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Pierre-Francois Loos 2020-06-10 13:25:04 +02:00
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BSEdyn.bib
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@ -1,7 +1,7 @@
%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/
%% Created for Pierre-Francois Loos at 2020-06-06 09:02:31 +0200
%% Created for Pierre-Francois Loos at 2020-06-10 12:38:29 +0200
%% Saved with string encoding Unicode (UTF-8)
@ -17,7 +17,8 @@
Pages = {989},
Title = {Damping of small-amplitude nuclear collective motion},
Volume = {51},
Year = {1988}}
Year = {1988},
Bdsk-Url-1 = {https://doi.org/10.1088/0034-4885/51/7/002}}
@article{Sakkinen_2012,
Author = {N. Sakkinen and M. Manninen and R. van Leeuwen},
@ -148,12 +149,12 @@
@article{Loos_2020c,
Author = {P. F. Loos and A. Scemama and M. Boggio-Pasqua and D. Jacquemin},
Date-Added = {2020-05-18 22:13:24 +0200},
Date-Modified = {2020-05-29 10:31:08 +0200},
Date-Modified = {2020-06-10 12:38:21 +0200},
Doi = {10.1021/acs.jctc.0c00227},
Journal = {J. Chem. Theory Comput.},
Pages = {XXXX},
Pages = {3720--3736},
Title = {A Mountaineering Strategy to Excited States: Highly-Accurate Energies and Benchmarks for Exotic Molecules and Radicals},
Volume = {XX},
Volume = {16},
Year = {2020},
Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.9b01216}}

239
BSEdyn.tex
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@ -266,7 +266,7 @@ It is important to note that, although all the studies mentioned above are clear
However, it does permit to recover, for transitions with a dominant single-excitation character, additional relaxation effects coming from higher excitations (and, in particular, non-interacting double excitations).
These higher excitations would be explicitly present in the BSE Hamiltonian by ``unfolding'' the dynamical BSE kernel, and one would recover a linear eigenvalue problem with, nonetheless, a much larger dimension.
Based on a rather simple model (the Hubbard dimer) which permits to analytically solve the dynamical equations, Romaniello and coworkers \cite{Romaniello_2009b,Sangalli_2011} evidenced that one can genuinely access additional excitations by solving the non-linear, frequency-dependent eigenvalue problem.
Based on a simple two-level model which permits to analytically solve the dynamical equations, Romaniello and coworkers \cite{Romaniello_2009b,Sangalli_2011} evidenced that one can genuinely access additional excitations by solving the non-linear, frequency-dependent eigenvalue problem.
For this particular system, it was shown that a BSE kernel based on the random-phase approximation (RPA) produces indeed double excitations but also unphysical excitations. \cite{Romaniello_2009b}
The appearance of these spurious excitations was attributed to the self-screening problem. \cite{Romaniello_2009a}
This was fixed in a follow-up paper by Sangalli \textit{et al.} \cite{Sangalli_2011} thanks to the design of a number-conserving approach based on the second RPA. \cite{Wambach_1988}
@ -732,7 +732,7 @@ All the static and dynamic BSE calculations have been performed with the softwar
\label{tab:N2}
}
\begin{ruledtabular}
\begin{tabular}{llddddddddd}
\begin{tabular}{lcddddddddd}
& & \mc{3}{c}{cc-pVDZ ($\Eg^{\GW} = 20.71$ eV)}
& \mc{3}{c}{cc-pVTZ ($\Eg^{\GW} = 20.21$ eV)}
& \mc{3}{c}{cc-pVQZ ($\Eg^{\GW} = 20.05$ eV)} \\
@ -805,79 +805,86 @@ In accordance with the success of the dTDA, the remaining calculations of the pr
\label{tab:BigTabSi}
}
\begin{ruledtabular}
\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}
\begin{tabular}{llcdddddddddd}
& & & \mc{5}{c}{BSE@{\GOWO}@HF} & \mc{5}{c}{Wave function-based methods} \\
\cline{4-8} \cline{9-13}
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
& 6.07 & 7.97 & 7.91 & 7.96 & 7.84 \\
% & 7.33 & 7.59 & 7.56 & 7.52 & 7.96 \\
\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 \\
\\
\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 \\
& $^1A_2(n \ra 3p)$ & 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 \\
& $^1A_1(n \ra 3s)$ & 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{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 \\
& $^1A_2(n \ra 3p)$ & Ryd. & & 9.79 & 9.72 & -0.07 & 1.005
& 9.41 & 8.84 & 9.36 & 8.89 & 8.92 \\
& $^1A_1(n \ra 3s)$ & Ryd. & & 10.42 & 10.35 & -0.07 & 1.006
& 9.99 & 9.52 & 9.96 & 9.58 & 9.52 \\
\\
\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 \\
& 9.66 & 9.48 & 9.41 & 9.44 & 9.34 \\
& $^1\Sigma_u^-(\pi \ra \pis)$ & Val. & & 10.11 & 9.66 & -0.45 & 1.029
& 10.31 & 10.26 & 10.00 & 10.32 & 9.88 \\
& 10.31 & 10.26 & 10.00 & 10.32 & 9.88 \\
& $^1\Delta_u(\pi \ra \pis)$ & Val. & & 10.75 & 10.33 & -0.42 & 1.030
& 10.85 & 10.79 & 10.44 & 10.86 & 10.29 \\
& $^1\Sigma_g^+$ & Ryd. & & 13.60 & 13.57 & -0.03 & 1.003
& 13.67 & 12.99 & 13.15 & 12.83 & 12.98 \\
& $^1\Pi_u$ & Ryd. & & 13.98 & 13.94 & -0.04 & 1.004
& 13.64 & 13.32 & 13.43 & 13.15 & 13.03 \\
& $^1\Sigma_u^+$ & Ryd. & & 13.98 & 13.91 & -0.07 & 1.008
& 13.75 & 13.07 & 13.26 & 12.89 & 13.09 \\
& $^1\Pi_u$ & Ryd. & & 14.24 & 14.21 & -0.03 & 1.002
& 14.52 & 14.00 & 13.67 & 13.96 & 13.46 \\
& 10.85 & 10.79 & 10.44 & 10.86 & 10.29 \\
& $^1\Sigma_g^+$ & Ryd. & & 13.60 & 13.57 & -0.03 & 1.003
& 13.67 & 12.99 & 13.15 & 12.83 & 12.98 \\
& $^1\Pi_u$ & Ryd. & & 13.98 & 13.94 & -0.04 & 1.004
& 13.64 & 13.32 & 13.43 & 13.15 & 13.03 \\
& $^1\Sigma_u^+$ & Ryd. & & 13.98 & 13.91 & -0.07 & 1.008
& 13.75 & 13.07 & 13.26 & 12.89 & 13.09 \\
& $^1\Pi_u$ & Ryd. & & 14.24 & 14.21 & -0.03 & 1.002
& 14.52 & 14.00 & 13.67 & 13.96 & 13.46 \\
\\
\ce{CO} & $^1\Pi(n \ra \pis)$ & 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{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} & $^1A''(n \ra \pis)$ & 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 \\
& $^1A'$ & 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 \\
& 1.80 & 1.68 & 1.76 & 1.74 & 1.74 \\
& $^1A'$ & Ryd. & & 7.05 & 7.01 & -0.04 & 1.003
& 5.81 & 5.73 & 6.30 & 5.72 & 6.27 \\
\\
\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 \\
& 7.28 & 7.24 & 7.15 & 7.26 & 7.10 \\
& $^1\Delta_{u}(\pi \ra \pis)$ & Val. & & 7.74 & 7.46 & -0.29 & 1.025
& 7.62 & 7.56 & 7.48 & 7.59 & 7.44\\
& 7.62 & 7.56 & 7.48 & 7.59 & 7.44\\
\\
%T2: check state ordering in BSE calculation
\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 \\
& $^1B_{1u}(\pi \ra \pis)$ & 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 \\
& $^1B_{1g}(\pi \ra 3p)$ & 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{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 \\
& $^1B_{1u}(\pi \ra \pis)$ & Val. & & 8.18 & 8.03 & -0.15 & 1.022
& 7.95 & 7.91 & 8.02 & 7.92 & 7.93 \\
& $^1B_{1g}(\pi \ra 3p)$ & Ryd. & & 8.29 & 8.26 & -0.03 & 1.003
& 8.01 & 7.99 & 8.08 & 7.95 & 8.08 \\
\\
\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 \\
\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 \\
\hline
MAE & & & & 0.65 & 0.50 & &
& 0.41 & 0.24 & 0.14 & 0.25 & 0.00 \\
MSE & & & & 0.65 & 0.48 & &
& 0.12 & 0.00 & 0.13 & 0.00 & 0.00 \\
\end{tabular}
\end{ruledtabular}
\end{table*}
@ -892,64 +899,69 @@ In accordance with the success of the dTDA, the remaining calculations of the pr
\label{tab:BigTabTr}
}
\begin{ruledtabular}
\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}
\begin{tabular}{llcdddddddddd}
& & & \mc{5}{c}{BSE@{\GOWO}@HF} & \mc{5}{c}{Wave function-based methods} \\
\cline{4-8} \cline{9-13}
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} & $^3B_1(n \ra 3s)$ & Ryd. & 13.58 & 7.62 & 7.48 & -0.14 & 1.009
& 7.25 & 6.86 & 7.20 & 6.91 & 6.92 \\
% & 6.55 & 6.75 & 7.12 & 6.72 & 7.04 \\
& $^3A_2(n \ra 3p)$ & Ryd. & & 9.61 & 9.50 & -0.11 & 1.007
& 9.24 & 8.72 & 9.20 & 8.77 & 8.91 \\
% & 8.22 & 8.45 & 8.77 & 8.54 & 8.92 \\
& $^3A_1(n \ra 3s)$ & Ryd. & & 9.80 & 9.66 & -0.14 & 1.008
& 9.54 & 9.15 & 9.49 & 9.20 & 9.30 \\
% & 8.60 & 8.82 & 9.24 & 8.79 & 9.11 \\
\ce{H2O} & $^3B_1(n \ra 3s)$ & Ryd. & 13.58 & 7.62 & 7.48 & -0.14 & 1.009
& 7.25 & 6.86 & 7.20 & 6.91 & 6.92 \\
& $^3A_2(n \ra 3p)$ & Ryd. & & 9.61 & 9.50 & -0.11 & 1.007
& 9.24 & 8.72 & 9.20 & 8.77 & 8.91 \\
& $^3A_1(n \ra 3s)$ & Ryd. & & 9.80 & 9.66 & -0.14 & 1.008
& 9.54 & 9.15 & 9.49 & 9.20 & 9.30 \\
\\
\ce{N2} & $^3\Sigma_u^+(\pi \ra \pis)$ & Val. & 19.20 & 8.02 & 7.38 & -0.64 & 1.032 & 8.20 & 8.15 & 7.66 & 8.19 & 7.70 \\
& $^3\Pi_g(n \ra \pis)$ & Val. & & 8.66 & 8.10 & -0.56 & 1.031 & 8.33 & 8.20 & 8.09 & 8.19 & 8.01 \\
& $^3\Delta_u(\pi \ra \pis)$ & Val. & & 9.04 & 8.48 & -0.56 & 1.031 & 9.30 & 9.25 & 8.91 & 9.30 & 8.87 \\
& $^3\Sigma_u^-(\pi \ra \pis)$ & Val. & & 10.11 & 9.66 & -0.45 & 1.029 & 10.29 & 10.23 & 9.83 & 10.29 & 9.66 \\
\ce{N2} & $^3\Sigma_u^+(\pi \ra \pis)$ & Val. & 19.20 & 8.02 & 7.38 & -0.64 & 1.032
& 8.20 & 8.15 & 7.66 & 8.19 & 7.70 \\
& $^3\Pi_g(n \ra \pis)$ & Val. & & 8.66 & 8.10 & -0.56 & 1.031
& 8.33 & 8.20 & 8.09 & 8.19 & 8.01 \\
& $^3\Delta_u(\pi \ra \pis)$ & Val. & & 9.04 & 8.48 & -0.56 & 1.031
& 9.30 & 9.25 & 8.91 & 9.30 & 8.87 \\
& $^3\Sigma_u^-(\pi \ra \pis)$ & Val. & & 10.11 & 9.66 & -0.45 & 1.029
& 10.29 & 10.23 & 9.83 & 10.29 & 9.66 \\
\\
\ce{CO} & $^3\Pi(n \ra \pis)$ & Val. & 16.46 & 6.80 & 6.25 & -0.55 & 1.031 & 6.51 & 6.45 & 6.36 & 6.42 & 6.28 \\
& $^3\Sigma^+(\pi \ra \pis)$ & Val. & & 8.56 & 8.06 & -0.50 & 1.025 & 8.63 & 8.54 & 8.34 & 8.72 & 8.45 \\
& $^3\Delta(\pi \ra \pis)$ & Val. & & 9.39 & 8.96 & -0.43 & 1.024 & 9.44 & 9.33 & 9.23 & 9.56 & 9.27 \\
& $^3\Sigma_u^-(\pi \ra \pis)$ & Val. & & 10.25 & 9.90 & -0.35 & 1.023 & 10.10 & 10.01 & 9.81 & 10.27 & 9.80 \\
& $^3\Sigma_u^+$ & Ryd. & & 11.17 & 11.07 & -0.10 & 1.008 & 10.98 & 10.83 & 10.71 & 10.60 & 10.47 \\
\ce{CO} & $^3\Pi(n \ra \pis)$ & Val. & 16.46 & 6.80 & 6.25 & -0.55 & 1.031
& 6.51 & 6.45 & 6.36 & 6.42 & 6.28 \\
& $^3\Sigma^+(\pi \ra \pis)$ & Val. & & 8.56 & 8.06 & -0.50 & 1.025
& 8.63 & 8.54 & 8.34 & 8.72 & 8.45 \\
& $^3\Delta(\pi \ra \pis)$ & Val. & & 9.39 & 8.96 & -0.43 & 1.024
& 9.44 & 9.33 & 9.23 & 9.56 & 9.27 \\
& $^3\Sigma_u^-(\pi \ra \pis)$ & Val. & & 10.25 & 9.90 & -0.35 & 1.023
& 10.10 & 10.01 & 9.81 & 10.27 & 9.80 \\
& $^3\Sigma_u^+$ & Ryd. & & 11.17 & 11.07 & -0.10 & 1.008
& 10.98 & 10.83 & 10.71 & 10.60 & 10.47 \\
\\
\ce{HNO} & $^3A''(n \ra \pis)$ & Val. & 11.71 & 1.27 & 0.67 & -0.60 & 1.036
& 0.91 & 0.78 & 0.85 & 0.84 & 0.88 \\
% & -0.47 & -0.61 & 0.36 & -0.49 & -0.58 \\
& 0.91 & 0.78 & 0.85 & 0.84 & 0.88 \\
& $^3A'(\pi \ra \pis)$ & Val. & & 5.55 & 4.87 & -0.69 & 1.037
& 5.72 & 5.46 & 5.49 & 5.44 & 5.61 \\
% & 4.73 & 4.46 & 5.27 & 4.55 & 4.57 \\
& 5.72 & 5.46 & 5.49 & 5.44 & 5.61 \\
\\
\ce{C2H2} & $^3\Sigma_{u}^+(\pi \ra \pis)$ & Val. & 12.28 & 5.83 & 5.32 & -0.51 & 1.031
& 5.79 & 5.75 & 5.45 & 5.76 & 5.53 \\
& 5.79 & 5.75 & 5.45 & 5.76 & 5.53 \\
& $^3\Delta_{u}(\pi \ra \pis)$ & Val. & & 6.64 & 6.23 & -0.41 & 1.028
& 6.62 & 6.57 & 6.41 & 6.60 & 6.40 \\
& 6.62 & 6.57 & 6.41 & 6.60 & 6.40 \\
& $^3\Sigma_{u}^-(\pi \ra \pis)$ & Val. & & 7.37 & 7.05 & -0.32 & 1.026
& 7.31 & 7.27 & 7.12 & 7.29 & 7.08 \\
& 7.31 & 7.27 & 7.12 & 7.29 & 7.08 \\
\\
\ce{C2H4} & $^3B_{1u}(\pi \ra \pis)$ & Val. & 11.49 & 4.95 & 4.49 & -0.46 & 1.032
& 4.62 & 4.59 & 4.46 & 4.59 & 4.54 \\
% & 4.07 & 3.84 & 4.54 & 3.92 & 3.55 \\
& $^3B_{3u}(\pi \ra 3s)$ & Ryd. & & 7.46 & 7.42 & -0.04 & 1.004
& 7.26 & 7.23 & 7.29 & 7.19 & 7.23 \\
% & 6.54 & 6.74 & 6.90 & 6.83 & 7.41 \\
& $^3B_{1g}(\pi \ra 3p)$ & Ryd. & & 8.23 & 8.19 & -0.04 & 1.004
& 7.97 & 7.95 & 8.03 & 7.91 & 7.98 \\
% & 7.14 & 7.34 & 7.46 & 7.45 & 7.53 \\
\ce{C2H4} & $^3B_{1u}(\pi \ra \pis)$ & Val. & 11.49 & 4.95 & 4.49 & -0.46 & 1.032
& 4.62 & 4.59 & 4.46 & 4.59 & 4.54 \\
& $^3B_{3u}(\pi \ra 3s)$ & Ryd. & & 7.46 & 7.42 & -0.04 & 1.004
& 7.26 & 7.23 & 7.29 & 7.19 & 7.23 \\
& $^3B_{1g}(\pi \ra 3p)$ & Ryd. & & 8.23 & 8.19 & -0.04 & 1.004
& 7.97 & 7.95 & 8.03 & 7.91 & 7.98 \\
\\
\ce{CH2O} & $^3A_2(n \ra \pis)$ & Val. & 12.00 & 4.28 & 3.87 & -0.40 & 1.027 & 3.58 & 3.46 & 3.56 & 3.59 & 3.58 \\
& $^3A_1(\pi \ra \pis)$ & Val. & & 6.31 & 5.75 & -0.56 & 1.033 & 6.27 & 6.20 & 5.97 & 6.30 & 6.06 \\
& $^3B_2(n \ra 3s)$ & Ryd. & & 7.60 & 7.56 & -0.05 & 1.002 & 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 \\
\ce{CH2O} & $^3A_2(n \ra \pis)$ & Val. & 12.00 & 4.28 & 3.87 & -0.40 & 1.027
& 3.58 & 3.46 & 3.56 & 3.59 & 3.58 \\
& $^3A_1(\pi \ra \pis)$ & Val. & & 6.31 & 5.75 & -0.56 & 1.033
& 6.27 & 6.20 & 5.97 & 6.30 & 6.06 \\
& $^3B_2(n \ra 3s)$ & Ryd. & & 7.60 & 7.56 & -0.05 & 1.002
& 6.66 & 6.39 & 7.08 & 6.44 & 7.06 \\
\hline
MAE & & & & 0.39 & 0.29 & &
& 0.25 & 0.21 & 0.09 & 0.22 & 0.00 \\
MSE & & & & 0.39 & 0.01 & &
& 0.21 & 0.08 & 0.04 & 0.12 & 0.00 \\
\end{tabular}
\end{ruledtabular}
\end{table*}
@ -971,14 +983,13 @@ Moreover, we have observed that an iterative, self-consistent resolution [where
\label{tab:BigMol}
}
\begin{ruledtabular}
\begin{tabular}{llldddddd}
\begin{tabular}{llcdddddd}
& & & \mc{5}{c}{BSE@{\GOWO}@HF} \\
\cline{4-8}
Molecule & State & Nature & \tabc{$\Eg^{\GW}$} & \tabc{$\Om{s}{\stat}$} & \tabc{$\Om{s}{\dyn}$} & \tabc{$\Delta\Om{s}{\dyn}$} & \tabc{$Z_{s}$} & \tabc{CC3} \\
\hline
acrolein & $^1A''(n \ra \pis)$ & Val. & 11.67 & 4.62 & 4.28 & -0.35 & 1.030 & 3.77 \\
& $^1A'(n \ra \pis)$ & Val. & & 6.86 & 6.70 & -0.16 & 1.023 & 6.67 \\
& $^1A''(n \ra \pis)$ & Val. & & 7.85 & 7.71 & -0.14 & 1.012 & 6.75 \\
& $^1A'(n \ra 3s)$ & Ryd. & & 7.57 & 7.53 & -0.04 & 1.004 & 6.99 \\
\\
& $^3A''(n \ra \pis)$ & Val. & & 3.97 & 3.54 & -0.43 & 1.031 & 3.47 \\
@ -986,15 +997,31 @@ Moreover, we have observed that an iterative, self-consistent resolution [where
\\
butadiene & $^1B_u(\pi \ra \pis)$ & Val. & 9.88 & 6.25 & 6.13 & -0.12 & 1.019 & 6.25 \\
& $^1A_g(\pi \ra \pis)$ & Val. & & 6.88 & 6.86 & -0.03 & 1.003 & 6.68 \\
\\
& $^3B_u(\pi \ra \pis)$ & Val. & & 3.68 & 3.25 & -0.43 & 1.032 & 3.36 \\
& $^3A_g(\pi \ra \pis)$ & Val. & & 5.51 & 5.01 & -0.50 & 1.040 & 5.21 \\
& $^3B_g(\pi \ra 3s)$ & Ryd. & & 6.29 & 6.25 & -0.04 & 1.005 & 6.20 \\
\\
diacetylene & $^1\Sigma_u^-(\pi \ra \pis)$ & Val. & 11.01 & 5.62 & 5.35 & -0.28 & 1.025 & 5.44 \\
& $^1\Delta_u(\pi \ra \pis)$ & Val. & & 5.87 & 5.63 & -0.25 & 1.024 & 5.69 \\
\\
& $^3\Sigma_u^+(\pi \ra \pis)$ & Val. & & 4.30 & 3.82 & -0.49 & 1.031 & 4.06 \\
& $^3\Delta_u(\pi \ra \pis)$ & Val. & & 5.04 & 4.68 & -0.36 & 1.027 & 4.86 \\
\\
glyoxal & $^1A_u(n \ra \pis)$ & Val. & 10.90 & 3.46 & 3.14 & -0.33 & 1.028 & 2.90 \\
& $^1B_g(n \ra \pis)$ & Val. & & 4.96 & 4.55 & -0.41 & 1.034 & 4.30 \\
& $^1B_u(n \ra 3p)$ & Ryd. & & 7.90 & 7.86 & -0.04 & 1.004 & 7.55 \\
\\
streptocyanine & $^1B_2(\pi \ra \pis)$ & Val. & 13.79 & 7.66 & 7.51 & -0.15 & 1.019 & 7.14 \\
& $^3A_u(n \ra \pis)$ & Val. & & 2.77 & 2.38 & -0.39 & 1.028 & 2.49 \\
& $^3B_g(n \ra \pis)$ & Val. & & 4.23 & 3.75 & -0.48 & 1.034 & 3.91 \\
& $^3B_u(\pi \ra \pis)$ & Val. & & 5.01 & 4.47 & -0.55 & 1.034 & 5.20 \\
& $^3A_g(\pi \ra \pis)$ & Val. & & 6.22 & 5.61 & -0.61 & 1.038 & 6.34 \\
\\
streptocyanine & $^1B_2(\pi \ra \pis)$ & Val. & 13.79 & 7.66 & 7.51 & -0.15 & 1.019 & 7.14 \\
& $^3B_2(\pi \ra \pis)$ & Val. & & 5.39 & 5.10 & -0.29 & 1.021 & 5.48 \\
\hline
MAE & & & & 0.30 & 0.26 & & & 0.00 \\
MSE & & & & 0.27 & -0.04 & & & 0.00 \\
\end{tabular}
\end{ruledtabular}
\end{table}

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