From f61c78f3bd909e4df4b4f8df3766ad08550146db Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Mon, 1 Jun 2020 22:42:36 +0200 Subject: [PATCH] TBE --- BSEdyn.bib | 34 +++++++++++++++++--- BSEdyn.tex | 93 +++++++++++++++++++++++++++--------------------------- 2 files changed, 75 insertions(+), 52 deletions(-) diff --git a/BSEdyn.bib b/BSEdyn.bib index 8eaaf75..bd9eb90 100644 --- a/BSEdyn.bib +++ b/BSEdyn.bib @@ -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}, diff --git a/BSEdyn.tex b/BSEdyn.tex index 6d0fcb8..5e5b07d 100644 --- a/BSEdyn.tex +++ b/BSEdyn.tex @@ -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*}