 & 9.34 \\
& $^1\Sigma_u^-(\pi \ra \pis)$ & & 10.11 & 9.66 & -0.45 & 1.029
& $^1\Sigma_u^-(\pi \ra \pis)$ & Val. & & 10.11 & 9.66 & -0.45 & 1.029
& 10.31 & 10.26 & 10.00 & 10.32 & 9.88 \\
& $^1\Delta_u(\pi \ra \pis)$ & & 10.75 & 10.33 & -0.42 & 1.030
& $^1\Delta_u(\pi \ra \pis)$ & Val. & & 10.75 & 10.33 & -0.42 & 1.030
& 10.85 & 10.79 & 10.44 & 10.86 & 10.29 \\
& $^1\Sigma_g^+$(R) & & 13.60 & 13.57 & -0.03 & 1.003
& $^1\Sigma_g^+$ & Ryd. & & 13.60 & 13.57 & -0.03 & 1.003
& 13.67 & 12.99 & 13.15 & 12.83 & 12.98 \\
& $^1\Pi_u$(R) & & 13.98 & 13.94 & -0.04 & 1.004
& $^1\Pi_u$ & Ryd. & & 13.98 & 13.94 & -0.04 & 1.004
& 13.64 & 13.32 & 13.43 & 13.15 & 13.03 \\
& $^1\Sigma_u^+$(R) & & 13.98 & 13.91 & -0.07 & 1.008
& $^1\Sigma_u^+$ & Ryd. & & 13.98 & 13.91 & -0.07 & 1.008
& 13.75 & 13.07 & 13.26 & 12.89 & 13.09 \\
& $^1\Pi_u$(R) & & 14.24 & 14.21 & -0.03 & 1.002
& $^1\Pi_u$ & Ryd. & & 14.24 & 14.21 & -0.03 & 1.002
& 14.52 & 14.00 & 13.67 & 13.96 & 13.46 \\
\\
\ce{CO} & $^1\Pi(n \ra \pis)$ & 16.46 & 9.54 & 9.19 & -0.34 & 1.029 & 8.78 & 8.69 & 8.59 & 8.64 & 8.49 \\
& $^1\Sigma^-(\pi \ra \pis)$ & & 10.25 & 9.90 & -0.35 & 1.023 & 10.13 & 10.03 & 9.99 & 10.30 & 9.92 \\
& $^1\Delta(\pi \ra \pis)$ & & 10.71 & 10.39 & -0.32 & 1.023 & 10.41 & 10.30 & 10.12 & 10.60 & 10.06 \\
& $^1\Sigma^+$(R) & & 11.88 & 11.85 & -0.03 & 1.005 & 11.48 & 11.32 & 11.22 & 11.11 & 10.95 \\
& $^1\Sigma^+$(R) & & 12.39 & 12.37 & -0.02 & 1.003 & 11.71 & 11.83 & 11.75 & 11.63 & 11.52 \\
& $^1\Pi$(R) & & 12.37 & 12.32 & -0.05 & 1.004 & 12.06 & 12.03 & 11.96 & 11.83 & 11.72 \\
\ce{CO} & $^1\Pi(n \ra \pis)$ & Val. & 16.46 & 9.54 & 9.19 & -0.34 & 1.029 & 8.78 & 8.69 & 8.59 & 8.64 & 8.49 \\
& $^1\Sigma^-(\pi \ra \pis)$ & Val. & & 10.25 & 9.90 & -0.35 & 1.023 & 10.13 & 10.03 & 9.99 & 10.30 & 9.92 \\
& $^1\Delta(\pi \ra \pis)$ & Val. & & 10.71 & 10.39 & -0.32 & 1.023 & 10.41 & 10.30 & 10.12 & 10.60 & 10.06 \\
& $^1\Sigma^+$ & Ryd. & & 11.88 & 11.85 & -0.03 & 1.005 & 11.48 & 11.32 & 11.22 & 11.11 & 10.95 \\
& $^1\Sigma^+$ & Ryd. & & 12.39 & 12.37 & -0.02 & 1.003 & 11.71 & 11.83 & 11.75 & 11.63 & 11.52 \\
& $^1\Pi$ & Ryd. & & 12.37 & 12.32 & -0.05 & 1.004 & 12.06 & 12.03 & 11.96 & 11.83 & 11.72 \\
\\
\ce{HNO} & $^1A''(n \ra \pis)$ & 11.71 & 2.46 & 1.98 & -0.48 & 1.035
\ce{HNO} & $^1A''(n \ra \pis)$ & Val. & 11.71 & 2.46 & 1.98 & -0.48 & 1.035
& 1.80 & 1.68 & 1.76 & 1.74 & 1.74 \\
% & 1.55 & 1.51 & 0.99 & 1.51 & 1.46 \\
& $^1A'$(R) & & 7.05 & 7.01 & -0.04 & 1.003
& $^1A'$ & Ryd. & & 7.05 & 7.01 & -0.04 & 1.003
& 5.81 & 5.73 & 6.30 & 5.72 & 6.27 \\
% & 5.63 & 5.85 & 6.22 & 5.94 & 6.33 \\
\\
\ce{C2H2} & $^1\Sigma_{u}^-(\pi \ra \pis)$ & 12.28 & 7.37 & 7.05 & -0.32 & 1.026
\ce{C2H2} & $^1\Sigma_{u}^-(\pi \ra \pis)$ & Val. & 12.28 & 7.37 & 7.05 & -0.32 & 1.026
& 7.28 & 7.24 & 7.15 & 7.26 & 7.10 \\
& $^1\Delta_{u}(\pi \ra \pis)$ & & 7.74 & 7.46 & -0.29 & 1.025
& $^1\Delta_{u}(\pi \ra \pis)$ & Val. & & 7.74 & 7.46 & -0.29 & 1.025
& 7.62 & 7.56 & 7.48 & 7.59 & 7.44\\
\\
%T2: check state ordering in BSE calculation
\ce{C2H4} & $^1B_{3u}(\pi \ra 3s)$ & 11.49 & 7.64 & 7.62 & -0.03 & 1.004
\ce{C2H4} & $^1B_{3u}(\pi \ra 3s)$ & Ryd. & 11.49 & 7.64 & 7.62 & -0.03 & 1.004
& 7.35 & 7.34 & 7.42 & 7.29 & 7.39 \\
% & 6.63 & 6.88 & 6.94 & 6.93 & 7.57 \\
& $^1B_{1u}(\pi \ra \pis)$ & & 8.18 & 8.03 & -0.15 & 1.022
& $^1B_{1u}(\pi \ra \pis)$ & Val. & & 8.18 & 8.03 & -0.15 & 1.022
& 7.95 & 7.91 & 8.02 & 7.92 & 7.93 \\
% & 8.06 & 7.51 & 7.50 & 7.46 & 7.64 \\
& $^1B_{1g}(\pi \ra 3p)$ & & 8.29 & 8.26 & -0.03 & 1.003
& $^1B_{1g}(\pi \ra 3p)$ & Ryd. & & 8.29 & 8.26 & -0.03 & 1.003
& 8.01 & 7.99 & 8.08 & 7.95 & 8.08 \\
% & 7.18 & 7.45 & 7.47 & 7.54 & 8.15 \\
\\
\ce{CH2O} & $^1A_2(n \ra \pis)$ & 12.00 & 5.03 & 4.68 & -0.35 & 1.027 & 4.04 & 3.92 & 4.01 & 4.07 & 3.98 \\
& $^1B_2(n \ra 3s)$ & & 7.87 & 7.85 & -0.02 & 1.001 & 6.64 & 6.50 & 7.23 & 6.56 & 7.23 \\
& $^1B_2(n \ra 3p)$ & & 8.76 & 8.72 & -0.04 & 1.003 & 7.56 & 7.53 & 8.12 & 7.57 & 8.13 \\
& $^1A_1(n \ra 3p)$ & & 8.85 & 8.84 & -0.01 & 1.000 & 8.16 & 7.47 & 8.21 & 7.52 & 8.23 \\
& $^1A_2(n \ra 3p)$ & & 8.87 & 8.85 & -0.02 & 1.002 & 8.04 & 7.99 & 8.65 & 8.04 & 8.67 \\
& $^1B_1(\si \ra \pis)$ & & 10.18 & 9.77 & -0.42 & 1.032 & 9.38 & 9.17 & 9.28 & 9.32 & 9.22 \\
& $^1A_1(\pi \ra \pis)$ & & 10.05 & 9.81 & -0.24 & 1.026 & 9.08 & 9.46 & 9.67 & 9.54 & 9.43 \\
\ce{CH2O} & $^1A_2(n \ra \pis)$ & Val. & 12.00 & 5.03 & 4.68 & -0.35 & 1.027 & 4.04 & 3.92 & 4.01 & 4.07 & 3.98 \\
& $^1B_2(n \ra 3s)$ & Ryd. & & 7.87 & 7.85 & -0.02 & 1.001 & 6.64 & 6.50 & 7.23 & 6.56 & 7.23 \\
& $^1B_2(n \ra 3p)$ & Ryd. & & 8.76 & 8.72 & -0.04 & 1.003 & 7.56 & 7.53 & 8.12 & 7.57 & 8.13 \\
& $^1A_1(n \ra 3p)$ & Ryd. & & 8.85 & 8.84 & -0.01 & 1.000 & 8.16 & 7.47 & 8.21 & 7.52 & 8.23 \\
& $^1A_2(n \ra 3p)$ & Ryd. & & 8.87 & 8.85 & -0.02 & 1.002 & 8.04 & 7.99 & 8.65 & 8.04 & 8.67 \\
& $^1B_1(\si \ra \pis)$ & Val. & & 10.18 & 9.77 & -0.42 & 1.032 & 9.38 & 9.17 & 9.28 & 9.32 & 9.22 \\
& $^1A_1(\pi \ra \pis)$ & Val. & & 10.05 & 9.81 & -0.24 & 1.026 & 9.08 & 9.46 & 9.67 & 9.54 & 9.43 \\
\end{tabular}
\end{ruledtabular}
\end{table*}
%\end{squeezetable}
\end{squeezetable}
%%% TABLE II %%%
%\begin{squeezetable}
\begin{squeezetable}
\begin{table*}
\caption{
Triplet excitation energies (in eV) for various molecules obtained with the aug-cc-pVTZ basis set computed at various levels of theory.
@ -899,68 +903,68 @@ In accordance with the success of the dTDA, the remaining calculations of the pr
\label{tab:BigTabTr}
}
\begin{ruledtabular}
\begin{tabular}{lldddddddddd}
& & \mc{5}{c}{BSE@{\GOWO}@HF} & \mc{5}{c}{Wave function-based methods} \\%& \mc{5}{c}{Density-based methods} \\
\cline{3-7} \cline{8-12} %\cline{13-17}
Mol. & State & \tabc{$\Eg^{\GW}$} & \tabc{$\Om{s}{\stat}$} & \tabc{$\Om{s}{\dyn}$} & \tabc{$\Delta\Om{s}{\dyn}$} & \tabc{$Z_{s}$}
\begin{tabular}{llldddddddddd}
& & & \mc{5}{c}{BSE@{\GOWO}@HF} & \mc{5}{c}{Wave function-based methods} \\%& \mc{5}{c}{Density-based methods} \\
\cline{4-8} \cline{8-13} %\cline{13-17}
Mol. & State & Nature & \tabc{$\Eg^{\GW}$} & \tabc{$\Om{s}{\stat}$} & \tabc{$\Om{s}{\dyn}$} & \tabc{$\Delta\Om{s}{\dyn}$} & \tabc{$Z_{s}$}
& \tabc{CIS(D)} & \tabc{ADC(2)} & \tabc{CCSD} & \tabc{CC2} & \tabc{TBE} \\
% & \tabc{B3LYP} & \tabc{PBE0} & \tabc{M06-2X} & \tabc{CAM-B3LYP} & \tabc{LC-$\omega$HPBE} \\
\hline
\ce{H2O} & $^3B_1(n \ra 3s)$ & 13.58 & 8.14 & 7.98 & -0.15 & 1.014
\ce{H2O} & $^3B_1(n \ra 3s)$ & Ryd. & 13.58 & 8.14 & 7.98 & -0.15 & 1.014
& 7.25 & 6.86 & 7.20 & 6.91 & 6.92 \\
% & 6.55 & 6.75 & 7.12 & 6.72 & 7.04 \\
& $^3A_2(n \ra 3p)$ & & 9.97 & 9.89 & -0.07 & 1.008
& $^3A_2(n \ra 3p)$ & Ryd. & & 9.97 & 9.89 & -0.07 & 1.008
& 9.24 & 8.72 & 9.20 & 8.77 & 8.91 \\
% & 8.22 & 8.45 & 8.77 & 8.54 & 8.92 \\
& $^3A_1(n \ra 3s)$ & & 10.28 & 10.13 & -0.15 & 1.012
& $^3A_1(n \ra 3s)$ & Ryd. & & 10.28 & 10.13 & -0.15 & 1.012
& 9.54 & 9.15 & 9.49 & 9.20 & 9.30 \\
% & 8.60 & 8.82 & 9.24 & 8.79 & 9.11 \\
\\
\ce{N2} & $^3\Sigma_u^+(\pi \ra \pis)$ & 19.20 & 9.50 & 8.46 & -1.04 & 1.060 & 8.20 & 8.15 & 7.66 & 8.19 & 7.70 \\
& $^3\Pi_g(n \ra \pis)$ & & 9.85 & 9.27 & -0.58 & 1.050 & 8.33 & 8.20 & 8.09 & 8.19 & 8.01 \\
& $^3\Delta_u(\pi \ra \pis)$ & & 10.19 & 9.24 & -0.95 & 1.060 & 9.30 & 9.25 & 8.91 & 9.30 & 8.87 \\
& $^3\Sigma_u^-(\pi \ra \pis)$ & & 10.89 & 10.06 & -0.82 & 1.058 & 10.29 & 10.23 & 9.83 & 10.29 & 9.66 \\
\ce{N2} & $^3\Sigma_u^+(\pi \ra \pis)$ & Val. & 19.20 & 9.50 & 8.46 & -1.04 & 1.060 & 8.20 & 8.15 & 7.66 & 8.19 & 7.70 \\
& $^3\Pi_g(n \ra \pis)$ & Val. & & 9.85 & 9.27 & -0.58 & 1.050 & 8.33 & 8.20 & 8.09 & 8.19 & 8.01 \\
& $^3\Delta_u(\pi \ra \pis)$ & Val. & & 10.19 & 9.24 & -0.95 & 1.060 & 9.30 & 9.25 & 8.91 & 9.30 & 8.87 \\
& $^3\Sigma_u^-(\pi \ra \pis)$ & Val. & & 10.89 & 10.06 & -0.82 & 1.058 & 10.29 & 10.23 & 9.83 & 10.29 & 9.66 \\
\\
\ce{CO} & $^3\Pi(n \ra \pis)$ & 16.46 & 8.10 & 7.33 & -0.77 & 1.055 & 6.51 & 6.45 & 6.36 & 6.42 & 6.28 \\
& $^3\Sigma^+(\pi \ra \pis)$ & & 9.61 & 9.04 & -0.57 & 1.037 & 8.63 & 8.54 & 8.34 & 8.72 & 8.45 \\
& $^3\Delta(\pi \ra \pis)$ & & 10.20 & 9.69 & -0.50 & 1.036 & 9.44 & 9.33 & 9.23 & 9.56 & 9.27 \\
& $^3\Sigma_u^-(\pi \ra \pis)$ & & 10.79 & 10.38 & -0.42 & 1.034 & 10.10 & 10.01 & 9.81 & 10.27 & 9.80 \\
& $^3\Sigma_u^+$(R) & & 11.48 & 11.38 & -0.10 & 1.010 & 10.98 & 10.83 & 10.71 & 10.60 & 10.47 \\
\ce{CO} & $^3\Pi(n \ra \pis)$ & Val. & 16.46 & 8.10 & 7.33 & -0.77 & 1.055 & 6.51 & 6.45 & 6.36 & 6.42 & 6.28 \\
& $^3\Sigma^+(\pi \ra \pis)$ & Val. & & 9.61 & 9.04 & -0.57 & 1.037 & 8.63 & 8.54 & 8.34 & 8.72 & 8.45 \\
& $^3\Delta(\pi \ra \pis)$ & Val. & & 10.20 & 9.69 & -0.50 & 1.036 & 9.44 & 9.33 & 9.23 & 9.56 & 9.27 \\
& $^3\Sigma_u^-(\pi \ra \pis)$ & Val. & & 10.79 & 10.38 & -0.42 & 1.034 & 10.10 & 10.01 & 9.81 & 10.27 & 9.80 \\
& $^3\Sigma_u^+$ & Ryd. & & 11.48 & 11.38 & -0.10 & 1.010 & 10.98 & 10.83 & 10.71 & 10.60 & 10.47 \\
\\
\ce{HNO} & $^3A''(n \ra \pis)$ & 11.71 & 3.05 & 2.35 & -0.71 & 1.069
\ce{HNO} & $^3A''(n \ra \pis)$ & Val. & 11.71 & 3.05 & 2.35 & -0.71 & 1.069
& 0.91 & 0.78 & 0.85 & 0.84 & 0.88 \\
% & -0.47 & -0.61 & 0.36 & -0.49 & -0.58 \\
& $^3A'(\pi \ra \pis)$ & & 6.69 & 6.70 & 0.01 & 1.000
& $^3A'(\pi \ra \pis)$ & Val. & & 6.69 & 6.70 & 0.01 & 1.000
& 5.72 & 5.46 & 5.49 & 5.44 & 5.61 \\
% & 4.73 & 4.46 & 5.27 & 4.55 & 4.57 \\
\\
\ce{C2H2} & $^3\Sigma_{u}^+(\pi \ra \pis)$ & 12.28 & 7.22 & 6.48 & -0.73 & 1.056
\ce{C2H2} & $^3\Sigma_{u}^+(\pi \ra \pis)$ & Val. & 12.28 & 7.22 & 6.48 & -0.73 & 1.056
& 5.79 & 5.75 & 5.45 & 5.76 & 5.53 \\
& $^3\Delta_{u}(\pi \ra \pis)$ & & 7.70 & 7.08 & -0.62 & 1.053
& $^3\Delta_{u}(\pi \ra \pis)$ & Val. & & 7.70 & 7.08 & -0.62 & 1.053
& 6.62 & 6.57 & 6.41 & 6.60 & 6.40 \\
& $^3\Sigma_{u}^-(\pi \ra \pis)$ & & 8.16 & 7.66 & -0.51 & 1.049
& $^3\Sigma_{u}^-(\pi \ra \pis)$ & Val. & & 8.16 & 7.66 & -0.51 & 1.049
& 7.31 & 7.27 & 7.12 & 7.29 & 7.08 \\
\\
\ce{C2H4} & $^3B_{1u}(\pi \ra \pis)$ & 11.49 & 6.54 & 5.85 & -0.69 & 1.065
\ce{C2H4} & $^3B_{1u}(\pi \ra \pis)$ & Val. & 11.49 & 6.54 & 5.85 & -0.69 & 1.065
& 4.62 & 4.59 & 4.46 & 4.59 & 4.54 \\
% & 4.07 & 3.84 & 4.54 & 3.92 & 3.55 \\
& $^3B_{3u}(\pi \ra 3s)$ & & 7.61 & 7.55 & -0.06 & 1.008
& $^3B_{3u}(\pi \ra 3s)$ & Ryd. & & 7.61 & 7.55 & -0.06 & 1.008
& 7.26 & 7.23 & 7.29 & 7.19 & 7.23 \\
% & 6.54 & 6.74 & 6.90 & 6.83 & 7.41 \\
& $^3B_{1g}(\pi \ra 3p)$ & & 8.36 & 8.31 & -0.05 & 1.006 % 4th state in BSE
& $^3B_{1g}(\pi \ra 3p)$ & Ryd. & & 8.36 & 8.31 & -0.05 & 1.006 % 4th state in BSE
& 7.97 & 7.95 & 8.03 & 7.91 & 7.98 \\
% & 7.14 & 7.34 & 7.46 & 7.45 & 7.53 \\
\\
\ce{CH2O} & $^3A_2(n \ra \pis)$ & 12.00 & 5.53 & 5.05 & -0.47 & 1.049 & 3.58 & 3.46 & 3.56 & 3.59 & 3.58 \\
& $^3A_1(\pi \ra \pis)$ & & 8.15 & 7.32 & -0.83 & 1.067 & 6.27 & 6.20 & 5.97 & 6.30 & 6.06 \\
& $^3B_2(n \ra 3s)$ & & 7.51 & 7.54 & 0.03 & 0.994 & 6.66 & 6.39 & 7.08 & 6.44 & 7.06 \\
\ce{CH2O} & $^3A_2(n \ra \pis)$ & Val. & 12.00 & 5.53 & 5.05 & -0.47 & 1.049 & 3.58 & 3.46 & 3.56 & 3.59 & 3.58 \\
& $^3A_1(\pi \ra \pis)$ & Val. & & 8.15 & 7.32 & -0.83 & 1.067 & 6.27 & 6.20 & 5.97 & 6.30 & 6.06 \\
& $^3B_2(n \ra 3s)$ & Ryd. & & 7.51 & 7.54 & 0.03 & 0.994 & 6.66 & 6.39 & 7.08 & 6.44 & 7.06 \\
% & $^3B_2(n \ra 3p)$* & & 8.62 & 8.61 & -0.00 & 0.998 & 7.52 & 7.41 & 7.94 & 7.45 & 7.94 \\
% & $^3A_1(n \ra 3p)$* & & 8.75 & 8.69 & -0.06 & 1.007 & 7.68 & 7.40 & 8.09 & 7.44 & 8.10 \\
% & $^3B_1(n \ra 3d)$* & & 8.82 & 8.82 & -0.01 & 1.000 & 8.57 & 8.39 & 8.43 & 8.52 & 8.42 \\
\end{tabular}
\end{ruledtabular}
\end{table*}
%\end{squeezetable}
\end{squeezetable}
Tables \ref{tab:BigTabSi} and \ref{tab:BigTabTr} report, respectively, singlet and triplet excitation energies for various molecules computed at the BSE@{\GOWO}@HF level and with the aug-cc-pVTZ basis set.
For comparative purposes, excitation energies obtained with the same basis set and several second-order wave function methods [CIS(D), ADC(2), CCSD, and CC2] are also reported.
@ -975,28 +979,35 @@ Moreover, we have observed that an iterative, self-consistent resolution [where
\caption{
Singlet excitation energies (in eV) for various molecules obtained with the aug-cc-pVDZ basis set computed at various levels of theory.
The dynamical correction is computed in the dTDA.
V and R stand for valence and Rydberg, respectively.
\label{tab:BigTabSi}
}
\begin{ruledtabular}
\begin{tabular}{lldddddd}
& & \mc{5}{c}{BSE@{\GOWO}@HF} \\
\cline{3-7}
Mol. & State & \tabc{$\Eg^{\GW}$} & \tabc{$\Om{s}{\stat}$} & \tabc{$\Om{s}{\dyn}$} & \tabc{$\Delta\Om{s}{\dyn}$} & \tabc{$Z_{s}$} & \tabc{TBE} \\
\begin{tabular}{llldddddd}
& & & \mc{5}{c}{BSE@{\GOWO}@HF} \\
\cline{4-8}
Mol. & State & Nature & \tabc{$\Eg^{\GW}$} & \tabc{$\Om{s}{\stat}$} & \tabc{$\Om{s}{\dyn}$} & \tabc{$\Delta\Om{s}{\dyn}$} & \tabc{$Z_{s}$} & \tabc{TBE} \\
\hline
streptocyanine & $^1B_2(\pi \ra \pis)$ & 7.66 & 7.51 & -0.15 & 1.019 & 7.13 \\
& $^3B_2(\pi \ra \pis)$ & 6.52 & 6.11 & -0.41 & 1.042 & 5.52 \\
acrolein & $^1A''(n \ra \pis)$ & Val. & \\
\\
diacetylene & $^1\Sigma_u^-(\pi \ra \pis)$ \\
& $^1\Delta_u(\pi \ra \pis)$ \\
& $^3\Sigma_u^+(\pi \ra \pis)$ \\
& $^3\Delta_u(\pi \ra \pis)$ \\
butadiene & $^1B_u(\pi \ra \pis)$ & Val. & 9.88 & 6.25 & 6.13 & -0.12 & 1.019 \\
& $^1A_g(\pi \ra \pis)$ & Val. & & 6.88 & 6.86 & -0.03 & 1.003 \\
& $^3B_u(\pi \ra \pis)$ & Val. & & 5.09 & 4.61 & -0.48 & 1.054 \\
\\
butadiene & $^1B_u(\pi \ra \pis)$ \\
& $^1B_g(\pi \ra 3s)$ \\
& $^1A_g(\pi \ra \pis)$ \\
acrolein & \\
glyoxal & \\
diacetylene & $^1\Sigma_u^-(\pi \ra \pis)$ & Val. \\
& $^1\Delta_u(\pi \ra \pis)$ & Val. \\
& $^3\Sigma_u^+(\pi \ra \pis)$ & Val. \\
& $^3\Delta_u(\pi \ra \pis)$ & Val. \\
\\
glyoxal & $^1A_u(n \ra \pis)$ & Val. & 10.90 & 3.46 & 3.14 & -0.33 & 1.028 \\
& $^1B_g(n \ra \pis)$ & Val. & & 4.96 & 4.55 & -0.41 & 1.034 \\
& $^1B_g(n \ra \pis)$ & Val. & & & & & \\
& $^1B_u(n \ra 3p)$ & Ryd. & & & & & \\
& $^3A_u(n \ra \pis)$ & Val. & & 3.94 & 3.57 & -0.37 & 1.045 \\
& $^3B_g(n \ra \pis)$ & Val. & & 5.70 & 5.30 & -0.40 & 1.051 \\
& $^3B_u(\pi \ra \pis)$ & Val. & & 6.69 & 6.07 & -0.62 & 1.057 \\
\\
streptocyanine & $^1B_2(\pi \ra \pis)$ & Val. & 7.66 & 7.51 & -0.15 & 1.019 & 7.13 \\
& $^3B_2(\pi \ra \pis)$ & Val. & 6.52 & 6.11 & -0.41 & 1.042 & 5.52 \\
\end{tabular}
\end{ruledtabular}
\end{table*}

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