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BSEdyn.bib
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@ -1,13 +1,37 @@
%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/
%% Created for Pierre-Francois Loos at 2020-05-29 13:02:34 +0200
%% Created for Pierre-Francois Loos at 2020-06-01 08:13:45 +0200
%% Saved with string encoding Unicode (UTF-8)
@article{Sakkinen_2012,
Author = {N. Sakkinen and M. Manninen and R. van Leeuwen},
Date-Added = {2020-06-01 08:10:19 +0200},
Date-Modified = {2020-06-01 08:13:10 +0200},
Doi = {10.1088/1367-2630/14/1/013032},
Journal = {New J. Phys.},
Pages = {013032},
Title = {The Kadanoff-Baym approach to double excitations in finite systems},
Volume = {14},
Year = {2012},
Bdsk-Url-1 = {https://doi.org/10.1088/1367-2630/14/1/013032}}
@article{Myohanen_2008,
Author = {P. My{\"o}h{\"a}nen and A. Stan and G. Stefanucci and R. van Leeuwen},
Date-Added = {2020-06-01 08:08:11 +0200},
Date-Modified = {2020-06-01 08:09:43 +0200},
Doi = {10.1209/0295-5075/84/67001},
Journal = {Europhys. Lett.},
Pages = {67001},
Title = {A many-body approach to quantum transport dynamics: Initial correlations and memory effects},
Volume = {84},
Year = {2008},
Bdsk-Url-1 = {https://doi.org/10.1209/0295-5075/84/67001}}
@article{Loos_2020b,
Author = {P. F. Loos and F. Lipparini and M. Boggio-Pasqua and A. Scemama and D. Jacquemin},
Date-Added = {2020-05-29 10:29:27 +0200},
@ -2370,9 +2394,9 @@
Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.74.2327}}
@article{Veril_2018,
Author = {M. Veril and P. Romaniello and J. A. Berger and P. F. Loos},
Author = {M. V{\'e}ril and P. Romaniello and J. A. Berger and P. F. Loos},
Date-Added = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-06-01 08:13:45 +0200},
Doi = {10.1021/acs.jctc.8b00745},
Journal = {J. Chem. Theory Comput.},
Pages = {5220},
@ -9937,10 +9961,10 @@
Year = {2010},
Bdsk-Url-1 = {https://doi.org/10.1038/nchem.720}}
@article{Sil08,
@article{Silva-Junior_2008,
Author = {Silva-Junior, M. R. and Schreiber, M. and Sauer, S. P. A. and Thiel, W.},
Date-Added = {2020-01-01 21:36:51 +0100},
Date-Modified = {2020-01-01 21:36:52 +0100},
Date-Modified = {2020-06-01 08:12:42 +0200},
Journal = {J. Chem. Phys.},
Pages = {104103},
Title = {Benchmarks for Electronically Excited States: Time-Dependent Density Functional Theory and Density Functional Theory Based Multireference Configuration Interaction},

93
BSEdyn.tex
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@ -251,7 +251,7 @@ and they are, moreover, a real challenge for high-level computational methods. \
Double excitations play also a significant role in the correct location of the excited states of polyenes that are closely related to rhodopsin which is involved in the visual transduction. \cite{Olivucci_2010,Robb_2007,Manathunga_2016}
In butadiene, for example, while the bright $1 ^1B_u$ state has a clear $\HOMO \ra \LUMO$ single-excitation character, the dark $2 ^1A_g$ state includes a substantial fraction of doubly-excited character from the $\HOMO^2 \ra \LUMO^2$ double excitation (roughly $30\%$), yet dominant contributions from the $\HOMO-1 \ra \LUMO$ and $\HOMO \ra \LUMO+1$ single excitations. \cite{Maitra_2004,Cave_2004,Saha_2006,Watson_2012,Shu_2017,Barca_2018a,Barca_2018b,Loos_2019}
Going beyond the static approximation is tricky and very few groups have dared to take the plunge. \cite{Strinati_1988,Rohlfing_2000,Sottile_2003,Ma_2009a,Ma_2009b,Romaniello_2009b,Sangalli_2011,Huix-Rotllant_2011,Zhang_2013,Rebolini_2016,Olevano_2019,Lettmann_2019}
Going beyond the static approximation is tricky and very few groups have dared to take the plunge. \cite{Strinati_1988,Rohlfing_2000,Sottile_2003,Myohanen_2008,Ma_2009a,Ma_2009b,Romaniello_2009b,Sangalli_2011,Huix-Rotllant_2011,Sakkinen_2012,Zhang_2013,Rebolini_2016,Olevano_2019,Lettmann_2019}
Nonetheless, it is worth mentioning the seminal work of Strinati on core excitons in semiconductors, \cite{Strinati_1982,Strinati_1984,Strinati_1988} in which the dynamical screening effects were taken into account through the dielectric matrix, and where he observed an increase of the binding energy over its value for static screening and a narrowing of the Auger width below its value for a core hole.
Following Strinati's footsteps, Rohlfing and coworkers have developed an efficient way of taking into account, thanks to first-order perturbation theory, the dynamical effects via a plasmon-pole approximation combined with the Tamm-Dancoff approximation (TDA). \cite{Rohlfing_2000,Ma_2009a,Ma_2009b,Baumeier_2012b}
With such a scheme, they have been able to compute the excited states of biological chromophores, showing that taking into account the electron-hole dynamical screening is important for an accurate description of the lowest $n \ra \pi^*$ excitations. \cite{Ma_2009a,Ma_2009b,Baumeier_2012b}
@ -785,7 +785,7 @@ All the BSE calculations have been performed with the $GW$ software, \texttt{QuA
& & \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{$Z_{s}$}
& \tabc{CIS(D)} & \tabc{ADC(2)} & \tabc{CCSD} & \tabc{CC2} & \tabc{CC3} \\
& \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
@ -793,63 +793,62 @@ All the BSE calculations have been performed with the $GW$ software, \texttt{QuA
% & 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
& 7.62 & 7.18 & 7.60 & 7.23 & 7.65 \\
& 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
& 9.41 & 8.84 & 9.36 & 8.89 & 9.43 \\
& 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
& 9.99 & 9.52 & 9.96 & 9.58 & 10.00 \\
& 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
& 9.66 & 9.48 & 9.41 & 9.44 & 9.34 \\
% & 9.23 & \\
& $^1\Sigma_u^-(\pi \ra \pis)$ & & 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
& 10.85 & 10.79 & 10.44 & 10.86 & 10.29 \\
& $^1\Sigma_g^+$(R) & & 13.60 & 13.57 & -0.03 & 1.003
& 13.67 & 12.99 & 13.15 & 12.83 & 13.01 \\
& 13.67 & 12.99 & 13.15 & 12.83 & 12.98 \\
& $^1\Pi_u$(R) & & 13.98 & 13.94 & -0.04 & 1.004
& 13.64 & 13.32 & 13.43 & 13.15 & 13.22 \\
& 13.64 & 13.32 & 13.43 & 13.15 & 13.03 \\
& $^1\Sigma_u^+$(R) & & 13.98 & 13.91 & -0.07 & 1.008
& 13.75 & 13.07 & 13.26 & 12.89 & 13.12 \\
& 13.75 & 13.07 & 13.26 & 12.89 & 13.09 \\
& $^1\Pi_u$(R) & & 14.24 & 14.21 & -0.03 & 1.002
& 14.52 & 14.00 & 13.67 & 13.96 & 13.49 \\
& 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 & 9.99 \\
& $^1\Delta(\pi \ra \pis)$ & & 10.71 & 10.39 & -0.32 & 1.023 & 10.41 & 10.30 & 10.12 & 10.60 & 10.12 \\
& $^1\Sigma^+$(R) & & 11.88 & 11.85 & -0.03 & 1.005 & 11.48 & 11.32 & 11.22 & 11.11 & 10.94 \\
& $^1\Sigma^+$(R) & & 12.39 & 12.37 & -0.02 & 1.003 & 11.71 & 11.83 & 11.75 & 11.63 & 11.49 \\
& $^1\Pi$(R) & & 12.37 & 12.32 & -0.05 & 1.004 & 12.06 & 12.03 & 11.96 & 11.83 & 11.69 \\
& $^1\Sigma^-(\pi \ra \pis)$ & & 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{HNO} & $^1A''(n \ra \pis)$ & 11.71 & 2.46 & 1.98 & -0.48 & 1.035
& 1.80 & 1.68 & 1.76 & 1.74 & 1.75 \\
& 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
& 5.81 & 5.73 & 6.30 & 5.72 & 6.26 \\
& 5.81 & 5.73 & 6.30 & 5.72 & 6.27 \\
% & 5.63 & 5.85 & 6.22 & 5.94 & 6.33 \\
\\
%T2: check state ordering in BSE calculation
\ce{C2H4} & $^1B_{3u}(\pi \ra 3s)$ & 11.49 & 7.64 & 7.62 & -0.03 & 1.004
& 7.35 & 7.34 & 7.42 & 7.29 & 7.35 \\
& 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
& 7.95 & 7.91 & 8.02 & 7.92 & 7.91 \\
& 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
& 8.01 & 7.99 & 8.08 & 7.95 & 8.03 \\
& 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 & 3.97 \\
& $^1B_2(n \ra 3s)$ & & 7.87 & 7.85 & -0.02 & 1.001 & 6.64 & 6.50 & 7.23 & 6.56 & 7.18 \\
& $^1B_2(n \ra 3p)$ & & 8.76 & 8.72 & -0.04 & 1.003 & 7.56 & 7.53 & 8.12 & 7.57 & 8.07 \\
& $^1A_1(n \ra 3p)$ & & 8.85 & 8.84 & -0.01 & 1.000 & 8.16 & 7.47 & 8.21 & 7.52 & 8.18 \\
& $^1A_2(n \ra 3p)$ & & 8.87 & 8.85 & -0.02 & 1.002 & 8.04 & 7.99 & 8.65 & 8.04 & 8.64 \\
& $^1B_1(\si \ra \pis)$ & & 10.18 & 9.77 & -0.42 & 1.032 & 9.38 & 9.17 & 9.28 & 9.32 & 9.19 \\
& $^1A_1(\pi \ra \pis)$ & & 10.05 & 9.81 & -0.24 & 1.026 & 9.08 & 9.46 & 9.67 & 9.54 & 9.48 \\
\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 \\
\end{tabular}
\end{ruledtabular}
\end{table*}
@ -868,53 +867,53 @@ All the BSE calculations have been performed with the $GW$ software, \texttt{QuA
& & \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{$Z_{s}$}
& \tabc{CIS(D)} & \tabc{ADC(2)} & \tabc{CCSD} & \tabc{CC2} & \tabc{CC3} \\
& \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
& 7.25 & 6.86 & 7.20 & 6.91 & 7.28 \\
& 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
& 9.24 & 8.72 & 9.20 & 8.77 & 9.26 \\
& 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
& 9.54 & 9.15 & 9.49 & 9.20 & 9.56 \\
& 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 & 7.68 \\
& $^3\Pi_g(n \ra \pis)$ & & 9.85 & 9.27 & -0.58 & 1.050 & 8.33 & 8.20 & 8.09 & 8.19 & 8.04 \\
\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 & 9.68 \\
& $^3\Sigma_u^-(\pi \ra \pis)$ & & 10.89 & 10.06 & -0.82 & 1.058 & 10.29 & 10.23 & 9.83 & 10.29 & 9.66 \\
\\
\ce{CO} & $^3\Pi(n \ra \pis)$ & 16.46 & 8.10 & 7.33 & -0.77 & 1.055 & 6.51 & 6.45 & 6.36 & 6.42 & 6.30 \\
\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 & 9.30 \\
& $^3\Sigma_u^-(\pi \ra \pis)$ & & 10.79 & 10.38 & -0.42 & 1.034 & 10.10 & 10.01 & 9.81 & 10.27 & 9.82 \\
& $^3\Sigma_u^+$(R) & & 11.48 & 11.38 & -0.10 & 1.010 & 10.98 & 10.83 & 10.71 & 10.60 & 10.45 \\
& $^3\Delta(\pi \ra \pis)$ & & 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{HNO} & $^3A''(n \ra \pis)$ & 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
& 5.72 & 5.46 & 5.49 & 5.44 & 5.59 \\
& 5.72 & 5.46 & 5.49 & 5.44 & 5.61 \\
% & 4.73 & 4.46 & 5.27 & 4.55 & 4.57 \\
\\
\ce{C2H4} & $^3B_{1u}(\pi \ra \pis)$ & 11.49 & 6.54 & 5.85 & -0.69 & 1.065
& 4.62 & 4.59 & 4.46 & 4.59 & 4.53 \\
& 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
& 7.26 & 7.23 & 7.29 & 7.19 & 7.24 \\
& 7.26 & 7.23 & 7.29 & 7.19 & 7.23 \\
% & 6.54 & 6.74 & 6.90 & 6.83 & 7.41 \\
& $^3B_{1g}(\pi \ra 3p)$ & & 8.34 & 8.31 & -0.03 & 1.003
& 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 & 3.57 \\
& $^3A_1(\pi \ra \pis)$ & & 8.15 & 7.32 & -0.83 & 1.067 & 6.27 & 6.20 & 5.97 & 6.30 & 6.05 \\
& $^3B_2(n \ra 3s)$ & & 7.51 & 7.54 & 0.03 & 0.994 & 6.66 & 6.39 & 7.08 & 6.44 & 7.03 \\
& $^3B_2(n \ra 3p)$ & & 8.62 & 8.61 & -0.00 & 0.998 & 7.52 & 7.41 & 7.94 & 7.45 & 7.92 \\
& $^3A_1(n \ra 3p)$ & & 8.75 & 8.69 & -0.06 & 1.007 & 7.68 & 7.40 & 8.09 & 7.44 & 8.08 \\
& $^3B_1(n \ra 3d)$ & & 8.82 & 8.82 & -0.01 & 1.000 & 8.57 & 8.39 & 8.43 & 8.52 & 8.41 \\
\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 \\
& $^3B_2(n \ra 3p)$ & & 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*}