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C2H4

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Pierre-Francois Loos 2020-05-21 14:08:14 +02:00
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BSEdyn.tex
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@ -627,11 +627,10 @@ Although it might be reduced to $\order*{\Norb^4}$ operations with standard reso
All systems under investigation have close-shell singlet ground states. All systems under investigation have close-shell singlet ground states.
We then adopt a restricted formalism throughout this work. We then adopt a restricted formalism throughout this work.
The $GW$ calculations performed to obtain the screened Coulomb operator and the quasiparticle energies are done using a (restricted) HF starting point. The $GW$ calculations performed to obtain the screened Coulomb operator and the quasiparticle energies are done using a (restricted) HF starting point.
Perturbative $GW$ (or {\GOWO}) \cite{Hybertsen_1985a, Hybertsen_1986} and partially self-consistent ev$GW$ \cite{Hybertsen_1986,Shishkin_2007,Blase_2011,Faber_2011}calculations are employed as starting points to compute the BSE neutral excitations. Perturbative $GW$ (or {\GOWO}) \cite{Hybertsen_1985a, Hybertsen_1986} quasiparticle energies are employed as starting points to compute the BSE neutral excitations.
For both {\GOWO} and {\evGW}, the entire set of orbitals are corrected. For both {\GOWO} and {\evGW}, the entire set of orbitals are corrected.
In the case of {\GOWO}, the quasiparticle energies are obtained by linearizing the frequency-dependent quasiparticle equation. In the case of {\GOWO}, the quasiparticle energies are obtained by linearizing the frequency-dependent quasiparticle equation.
For ev$GW$, the convergence criterion has been set to $10^{-5}$. Further details about our implementation of {\GOWO} can be found in Refs.~\onlinecite{Loos_2018b,Veril_2018}.
Further details about our implementation of {\GOWO} and {\evGW} can be found in Refs.~\onlinecite{Loos_2018b,Veril_2018}.
As one-electron basis sets, we employ the augmented Dunning family (aug-cc-pVXZ) defined with cartesian Gaussian functions. As one-electron basis sets, we employ the augmented Dunning family (aug-cc-pVXZ) defined with cartesian Gaussian functions.
Finally, the infinitesimal $\eta$ is set to $100$ meV for all calculations. Finally, the infinitesimal $\eta$ is set to $100$ meV for all calculations.
@ -685,48 +684,47 @@ All the BSE calculations have been performed with our locally developed $GW$ sof
\label{tab:BigTabSi} \label{tab:BigTabSi}
} }
\begin{ruledtabular} \begin{ruledtabular}
\begin{tabular}{llddddddddddddddd} \begin{tabular}{lldddddddddd}
& & \mc{5}{c}{BSE@{\GOWO}@HF} & \mc{5}{c}{BSE@{\evGW}@HF} \\ & & \mc{5}{c}{BSE@{\GOWO}@HF} \\
\cline{3-7} \cline{8-12} \cline{3-7}
Mol. & State & \tabc{$\Eg^{\GW}$} & \tabc{$\Om{m}{\stat}$} & \tabc{$\Om{m}{\dyn}$} & \tabc{$\Delta\Om{m}{\dyn}$} & \tabc{$Z_{m}$} Mol. & State & \tabc{$\Eg^{\GW}$} & \tabc{$\Om{m}{\stat}$} & \tabc{$\Om{m}{\dyn}$} & \tabc{$\Delta\Om{m}{\dyn}$} & \tabc{$Z_{m}$}
& \tabc{$\Eg^{\GW}$} & \tabc{$\Om{m}{\stat}$} & \tabc{$\Om{m}{\dyn}$} & \tabc{$\Delta\Om{m}{\dyn}$} & \tabc{$Z_{m}$}
& \tabc{CIS(D)} & \tabc{ADC(2)} & \tabc{CCSD} & \tabc{CC2} & \tabc{CC3} \\ & \tabc{CIS(D)} & \tabc{ADC(2)} & \tabc{CCSD} & \tabc{CC2} & \tabc{CC3} \\
\hline \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 \\ \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} & $^1B_1(n \ra 3s)$ & 13.58 & 8.09 & 8.00 & -0.09 & 1.007 & & & & & & 7.62 & 7.18 & 7.60 & 7.23 & 7.65 \\ \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 \\
& $^1A_2(n \ra 3p)$ & & 9.79 & 9.72 & -0.07 & 1.005 & & & & & & 9.41 & 8.84 & 9.36 & 8.89 & 9.43 \\ & $^1A_2(n \ra 3p)$ & & 9.79 & 9.72 & -0.07 & 1.005 & 9.41 & 8.84 & 9.36 & 8.89 & 9.43 \\
& $^1A_1(n \ra 3s)$ & & 10.42 & 10.35 & -0.07 & 1.006 & & & & & & 9.99 & 9.52 & 9.96 & 9.58 & 10.00 \\ & $^1A_1(n \ra 3s)$ & & 10.42 & 10.35 & -0.07 & 1.006 & 9.99 & 9.52 & 9.96 & 9.58 & 10.00 \\
\\ \\
\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 \\ \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 \\
& $^1\Sigma_u^-(\pi \ra \pis)$ & & 10.11 & 9.66 & -0.45 & 1.029 & & & & & & 10.31 & 10.26 & 10.00 & 10.32 & 9.88 \\ & $^1\Sigma_u^-(\pi \ra \pis)$ & & 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 \\ & $^1\Delta_u(\pi \ra \pis)$ & & 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 \\ & $^1\Sigma_g^+$(R) & & 13.60 & 13.57 & -0.03 & 1.003 & 13.67 & 12.99 & 13.15 & 12.83 & 13.01 \\
& $^1\Pi_u$(R) & & 13.98 & 13.94 & -0.04 & 1.004 & & & & & & 13.64 & 13.32 & 13.43 & 13.15 & 13.22 \\ & $^1\Pi_u$(R) & & 13.98 & 13.94 & -0.04 & 1.004 & 13.64 & 13.32 & 13.43 & 13.15 & 13.22 \\
& $^1\Sigma_u^+$(R) & & 13.98 & 13.91 & -0.07 & 1.008 & & & & & & 13.75 & 13.07 & 13.26 & 12.89 & 13.12 \\ & $^1\Sigma_u^+$(R) & & 13.98 & 13.91 & -0.07 & 1.008 & 13.75 & 13.07 & 13.26 & 12.89 & 13.12 \\
& $^1\Pi_u$(R) & & 14.24 & 14.21 & -0.03 & 1.002 & & & & & & 14.52 & 14.00 & 13.67 & 13.96 & 13.49 \\ & $^1\Pi_u$(R) & & 14.24 & 14.21 & -0.03 & 1.002 & 14.52 & 14.00 & 13.67 & 13.96 & 13.49 \\
\\ \\
\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 \\ \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 \\ & $^1\Sigma^-(\pi \ra \pis)$ & & 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 \\ & $^1\Delta(\pi \ra \pis)$ & & 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) & & 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 \\ & $^1\Sigma^+$(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 \\ & $^1\Pi$(R) & & 12.37 & 12.32 & -0.05 & 1.004 & 12.06 & 12.03 & 11.96 & 11.83 & 11.69 \\
\\ \\
\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 \\ \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 \\
& $^1A'$(R) & & 7.05 & 7.01 & -0.037 & 1.003 & & & & & & 5.81 & 5.73 & 6.30 & 5.72 & 6.26 \\ & $^1A'$(R) & & 7.05 & 7.01 & -0.037 & 1.003 & 5.81 & 5.73 & 6.30 & 5.72 & 6.26 \\
\\ \\
\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 \\ \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 \\
& $^1B_{1u}(\pi \ra \pis)$ & & 8.18 & 8.03 & -0.15 & 1.022 & & & & & & 7.95 & 7.91 & 8.02 & 7.92 & 7.91 \\ & $^1B_{1u}(\pi \ra \pis)$ & & 8.18 & 8.03 & -0.15 & 1.022 & 7.95 & 7.91 & 8.02 & 7.92 & 7.91 \\
& $^1B_{1g}(\pi \ra 3p)$ & & 8.29 & 8.26 & -0.03 & 1.003 & & & & & & 8.01 & 7.99 & 8.08 & 7.95 & 8.03 \\ & $^1B_{1g}(\pi \ra 3p)$ & & 8.29 & 8.26 & -0.03 & 1.003 & 8.01 & 7.99 & 8.08 & 7.95 & 8.03 \\
\\ \\
\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 \\ \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 \\ & $^1B_2(n \ra 3s)$ & & 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 \\ & $^1B_2(n \ra 3p)$ & & 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 \\ & $^1A_1(n \ra 3p)$ & & 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 \\ & $^1A_2(n \ra 3p)$ & & 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 \\ & $^1B_1(\si \ra \pis)$ & & 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 \\ & $^1A_1(\pi \ra \pis)$ & & 10.05 & 9.81 & -0.24 & 1.026 & 9.08 & 9.46 & 9.67 & 9.54 & 9.48 \\
\end{tabular} \end{tabular}
\end{ruledtabular} \end{ruledtabular}
\end{table*} \end{table*}
@ -739,41 +737,40 @@ All the BSE calculations have been performed with our locally developed $GW$ sof
\label{tab:BigTabTr} \label{tab:BigTabTr}
} }
\begin{ruledtabular} \begin{ruledtabular}
\begin{tabular}{llddddddddddddddd} \begin{tabular}{lldddddddddd}
& & \mc{5}{c}{BSE@{\GOWO}@HF} & \mc{5}{c}{BSE@{\evGW}@HF} \\ & & \mc{5}{c}{BSE@{\GOWO}@HF} \\
\cline{3-7} \cline{8-12} \cline{3-7}
Mol. & State & \tabc{$\Eg^{\GW}$} & \tabc{$\Om{m}{\stat}$} & \tabc{$\Om{m}{\dyn}$} & \tabc{$\Delta\Om{m}{\dyn}$} & \tabc{$Z_{m}$} Mol. & State & \tabc{$\Eg^{\GW}$} & \tabc{$\Om{m}{\stat}$} & \tabc{$\Om{m}{\dyn}$} & \tabc{$\Delta\Om{m}{\dyn}$} & \tabc{$Z_{m}$}
& \tabc{$\Eg^{\GW}$} & \tabc{$\Om{m}{\stat}$} & \tabc{$\Om{m}{\dyn}$} & \tabc{$\Delta\Om{m}{\dyn}$} & \tabc{$Z_{m}$}
& \tabc{CIS(D)} & \tabc{ADC(2)} & \tabc{CCSD} & \tabc{CC2} & \tabc{CC3} \\ & \tabc{CIS(D)} & \tabc{ADC(2)} & \tabc{CCSD} & \tabc{CC2} & \tabc{CC3} \\
\hline \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 \\ \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 \\
& $^3A_2(n \ra 3p)$ & & 9.97 & 9.89 & -0.07 & 1.008 & & & & & & 9.24 & 8.72 & 9.20 & 8.77 & 9.26 \\ & $^3A_2(n \ra 3p)$ & & 9.97 & 9.89 & -0.07 & 1.008 & 9.24 & 8.72 & 9.20 & 8.77 & 9.26 \\
& $^3A_1(n \ra 3s)$ & & 10.28 & 10.13 & -0.15 & 1.012 & & & & & & 9.54 & 9.15 & 9.49 & 9.20 & 9.56 \\ & $^3A_1(n \ra 3s)$ & & 10.28 & 10.13 & -0.15 & 1.012 & 9.54 & 9.15 & 9.49 & 9.20 & 9.56 \\
\\ \\
\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 \\ \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 \\ & $^3\Pi_g(n \ra \pis)$ & & 9.85 & 9.27 & -0.58 & 1.050 & 8.33 & 8.20 & 8.09 & 8.19 & 8.04 \\
& $^3\Delta_u(\pi \ra \pis)$ & & 10.19 & 9.24 & -0.95 & 1.060 & & & & & & 9.30 & 9.25 & 8.91 & 9.30 & 8.87 \\ & $^3\Delta_u(\pi \ra \pis)$ & & 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 & 9.68 \\
\\ \\
\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 & 6.30 \\
& $^3\Sigma^+(\pi \ra \pis)$ & & 9.61 & 9.04 & -0.57 & 1.037 & & & & & & 8.63 & 8.54 & 8.34 & 8.72 & 8.45 \\ & $^3\Sigma^+(\pi \ra \pis)$ & & 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 \\ & $^3\Delta(\pi \ra \pis)$ & & 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 \\ & $^3\Sigma_u^-(\pi \ra \pis)$ & & 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 \\ & $^3\Sigma_u^+$(R) & & 11.48 & 11.38 & -0.10 & 1.010 & 10.98 & 10.83 & 10.71 & 10.60 & 10.45 \\
\\ \\
\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 \\ \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 \\
& $^3A'(\pi \ra \pis)$ & & 6.69 & 6.70 & 0.01 & 1.000 & & & & & & 5.72 & 5.46 & 5.49 & 5.44 & 5.59 \\ & $^3A'(\pi \ra \pis)$ & & 6.69 & 6.70 & 0.01 & 1.000 & 5.72 & 5.46 & 5.49 & 5.44 & 5.59 \\
\\ \\
\ce{C2H4} & $^3B_{1u}(\pi \ra \pis)$ & 11.49 & 6.54 & & & & & & & & & 4.62 & 4.59 & 4.46 & 4.59 & 4.53 \\ \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 \\
& $^3B_{3u}(\pi \ra 3s)$ & & 7.61 & & & & & & & & & 7.26 & 7.23 & 7.29 & 7.19 & 7.24 \\ & $^3B_{3u}(\pi \ra 3s)$ & & 7.61 & 7.55 & -0.06 & 1.008 & 7.26 & 7.23 & 7.29 & 7.19 & 7.24 \\
& $^3B_{1g}(\pi \ra 3p)$ & & 8.34 & & & & & & & & & 7.97 & 7.95 & 8.03 & 7.91 & 7.98 \\ & $^3B_{1g}(\pi \ra 3p)$ & & 8.34 & 8.31 & -0.03 & 1.003 & 7.97 & 7.95 & 8.03 & 7.91 & 7.98 \\
\\ \\
\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 \\ \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 \\ & $^3A_1(\pi \ra \pis)$ & & 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 \\ & $^3B_2(n \ra 3s)$ & & 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 \\ & $^3B_2(n \ra 3p)$ & & 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 \\ & $^3A_1(n \ra 3p)$ & & 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 \\ & $^3B_1(n \ra 3d)$ & & 8.82 & 8.82 & -0.01 & 1.000 & 8.57 & 8.39 & 8.43 & 8.52 & 8.41 \\
\end{tabular} \end{tabular}
\end{ruledtabular} \end{ruledtabular}
\end{table*} \end{table*}