From e58852aff0379c04cfb3bae125eeda8a6e9c1488 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Wed, 16 Mar 2022 17:19:37 +0100 Subject: [PATCH] sup --- Manuscript/CASPT3.tex | 840 +-------------------------------- Manuscript/sup_CASPT3.tex | 943 ++++++++++++++++++++++++++++++++++++++ 2 files changed, 948 insertions(+), 835 deletions(-) create mode 100644 Manuscript/sup_CASPT3.tex diff --git a/Manuscript/CASPT3.tex b/Manuscript/CASPT3.tex index 9716d25..44f7224 100644 --- a/Manuscript/CASPT3.tex +++ b/Manuscript/CASPT3.tex @@ -140,7 +140,11 @@ Third-order version have been developed but rarely used and accuracy still need Pioneering work along these lines is due to Werner which develops a CASPT3 code in MOLPRO \cite{Werner_2020} based on a hack of the MRCI module. \cite{Werner_1996} There is also the NEVPT3 method of Angeli and coworkers. \cite{Angeli_2006} - +\begin{figure} + \includegraphics[width=\linewidth,viewport=1.cm 10cm 18cm 27cm,clip]{mol.pdf} + \caption{Various molecular systems considered in this study. + \label{fig:mol}} +\end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Computational details} @@ -149,840 +153,6 @@ There is also the NEVPT3 method of Angeli and coworkers. \cite{Angeli_2006} All the CASPT2 and CASPT3 calculations have been carried out with MOLPRO within the RS2 and RS3 schemes. \cite{Werner_2020} Both methods have been tested with and without IPEA (labeled as NOIPEA). -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of acetaldehyde.} - \label{tab:acetaldehyde} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a',a'')$ & $(A',A'')$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline -$^1A''(n,\pis)$ &(3,2) &(1,1) &4.62$^a$ &4.35$^a$ &4.13$^a$ &4.44$^a$ &4.41$^a$ &4.31\\ -$^3A''(n,\pis)$ &(3,2) &(1,1) &4.28$^a$ &3.94$^a$ &3.71$^a$ &4.06$^a$ &4.03$^a$ &3.97\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Reference (6e,5o) active space including valence $\nO$, $\piCO$, $\sigCO$, $\pisCO$ and $\sigsCO$ orbitals. -\end{table*} - - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of acetone.} - \label{tab:acetone} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State &Active space &State-average &CASSCF &CASPT2 &CASPT2 &CASPT3 &CASPT3 &TBE \\ - &$(a_1,b_1,b_2,a_2)$ &$(A_1,B_1,B_2,A_2)$ & &IPEA &NOIPEA &IPEA &NOIPEA & \\ - \hline - $^1A_2(n,\pis)$ &(2,3,1,0) &(1,0,0,2) &4.77$^a$ &4.44$^a$ &4.19$^a$ &4.57$^a$ &4.55$^a$ &4.47\\ - $^1B_2(n,3s)$ &(4,2,1,0) &(1,0,2,0) &5.50$^b$ &6.46$^b$ &6.35$^b$ &6.64$^b$ &6.67$^b$ &6.46\\ - $^1A_2(n,3p_x)$ &(2,3,1,0) &(1,0,0,2) &7.46$^a$ &7.80$^a$ &7.55$^a$ &7.76$^a$ &7.68$^a$ &7.47\\ - $^1A_1(n,3p_y)$ &(2,2,2,0) &(2,0,0,0) &7.03$^c$ &7.67$^c$ &7.46$^c$ &7.76$^c$ &7.75$^c$ &7.51\\ - $^1B_2(n,3p_z)$ &(4,2,1,0) &(1,0,2,0) &6.44$^b$ &7.56$^b$ &7.47$^b$ &7.73$^b$ &7.76$^b$ &7.62\\ - $^3A_2(n,\pis)$ &(2,2,1,0) &(1,0,0,1) &4.47$^d$ &4.13$^d$ &3.89$^d$ &4.27$^d$ &4.24$^d$ &4.13\\ - $^3A_1(\pi,\pis)$ &(2,2,0,0) &(2,0,0,0) &6.22$^e$ &6.24$^e$ &6.07$^e$ &6.26$^e$ &6.22$^e$ &6.25\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Using reference (6e,6o) active space including valence $\pi$, $\nO$, $\sigCO$, $\sigsCO$ and $3p_x$ orbitals. - $^b$Using reference (6e,7o) active space including valence $\pi$, $\nO$, $\sigCO$, $\sigsCO$, $3s$ and $3p_z$ orbitals. - $^c$Using reference (6e,6o) active space including valence $\pi$, $\nO$, $\sigCO$, $\sigsCO$ and $3p_y$ orbitals. - $^d$Using reference (6e,5o) active space including valence $\pi$, $\nO$, $\sigCO$ and $\sigsCO$ orbitals. - $^e$Using reference (4e,4o) active space including valence $\pi$, $\sigCO$, $\sigsCO$ orbitals. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of acrolein.} - \label{tab:acrolein} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a',a'')$ & $(A',A'')$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1A''(n,\pis)$ &(1,5) &(1,3) &3.48$^c$ &3.58$^c$ &3.46$^c$ &3.66$^c$ &3.66$^c$ &3.78\\ - $^1A'(\pi,\pis)$ &(2,4) &(4,0) &8.84$^d$ &6.93$^d$ &6.28$^d$ &7.18$^d$ &7.05$^d$ &6.69\\ - $^1A''(n,\pis)$ &(1,5) &(1,3) &6.76$^{c,e}$&6.79$^{a,e}$&6.34$^{a,e}$&6.88$^{a,e}$&6.80$^{a,e}$&6.72\\ - $^1A'(n,3s)$ &(2,4) &(4,0) &7.20$^d$ &7.21$^d$ &6.98$^d$ &7.20$^d$ &7.16$^d$ &7.08\\ - $^1A'(\pi^2,\pis^2)$&(2,4) &(4,0) &7.91$^d$ &8.10$^d$ &7.75$^d$ &8.02$^d$ &7.95$^d$ &7.87\\ - $^3A''(n,\pis)$ &(1,5) &(1,3) &3.25$^c$ &3.28$^c$ &3.15$^c$ &3.39$^c$ &3.40$^c$ &3.51\\ - $^3A'(\pi,\pis)$ &(2,4) &(4,0) &3.89$^d$ &4.01$^d$ &3.78$^d$ &3.96$^d$ &3.91$^d$ &3.94\\ - $^3A'(\pi,\pis)$ &(2,4) &(4,0) &5.89$^d$ &6.20$^d$ &5.93$^d$ &6.10$^d$ &6.02$^d$ &6.18\\ - $^3A''(n,\pis)$ &(1,5) &(1,3) &6.67$^{c,e}$&6.65$^{c,e}$&6.21$^{c,e}$&6.74$^{c,e}$&6.66$^{c,e}$&6.54\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Using reference (12e,12o) active space including valence $\pi$, $\sigCC$, $\sigsCO$, $\sigsCC$, $\sigsCO$, $\nO$ and $3s$ orbitals. - $^b$Level shift det to \SI{0.4}{\hartree}. - $^c$Using reference (6e,6o) active space including valence $\pi$, $\nO$ and $3p_z$ orbitals. - $^d$Using reference (6e,6o) active space including valence $\pi$, $\nO$ and $3s$ orbitals. - $^e$Substantial Rydberg and doubly-excited character. - $^f$Substantial doubly-excited character. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of benzene.} - \label{tab:benzene} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_g,b_{3u},b_{2u},b_{1g},b_{1u},b_{2g},b_{3g},a_u)$ & $(A_g,B_{3u},B_{2u},B_{1g},B_{1u},B_{2g},B_{3g},A_u)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1B_{2u}(\pi,\pis)$ &(0,0,0,0,2,1,2,1) &(1,1,0,0,0,0,0,0) &4.98$^a$ &5.14$^a$ &4.66$^a$ &5.09$^a$ &5.01$^a$ &5.06\\ - $^1B_{1u}(\pi,\pis)$ &(0,0,0,0,4,1,2,2) &(1,1,2,0,0,0,0,0) &7.27$^b$ &6.65$^b$ &6.23$^b$ &6.67$^b$ &6.58$^b$ &6.45\\ - $^1E_{1g}(\pi,3s)$ &(1,0,0,0,2,1,2,1) &(1,0,0,0,0,1,1,0) &5.90$^c$ &6.70$^c$ &6.57$^c$ &6.56$^c$ &6.51$^c$ &6.52\\ - $^1A_{2u}(\pi,3p_{x,y})$ &(0,1,1,0,2,1,2,1) &(1,0,0,0,2,0,0,1) &6.14$^d$ &7.21$^d$ &7.07$^d$ &7.07$^d$ &7.02$^d$ &7.08\\ - $^1E_{2u}(\pi,3p_{x,y})$ &(0,1,1,0,2,1,2,1) &(1,0,0,0,2,0,0,1) &6.21$^d$ &7.26$^d$ &7.12$^d$ &7.13$^d$ &7.08$^d$ &7.15\\ - $^1E_{2g}(\pi^2,\pis^2)$ &(0,0,0,0,2,1,2,1) &(2,0,0,1,0,0,0,0) &8.10$^a$ &8.31$^a$ &7.82$^{a,e}$ &8.26$^a$ &8.16$^{a,e}$ &8.28\\ - $^3B_{1u}(\pi,\pis)$ &(0,0,0,0,4,1,2,2) &(1,0,1,0,0,0,0,0) &3.85$^b$ &4.22$^b$ &3.92$^b$ &4.14$^b$ &4.08$^b$ &4.16\\ - $^3E_{1u}(\pi,\pis)$ &(0,0,0,0,4,1,2,2) &(1,1,1,0,0,0,0,0) &4.85$^b$ &4.89$^b$ &4.51$^b$ &4.87$^b$ &4.80$^b$ &4.85\\ - $^3B_{2u}(\pi,\pis)$ &(0,0,0,0,4,1,2,2) &(1,1,0,0,0,0,0,0) &6.75$^b$ &5.85$^b$ &5.40$^b$ &5.90$^b$ &5.81$^b$ &5.81\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Using reference (6e,6o) active space including valence $\pi$ orbitals. - $^b$Using reference (6e,9o) active space including valence $\pi$ and three $3p_z$ orbitals. - $^c$Using reference (6e,7o) active space including valence $\pi$ and $3s$ orbitals. - $^d$Using reference (6e,8o) active space including valence $\pi$, $3p_x$ and $3p_y$ orbitals. - $^e$Level shift set to \SI{0.4}{\hartree}. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of butadiene.} - \label{tab:butadiene} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_g,a_u,b_u,b_g)$ & $(A_g,A_u,B_u,B_g)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1B_u(\pi,\pis)$ &(0,4,0,4) &(1,0,2,0) &6.65$^a$ &6.76$^a$ &6.52$^a$ &6.72$^a$ &6.65$^a$ &6.22\\ - $^1B_g(\pi,3s)$ &(4,2,3,2) &(1,0,0,1) &5.94$^b$ &6.49$^b$ &6.32$^b$ &6.43$^b$ &6.38$^b$ &6.33\\ - $^1A_g(\pi^2,\pis^2)$ &(3,2,3,2) &(2,0,0,0) &6.99$^c$ &6.74$^c$ &6.30$^{c,d}$ &6.73$^c$ &6.66$^{c,d}$ &6.50\\ - $^1A_u(\pi,3p_x)$ &(3,2,5,2) &(1,2,0,0) &5.95$^e$ &6.74$^e$ &6.64$^e$ &6.70$^e$ &6.67$^e$ &6.64\\ - $^1A_u(\pi,3p_y)$ &(3,2,5,2) &(1,2,0,0) &6.12$^e$ &6.95$^e$ &6.84$^e$ &6.90$^e$ &6.86$^e$ &6.80\\ - $^1B_u(\pi,3p_z)$ &(0,4,0,4) &(1,0,2,0) &7.93$^a$ &7.60$^a$ &7.30$^a$ &7.62$^a$ &7.54$^a$ &7.68\\ - $^3B_u(\pi,\pis)$ &(3,2,3,2) &(1,0,1,0) &3.55$^c$ &3.40$^c$ &3.19$^c$ &3.40$^c$ &3.35$^c$ &3.36\\ - $^3A_g(\pi,\pis)$ &(3,2,3,2) &(2,0,0,0) &5.52$^c$ &5.32$^c$ &4.93$^c$ &5.29$^c$ &5.19$^c$ &5.20\\ - $^3B_g(\pi,3s)$ &(4,2,3,2) &(1,0,0,1) &5.89$^b$ &6.44$^b$ &6.27$^b$ &6.38$^b$ &6.33$^b$ &6.29\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Using reference (4e,8o) active space including valence $\pi$ and four $3p_z$. - $^b$Using reference (10e,11o) active space including valence $\pi$, $\sigCC$, $\sigsCC$ and $3s$ orbitals. - $^c$Using reference (10e,10o) active space including valence $\pi$, $\sigCC$ and $\sigsCC$ orbitals. - $^d$Level shift set to \SI{0.4}{\hartree}. - $^e$Using reference (10e,12o) active space including valence $\pi$, $\sigCC$, $\sigsCC$, $3p_x$ and $3p_y$ orbitals. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of carbon trimer.} - \label{tab:carbon_trimer} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_g,b_{3u},b_{2u},b_{1g},b_{1u},b_{2g},b_{3g},a_u)$ & $(A_g,B_{3u},B_{2u},B_{1g},B_{1u},B_{2g},B_{3g},A_u)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $1\Delta_g(n^2,\pis^2)$ &(3,2,2,0,3,1,1,0) &(2,0,0,1,0,0,0,0) &4.98$^a$ &5.08$^a$ &4.85$^{a,b}$ &5.20$^a$ &5.19$^{a,c}$ &5.22\\ - $1\Sigma_g^+(n^2,\pis^2)$ &(3,2,2,0,3,1,1,0) &(2,0,0,0,0,0,0,0) &5.84$^a$ &5.82$^a$ &5.58$^{a,c}$ &5.92$^a$ &5.89$^{a,b}$ &5.91\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$All calculations using a full valence (12e,12o) active space. - $^b$Level shift set to \SI{0.4}{\hartree}. - $^c$Level shift set to \SI{0.5}{\hartree}. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of cyanoacetylene.$^a$} - \label{tab:cyanoacetylene} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1\Sigma^-(\pi,\pis)$ &(0,4,4,0) &(1,0,0,1) &6.54 &5.85 &5.47 &5.89 &5.81 &5.80\\ - $^1\Delta(\pi,\pis)$ &(0,4,4,0) &(2,0,0,1) &6.80 &6.13 &5.78 &6.17 &6.09 &6.07\\ - $^3\Sigma^+(\pi,\pis)$ &(0,4,4,0) &(2,0,0,0) &4.86 &4.45 &4.04 &4.52 &4.45 &4.44\\ - $^3\Delta(\pi,\pis)$ &(0,4,4,0) &(2,0,0,1) &5.64 &5.21 &4.86 &5.26 &5.19 &5.21\\ - $^1A''[F](\pi,\pis)$ &($a'$:4,$a''$:4) &($A'$:1,$A''$:1) &4.30 &3.67 &3.47 &3.64 &3.58 &3.54\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$All calculations using a full valence $\pi$ active space of (8e,8o). -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of cyanoformaldehyde.} - \label{tab:cyanoformaldehyde} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a',a'')$ & $(A',A'')$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1A''(n,\pis)$ &(3,4) &(1,2) &4.02$^a$ &3.98$^a$ &3.67$^a$ &3.94$^a$ &3.89$^a$ &3.81\\ - $^1A''(\pi,\pis)$ &(3,4) &(1,2) &7.61$^a$ &6.79$^a$ &6.43$^a$ &6.77$^a$ &6.67$^a$ &6.46\\ - $^3A''(n,\pis)$ &(3,4) &(1,1) &3.52$^a$ &3.46$^a$ &3.25$^a$ &3.51$^a$ &3.50$^a$ &3.44\\ - $^3A'(\pi,\pis)$ &(2,4) &(2,0) &4.98$^b$ &5.25$^b$ &5.03$^b$ &5.16$^b$ &5.12$^b$ &5.01\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Using reference (8e,7o) active space including valence $\pi$ and $\nO$ orbitals. - $^b$Using reference (6e,6o) active space including valence $\pi$ orbitals. -\end{table*} - - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of cyanogen.$^a$} - \label{tab:cyanogen} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_g,b_{3u},b_{2u},b_{1g},b_{1u},b_{2g},b_{3g},a_u)$ & $(A_g,B_{3u},B_{2u},B_{1g},B_{1u},B_{2g},B_{3g},A_u)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1\Sigma_u^-(\pi,\pis)$ &(0,2,2,0,0,2,2,0) &(1,0,0,0,0,0,0,1) &7.14 &6.40 &6.03 &6.46 &6.39 &6.39\\ - $^1\Delta_u(\pi,\pis)$ &(0,2,2,0,0,2,2,0) &(1,0,0,0,1,0,0,1) &7.46 &6.70 &6.35 &6.75 &6.68 &6.66\\ - $^3\Sigma_u^+(\pi,\pis)$ &(0,2,2,0,0,2,2,0) &(1,0,0,0,1,0,0,0) &5.28 &4.85 &4.46 &4.95 &4.89 &4.91\\ - $^1\Sigma_u^-[F](\pi,\pis)$ &(0,2,2,0,0,2,2,0) &(1,0,0,0,0,0,0,1) &5.68 &5.07 &4.75 &5.11 &5.04 &5.05\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$All calculations using a full valence $\pi$ active space of (8e,8o). -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of cyclopentadiene.} - \label{tab:cyclopentadiene} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1B_2(\pi,\pis)$ &(0,4,0,2) &(1,0,2,0) &6.71$^a$ &5.96$^a$ &5.62$^a$ &6.06$^a$ &5.99$^a$ &5.56\\ - $^1A_2(\pi,3s)$ &(2,2,0,2) &(1,0,0,2) &5.21$^b$ &5.88$^b$ &5.78$^b$ &5.81$^b$ &5.77$^b$ &5.78\\ - $^1B_1(\pi,3p_y)$ &(0,2,1,2) &(1,1,0,0) &6.08$^c$ &6.59$^c$ &6.44$^c$ &6.47$^c$ &6.41$^c$ &6.41\\ - $^1A_2(\pi,3p_z)$ &(2,2,0,2) &(1,0,0,2) &5.78$^b$ &6.55$^b$ &6.46$^b$ &6.45$^b$ &6.41$^b$ &6.46\\ - $^1B_2(\pi,3p_x)$ &(0,4,0,2) &(1,0,2,0) &6.16$^a$ &6.72$^a$ &6.56$^a$ &6.61$^a$ &6.54$^a$ &6.56\\ - $^1A_1(\pi,\pis)$ &(0,2,0,2) &(3,0,0,0) &6.49$^{d,e}$ &6.63$^{d,e}$ &6.13$^{d,e}$ &6.59$^{d,e}$ &6.50$^{d,e}$ &6.52\\ - $^3B_2(\pi,\pis)$ &(0,2,0,2) &(1,0,1,0) &3.26$^d$ &3.34$^d$ &3.09$^d$ &3.31$^d$ &3.26$^d$ &3.31\\ - $^3A_1(\pi,\pis)$ &(0,2,0,2) &(3,0,0,0) &4.92$^d$ &5.14$^d$ &4.78$^d$ &5.10$^d$ &5.03$^d$ &5.11\\ - $^3A_2(\pi,3s)$ &(1,2,0,2) &(1,0,0,1) &5.53$^f$ &5.91$^f$ &5.74$^f$ &5.81$^f$ &5.75$^f$ &5.73\\ - $^3B_1(\pi,3p_y)$ &(0,2,1,2) &(1,1,0,0) &6.05$^c$ &6.56$^c$ &6.40$^c$ &6.43$^c$ &6.37$^c$ &6.36\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Using reference (4e,6o) active space including valence $\pi$ and two $3p_x$ orbitals. - $^b$Using reference (4e,6o) active space including valence $\pi$, $3s$ and $3p_z$ orbitals. - $^c$Using reference (4e,5o) active space including valence $\pi$ and $3p_y$ orbitals. - $^d$Using reference (4e,4o) active space including valence $\pi$ orbitals. - $^e$Strong double-excitation character. - $^f$Using reference (4e,5o) active space including valence $\pi$ and $3s$ orbitals. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of cyclopropene.} - \label{tab:cyclopropene} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1B_1(\sig,\pis)$ &(3,1,3,1) &(1,1,0,0) &7.48$^a$ &6.86$^a$ &6.58$^a$ &6.85$^a$ &6.77$^a$ &6.68\\ - $^1B_2(\pi,\pis)$ &(3,1,3,1) &(1,0,1,0) &7.47$^a$ &6.89$^a$ &6.47$^a$ &6.96$^a$ &6.87$^a$ &6.79\\ - $^3B_2(\pi,\pis)$ &(3,1,3,1) &(1,0,1,0) &4.60$^a$ &4.47$^a$ &4.27$^a$ &4.46$^a$ &4.40$^a$ &4.38\\ - $^3B_1(\sig,\pis)$ &(3,1,3,1) &(1,1,0,0) &7.08$^a$ &6.56$^a$ &6.32$^a$ &6.55$^a$ &6.47$^a$ &6.45\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Reference (8e,8o) active space including valence $\piCC$, $\sigCC$ and $\pisCC$, $\sigsCC$ orbitals. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of cyclopropenethione.} - \label{tab:cyclopropenethione} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1A_2(n,\pis)$ &(0,3,1,1) &(1,0,0,1) &3.44$^a$ &3.43$^a$ &3.14$^a$ &3.46$^a$ &3.40$^a$ &3.41\\ - $^1B_1(n,\pis)$ &(0,3,1,1) &(1,1,0,0) &3.57$^a$ &3.45$^a$ &3.17$^a$ &3.52$^a$ &3.46$^a$ &3.45\\ - $^1B_2(\pi,\pis)$ &(2,3,1,1) &(1,0,3,0) &4.51$^b$ &4.64$^b$ &4.35$^b$ &4.66$^b$ &4.61$^b$ &4.60\\ - $^1B_2(n,3s)$ &(2,3,1,1) &(1,0,3,0) &4.59$^b$ &5.25$^b$ &5.15$^b$ &5.25$^b$ &5.22$^b$ &5.34\\ - $^1A_1(\pi,\pis)$ &(0,3,0,1) &(2,0,0,0) &6.46$^c$ &5.84$^c$ &5.32$^c$ &5.88$^c$ &5.75$^c$ &5.46\\ - $^1B_2(n,3p_z)$ &(2,3,1,1) &(1,0,3,0) &5.27$^b$ &5.93$^b$ &5.86$^b$ &5.92$^b$ &5.90$^b$ &5.92\\ - $^3A_2(n,\pis)$ &(0,3,1,1) &(1,0,0,1) &3.26$^a$ &3.28$^a$ &3.00$^a$ &3.33$^a$ &3.28$^a$ &3.28\\ - $^3B_1(n,\pis)$ &(0,3,1,1) &(1,1,0,0) &3.51$^a$ &3.35$^a$ &3.07$^a$ &3.42$^a$ &3.36$^a$ &3.32\\ - $^3B_2(\pi,\pis)$ &(2,3,1,1) &(1,0,3,0) &3.80$^b$ &3.97$^b$ &3.75$^b$ &3.99$^b$ &3.95$^b$ &4.01\\ - $^3A_1(\pi,\pis)$ &(0,3,0,1) &(2,0,0,0) &3.83$^c$ &4.01$^c$ &3.77$^c$ &4.00$^c$ &3.95$^c$ &4.01\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Using reference (6e,5o) active space including valence $\pi$ and $\nS$. - $^b$Using reference (6e,7o) active space including valence $\pi$, $\nS$, $3s$ and $3p_z$. - $^c$Using reference (4e,4o) active space including valence $\pi$. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of cyclopropenone.} - \label{tab:cyclopropenone} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1B_1(n,\pis)$ &(2,3,1,1) &(1,3,0,0) &4.92$^a$ &4.12$^a$ &3.75$^a$ &4.40$^a$ &4.38$^a$ &4.26\\ - $^1A_2(n,\pis)$ &(0,4,2,1) &(1,0,0,3) &5.64$^b$ &5.62$^b$ &5.31$^b$ &5.67$^b$ &5.64$^b$ &5.55\\ - $^1B_2(n,3s)$ &(2,3,1,1) &(1,0,3,0) &5.68$^a$ &6.28$^a$ &6.21$^a$ &6.41$^a$ &6.44$^a$ &6.34\\ - $^1B_2(\pi,\pis)$ &(2,3,1,1) &(1,0,3,0) &6.40$^a$ &6.54$^a$ &6.20$^a$ &6.63$^a$ &6.62$^a$ &6.54\\ - $^1B_2(n,3p_z)$ &(2,3,1,1) &(1,0,3,0) &6.35$^a$ &6.84$^a$ &6.70$^a$ &6.99$^a$ &7.01$^a$ &6.98\\ - $^1A_1(n,3p_y)$ &(0,4,2,1) &(4,0,0,0) &6.84$^b$ &7.27$^b$ &7.03$^b$ &7.26$^b$ &7.24$^b$ &7.02\\ - $^1A_1(\pi,\pis)$ &(0,4,2,1) &(4,0,0,0) &10.42$^b$ &8.96$^b$ &8.11$^b$ &9.21$^b$ &9.07$^b$ &8.28\\ - $^3B_1(n,\pis)$ &(2,3,1,1) &(1,3,0,0) &4.72$^a$ &3.65$^a$ &3.28$^a$ &4.00$^a$ &3.98$^a$ &3.93\\ - $^3B_2(\pi,\pis)$ &(2,3,1,1) &(1,0,3,0) &4.39$^a$ &4.76$^a$ &4.60$^a$ &4.76$^a$ &4.74$^a$ &4.88\\ - $^3A_2(n,\pis)$ &(0,4,2,1) &(1,0,0,3) &5.40$^b$ &5.36$^b$ &5.06$^b$ &5.44$^b$ &5.42$^b$ &5.35\\ - $^3A_1(\pi,\pis)$ &(0,4,2,1) &(4,0,0,0) &6.59$^b$ &6.93$^b$ &6.61$^b$ &6.86$^b$ &6.82$^b$ &6.79\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Using reference (6e,7o) active space including valence $\pi$, $\nO$, $3s$ and $3p_z$. - $^b$Using reference (6e,7o) active space including valence $\pi$, $\nO$, $3p_x$ and $3p_y$. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of diacetylene.$^a$} - \label{tab:diacetylene} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_g,b_{3u},b_{2u},b_{1g},b_{1u},b_{2g},b_{3g},a_u)$ & $(A_g,B_{3u},B_{2u},B_{1g},B_{1u},B_{2g},B_{3g},A_u)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1\Sigma_u^-(\pi,\pis)$ &(0,2,2,0,0,2,2,0) &(1,0,0,0,0,0,0,1) &6.13 &5.42 &5.01 &5.45 &5.36 &5.33\\ - $^1\Delta_u(\pi,\pis)$ &(0,2,2,0,0,2,2,0) &(1,0,0,0,1,0,0,1) &6.39 &5.68 &5.30 &5.72 &5.63 &5.61\\ - $^3\Sigma_u^+(\pi,\pis)$ &(0,2,2,0,0,2,2,0) &(1,0,0,0,1,0,0,0) &4.54 &4.11 &3.67 &4.17 &4.09 &4.10\\ - $^3\Delta_u(\pi,\pis)$ &(0,2,2,0,0,2,2,0) &(1,0,0,0,1,0,0,1) &5.28 &4.82 &4.45 &4.86 &4.78 &4.78\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$All calculations using a full valence $\pi$ active space of (8e,8o). -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of diazomethane.} - \label{tab:diazomethane} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline -$^1A_2(\pi,\pis)$ &(4,3,2,0) &(1,0,0,1) &3.27$^a$ &3.13$^a$ &2.92$^a$ &3.09$^a$ &3.04$^a$ &3.14\\ -$^1B_1(\pi,3s)$ &(5,3,2,0) &(1,1,0,0) &4.59$^b$ &5.50$^b$ &5.30$^b$ &5.48$^b$ &5.45$^b$ &5.54\\ -$^1A_1(\pi,\pis)$ &(4,4,2,0) &(3,0,0,0) &5.65$^c$ &6.21$^c$ &5.92$^c$ &6.18$^c$ &6.13$^c$ &5.90\\ -$^3A_2(\pi,\pis)$ &(4,3,2,0) &(1,0,0,1) &3.02$^a$ &2.87$^a$ &2.67$^a$ &2.84$^a$ &2.79$^a$ &2.79\\ -$^3A_1(\pi,\pis)$ &(4,3,2,0) &(2,0,0,0) &4.27$^a$ &4.10$^a$ &3.88$^a$ &4.06$^a$ &4.01$^a$ &4.05\\ -$^3B_1(\pi,3s)$ &(5,3,2,0) &(1,1,0,0) &4.45$^b$ &5.34$^b$ &5.15$^b$ &5.33$^b$ &5.30$^b$ &5.35\\ -$^3A_1(\pi,3p)$ &(4,4,2,0) &(3,0,0,0) &6.34$^c$ &7.00$^c$ &6.76$^c$ &6.96$^c$ &6.91$^c$ &6.82\\ -$^1A''[F](\pi,\pis)$ &($a'$:6,$a''$:3) &($A'$:1,$A''$:1) &0.72$^a$ &0.69$^a$ &0.52$^a$ &0.66$^a$ &0.62$^a$ &0.71\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Reference (10e,9o) active space including valence $\pi$, $\sigCN$, $\sigNN$ and $\sigsCN$, $\sigsNN$ orbitals. - $^b$Reference (10e,10o) active space including valence $\pi$, $\sigCN$, $\sigNN$ and $\sigsCN$, $\sigsNN$, Rydberg $3s$ orbitals. - $^c$Reference (10e,10o) active space including valence $\pi$, $\sigCN$, $\sigNN$ and $\sigsCN$, $\sigsNN$, Rydberg $3p$ orbitals. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of formamide.} - \label{tab:formamide} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a',a'')$ & $(A',A'')$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1A''(n,\pis)$ &(5,3) &(1,1) &5.95$^a$ &5.66$^a$ &5.45$^a$ &5.71$^a$ &5.67$^a$ &5.65\\ - $^1A'(n,3s)$ &(7,3) &(4,0) &6.17$^b$ &6.80$^b$ &6.64$^b$ &6.82$^b$ &6.81$^b$ &6.77\\ - $^1A'(n,3p)$ &(7,3) &(4,0) &6.74$^b$ &7.45$^b$ &7.32$^b$ &7.46$^b$ &7.46$^b$ &7.38\\ - $^1A'(\pi,\pis)$ &(7,3) &(4,0) &8.80$^b$ &7.88$^b$ &7.13$^b$ &7.95$^b$ &7.78$^b$ &7.63\\ - $^3A''(n,\pis)$ &(5,3) &(1,1) &5.89$^a$ &5.36$^a$ &5.16$^a$ &5.41$^a$ &5.37$^a$ &5.38\\ - $^3A'(\pi,\pis)$ &(4,3) &(2,0) &6.10$^c$ &5.88$^c$ &5.62$^c$ &5.91$^c$ &5.87$^c$ &5.81\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Reference (10e,8o) active space including valence $\pi$, $\nO$, $\sigCN$, $\sigCO$ and $\sigsCN$, $\sigsCO$ orbitals. - $^b$Reference (10e,10o) active space including valence $\pi$, $\nO$, $\sigCN$, $\sigCO$ and $\sigsCN$, $\sigsCO$, Rydberg $3s$ and $3p$ orbitals. - $^c$Reference (8e,7o) active space including valence $\pi$, $\sigCN$, $\sigCO$ and $\sigsCN$, $\sigsCO$ orbitals. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of furan.} - \label{tab:furan} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1A_2(\pi,3s)$ &(2,3,0,2) &(1,0,0,2) &5.26$^a$ &6.16$^a$ &6.04$^a$ &6.06$^a$ &6.02$^a$ &6.09\\ - $^1B_2(\pi,\pis)$ &(0,4,0,2) &(1,0,2,0) &7.78$^b$ &6.59$^b$ &6.02$^b$ &6.80$^b$ &6.71$^b$ &6.37\\ - $^1A_1(\pi,\pis)$ &(0,3,0,2) &(3,0,0,0) &6.73$^{c,d}$ &6.66$^{c,d}$ &6.10$^{c,d}$ &6.69$^{c,d}$ &6.62$^{c,d}$ &6.56\\ - $^1B_1(\pi,3p_y)$ &(0,3,1,2) &(1,1,0,0) &6.07$^e$ &6.79$^e$ &6.63$^e$ &6.65$^e$ &6.60$^e$ &6.64\\ - $^1A_2(\pi,3p_z)$ &(2,3,0,2) &(1,0,0,2) &5.87$^a$ &6.87$^a$ &6.77$^a$ &6.76$^a$ &6.72$^a$ &6.81\\ - $^1B_2(\pi,3p_x)$ &(0,4,0,2) &(1,0,2,0) &6.54$^b$ &7.11$^b$ &6.84$^b$ &6.96$^b$ &6.88$^b$ &7.24\\ - $^3B_2(\pi,\pis)$ &(0,3,0,2) &(1,0,1,0) &3.94$^c$ &4.26$^c$ &4.01$^c$ &4.17$^c$ &4.12$^c$ &4.20\\ - $^3A_1(\pi,\pis)$ &(0,3,0,2) &(3,0,0,0) &5.41$^c$ &5.50$^c$ &5.09$^c$ &5.47$^c$ &5.40$^c$ &5.46\\ - $^3A_2(\pi,3s)$ &(1,3,0,2) &(1,0,0,1) &5.57$^f$ &6.16$^f$ &5.99$^f$ &6.05$^f$ &5.99$^f$ &6.02\\ - $^3B_1(\pi,3p_y)$ &(0,3,1,2) &(1,1,0,0) &6.04$^e$ &6.76$^e$ &6.60$^e$ &6.62$^e$ &6.56$^e$ &6.59\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Using reference (6e,7o) active space including valence $\pi$, $3s$ and $3p_z$ orbitals. - $^b$Using reference (6e,6o) active space including valence $\pi$ and $3p_x$ orbitals. - $^c$Using reference (6e,5o) active space including valence $\pi$ orbitals. - $^d$Strong double-excitation character. - $^e$Using reference (6e,6o) active space including valence $\pi$ and $3p_y$ orbitals. - $^f$Using reference (6e,6o) active space including valence $\pi$ and $3s$ orbitals. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of imidazole.} - \label{tab:imidazole} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a',a'')$ & $(A',A'')$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1A''(\pi,3s)$ &(2,5) &(1,3) &5.04$^a$ &5.88$^a$ &5.66$^a$ &5.74$^a$ &5.68$^a$ &5.70\\ - $^1A'(\pi,3p)$ &(0,9) &(3,0) &6.18$^b$ &6.69$^b$ &6.45$^b$ &6.61$^b$ &6.56$^b$ &6.41\\ - $^1A''(\pi,3p)$ &(4,6) &(1,7) &5.43$^c$ &6.57$^c$ &6.47$^c$ &6.47$^c$ &6.44$^c$ &6.50\\ - $^1A''(n,\pis)$ &(2,5) &(1,3) &7.13$^a$ &6.94$^a$ &6.57$^a$ &6.92$^a$ &6.85$^a$ &6.73\\ - $^1A''(\pi,3p)$ &(4,6) &(1,7) &5.74$^c$ &6.87$^c$ &6.67$^c$ &6.79$^c$ &6.77$^c$ &---\\ - $^1A''(\pi,3s)$ &(4,6) &(1,7) &5.68$^c$ &6.89$^c$ &6.70$^c$ &6.82$^c$ &6.79$^c$ &---\\ - $^1A'(\pi,\pis)$ &(0,9) &(3,0) &6.73$^b$ &6.88$^b$ &6.46$^b$ &6.89$^b$ &6.83$^b$ &6.87\\ - $^1A'(n,3s)$ &(2,5) &(2,0) &6.36$^a$ &7.10$^a$ &6.91$^a$ &7.09$^a$ &7.07$^a$ &7.02\\ - $^3A'(\pi,\pis)$ &(0,9) &(3,0) &4.55$^b$ &4.78$^b$ &4.53$^b$ &4.73$^b$ &4.68$^b$ &4.73\\ - $^3A''(\pi,3s)$ &(2,5) &(1,3) &5.03$^a$ &5.86$^a$ &5.63$^a$ &5.72$^a$ &5.66$^a$ &5.66\\ - $^3A'(\pi,\pis)$ &(0,9) &(3,0) &5.69$^b$ &5.85$^b$ &5.48$^b$ &5.80$^b$ &5.72$^b$ &5.74\\ - $^3A''(n,\pis)$ &(2,5) &(1,3) &6.58$^a$ &6.44$^a$ &6.10$^a$ &6.43$^a$ &6.37$^a$ &6.31\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Using reference $(8e,7o)$ active space including valence $\pi$, $\nN$ and $3s$ orbitals. - $^b$Using reference $(6e,9o)$ active space including valence $\pi$ and four $3p_z$ orbitals. - $^c$Using reference $(8e,10o)$ active space including valence $\pi$, $\nN$, $3s$ and three $3p$ orbitals. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of isobutene.} - \label{tab:isobutene} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1B_1(\pi,3s)$ &(3,2,0,0) &(1,1,0,0) &6.21$^a$ &6.74$^a$ &6.59$^a$ &6.64$^a$ &6.57$^a$ &6.46\\ - $^1A_1(\pi,3p_x)$ &(2,3,0,0) &(2,0,0,0) &6.90$^b$ &7.32$^b$ &7.14$^b$ &7.24$^b$ &7.18$^b$ &7.01\\ - $^3A_1(\pi,\pis)$ &(2,2,0,0) &(2,0,0,0) &4.66$^c$ &4.59$^c$ &4.41$^c$ &4.58$^c$ &4.53$^c$ &4.53\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Using reference (4e,5o) active space including valence $\pi$, $\sigCC$, $\sigsCC$ and $3s$ orbitals. - $^b$Using reference (4e,5o) active space including valence $\pi$, $\sigCC$, $\sigsCC$ and $3p_x$ orbitals. - $^c$Using reference (4e,4o) active space including valence $\pi$, $\sigCC$ and $\sigsCC$ orbitals. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of ketene.} - \label{tab:ketene} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline -$^1A2(\pi,\pis)$ &(4,3,2,0) &(1,0,0,1) &3.98$^a$ &3.92$^a$ &3.70$^a$ &3.90$^a$ &3.85$^a$ &3.86\\ -$^1B1(\pi,3s)$ &(5,3,2,0) &(1,1,0,0) &5.22$^b$ &5.99$^b$ &5.79$^b$ &6.00$^b$ &5.97$^b$ &6.01\\ -$^1A2(\pi,3p)$ &(4,3,3,0) &(1,0,0,2) &6.38$^c$ &7.25$^c$ &7.05$^c$ &7.19$^c$ &7.15$^c$ &7.18\\ -$^3A2(\pi,\pis)$ &(4,3,2,0) &(1,0,0,1) &3.92$^a$ &3.81$^a$ &3.59$^a$ &3.79$^a$ &3.74$^a$ &3.77\\ -$^3A1(\pi,\pis)$ &(4,3,2,0) &(2,0,0,0) &5.79$^a$ &5.65$^a$ &5.43$^a$ &5.63$^a$ &5.59$^a$ &5.61\\ -$^3B1(\pi,3s)$ &(5,3,2,0) &(1,1,0,0) &5.05$^b$ &5.79$^b$ &5.60$^b$ &5.80$^b$ &5.77$^b$ &5.79\\ -$^3A2(\pi,3p)$ &(4,3,3,0) &(1,0,0,2) &6.35$^c$ &7.22$^c$ &7.01$^c$ &7.15$^c$ &7.11$^c$ &7.12\\ -$^1A''[F](\pi,\pis)$ &($a'$:6,$a''$:3) &($A'$:1,$A''$:1) &0.95$^a$ &1.05$^a$ &0.88$^a$ &1.00$^a$ &0.95$^a$ &1.00\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Reference (10e,9o) active space including valence $\pi$, $\sigCC$, $\sigCO$ and $\sigsCC$, $\sigsCO$ orbitals. - $^b$Reference (10e,10o) active space including valence $\pi$, $\sigCC$, $\sigCO$ and $\sigsCC$, $\sigsCO$, Rydberg $3s$ orbitals. - $^c$Reference (10e,10o) active space including valence $\pi$, $\sigCC$, $\sigCO$ and $\sigsCC$, $\sigsCO$, Rydberg $3p$ orbitals. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of methylenecyclopropene.} - \label{tab:methylenecyclopropene} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1B_2(\pi,\pis)$ &(0,3,0,1) &(1,0,1,0) &4.47$^a$ &4.40$^a$ &4.12$^a$ &4.39$^a$ &4.33$^a$ &4.28\\ - $^1B_1(\pi,3s)$ &(1,3,0,1) &(1,1,0,0) &4.92$^b$ &5.57$^b$ &5.44$^b$ &5.46$^b$ &5.41$^b$ &5.44\\ - $^1A_2(\pi,3p_y)$ &(0,3,1,1) &(1,0,0,1) &5.37$^b$ &6.09$^b$ &5.97$^b$ &5.97$^b$ &5.92$^b$ &5.96\\ - $^1A_1(\pi,3p_x)$ &(0,6,0,1) &(5,0,0,0) &5.37$^c$ &6.26$^c$ &6.16$^c$ &6.17$^c$ &6.13$^c$ &6.12\\ - $^3B_2(\pi,\pis)$ &(0,3,0,1) &(1,0,1,0) &3.44$^a$ &3.57$^a$ &3.34$^a$ &3.55$^a$ &3.49$^a$ &3.49\\ - $^3A_1(\pi,\pis)$ &(0,5,0,1) &(4,0,0,0) &4.60$^d$ &4.82$^d$ &4.58$^d$ &4.77$^d$ &4.72$^d$ &4.74\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Using reference (4e,4o) active space including valence $\pi$. - $^b$Using reference (4e,5o) active space including valence $\pi$ and $3s$. - $^c$Using reference (4e,5o) active space including valence $\pi$ and $3p_y$. - $^d$Using reference (4e,7o) active space including valence $\pi$, two $3p_x$ and one $3d_{xz}$. - $^e$Using reference (4e,6o) active space including valence $\pi$, one $3p_x$ and one $3d_{xz}$. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of nitrosomethane.} - \label{tab:nitrosomethane} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a',a'')$ & $(A',A'')$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline -$^1A''(n,\pis)$ &(4,2) &(1,1) &2.12$^a$ &1.84$^a$ &1.60$^a$ &1.94$^a$ &1.91$^a$ &1.96\\ -$^1A'(n^2,\pis^2)$ &(4,2) &(2,0) &4.74$^a$ &4.69$^a$ &4.67$^a$ &4.71$^a$ &4.71$^a$ &4.76\\ -$^1A'(n,3s)$ &(5,2) &(3,0) &5.87$^b$ &6.32$^b$ &6.07$^b$ &6.34$^b$ &6.31$^b$ &6.29\\ -$^3A''(n,\pis)$ &(4,2) &(1,1) &1.31$^a$ &1.00$^a$ &0.75$^a$ &1.12$^a$ &1.09$^a$ &1.16\\ -$^3A'(\pi,\pis)$ &(2,2) &(2,0) &5.52$^c$ &5.52$^c$ &5.37$^c$ &5.54$^c$ &5.50$^c$ &5.60\\ -$^1A''[F](n,\pis)$ &(4,2) &(1,1) &1.83$^a$ &1.55$^a$ &1.32$^a$ &1.66$^a$ &1.62$^a$ &1.67\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Reference (8e,6o) active space including valence $\nO$, $\nN$, $\piNO$, $\sigNO$ and $\sigsNO$, $\pisNO$ orbitals. - $^b$Reference (8e,7o) active space including valence $\nO$, $\nN$, $\piNO$, $\sigNO$ and $\sigsNO$, $\pisNO$, Rydberg 3s orbitals. - $^c$Reference (4e,4o) active space including valence $\piNO$, $\sigNO$ and $\sigsNO$, $\pisNO$ orbitals. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of propynal.} - \label{tab:propynal} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a',a'')$ & $(A',A'')$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1A''(n,\pis)$ &(3,4) &(1,2) &4.00$^a$ &3.92$^a$ &3.64$^a$ &3.90$^a$ &3.86$^a$ &3.80\\ - $^1A''(\pi,\pis)$ &(3,4) &(1,2) &6.62$^a$ &5.82$^a$ &5.49$^a$ &5.81$^a$ &5.72$^a$ &5.54\\ - $^3A''(n,\pis)$ &(3,4) &(1,1) &3.52$^a$ &3.48$^a$ &3.26$^a$ &3.52$^a$ &3.50$^a$ &3.47\\ - $^3A'(\pi,\pis)$ &(2,4) &(2,0) &4.69$^b$ &4.59$^b$ &4.30$^b$ &4.59$^b$ &4.54$^b$ &4.47\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Using reference (8e,7o) active space including valence $\pi$ and $\nO$ orbitals. - $^b$Using reference (6e,6o) active space including valence $\pi$ orbitals. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of pyrazine.} - \label{tab:pyrazine} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_g,b_{3u},b_{2u},b_{1g},b_{1u},b_{2g},b_{3g},a_u)$ & $(A_g,B_{3u},B_{2u},B_{1g},B_{1u},B_{2g},B_{3g},A_u)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1B_{3u}(n,\pis)$ &(1,2,0,1,1,2,0,1) &(1,1,0,0,0,0,0,0) &4.76a &4.09a &3.66a &4.31a &4.30a &4.15\\ - $^1A_{u}(n,\pis)$ &(1,2,0,1,1,2,0,1) &(1,0,0,0,0,0,0,1) &5.90a &4.76a &4.26a &5.10a &5.10a &4.98\\ - $^1B_{2u}(\pi,\pis)$ &(0,2,0,1,0,2,0,1) &(1,0,1,0,0,0,0,0) &4.97b &5.13b &4.65b &5.09b &5.03b &5.02\\ - $^1B_{2g}(n,\pis)$ &(1,2,0,1,1,2,0,1) &(1,0,0,0,0,1,0,0) &5.80a &5.68a &5.27a &5.73a &5.70a &5.71\\ - $^1A_{g}(n,3s)$ &(2,2,0,1,1,2,0,1) &(2,0,0,0,0,0,0,0) &6.69c &6.66c &6.27c &6.81c &6.80c &6.65\\ - $^1B_{1g}(n,\pis)$ &(1,2,0,1,1,2,0,1) &(1,0,0,1,0,0,0,0) &7.16a &6.61a &6.07a &6.78a &6.76a &6.74\\ - $^1B_{1u}(\pi,\pis)$ &(0,4,0,1,0,2,0,2) &(1,0,0,0,3,0,0,0) &8.04d &7.14d &6.72d &7.20d &7.12d &6.88\\ - $^1B_{1g}(\pi,3s)$ &(1,2,0,1,0,2,0,1) &(1,0,0,1,0,0,0,0) &6.73e &7.41e &7.27e &7.24e &7.18e &7.21\\ - $^1B_{2u}(n,3p_y)$ &(1,2,1,1,1,2,0,1) &(1,0,2,0,0,0,0,0) &7.49f &7.34f &6.93f &7.43f &7.40f &7.24\\ - $^1B_{1u}(n,3p_z)$ &(1,2,0,1,2,2,0,1) &(1,0,0,0,3,0,0,0) &7.83g &7.55g &7.08g &7.64g &7.59g &7.44\\ - $^1B_{1u}(\pi,\pis)$ &(0,4,0,1,0,2,0,2) &(1,0,0,0,3,0,0,0) &9.65d &8.59d &7.96d &8.68d &8.57d &7.98\\ - $^3B_{3u}(n,\pis)$ &(1,2,0,1,1,2,0,1) &(1,1,0,0,0,0,0,0) &4.16a &3.49a &3.08a &3.72a &3.71a &3.59\\ - $^3B_{1u}(\pi,\pis)$ &(0,4,0,1,0,2,0,2) &(1,0,0,0,2,0,0,0) &3.98d &4.44d &4.15d &4.34d &4.28d &4.35\\ - $^3B_{2u}(\pi,\pis)$ &(0,2,0,1,0,2,0,1) &(1,0,1,0,0,0,0,0) &4.62b &4.44b &4.09b &4.47b &4.41b &4.39\\ - $^3A_{u}(n,\pis)$ &(1,2,0,1,1,2,0,1) &(1,0,0,0,0,0,0,1) &5.85a &4.73a &4.21a &5.07a &5.07a &4.93\\ - $^3B_{2g}(n,\pis)$ &(1,2,0,1,1,2,0,1) &(1,0,0,0,0,1,0,0) &5.25a &5.04a &4.66a &5.14a &5.11a &5.08\\ - $^3B_{1u}(\pi,\pis)$ &(0,4,0,1,0,2,0,2) &(1,0,0,0,2,0,0,0) &5.15d &5.29d &4.92d &5.25d &5.19d &5.28\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Using reference (10e,8o) active space including valence $\pi$ and $\nN$ orbitals. - $^b$Using reference (6e,6o) active space including valence $\pi$ orbitals. - $^c$Using reference (10e,9o) active space including valence $\pi$, $\nN$ and $3s$ orbitals. - $^d$Using reference (6e,9o) active space including valence $\pi$ and three $3p_x$ orbitals. - $^e$Using reference (6e,7o) active space including valence $\pi$ and $3s$ orbitals. - $^f$Using reference (10e,9o) active space including valence $\pi$, $\nN$ and $3p_y$ orbitals. - $^g$Using reference (10e,9o) active space including valence $\pi$, $\nN$ and $3p_z$ orbitals. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of pyridazine.} - \label{tab:pyridazine} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1B_1(n,\pis)$ &(1,3,1,3) &(1,1,0,0) &4.29$^a$ &3.74$^a$ &3.36$^a$ &3.94$^a$ &3.92$^a$ &3.83\\ - $^1A_2(n,\pis)$ &(1,3,1,3) &(1,0,0,1) &4.83$^a$ &4.29$^a$ &3.87$^a$ &4.49$^a$ &4.48$^a$ &4.37\\ - $^1A_1(\pi,\pis)$ &(0,3,0,3) &(2,0,0,0) &5.12$^b$ &5.34$^b$ &4.87$^b$ &5.30$^b$ &5.25$^b$ &5.26\\ - $^1A_2(n,\pis)$ &(1,3,1,3) &(1,0,0,2) &6.26$^a$ &5.73$^a$ &5.19$^a$ &5.93$^a$ &5.89$^a$ &5.72\\ - $^1B_2(n,3s)$ &(2,3,1,3) &(1,0,1,0) &5.99$^c$ &6.18$^c$ &5.90$^c$ &6.28$^c$ &6.27$^c$ &6.17\\ - $^1B_1(n,\pis)$ &(1,3,1,3) &(1,2,0,0) &7.16$^a$ &6.50$^a$ &5.94$^a$ &6.72$^a$ &6.67$^a$ &6.37\\ - $^1B_2(\pi,\pis)$ &(0,5,0,4) &(1,0,1,0) &7.54$^d$ &7.26$^d$ &6.82$^d$ &7.25$^d$ &7.17$^d$ &6.75\\ - $^3B_1(n,\pis)$ &(1,3,1,3) &(1,1,0,0) &3.60$^a$ &3.08$^a$ &2.72$^a$ &3.29$^a$ &3.28$^a$ &3.19\\ - $^3A_2(n,\pis)$ &(1,3,1,3) &(1,0,0,1) &4.49$^a$ &4.01$^a$ &3.59$^a$ &4.20$^a$ &4.18$^a$ &4.11\\ - $^3B_2(\pi,\pis)$ &(0,3,0,3) &(1,0,1,0) &3.93$^b$ &4.44$^b$ &4.13$^b$ &4.30$^b$ &4.24$^b$ &4.34\\ - $^3A_1(\pi,\pis)$ &(0,3,0,3) &(2,0,0,0) &4.93$^b$ &4.87$^b$ &4.48$^b$ &4.89$^b$ &4.83$^b$ &4.82\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Using reference (10e,8o) active space including valence $\pi$ and $\nN$ orbitals. - $^b$Using reference (6e,6o) active space including valence $\pi$ orbitals. - $^c$Using reference (10e,9o) active space including valence $\pi$, $\nN$ and $3s$ orbitals. - $^d$Using reference (6e,9o) active space including valence $\pi$, $\nN$ and three $3p_x$ orbitals. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of pyridine.} - \label{tab:pyridine} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1B_1(n,\pis)$ &(1,4,1,2) &(1,2,0,0) &5.43$^a$ &5.15$^a$ &4.81$^a$ &5.18$^a$ &5.13$^a$ &4.95\\ - $^1B_2(\pi,\pis)$ &(0,7,0,3) &(1,0,2,0) &5.03$^b$ &5.18$^b$ &4.76$^b$ &5.15$^b$ &5.09$^b$ &5.14\\ - $^1A_2(n,\pis)$ &(2,4,0,2) &(1,0,0,2) &6.30$^c$ &5.46$^c$ &5.03$^c$ &5.63$^c$ &5.59$^c$ &5.40\\ - $^1A_1(\pi,\pis)$ &(0,4,0,2) &(2,0,0,0) &7.90$^d$ &6.92$^d$ &6.27$^d$ &7.04$^d$ &6.93$^d$ &6.62\\ - $^1A_1(n,3s)$ &(2,4,0,2) &(2,0,0,0) &6.40$^c$ &6.90$^c$ &6.67$^c$ &6.97$^c$ &6.96$^c$ &6.76\\ - $^1A_2(\pi,3s)$ &(2,4,0,2) &(1,0,0,2) &6.60$^c$ &7.08$^c$ &6.87$^c$ &6.88$^c$ &6.80$^c$ &6.82\\ - $^1B_2(\pi,\pis)$ &(0,7,0,3) &(1,0,2,0) &7.45$^b$ &7.92$^b$ &7.67$^b$ &7.80$^b$ &7.73$^b$ &7.40\\ - $^1B_1(\pi,3p_y)$ &(1,4,1,2) &(1,2,0,0) &7.12$^a$ &7.70$^a$ &7.51$^a$ &7.48$^a$ &7.40$^a$ &7.38\\ - $^1A_1(\pi,\pis)$ &(0,4,0,2) &(4,0,0,0) &9.49$^d$ &7.66$^d$ &6.63$^d$ &7.87$^d$ &7.70$^d$ &7.39\\ - $^3A_1(\pi,\pis)$ &(0,4,0,2) &(2,0,0,0) &3.98$^d$ &4.40$^d$ &4.06$^d$ &4.29$^d$ &4.22$^d$ &4.30\\ - $^3B_1(n,\pis)$ &(1,4,0,2) &(1,1,0,0) &4.65$^e$ &4.48$^e$ &4.21$^e$ &4.57$^e$ &4.55$^e$ &4.46\\ - $^3B_2(\pi,\pis)$ &(0,7,0,3) &(1,0,2,0) &4.83$^b$ &4.86$^b$ &4.53$^b$ &4.81$^b$ &4.74$^b$ &4.79\\ - $^3A_1(\pi,\pis)$ &(0,4,0,2) &(3,0,0,0) &5.11$^d$ &5.09$^d$ &4.63$^d$ &5.09$^d$ &5.02$^d$ &5.04\\ - $^3A_2(n,\pis)$ &(1,4,0,2) &(1,0,0,1) &5.94$^e$ &5.33$^e$ &4.96$^e$ &5.53$^e$ &5.51$^e$ &5.36\\ - $^3B_2(\pi,\pis)$ &(0,7,0,3) &(1,0,2,0) &6.93$^b$ &6.40$^b$ &5.99$^b$ &6.43$^b$ &6.35$^b$ &6.24\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Using reference (8e,8o) active space including valence $\pi$, $\nN$ and $3p_y$ orbitals. - $^b$Using reference (6e,10o) active space including valence $\pi$ and four $3p_x$ orbitals. - $^c$Using reference (8e,8o) active space including valence $\pi$, $\nN$ and $3s$ orbitals. - $^d$Using reference (6e,6o) active space including valence $\pi$ orbitals. - $^e$Using reference (8e,7o) active space including valence $\pi$ and $\nN$ orbitals. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of pyrimidine.} - \label{tab:pyrimidine} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1B_1(n,\pis)$ &(1,4,1,2) &(1,1,0,0) &4.85$^a$ &4.44$^a$ &4.07$^a$ &4.58$^a$ &4.55$^a$ &4.44\\ - $^1A_2(n,\pis)$ &(1,4,1,2) &(1,0,0,1) &5.52$^a$ &4.80$^a$ &4.36$^a$ &5.02$^a$ &5.00$^a$ &4.85\\ - $^1B_2(\pi,\pis)$ &(0,6,0,3) &(1,0,1,0) &5.28$^b$ &5.42$^b$ &4.98$^b$ &5.41$^b$ &5.36$^b$ &5.38\\ - $^1A_2(n,\pis)$ &(1,4,1,2) &(1,0,0,2) &6.70$^a$ &5.92$^a$ &5.32$^a$ &6.16$^a$ &6.10$^a$ &5.92\\ - $^1B_1(n,\pis)$ &(1,4,1,2) &(1,2,0,0) &7.20$^a$ &6.31$^a$ &5.65$^a$ &6.58$^a$ &6.53$^a$ &6.26\\ - $^1B_2(n,3s)$ &(2,4,1,2) &(1,0,2,0) &6.86$^c$ &6.85$^c$ &6.50$^c$ &6.89$^c$ &6.86$^c$ &6.70\\ - $^1A_1(\pi,\pis)$ &(0,6,0,3) &(2,0,0,0) &7.69$^b$ &7.31$^b$ &6.94$^b$ &7.29$^b$ &7.22$^b$ &6.88\\ - $^3B_1(n,\pis)$ &(1,4,1,2) &(1,1,0,0) &4.45$^a$ &4.05$^a$ &3.67$^a$ &4.20$^a$ &4.18$^a$ &4.09\\ - $^3A_1(\pi,\pis)$ &(0,6,0,3) &(2,0,0,0) &4.22$^b$ &4.57$^b$ &4.25$^b$ &4.51$^b$ &4.44$^b$ &4.51\\ - $^3A_2(n,\pis)$ &(1,4,1,2) &(1,0,0,1) &5.20$^a$ &4.63$^a$ &4.16$^a$ &4.81$^a$ &4.78$^a$ &4.66\\ - $^3B_2(\pi,\pis)$ &(0,4,0,2) &(1,0,1,0) &5.10$^d$ &5.01$^d$ &4.60$^d$ &5.03$^d$ &4.97$^d$ &4.96\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Using reference (10e,8o) active space including valence $\pi$ and $\nN$ orbitals. - $^b$Using reference (6e,9o) active space including valence $\pi$ and three $3p_x$ orbitals. - $^c$Using reference (10e,9o) active space including valence $\pi$, $\nN$ and $3s$ orbitals. - $^d$Using reference (6e,6o) active space including valence $\pi$ orbitals. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of pyrrole.} - \label{tab:pyrrole} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1A_2(\pi,3s)$ &(1,3,0,2) &(1,0,0,1) &4.49$^a$ &5.44$^a$ &5.23$^a$ &5.28$^a$ &5.23$^a$ &5.24\\ - $^1B_1(\pi,3p_y)$ &(0,3,1,2) &(1,1,0,0) &5.22$^b$ &6.26$^b$ &6.07$^b$ &6.08$^b$ &6.02$^b$ &6.00\\ - $^1A_2(\pi,3p_z)$ &(2,3,0,2) &(1,0,0,2) &4.89$^c$ &6.16$^c$ &6.02$^c$ &6.01$^c$ &5.97$^c$ &6.00\\ - $^1B_2(\pi,\pis)$ &(0,4,0,2) &(1,0,2,0) &7.73$^d$ &6.62$^d$ &6.36$^d$ &6.45$^d$ &6.38$^d$ &6.26\\ - $^1A_1(\pi,\pis)$ &(0,3,0,2) &(3,0,0,0) &6.47$^e$ &6.41$^e$ &5.84$^e$ &6.43$^e$ &6.34$^e$ &6.30\\ - $^1B_2(\pi,3p_x)$ &(0,4,0,2) &(1,0,2,0) &5.82$^d$ &6.75$^d$ &6.11$^d$ &6.92$^d$ &6.82$^d$ &6.83\\ - $^3B_2(\pi,\pis)$ &(0,3,0,2) &(1,0,1,0) &4.24$^e$ &4.57$^e$ &4.30$^e$ &4.49$^e$ &4.44$^e$ &4.51\\ - $^3A_2(\pi,3s)$ &(1,3,0,2) &(1,0,0,1) &4.47$^a$ &5.41$^a$ &5.21$^a$ &5.26$^a$ &5.20$^a$ &5.21\\ - $^3A_1(\pi,\pis)$ &(0,3,0,2) &(3,0,0,0) &5.52$^e$ &5.50$^e$ &5.04$^e$ &5.49$^e$ &5.40$^e$ &5.45\\ - $^3B_1(\pi,3p_y)$ &(0,3,1,2) &(1,1,0,0) &5.18$^b$ &6.22$^b$ &6.03$^b$ &6.04$^b$ &5.98$^b$ &5.91\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Using reference (6e,6o) active space including valence $\pi$ and $3s$ orbitals. - $^b$Using reference (6e,6o) active space including valence $\pi$ and $3p_y$ orbitals. - $^c$Using reference (6e,7o) active space including valence $\pi$, $3s$ and $3p_z$ orbitals. - $^d$Using reference (6e,6o) active space including valence $\pi$ and $3p_x$ orbitals. - $^e$Using reference (6e,5o) active space including valence $\pi$ orbitals. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of streptocyanine.} - \label{tab:streptocyanine} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1B_2(\pi,\pis)$ &(2,2,2,1) &(1,0,1,0) &7.82$^a$ &7.17$^a$ &6.76$^a$ &7.28$^a$ &7.21$^a$ &7.13\\ - $^3B_2(\pi,\pis)$ &(2,2,2,1) &(1,0,1,0) &5.86$^a$ &5.49$^a$ &5.22$^a$ &5.54$^a$ &5.49$^a$ &5.52\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Reference (8e,7o) active space including valence $\pi$, two $\sigCN$ and two $\sigsCN$ orbitals. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of tetrazine.} - \label{tab:tetrazine} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_g,b_{3u},b_{2u},b_{1g},b_{1u},b_{2g},b_{3g},a_u)$ & $(A_g,B_{3u},B_{2u},B_{1g},B_{1u},B_{2g},B_{3g},A_u)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1B_{3u}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,1,0,0,0,0,0,0) &2.99$^a$ &2.31$^a$ &1.91$^a$ &2.54$^a$ &2.53$^a$ &2.47\\ - $^1A_{u}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,0,0,1) &4.37$^a$ &3.49$^a$ &3.00$^a$ &3.77$^a$ &3.78$^a$ &3.69\\ - $^1A_{g}(\rm double)$ &(1,2,1,1,1,2,1,1) &(2,0,0,0,0,0,0,0) &5.42$^a$ &4.69$^a$ &4.48$^a$ &4.85$^a$ &4.87$^a$ &---\\ - $^1B_{1g}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,1,0,0,0,0) &5.41$^a$ &4.83$^a$ &4.33$^a$ &5.02$^a$ &5.00$^a$ &4.93\\ - $^1B_{2u}(\pi,\pis)$ &(0,2,0,1,0,2,0,1) &(1,0,1,0,0,0,0,0) &5.04$^b$ &5.31$^b$ &4.84$^b$ &5.26$^b$ &5.23$^b$ &5.21\\ - $^1B_{2g}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,1,0,0) &5.43$^a$ &5.38$^a$ &4.90$^a$ &5.42$^a$ &5.38$^a$ &5.45\\ - $^1A_{u}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,0,0,2) &6.37$^a$ &5.51$^a$ &4.92$^a$ &5.80$^a$ &5.80$^a$ &5.53\\ - $^1B_{3g}(\rm double)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,0,1,0) &6.59$^a$ &5.85$^a$ &5.22$^a$ &6.20$^a$ &6.22$^a$ &---\\ - $^1B_{2g}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,2,0,0) &6.79$^a$ &5.96$^a$ &5.18$^a$ &6.27$^a$ &6.28$^a$ &6.12\\ - $^1B_{1g}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,2,0,0,0,0) &7.18$^{a,c}$ &6.59$^{a,c}$ &5.89$^{a,c}$ &6.79$^{a,c}$ &6.72$^{a,c}$ &6.91\\ - $^3B_{3u}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,1,0,0,0,0,0,0) &2.38$^a$ &1.70$^a$ &1.31$^a$ &1.94$^a$ &1.93$^a$ &1.85\\ - $^3A_{u}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,0,0,1) &4.06$^a$ &3.26$^a$ &2.78$^a$ &3.52$^a$ &3.52$^a$ &3.45\\ - $^3B_{1g}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,1,0,0,0,0) &4.66$^a$ &4.10$^a$ &3.62$^a$ &4.32$^a$ &4.30$^a$ &4.20\\ - $^3B_{1u}(\pi,\pis)$ &(0,4,0,1,0,2,0,2) &(1,0,0,0,2,0,0,0) &3.90$^d$ &4.55$^d$ &4.29$^d$ &4.39$^d$ &4.34$^d$ &4.49\\ - $^3B_{2u}(\pi,\pis)$ &(0,2,0,1,0,2,0,1) &(1,0,1,0,0,0,0,0) &4.68$^b$ &4.55$^b$ &4.20$^b$ &4.60$^b$ &4.55$^b$ &4.52\\ - $^3B_{2g}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,1,0,0) &5.17$^a$ &5.02$^a$ &4.53$^a$ &5.10$^a$ &5.07$^a$ &5.04\\ - $^3A_{u}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,0,0,2) &6.12$^a$ &5.07$^a$ &4.44$^a$ &5.41$^a$ &5.41$^a$ &5.11\\ - $^3B_{3g}(\rm double)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,0,1,0) &6.56$^a$ &5.39$^a$ &4.86$^a$ &5.83$^a$ &5.85$^a$ &---\\ - $^3B1u(\pi,\pis)$ &(0,4,0,1,0,2,0,2) &(1,0,0,0,2,0,0,0) &5.32$^d$ &5.46$^d$ &5.08$^d$ &5.44$^d$ &5.39$^d$ &5.42\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Using reference (14e,10o) active space including valence $\pi$ and $\nN$ orbitals. - $^b$Using reference (6e,6o) active space including valence $\pi$ orbitals. - $^c$Level shift set to \SI{0.4}{\hartree}. - $^d$Using reference (6e,9o) active space including valence $\pi$ and three $3p_x$ orbitals. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of thioacetone.} - \label{tab:thioacetone} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1A_2(n,\pis)$ &(2,2,1,0) &(1,0,0,1) &2.72$^a$ &2.58$^a$ &2.33$^a$ &2.60$^a$ &2.53$^a$ &2.53\\ - $^1B_2(n,3s)$ &(4,2,1,0) &(1,0,2,0) &4.80$^b$ &5.60$^b$ &5.48$^b$ &5.64$^b$ &5.61$^b$ &5.56\\ - $^1A_1(\pi,\pis)$ &(2,2,2,0) &(3,0,0,0) &6.94$^d$ &6.42$^d$ &5.98$^d$ &6.40$^d$ &6.26$^d$ &5.88\\ - $^1B_2(n,3p_z)$ &(4,2,1,0) &(1,0,2,0) &5.57$^b$ &6.51$^b$ &6.40$^b$ &6.53$^b$ &6.49$^b$ &6.51\\ - $^1A_1(n,3p_y)$ &(2,2,2,0) &(3,0,0,0) &6.24$^d$ &6.66$^d$ &6.41$^d$ &6.59$^d$ &6.50$^d$ &6.61\\ - $^3A_2(n,\pis)$ &(2,2,1,0) &(1,0,0,1) &2.52$^a$ &2.34$^a$ &2.09$^a$ &2.38$^a$ &2.31$^a$ &2.33\\ - $^3A_1(\pi,\pis)$ &(2,2,0,0) &(2,0,0,0) &3.52$^c$ &3.48$^c$ &3.29$^c$ &3.48$^c$ &3.43$^c$ &3.45\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Using reference (6e,5o) active space including valence $\pi$, $\nO$, $\sigCO$ and $\sigsCO$ orbitals. - $^b$Using reference (6e,7o) active space including valence $\pi$, $\nO$, $\sigCO$, $\sigsCO$, $3s$ and $3p_z$ orbitals. - $^c$Using reference (4e,4o) active space including valence $\pi$, $\sigCO$ and $\sigsCO$ orbitals. - $^d$Using reference (6e,6o) active space including valence $\pi$, $\nO$, $\sigCO$, $\sigsCO$ and $3p_y$ orbitals. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of thiophene.} - \label{tab:thiophene} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1A_1(\pi,\pis)$ &(0,3,0,2) &(3,0,0,0) &6.11$^a$ &5.84$^a$ &5.21$^a$ &5.89$^a$ &5.79$^a$ &5.64\\ - $^1B_2(\pi,\pis)$ &(0,5,0,2) &(1,0,2,0) &6.94$^b$ &6.35$^b$ &5.89$^b$ &6.44$^b$ &6.35$^b$ &5.98\\ - $^1A_2(\pi,3s)$ &(1,3,0,2) &(1,0,0,1) &5.70$^c$ &6.28$^c$ &6.07$^c$ &6.16$^c$ &6.10$^c$ &6.14\\ - $^1B_1(\pi,3p_y)$ &(0,3,1,2) &(1,1,0,0) &6.02$^d$ &6.21$^d$ &5.90$^d$ &6.16$^d$ &6.10$^d$ &6.14\\ - $^1A_2(\pi,3p_y)$ &(0,3,1,2) &(1,0,0,1) &6.05$^d$ &6.32$^d$ &5.98$^d$ &6.28$^d$ &6.21$^d$ &6.21\\ - $^1B_1(\pi,3s)$ &(1,3,1,2) &(1,2,0,0) &5.78$^e$ &6.57$^e$ &6.28$^e$ &6.51$^e$ &6.44$^e$ &6.49\\ - $^1B_2(\pi,3p_x)$ &(0,5,0,2) &(1,0,2,0) &6.80$^b$ &7.29$^b$ &7.03$^b$ &7.20$^b$ &7.13$^b$ &7.29\\ - $^1A_1(\pi,\pis)$ &(0,3,0,2) &(3,0,0,0) &8.29$^{a,f}$ &7.62$^{a,f}$ &6.85$^{a,f}$ &7.71$^{a,f}$ &7.56$^{a,f}$ &7.31\\ - $^3B_2(\pi,\pis)$ &(0,3,0,2) &(1,0,1,0) &3.68$^a$ &3.98$^a$ &3.71$^a$ &3.90$^a$ &3.84$^a$ &3.92\\ - $^3A_1(\pi,\pis)$ &(0,3,0,2) &(3,0,0,0) &4.97$^a$ &4.85$^a$ &4.39$^a$ &4.87$^a$ &4.79$^a$ &4.76\\ - $^3B_1(\pi,3p_y)$ &(0,3,1,2) &(1,1,0,0) &5.86$^d$ &5.97$^d$ &5.64$^d$ &5.94$^d$ &5.88$^d$ &5.93\\ - $^3A_2(\pi,3s)$ &(1,3,0,2) &(1,0,0,1) &5.65$^c$ &6.22$^c$ &6.01$^c$ &6.11$^c$ &6.04$^c$ &6.08\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Using reference (6e,5o) active space including valence $\pi$ orbitals. - $^b$Using reference (6e,7o) active space including valence $\pi$ and two $3p_x$ orbitals. - $^c$Using reference (6e,6o) active space including valence $\pi$ and $3s$ orbitals. - $^d$Using reference (6e,6o) active space including valence $\pi$ and $3p_y$ orbitals. - $^e$Using reference (6e,7o) active space including valence $\pi$, $3s$ and $3p_y$ orbitals. - $^f$Strong double-excitation character. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of thiopropynal.} - \label{tab:thiopropynal} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a',a'')$ & $(A',A'')$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1A''(n,\pis)$ &(3,4) &(1,1) &2.06$^a$ &2.05$^a$ &1.84$^a$ &2.05$^a$ &2.00$^a$ &2.03\\ - $^3A''(n,\pis)$ &(3,4) &(1,1) &1.85$^a$ &1.81$^a$ &1.60$^a$ &1.84$^a$ &1.79$^a$ &1.80\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Using reference (8e,7o) active space including valence $\pi$ and $\nO$ orbitals. -\end{table*} - -\begin{table*} - \caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of triazine.} - \label{tab:triazine} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ - & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ - \hline - $^1A_1''(n,\pis)$ &(2,4,1,2) &(1,2,0,2) &5.88$^a$ &4.62$^a$ &3.90$^a$ &5.00$^a$ &4.99$^a$ &4.72\\ - $^1A_2''(n,\pis)$ &(2,4,1,2) &(1,1,0,0) &5.14$^a$ &4.77$^a$ &4.39$^a$ &4.90$^a$ &4.87$^a$ &4.75\\ - $^1E''(n,\pis)$ &(2,4,1,2) &(1,2,0,2) &5.51$^a$ &4.76$^a$ &4.14$^a$ &5.01$^a$ &4.98$^a$ &4.78\\ - $^1A_2'(\pi,\pis)$ &(0,6,0,3) &(1,0,1,0) &5.55$^b$ &5.76$^b$ &5.32$^b$ &5.75$^b$ &5.72$^b$ &5.75\\ - $^1A_1'(\pi,\pis)$ &(0,6,0,3) &(2,0,0,0) &8.20$^b$ &7.43$^b$ &6.89$^b$ &7.50$^b$ &7.41$^b$ &7.24\\ - $^1E'(n,3s)$ &(3,4,1,2) &(2,0,2,0) &7.40$^c$ &7.48$^c$ &7.15$^c$ &7.53$^c$ &7.49$^c$ &7.32\\ - $^1E''(n,\pis)$ &(2,4,1,2) &(1,1,0,1) &8.26$^a$ &7.75$^a$ &7.04$^a$ &7.92$^a$ &7.90$^a$ &7.78\\ - $^1E'(\pi,\pis)$ &(0,6,0,3) &(4,0,3,0) &10.03$^b$ &8.65$^b$ &7.70$^b$ &8.83$^b$ &8.72$^b$ &7.94\\ - $^3A_2''(n,\pis)$ &(2,4,1,2) &(1,1,0,0) &4.74$^a$ &4.37$^a$ &3.99$^a$ &4.51$^a$ &4.49$^a$ &4.33\\ - $^3E''(n,\pis)$ &(2,4,1,2) &(1,2,0,2) &5.14$^a$ &4.47$^a$ &3.88$^a$ &4.71$^a$ &4.68$^a$ &4.51\\ - $^3A_1''(n,\pis)$ &(2,4,1,2) &(1,2,0,2) &5.88$^a$ &4.70$^a$ &3.94$^a$ &5.06$^a$ &5.04$^a$ &4.73\\ - $^3A_1'(\pi,\pis)$ &(0,6,0,3) &(2,0,0,0) &4.46$^b$ &4.88$^b$ &4.55$^b$ &4.81$^b$ &4.75$^b$ &4.85\\ - $^3E'(\pi,\pis)$ &(0,6,0,3) &(3,0,1,0) &5.57$^b$ &5.62$^b$ &5.20$^b$ &5.62$^b$ &5.57$^b$ &5.59\\ - $^3A_2'(\pi,\pis)$ &(0,6,0,3) &(1,0,1,0) &7.70$^b$ &6.62$^b$ &6.12$^b$ &6.76$^b$ &6.68$^b$ &6.62\\ - \end{tabular} - \end{ruledtabular} - \flushleft - $^a$Using reference (12e,9o) active space including valence $\pi$ and $\nN$ orbitals. - $^b$Using reference (6e,9o) active space including valence $\pi$ and three $3p_x$ orbitals. - $^c$Using reference (12e,10o) active space including valence $\pi$, $\nN$ and $3s$ orbitals. -\end{table*} - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Results and discussion} \label{sec:res} diff --git a/Manuscript/sup_CASPT3.tex b/Manuscript/sup_CASPT3.tex new file mode 100644 index 0000000..123588d --- /dev/null +++ b/Manuscript/sup_CASPT3.tex @@ -0,0 +1,943 @@ +\documentclass[aip,jcp,reprint,noshowkeys,superscriptaddress,onecolumn]{revtex4-1} +\usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,wrapfig,txfonts,siunitx} +\usepackage[version=4]{mhchem} +%\usepackage{natbib} +%\bibliographystyle{achemso} + +\newcommand{\fk}[1]{\textcolor{blue}{#1}} + +\newcommand{\ie}{\textit{i.e.}} +\newcommand{\eg}{\textit{e.g.}} +\newcommand{\alert}[1]{\textcolor{black}{#1}} +\usepackage[normalem]{ulem} +\newcommand{\titou}[1]{\textcolor{red}{#1}} +\newcommand{\trashPFL}[1]{\textcolor{red}{\sout{#1}}} +\newcommand{\PFL}[1]{\titou{(\underline{\bf PFL}: #1)}} +\newcommand{\toto}[1]{\textcolor{green}{#1}} +\newcommand{\trashAS}[1]{\textcolor{green}{\sout{#1}}} +\newcommand{\AS}[1]{\toto{(\underline{\bf AS}: #1)}} +\newcommand{\ant}[1]{\textcolor{orange}{#1}} +\newcommand{\SupInf}{\textcolor{blue}{Supporting Information}} + +\newcommand{\mc}{\multicolumn} +\newcommand{\fnm}{\footnotemark} +\newcommand{\fnt}{\footnotetext} +\newcommand{\tabc}[1]{\multicolumn{1}{c}{#1}} +\newcommand{\QP}{\textsc{quantum package}} + +\newcommand{\sig}{\sigma} +\newcommand{\sigs}{\sigma^*} +\newcommand{\pis}{{\pi^*}} + +\newcommand{\nN}{{n_{\ce{N}}}} +\newcommand{\nO}{{n_{\ce{O}}}} +\newcommand{\nS}{{n_{\ce{S}}}} + +\newcommand{\sigCC}{\sig_{\ce{CC}}} +\newcommand{\sigsCC}{\sig_{\ce{CC}}^*} +\newcommand{\piCC}{\pi_{\ce{CC}}} +\newcommand{\pisCC}{\pi_{\ce{CC}}^*} + +\newcommand{\sigCN}{\sig_{\ce{CN}}} +\newcommand{\sigsCN}{\sig_{\ce{CN}}^*} +\newcommand{\piCN}{\pi_{\ce{CN}}} +\newcommand{\pisCN}{\pi_{\ce{CN}}^*} + +\newcommand{\sigNN}{\sig_{\ce{NN}}} +\newcommand{\sigsNN}{\sig_{\ce{NN}}^*} +\newcommand{\piNN}{\pi_{\ce{NN}}} +\newcommand{\pisNN}{\pi_{\ce{NN}}^*} + +\newcommand{\sigCO}{\sig_{\ce{CO}}} +\newcommand{\sigsCO}{\sig_{\ce{CO}}^*} +\newcommand{\piCO}{\pi_{\ce{CO}}} +\newcommand{\pisCO}{\pi_{\ce{CO}}^*} + +\newcommand{\sigNO}{\sig_{\ce{NO}}} +\newcommand{\sigsNO}{\sig_{\ce{NO}}^*} +\newcommand{\piNO}{\pi_{\ce{NO}}} +\newcommand{\pisNO}{\pi_{\ce{NO}}^*} + +\usepackage[ + colorlinks=true, + citecolor=blue, + breaklinks=true + ]{hyperref} +\urlstyle{same} + +\begin{document} + +% addresses +\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France} +\newcommand{\CEISAM}{Universit\'e de Nantes, CNRS, CEISAM UMR 6230, F-44000 Nantes, France} + +\title{Supporting Information for ``Benchmarking CASPT3 vertical excitation energies''} + +\author{Martial \surname{Boggio-Pasqua}} + \email{martial.boggio@irsamc.ups-tlse.fr} + \affiliation{\LCPQ} +\author{Denis \surname{Jacquemin}} + \affiliation{\CEISAM} +\author{Pierre-Fran\c{c}ois \surname{Loos}} + \email{loos@irsamc.ups-tlse.fr} + \affiliation{\LCPQ} + +% Abstract +\begin{abstract} +%\bigskip +%\begin{center} +% \boxed{\includegraphics[width=0.4\linewidth]{TOC}} +%\end{center} +%\bigskip +\end{abstract} + +% Title +\maketitle + +In the following Tables, we report the vertical transition energies (in eV) obtained with the aug-cc-pVTZ basis and computed with state-averaged CASSCF, state-specific CASPT2 and CASPT3 using a level shift of \SI{0.30}{\hartree} with or without an IPEA shift of \SI{0.25}{\hartree}. +The symbol $[F]$ indicates the calculation of emission from the lowest $S_1$ geometry, i.e., a vertical fluorescence. +The composition of the active space is specified in terms of number of active orbitals per irreducible representation. +The state-averaging procedure used is also described in terms of number of states per irreducible representation. +Note that, for all calculations, the ground state is systematically included in the state averaging +procedure even if it does not belong to the same irreducible representation. +The cartesian coordinates have been extracted from the QUEST database \cite{Veril_2021} and can be download at \url{https://lcpq.github.io/QUESTDB_website}. + +\begin{table*} + \caption{Vertical transition energies (eV) of acetaldehyde.} + \label{tab:acetaldehyde} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a',a'')$ & $(A',A'')$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline +$^1A''(n,\pis)$ &(3,2) &(1,1) &4.62$^a$ &4.35$^a$ &4.13$^a$ &4.44$^a$ &4.41$^a$ &4.31\\ +$^3A''(n,\pis)$ &(3,2) &(1,1) &4.28$^a$ &3.94$^a$ &3.71$^a$ &4.06$^a$ &4.03$^a$ &3.97\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Reference (6e,5o) active space including valence $\nO$, $\piCO$, $\sigCO$, $\pisCO$ and $\sigsCO$ orbitals. +\end{table*} + + +\begin{table*} + \caption{Vertical transition energies (eV) of acetone.} + \label{tab:acetone} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State &Active space &State-average &CASSCF &CASPT2 &CASPT2 &CASPT3 &CASPT3 &TBE \\ + &$(a_1,b_1,b_2,a_2)$ &$(A_1,B_1,B_2,A_2)$ & &IPEA &NOIPEA &IPEA &NOIPEA & \\ + \hline + $^1A_2(n,\pis)$ &(2,3,1,0) &(1,0,0,2) &4.77$^a$ &4.44$^a$ &4.19$^a$ &4.57$^a$ &4.55$^a$ &4.47\\ + $^1B_2(n,3s)$ &(4,2,1,0) &(1,0,2,0) &5.50$^b$ &6.46$^b$ &6.35$^b$ &6.64$^b$ &6.67$^b$ &6.46\\ + $^1A_2(n,3p_x)$ &(2,3,1,0) &(1,0,0,2) &7.46$^a$ &7.80$^a$ &7.55$^a$ &7.76$^a$ &7.68$^a$ &7.47\\ + $^1A_1(n,3p_y)$ &(2,2,2,0) &(2,0,0,0) &7.03$^c$ &7.67$^c$ &7.46$^c$ &7.76$^c$ &7.75$^c$ &7.51\\ + $^1B_2(n,3p_z)$ &(4,2,1,0) &(1,0,2,0) &6.44$^b$ &7.56$^b$ &7.47$^b$ &7.73$^b$ &7.76$^b$ &7.62\\ + $^3A_2(n,\pis)$ &(2,2,1,0) &(1,0,0,1) &4.47$^d$ &4.13$^d$ &3.89$^d$ &4.27$^d$ &4.24$^d$ &4.13\\ + $^3A_1(\pi,\pis)$ &(2,2,0,0) &(2,0,0,0) &6.22$^e$ &6.24$^e$ &6.07$^e$ &6.26$^e$ &6.22$^e$ &6.25\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Using reference (6e,6o) active space including valence $\pi$, $\nO$, $\sigCO$, $\sigsCO$ and $3p_x$ orbitals. + $^b$Using reference (6e,7o) active space including valence $\pi$, $\nO$, $\sigCO$, $\sigsCO$, $3s$ and $3p_z$ orbitals. + $^c$Using reference (6e,6o) active space including valence $\pi$, $\nO$, $\sigCO$, $\sigsCO$ and $3p_y$ orbitals. + $^d$Using reference (6e,5o) active space including valence $\pi$, $\nO$, $\sigCO$ and $\sigsCO$ orbitals. + $^e$Using reference (4e,4o) active space including valence $\pi$, $\sigCO$, $\sigsCO$ orbitals. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of acrolein.} + \label{tab:acrolein} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a',a'')$ & $(A',A'')$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1A''(n,\pis)$ &(1,5) &(1,3) &3.48$^c$ &3.58$^c$ &3.46$^c$ &3.66$^c$ &3.66$^c$ &3.78\\ + $^1A'(\pi,\pis)$ &(2,4) &(4,0) &8.84$^d$ &6.93$^d$ &6.28$^d$ &7.18$^d$ &7.05$^d$ &6.69\\ + $^1A''(n,\pis)$ &(1,5) &(1,3) &6.76$^{c,e}$&6.79$^{a,e}$&6.34$^{a,e}$&6.88$^{a,e}$&6.80$^{a,e}$&6.72\\ + $^1A'(n,3s)$ &(2,4) &(4,0) &7.20$^d$ &7.21$^d$ &6.98$^d$ &7.20$^d$ &7.16$^d$ &7.08\\ + $^1A'(\pi^2,\pis^2)$&(2,4) &(4,0) &7.91$^d$ &8.10$^d$ &7.75$^d$ &8.02$^d$ &7.95$^d$ &7.87\\ + $^3A''(n,\pis)$ &(1,5) &(1,3) &3.25$^c$ &3.28$^c$ &3.15$^c$ &3.39$^c$ &3.40$^c$ &3.51\\ + $^3A'(\pi,\pis)$ &(2,4) &(4,0) &3.89$^d$ &4.01$^d$ &3.78$^d$ &3.96$^d$ &3.91$^d$ &3.94\\ + $^3A'(\pi,\pis)$ &(2,4) &(4,0) &5.89$^d$ &6.20$^d$ &5.93$^d$ &6.10$^d$ &6.02$^d$ &6.18\\ + $^3A''(n,\pis)$ &(1,5) &(1,3) &6.67$^{c,e}$&6.65$^{c,e}$&6.21$^{c,e}$&6.74$^{c,e}$&6.66$^{c,e}$&6.54\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Using reference (12e,12o) active space including valence $\pi$, $\sigCC$, $\sigsCO$, $\sigsCC$, $\sigsCO$, $\nO$ and $3s$ orbitals. + $^b$Level shift det to \SI{0.4}{\hartree}. + $^c$Using reference (6e,6o) active space including valence $\pi$, $\nO$ and $3p_z$ orbitals. + $^d$Using reference (6e,6o) active space including valence $\pi$, $\nO$ and $3s$ orbitals. + $^e$Substantial Rydberg and doubly-excited character. + $^f$Substantial doubly-excited character. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of benzene.} + \label{tab:benzene} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_g,b_{3u},b_{2u},b_{1g},b_{1u},b_{2g},b_{3g},a_u)$ & $(A_g,B_{3u},B_{2u},B_{1g},B_{1u},B_{2g},B_{3g},A_u)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1B_{2u}(\pi,\pis)$ &(0,0,0,0,2,1,2,1) &(1,1,0,0,0,0,0,0) &4.98$^a$ &5.14$^a$ &4.66$^a$ &5.09$^a$ &5.01$^a$ &5.06\\ + $^1B_{1u}(\pi,\pis)$ &(0,0,0,0,4,1,2,2) &(1,1,2,0,0,0,0,0) &7.27$^b$ &6.65$^b$ &6.23$^b$ &6.67$^b$ &6.58$^b$ &6.45\\ + $^1E_{1g}(\pi,3s)$ &(1,0,0,0,2,1,2,1) &(1,0,0,0,0,1,1,0) &5.90$^c$ &6.70$^c$ &6.57$^c$ &6.56$^c$ &6.51$^c$ &6.52\\ + $^1A_{2u}(\pi,3p_{x,y})$ &(0,1,1,0,2,1,2,1) &(1,0,0,0,2,0,0,1) &6.14$^d$ &7.21$^d$ &7.07$^d$ &7.07$^d$ &7.02$^d$ &7.08\\ + $^1E_{2u}(\pi,3p_{x,y})$ &(0,1,1,0,2,1,2,1) &(1,0,0,0,2,0,0,1) &6.21$^d$ &7.26$^d$ &7.12$^d$ &7.13$^d$ &7.08$^d$ &7.15\\ + $^1E_{2g}(\pi^2,\pis^2)$ &(0,0,0,0,2,1,2,1) &(2,0,0,1,0,0,0,0) &8.10$^a$ &8.31$^a$ &7.82$^{a,e}$ &8.26$^a$ &8.16$^{a,e}$ &8.28\\ + $^3B_{1u}(\pi,\pis)$ &(0,0,0,0,4,1,2,2) &(1,0,1,0,0,0,0,0) &3.85$^b$ &4.22$^b$ &3.92$^b$ &4.14$^b$ &4.08$^b$ &4.16\\ + $^3E_{1u}(\pi,\pis)$ &(0,0,0,0,4,1,2,2) &(1,1,1,0,0,0,0,0) &4.85$^b$ &4.89$^b$ &4.51$^b$ &4.87$^b$ &4.80$^b$ &4.85\\ + $^3B_{2u}(\pi,\pis)$ &(0,0,0,0,4,1,2,2) &(1,1,0,0,0,0,0,0) &6.75$^b$ &5.85$^b$ &5.40$^b$ &5.90$^b$ &5.81$^b$ &5.81\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Using reference (6e,6o) active space including valence $\pi$ orbitals. + $^b$Using reference (6e,9o) active space including valence $\pi$ and three $3p_z$ orbitals. + $^c$Using reference (6e,7o) active space including valence $\pi$ and $3s$ orbitals. + $^d$Using reference (6e,8o) active space including valence $\pi$, $3p_x$ and $3p_y$ orbitals. + $^e$Level shift set to \SI{0.4}{\hartree}. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of butadiene.} + \label{tab:butadiene} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_g,a_u,b_u,b_g)$ & $(A_g,A_u,B_u,B_g)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1B_u(\pi,\pis)$ &(0,4,0,4) &(1,0,2,0) &6.65$^a$ &6.76$^a$ &6.52$^a$ &6.72$^a$ &6.65$^a$ &6.22\\ + $^1B_g(\pi,3s)$ &(4,2,3,2) &(1,0,0,1) &5.94$^b$ &6.49$^b$ &6.32$^b$ &6.43$^b$ &6.38$^b$ &6.33\\ + $^1A_g(\pi^2,\pis^2)$ &(3,2,3,2) &(2,0,0,0) &6.99$^c$ &6.74$^c$ &6.30$^{c,d}$ &6.73$^c$ &6.66$^{c,d}$ &6.50\\ + $^1A_u(\pi,3p_x)$ &(3,2,5,2) &(1,2,0,0) &5.95$^e$ &6.74$^e$ &6.64$^e$ &6.70$^e$ &6.67$^e$ &6.64\\ + $^1A_u(\pi,3p_y)$ &(3,2,5,2) &(1,2,0,0) &6.12$^e$ &6.95$^e$ &6.84$^e$ &6.90$^e$ &6.86$^e$ &6.80\\ + $^1B_u(\pi,3p_z)$ &(0,4,0,4) &(1,0,2,0) &7.93$^a$ &7.60$^a$ &7.30$^a$ &7.62$^a$ &7.54$^a$ &7.68\\ + $^3B_u(\pi,\pis)$ &(3,2,3,2) &(1,0,1,0) &3.55$^c$ &3.40$^c$ &3.19$^c$ &3.40$^c$ &3.35$^c$ &3.36\\ + $^3A_g(\pi,\pis)$ &(3,2,3,2) &(2,0,0,0) &5.52$^c$ &5.32$^c$ &4.93$^c$ &5.29$^c$ &5.19$^c$ &5.20\\ + $^3B_g(\pi,3s)$ &(4,2,3,2) &(1,0,0,1) &5.89$^b$ &6.44$^b$ &6.27$^b$ &6.38$^b$ &6.33$^b$ &6.29\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Using reference (4e,8o) active space including valence $\pi$ and four $3p_z$. + $^b$Using reference (10e,11o) active space including valence $\pi$, $\sigCC$, $\sigsCC$ and $3s$ orbitals. + $^c$Using reference (10e,10o) active space including valence $\pi$, $\sigCC$ and $\sigsCC$ orbitals. + $^d$Level shift set to \SI{0.4}{\hartree}. + $^e$Using reference (10e,12o) active space including valence $\pi$, $\sigCC$, $\sigsCC$, $3p_x$ and $3p_y$ orbitals. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of carbon trimer.} + \label{tab:carbon_trimer} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_g,b_{3u},b_{2u},b_{1g},b_{1u},b_{2g},b_{3g},a_u)$ & $(A_g,B_{3u},B_{2u},B_{1g},B_{1u},B_{2g},B_{3g},A_u)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $1\Delta_g(n^2,\pis^2)$ &(3,2,2,0,3,1,1,0) &(2,0,0,1,0,0,0,0) &4.98$^a$ &5.08$^a$ &4.85$^{a,b}$ &5.20$^a$ &5.19$^{a,c}$ &5.22\\ + $1\Sigma_g^+(n^2,\pis^2)$ &(3,2,2,0,3,1,1,0) &(2,0,0,0,0,0,0,0) &5.84$^a$ &5.82$^a$ &5.58$^{a,c}$ &5.92$^a$ &5.89$^{a,b}$ &5.91\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$All calculations using a full valence (12e,12o) active space. + $^b$Level shift set to \SI{0.4}{\hartree}. + $^c$Level shift set to \SI{0.5}{\hartree}. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of cyanoacetylene.$^a$} + \label{tab:cyanoacetylene} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1\Sigma^-(\pi,\pis)$ &(0,4,4,0) &(1,0,0,1) &6.54 &5.85 &5.47 &5.89 &5.81 &5.80\\ + $^1\Delta(\pi,\pis)$ &(0,4,4,0) &(2,0,0,1) &6.80 &6.13 &5.78 &6.17 &6.09 &6.07\\ + $^3\Sigma^+(\pi,\pis)$ &(0,4,4,0) &(2,0,0,0) &4.86 &4.45 &4.04 &4.52 &4.45 &4.44\\ + $^3\Delta(\pi,\pis)$ &(0,4,4,0) &(2,0,0,1) &5.64 &5.21 &4.86 &5.26 &5.19 &5.21\\ + $^1A''[F](\pi,\pis)$ &($a'$:4,$a''$:4) &($A'$:1,$A''$:1) &4.30 &3.67 &3.47 &3.64 &3.58 &3.54\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$All calculations using a full valence $\pi$ active space of (8e,8o). +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of cyanoformaldehyde.} + \label{tab:cyanoformaldehyde} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a',a'')$ & $(A',A'')$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1A''(n,\pis)$ &(3,4) &(1,2) &4.02$^a$ &3.98$^a$ &3.67$^a$ &3.94$^a$ &3.89$^a$ &3.81\\ + $^1A''(\pi,\pis)$ &(3,4) &(1,2) &7.61$^a$ &6.79$^a$ &6.43$^a$ &6.77$^a$ &6.67$^a$ &6.46\\ + $^3A''(n,\pis)$ &(3,4) &(1,1) &3.52$^a$ &3.46$^a$ &3.25$^a$ &3.51$^a$ &3.50$^a$ &3.44\\ + $^3A'(\pi,\pis)$ &(2,4) &(2,0) &4.98$^b$ &5.25$^b$ &5.03$^b$ &5.16$^b$ &5.12$^b$ &5.01\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Using reference (8e,7o) active space including valence $\pi$ and $\nO$ orbitals. + $^b$Using reference (6e,6o) active space including valence $\pi$ orbitals. +\end{table*} + + +\begin{table*} + \caption{Vertical transition energies (eV) of cyanogen.$^a$} + \label{tab:cyanogen} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_g,b_{3u},b_{2u},b_{1g},b_{1u},b_{2g},b_{3g},a_u)$ & $(A_g,B_{3u},B_{2u},B_{1g},B_{1u},B_{2g},B_{3g},A_u)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1\Sigma_u^-(\pi,\pis)$ &(0,2,2,0,0,2,2,0) &(1,0,0,0,0,0,0,1) &7.14 &6.40 &6.03 &6.46 &6.39 &6.39\\ + $^1\Delta_u(\pi,\pis)$ &(0,2,2,0,0,2,2,0) &(1,0,0,0,1,0,0,1) &7.46 &6.70 &6.35 &6.75 &6.68 &6.66\\ + $^3\Sigma_u^+(\pi,\pis)$ &(0,2,2,0,0,2,2,0) &(1,0,0,0,1,0,0,0) &5.28 &4.85 &4.46 &4.95 &4.89 &4.91\\ + $^1\Sigma_u^-[F](\pi,\pis)$ &(0,2,2,0,0,2,2,0) &(1,0,0,0,0,0,0,1) &5.68 &5.07 &4.75 &5.11 &5.04 &5.05\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$All calculations using a full valence $\pi$ active space of (8e,8o). +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of cyclopentadiene.} + \label{tab:cyclopentadiene} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1B_2(\pi,\pis)$ &(0,4,0,2) &(1,0,2,0) &6.71$^a$ &5.96$^a$ &5.62$^a$ &6.06$^a$ &5.99$^a$ &5.56\\ + $^1A_2(\pi,3s)$ &(2,2,0,2) &(1,0,0,2) &5.21$^b$ &5.88$^b$ &5.78$^b$ &5.81$^b$ &5.77$^b$ &5.78\\ + $^1B_1(\pi,3p_y)$ &(0,2,1,2) &(1,1,0,0) &6.08$^c$ &6.59$^c$ &6.44$^c$ &6.47$^c$ &6.41$^c$ &6.41\\ + $^1A_2(\pi,3p_z)$ &(2,2,0,2) &(1,0,0,2) &5.78$^b$ &6.55$^b$ &6.46$^b$ &6.45$^b$ &6.41$^b$ &6.46\\ + $^1B_2(\pi,3p_x)$ &(0,4,0,2) &(1,0,2,0) &6.16$^a$ &6.72$^a$ &6.56$^a$ &6.61$^a$ &6.54$^a$ &6.56\\ + $^1A_1(\pi,\pis)$ &(0,2,0,2) &(3,0,0,0) &6.49$^{d,e}$ &6.63$^{d,e}$ &6.13$^{d,e}$ &6.59$^{d,e}$ &6.50$^{d,e}$ &6.52\\ + $^3B_2(\pi,\pis)$ &(0,2,0,2) &(1,0,1,0) &3.26$^d$ &3.34$^d$ &3.09$^d$ &3.31$^d$ &3.26$^d$ &3.31\\ + $^3A_1(\pi,\pis)$ &(0,2,0,2) &(3,0,0,0) &4.92$^d$ &5.14$^d$ &4.78$^d$ &5.10$^d$ &5.03$^d$ &5.11\\ + $^3A_2(\pi,3s)$ &(1,2,0,2) &(1,0,0,1) &5.53$^f$ &5.91$^f$ &5.74$^f$ &5.81$^f$ &5.75$^f$ &5.73\\ + $^3B_1(\pi,3p_y)$ &(0,2,1,2) &(1,1,0,0) &6.05$^c$ &6.56$^c$ &6.40$^c$ &6.43$^c$ &6.37$^c$ &6.36\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Using reference (4e,6o) active space including valence $\pi$ and two $3p_x$ orbitals. + $^b$Using reference (4e,6o) active space including valence $\pi$, $3s$ and $3p_z$ orbitals. + $^c$Using reference (4e,5o) active space including valence $\pi$ and $3p_y$ orbitals. + $^d$Using reference (4e,4o) active space including valence $\pi$ orbitals. + $^e$Strong double-excitation character. + $^f$Using reference (4e,5o) active space including valence $\pi$ and $3s$ orbitals. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of cyclopropene.} + \label{tab:cyclopropene} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1B_1(\sig,\pis)$ &(3,1,3,1) &(1,1,0,0) &7.48$^a$ &6.86$^a$ &6.58$^a$ &6.85$^a$ &6.77$^a$ &6.68\\ + $^1B_2(\pi,\pis)$ &(3,1,3,1) &(1,0,1,0) &7.47$^a$ &6.89$^a$ &6.47$^a$ &6.96$^a$ &6.87$^a$ &6.79\\ + $^3B_2(\pi,\pis)$ &(3,1,3,1) &(1,0,1,0) &4.60$^a$ &4.47$^a$ &4.27$^a$ &4.46$^a$ &4.40$^a$ &4.38\\ + $^3B_1(\sig,\pis)$ &(3,1,3,1) &(1,1,0,0) &7.08$^a$ &6.56$^a$ &6.32$^a$ &6.55$^a$ &6.47$^a$ &6.45\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Reference (8e,8o) active space including valence $\piCC$, $\sigCC$ and $\pisCC$, $\sigsCC$ orbitals. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of cyclopropenethione.} + \label{tab:cyclopropenethione} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1A_2(n,\pis)$ &(0,3,1,1) &(1,0,0,1) &3.44$^a$ &3.43$^a$ &3.14$^a$ &3.46$^a$ &3.40$^a$ &3.41\\ + $^1B_1(n,\pis)$ &(0,3,1,1) &(1,1,0,0) &3.57$^a$ &3.45$^a$ &3.17$^a$ &3.52$^a$ &3.46$^a$ &3.45\\ + $^1B_2(\pi,\pis)$ &(2,3,1,1) &(1,0,3,0) &4.51$^b$ &4.64$^b$ &4.35$^b$ &4.66$^b$ &4.61$^b$ &4.60\\ + $^1B_2(n,3s)$ &(2,3,1,1) &(1,0,3,0) &4.59$^b$ &5.25$^b$ &5.15$^b$ &5.25$^b$ &5.22$^b$ &5.34\\ + $^1A_1(\pi,\pis)$ &(0,3,0,1) &(2,0,0,0) &6.46$^c$ &5.84$^c$ &5.32$^c$ &5.88$^c$ &5.75$^c$ &5.46\\ + $^1B_2(n,3p_z)$ &(2,3,1,1) &(1,0,3,0) &5.27$^b$ &5.93$^b$ &5.86$^b$ &5.92$^b$ &5.90$^b$ &5.92\\ + $^3A_2(n,\pis)$ &(0,3,1,1) &(1,0,0,1) &3.26$^a$ &3.28$^a$ &3.00$^a$ &3.33$^a$ &3.28$^a$ &3.28\\ + $^3B_1(n,\pis)$ &(0,3,1,1) &(1,1,0,0) &3.51$^a$ &3.35$^a$ &3.07$^a$ &3.42$^a$ &3.36$^a$ &3.32\\ + $^3B_2(\pi,\pis)$ &(2,3,1,1) &(1,0,3,0) &3.80$^b$ &3.97$^b$ &3.75$^b$ &3.99$^b$ &3.95$^b$ &4.01\\ + $^3A_1(\pi,\pis)$ &(0,3,0,1) &(2,0,0,0) &3.83$^c$ &4.01$^c$ &3.77$^c$ &4.00$^c$ &3.95$^c$ &4.01\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Using reference (6e,5o) active space including valence $\pi$ and $\nS$. + $^b$Using reference (6e,7o) active space including valence $\pi$, $\nS$, $3s$ and $3p_z$. + $^c$Using reference (4e,4o) active space including valence $\pi$. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of cyclopropenone.} + \label{tab:cyclopropenone} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1B_1(n,\pis)$ &(2,3,1,1) &(1,3,0,0) &4.92$^a$ &4.12$^a$ &3.75$^a$ &4.40$^a$ &4.38$^a$ &4.26\\ + $^1A_2(n,\pis)$ &(0,4,2,1) &(1,0,0,3) &5.64$^b$ &5.62$^b$ &5.31$^b$ &5.67$^b$ &5.64$^b$ &5.55\\ + $^1B_2(n,3s)$ &(2,3,1,1) &(1,0,3,0) &5.68$^a$ &6.28$^a$ &6.21$^a$ &6.41$^a$ &6.44$^a$ &6.34\\ + $^1B_2(\pi,\pis)$ &(2,3,1,1) &(1,0,3,0) &6.40$^a$ &6.54$^a$ &6.20$^a$ &6.63$^a$ &6.62$^a$ &6.54\\ + $^1B_2(n,3p_z)$ &(2,3,1,1) &(1,0,3,0) &6.35$^a$ &6.84$^a$ &6.70$^a$ &6.99$^a$ &7.01$^a$ &6.98\\ + $^1A_1(n,3p_y)$ &(0,4,2,1) &(4,0,0,0) &6.84$^b$ &7.27$^b$ &7.03$^b$ &7.26$^b$ &7.24$^b$ &7.02\\ + $^1A_1(\pi,\pis)$ &(0,4,2,1) &(4,0,0,0) &10.42$^b$ &8.96$^b$ &8.11$^b$ &9.21$^b$ &9.07$^b$ &8.28\\ + $^3B_1(n,\pis)$ &(2,3,1,1) &(1,3,0,0) &4.72$^a$ &3.65$^a$ &3.28$^a$ &4.00$^a$ &3.98$^a$ &3.93\\ + $^3B_2(\pi,\pis)$ &(2,3,1,1) &(1,0,3,0) &4.39$^a$ &4.76$^a$ &4.60$^a$ &4.76$^a$ &4.74$^a$ &4.88\\ + $^3A_2(n,\pis)$ &(0,4,2,1) &(1,0,0,3) &5.40$^b$ &5.36$^b$ &5.06$^b$ &5.44$^b$ &5.42$^b$ &5.35\\ + $^3A_1(\pi,\pis)$ &(0,4,2,1) &(4,0,0,0) &6.59$^b$ &6.93$^b$ &6.61$^b$ &6.86$^b$ &6.82$^b$ &6.79\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Using reference (6e,7o) active space including valence $\pi$, $\nO$, $3s$ and $3p_z$. + $^b$Using reference (6e,7o) active space including valence $\pi$, $\nO$, $3p_x$ and $3p_y$. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of diacetylene.$^a$} + \label{tab:diacetylene} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_g,b_{3u},b_{2u},b_{1g},b_{1u},b_{2g},b_{3g},a_u)$ & $(A_g,B_{3u},B_{2u},B_{1g},B_{1u},B_{2g},B_{3g},A_u)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1\Sigma_u^-(\pi,\pis)$ &(0,2,2,0,0,2,2,0) &(1,0,0,0,0,0,0,1) &6.13 &5.42 &5.01 &5.45 &5.36 &5.33\\ + $^1\Delta_u(\pi,\pis)$ &(0,2,2,0,0,2,2,0) &(1,0,0,0,1,0,0,1) &6.39 &5.68 &5.30 &5.72 &5.63 &5.61\\ + $^3\Sigma_u^+(\pi,\pis)$ &(0,2,2,0,0,2,2,0) &(1,0,0,0,1,0,0,0) &4.54 &4.11 &3.67 &4.17 &4.09 &4.10\\ + $^3\Delta_u(\pi,\pis)$ &(0,2,2,0,0,2,2,0) &(1,0,0,0,1,0,0,1) &5.28 &4.82 &4.45 &4.86 &4.78 &4.78\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$All calculations using a full valence $\pi$ active space of (8e,8o). +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of diazomethane.} + \label{tab:diazomethane} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline +$^1A_2(\pi,\pis)$ &(4,3,2,0) &(1,0,0,1) &3.27$^a$ &3.13$^a$ &2.92$^a$ &3.09$^a$ &3.04$^a$ &3.14\\ +$^1B_1(\pi,3s)$ &(5,3,2,0) &(1,1,0,0) &4.59$^b$ &5.50$^b$ &5.30$^b$ &5.48$^b$ &5.45$^b$ &5.54\\ +$^1A_1(\pi,\pis)$ &(4,4,2,0) &(3,0,0,0) &5.65$^c$ &6.21$^c$ &5.92$^c$ &6.18$^c$ &6.13$^c$ &5.90\\ +$^3A_2(\pi,\pis)$ &(4,3,2,0) &(1,0,0,1) &3.02$^a$ &2.87$^a$ &2.67$^a$ &2.84$^a$ &2.79$^a$ &2.79\\ +$^3A_1(\pi,\pis)$ &(4,3,2,0) &(2,0,0,0) &4.27$^a$ &4.10$^a$ &3.88$^a$ &4.06$^a$ &4.01$^a$ &4.05\\ +$^3B_1(\pi,3s)$ &(5,3,2,0) &(1,1,0,0) &4.45$^b$ &5.34$^b$ &5.15$^b$ &5.33$^b$ &5.30$^b$ &5.35\\ +$^3A_1(\pi,3p)$ &(4,4,2,0) &(3,0,0,0) &6.34$^c$ &7.00$^c$ &6.76$^c$ &6.96$^c$ &6.91$^c$ &6.82\\ +$^1A''[F](\pi,\pis)$ &($a'$:6,$a''$:3) &($A'$:1,$A''$:1) &0.72$^a$ &0.69$^a$ &0.52$^a$ &0.66$^a$ &0.62$^a$ &0.71\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Reference (10e,9o) active space including valence $\pi$, $\sigCN$, $\sigNN$ and $\sigsCN$, $\sigsNN$ orbitals. + $^b$Reference (10e,10o) active space including valence $\pi$, $\sigCN$, $\sigNN$ and $\sigsCN$, $\sigsNN$, Rydberg $3s$ orbitals. + $^c$Reference (10e,10o) active space including valence $\pi$, $\sigCN$, $\sigNN$ and $\sigsCN$, $\sigsNN$, Rydberg $3p$ orbitals. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of formamide.} + \label{tab:formamide} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a',a'')$ & $(A',A'')$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1A''(n,\pis)$ &(5,3) &(1,1) &5.95$^a$ &5.66$^a$ &5.45$^a$ &5.71$^a$ &5.67$^a$ &5.65\\ + $^1A'(n,3s)$ &(7,3) &(4,0) &6.17$^b$ &6.80$^b$ &6.64$^b$ &6.82$^b$ &6.81$^b$ &6.77\\ + $^1A'(n,3p)$ &(7,3) &(4,0) &6.74$^b$ &7.45$^b$ &7.32$^b$ &7.46$^b$ &7.46$^b$ &7.38\\ + $^1A'(\pi,\pis)$ &(7,3) &(4,0) &8.80$^b$ &7.88$^b$ &7.13$^b$ &7.95$^b$ &7.78$^b$ &7.63\\ + $^3A''(n,\pis)$ &(5,3) &(1,1) &5.89$^a$ &5.36$^a$ &5.16$^a$ &5.41$^a$ &5.37$^a$ &5.38\\ + $^3A'(\pi,\pis)$ &(4,3) &(2,0) &6.10$^c$ &5.88$^c$ &5.62$^c$ &5.91$^c$ &5.87$^c$ &5.81\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Reference (10e,8o) active space including valence $\pi$, $\nO$, $\sigCN$, $\sigCO$ and $\sigsCN$, $\sigsCO$ orbitals. + $^b$Reference (10e,10o) active space including valence $\pi$, $\nO$, $\sigCN$, $\sigCO$ and $\sigsCN$, $\sigsCO$, Rydberg $3s$ and $3p$ orbitals. + $^c$Reference (8e,7o) active space including valence $\pi$, $\sigCN$, $\sigCO$ and $\sigsCN$, $\sigsCO$ orbitals. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of furan.} + \label{tab:furan} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1A_2(\pi,3s)$ &(2,3,0,2) &(1,0,0,2) &5.26$^a$ &6.16$^a$ &6.04$^a$ &6.06$^a$ &6.02$^a$ &6.09\\ + $^1B_2(\pi,\pis)$ &(0,4,0,2) &(1,0,2,0) &7.78$^b$ &6.59$^b$ &6.02$^b$ &6.80$^b$ &6.71$^b$ &6.37\\ + $^1A_1(\pi,\pis)$ &(0,3,0,2) &(3,0,0,0) &6.73$^{c,d}$ &6.66$^{c,d}$ &6.10$^{c,d}$ &6.69$^{c,d}$ &6.62$^{c,d}$ &6.56\\ + $^1B_1(\pi,3p_y)$ &(0,3,1,2) &(1,1,0,0) &6.07$^e$ &6.79$^e$ &6.63$^e$ &6.65$^e$ &6.60$^e$ &6.64\\ + $^1A_2(\pi,3p_z)$ &(2,3,0,2) &(1,0,0,2) &5.87$^a$ &6.87$^a$ &6.77$^a$ &6.76$^a$ &6.72$^a$ &6.81\\ + $^1B_2(\pi,3p_x)$ &(0,4,0,2) &(1,0,2,0) &6.54$^b$ &7.11$^b$ &6.84$^b$ &6.96$^b$ &6.88$^b$ &7.24\\ + $^3B_2(\pi,\pis)$ &(0,3,0,2) &(1,0,1,0) &3.94$^c$ &4.26$^c$ &4.01$^c$ &4.17$^c$ &4.12$^c$ &4.20\\ + $^3A_1(\pi,\pis)$ &(0,3,0,2) &(3,0,0,0) &5.41$^c$ &5.50$^c$ &5.09$^c$ &5.47$^c$ &5.40$^c$ &5.46\\ + $^3A_2(\pi,3s)$ &(1,3,0,2) &(1,0,0,1) &5.57$^f$ &6.16$^f$ &5.99$^f$ &6.05$^f$ &5.99$^f$ &6.02\\ + $^3B_1(\pi,3p_y)$ &(0,3,1,2) &(1,1,0,0) &6.04$^e$ &6.76$^e$ &6.60$^e$ &6.62$^e$ &6.56$^e$ &6.59\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Using reference (6e,7o) active space including valence $\pi$, $3s$ and $3p_z$ orbitals. + $^b$Using reference (6e,6o) active space including valence $\pi$ and $3p_x$ orbitals. + $^c$Using reference (6e,5o) active space including valence $\pi$ orbitals. + $^d$Strong double-excitation character. + $^e$Using reference (6e,6o) active space including valence $\pi$ and $3p_y$ orbitals. + $^f$Using reference (6e,6o) active space including valence $\pi$ and $3s$ orbitals. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of imidazole.} + \label{tab:imidazole} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a',a'')$ & $(A',A'')$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1A''(\pi,3s)$ &(2,5) &(1,3) &5.04$^a$ &5.88$^a$ &5.66$^a$ &5.74$^a$ &5.68$^a$ &5.70\\ + $^1A'(\pi,3p)$ &(0,9) &(3,0) &6.18$^b$ &6.69$^b$ &6.45$^b$ &6.61$^b$ &6.56$^b$ &6.41\\ + $^1A''(\pi,3p)$ &(4,6) &(1,7) &5.43$^c$ &6.57$^c$ &6.47$^c$ &6.47$^c$ &6.44$^c$ &6.50\\ + $^1A''(n,\pis)$ &(2,5) &(1,3) &7.13$^a$ &6.94$^a$ &6.57$^a$ &6.92$^a$ &6.85$^a$ &6.73\\ + $^1A''(\pi,3p)$ &(4,6) &(1,7) &5.74$^c$ &6.87$^c$ &6.67$^c$ &6.79$^c$ &6.77$^c$ &---\\ + $^1A''(\pi,3s)$ &(4,6) &(1,7) &5.68$^c$ &6.89$^c$ &6.70$^c$ &6.82$^c$ &6.79$^c$ &---\\ + $^1A'(\pi,\pis)$ &(0,9) &(3,0) &6.73$^b$ &6.88$^b$ &6.46$^b$ &6.89$^b$ &6.83$^b$ &6.87\\ + $^1A'(n,3s)$ &(2,5) &(2,0) &6.36$^a$ &7.10$^a$ &6.91$^a$ &7.09$^a$ &7.07$^a$ &7.02\\ + $^3A'(\pi,\pis)$ &(0,9) &(3,0) &4.55$^b$ &4.78$^b$ &4.53$^b$ &4.73$^b$ &4.68$^b$ &4.73\\ + $^3A''(\pi,3s)$ &(2,5) &(1,3) &5.03$^a$ &5.86$^a$ &5.63$^a$ &5.72$^a$ &5.66$^a$ &5.66\\ + $^3A'(\pi,\pis)$ &(0,9) &(3,0) &5.69$^b$ &5.85$^b$ &5.48$^b$ &5.80$^b$ &5.72$^b$ &5.74\\ + $^3A''(n,\pis)$ &(2,5) &(1,3) &6.58$^a$ &6.44$^a$ &6.10$^a$ &6.43$^a$ &6.37$^a$ &6.31\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Using reference $(8e,7o)$ active space including valence $\pi$, $\nN$ and $3s$ orbitals. + $^b$Using reference $(6e,9o)$ active space including valence $\pi$ and four $3p_z$ orbitals. + $^c$Using reference $(8e,10o)$ active space including valence $\pi$, $\nN$, $3s$ and three $3p$ orbitals. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of isobutene.} + \label{tab:isobutene} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1B_1(\pi,3s)$ &(3,2,0,0) &(1,1,0,0) &6.21$^a$ &6.74$^a$ &6.59$^a$ &6.64$^a$ &6.57$^a$ &6.46\\ + $^1A_1(\pi,3p_x)$ &(2,3,0,0) &(2,0,0,0) &6.90$^b$ &7.32$^b$ &7.14$^b$ &7.24$^b$ &7.18$^b$ &7.01\\ + $^3A_1(\pi,\pis)$ &(2,2,0,0) &(2,0,0,0) &4.66$^c$ &4.59$^c$ &4.41$^c$ &4.58$^c$ &4.53$^c$ &4.53\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Using reference (4e,5o) active space including valence $\pi$, $\sigCC$, $\sigsCC$ and $3s$ orbitals. + $^b$Using reference (4e,5o) active space including valence $\pi$, $\sigCC$, $\sigsCC$ and $3p_x$ orbitals. + $^c$Using reference (4e,4o) active space including valence $\pi$, $\sigCC$ and $\sigsCC$ orbitals. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of ketene.} + \label{tab:ketene} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline +$^1A2(\pi,\pis)$ &(4,3,2,0) &(1,0,0,1) &3.98$^a$ &3.92$^a$ &3.70$^a$ &3.90$^a$ &3.85$^a$ &3.86\\ +$^1B1(\pi,3s)$ &(5,3,2,0) &(1,1,0,0) &5.22$^b$ &5.99$^b$ &5.79$^b$ &6.00$^b$ &5.97$^b$ &6.01\\ +$^1A2(\pi,3p)$ &(4,3,3,0) &(1,0,0,2) &6.38$^c$ &7.25$^c$ &7.05$^c$ &7.19$^c$ &7.15$^c$ &7.18\\ +$^3A2(\pi,\pis)$ &(4,3,2,0) &(1,0,0,1) &3.92$^a$ &3.81$^a$ &3.59$^a$ &3.79$^a$ &3.74$^a$ &3.77\\ +$^3A1(\pi,\pis)$ &(4,3,2,0) &(2,0,0,0) &5.79$^a$ &5.65$^a$ &5.43$^a$ &5.63$^a$ &5.59$^a$ &5.61\\ +$^3B1(\pi,3s)$ &(5,3,2,0) &(1,1,0,0) &5.05$^b$ &5.79$^b$ &5.60$^b$ &5.80$^b$ &5.77$^b$ &5.79\\ +$^3A2(\pi,3p)$ &(4,3,3,0) &(1,0,0,2) &6.35$^c$ &7.22$^c$ &7.01$^c$ &7.15$^c$ &7.11$^c$ &7.12\\ +$^1A''[F](\pi,\pis)$ &($a'$:6,$a''$:3) &($A'$:1,$A''$:1) &0.95$^a$ &1.05$^a$ &0.88$^a$ &1.00$^a$ &0.95$^a$ &1.00\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Reference (10e,9o) active space including valence $\pi$, $\sigCC$, $\sigCO$ and $\sigsCC$, $\sigsCO$ orbitals. + $^b$Reference (10e,10o) active space including valence $\pi$, $\sigCC$, $\sigCO$ and $\sigsCC$, $\sigsCO$, Rydberg $3s$ orbitals. + $^c$Reference (10e,10o) active space including valence $\pi$, $\sigCC$, $\sigCO$ and $\sigsCC$, $\sigsCO$, Rydberg $3p$ orbitals. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of methylenecyclopropene.} + \label{tab:methylenecyclopropene} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1B_2(\pi,\pis)$ &(0,3,0,1) &(1,0,1,0) &4.47$^a$ &4.40$^a$ &4.12$^a$ &4.39$^a$ &4.33$^a$ &4.28\\ + $^1B_1(\pi,3s)$ &(1,3,0,1) &(1,1,0,0) &4.92$^b$ &5.57$^b$ &5.44$^b$ &5.46$^b$ &5.41$^b$ &5.44\\ + $^1A_2(\pi,3p_y)$ &(0,3,1,1) &(1,0,0,1) &5.37$^b$ &6.09$^b$ &5.97$^b$ &5.97$^b$ &5.92$^b$ &5.96\\ + $^1A_1(\pi,3p_x)$ &(0,6,0,1) &(5,0,0,0) &5.37$^c$ &6.26$^c$ &6.16$^c$ &6.17$^c$ &6.13$^c$ &6.12\\ + $^3B_2(\pi,\pis)$ &(0,3,0,1) &(1,0,1,0) &3.44$^a$ &3.57$^a$ &3.34$^a$ &3.55$^a$ &3.49$^a$ &3.49\\ + $^3A_1(\pi,\pis)$ &(0,5,0,1) &(4,0,0,0) &4.60$^d$ &4.82$^d$ &4.58$^d$ &4.77$^d$ &4.72$^d$ &4.74\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Using reference (4e,4o) active space including valence $\pi$. + $^b$Using reference (4e,5o) active space including valence $\pi$ and $3s$. + $^c$Using reference (4e,5o) active space including valence $\pi$ and $3p_y$. + $^d$Using reference (4e,7o) active space including valence $\pi$, two $3p_x$ and one $3d_{xz}$. + $^e$Using reference (4e,6o) active space including valence $\pi$, one $3p_x$ and one $3d_{xz}$. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of nitrosomethane.} + \label{tab:nitrosomethane} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a',a'')$ & $(A',A'')$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline +$^1A''(n,\pis)$ &(4,2) &(1,1) &2.12$^a$ &1.84$^a$ &1.60$^a$ &1.94$^a$ &1.91$^a$ &1.96\\ +$^1A'(n^2,\pis^2)$ &(4,2) &(2,0) &4.74$^a$ &4.69$^a$ &4.67$^a$ &4.71$^a$ &4.71$^a$ &4.76\\ +$^1A'(n,3s)$ &(5,2) &(3,0) &5.87$^b$ &6.32$^b$ &6.07$^b$ &6.34$^b$ &6.31$^b$ &6.29\\ +$^3A''(n,\pis)$ &(4,2) &(1,1) &1.31$^a$ &1.00$^a$ &0.75$^a$ &1.12$^a$ &1.09$^a$ &1.16\\ +$^3A'(\pi,\pis)$ &(2,2) &(2,0) &5.52$^c$ &5.52$^c$ &5.37$^c$ &5.54$^c$ &5.50$^c$ &5.60\\ +$^1A''[F](n,\pis)$ &(4,2) &(1,1) &1.83$^a$ &1.55$^a$ &1.32$^a$ &1.66$^a$ &1.62$^a$ &1.67\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Reference (8e,6o) active space including valence $\nO$, $\nN$, $\piNO$, $\sigNO$ and $\sigsNO$, $\pisNO$ orbitals. + $^b$Reference (8e,7o) active space including valence $\nO$, $\nN$, $\piNO$, $\sigNO$ and $\sigsNO$, $\pisNO$, Rydberg 3s orbitals. + $^c$Reference (4e,4o) active space including valence $\piNO$, $\sigNO$ and $\sigsNO$, $\pisNO$ orbitals. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of propynal.} + \label{tab:propynal} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a',a'')$ & $(A',A'')$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1A''(n,\pis)$ &(3,4) &(1,2) &4.00$^a$ &3.92$^a$ &3.64$^a$ &3.90$^a$ &3.86$^a$ &3.80\\ + $^1A''(\pi,\pis)$ &(3,4) &(1,2) &6.62$^a$ &5.82$^a$ &5.49$^a$ &5.81$^a$ &5.72$^a$ &5.54\\ + $^3A''(n,\pis)$ &(3,4) &(1,1) &3.52$^a$ &3.48$^a$ &3.26$^a$ &3.52$^a$ &3.50$^a$ &3.47\\ + $^3A'(\pi,\pis)$ &(2,4) &(2,0) &4.69$^b$ &4.59$^b$ &4.30$^b$ &4.59$^b$ &4.54$^b$ &4.47\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Using reference (8e,7o) active space including valence $\pi$ and $\nO$ orbitals. + $^b$Using reference (6e,6o) active space including valence $\pi$ orbitals. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of pyrazine.} + \label{tab:pyrazine} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_g,b_{3u},b_{2u},b_{1g},b_{1u},b_{2g},b_{3g},a_u)$ & $(A_g,B_{3u},B_{2u},B_{1g},B_{1u},B_{2g},B_{3g},A_u)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1B_{3u}(n,\pis)$ &(1,2,0,1,1,2,0,1) &(1,1,0,0,0,0,0,0) &4.76a &4.09a &3.66a &4.31a &4.30a &4.15\\ + $^1A_{u}(n,\pis)$ &(1,2,0,1,1,2,0,1) &(1,0,0,0,0,0,0,1) &5.90a &4.76a &4.26a &5.10a &5.10a &4.98\\ + $^1B_{2u}(\pi,\pis)$ &(0,2,0,1,0,2,0,1) &(1,0,1,0,0,0,0,0) &4.97b &5.13b &4.65b &5.09b &5.03b &5.02\\ + $^1B_{2g}(n,\pis)$ &(1,2,0,1,1,2,0,1) &(1,0,0,0,0,1,0,0) &5.80a &5.68a &5.27a &5.73a &5.70a &5.71\\ + $^1A_{g}(n,3s)$ &(2,2,0,1,1,2,0,1) &(2,0,0,0,0,0,0,0) &6.69c &6.66c &6.27c &6.81c &6.80c &6.65\\ + $^1B_{1g}(n,\pis)$ &(1,2,0,1,1,2,0,1) &(1,0,0,1,0,0,0,0) &7.16a &6.61a &6.07a &6.78a &6.76a &6.74\\ + $^1B_{1u}(\pi,\pis)$ &(0,4,0,1,0,2,0,2) &(1,0,0,0,3,0,0,0) &8.04d &7.14d &6.72d &7.20d &7.12d &6.88\\ + $^1B_{1g}(\pi,3s)$ &(1,2,0,1,0,2,0,1) &(1,0,0,1,0,0,0,0) &6.73e &7.41e &7.27e &7.24e &7.18e &7.21\\ + $^1B_{2u}(n,3p_y)$ &(1,2,1,1,1,2,0,1) &(1,0,2,0,0,0,0,0) &7.49f &7.34f &6.93f &7.43f &7.40f &7.24\\ + $^1B_{1u}(n,3p_z)$ &(1,2,0,1,2,2,0,1) &(1,0,0,0,3,0,0,0) &7.83g &7.55g &7.08g &7.64g &7.59g &7.44\\ + $^1B_{1u}(\pi,\pis)$ &(0,4,0,1,0,2,0,2) &(1,0,0,0,3,0,0,0) &9.65d &8.59d &7.96d &8.68d &8.57d &7.98\\ + $^3B_{3u}(n,\pis)$ &(1,2,0,1,1,2,0,1) &(1,1,0,0,0,0,0,0) &4.16a &3.49a &3.08a &3.72a &3.71a &3.59\\ + $^3B_{1u}(\pi,\pis)$ &(0,4,0,1,0,2,0,2) &(1,0,0,0,2,0,0,0) &3.98d &4.44d &4.15d &4.34d &4.28d &4.35\\ + $^3B_{2u}(\pi,\pis)$ &(0,2,0,1,0,2,0,1) &(1,0,1,0,0,0,0,0) &4.62b &4.44b &4.09b &4.47b &4.41b &4.39\\ + $^3A_{u}(n,\pis)$ &(1,2,0,1,1,2,0,1) &(1,0,0,0,0,0,0,1) &5.85a &4.73a &4.21a &5.07a &5.07a &4.93\\ + $^3B_{2g}(n,\pis)$ &(1,2,0,1,1,2,0,1) &(1,0,0,0,0,1,0,0) &5.25a &5.04a &4.66a &5.14a &5.11a &5.08\\ + $^3B_{1u}(\pi,\pis)$ &(0,4,0,1,0,2,0,2) &(1,0,0,0,2,0,0,0) &5.15d &5.29d &4.92d &5.25d &5.19d &5.28\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Using reference (10e,8o) active space including valence $\pi$ and $\nN$ orbitals. + $^b$Using reference (6e,6o) active space including valence $\pi$ orbitals. + $^c$Using reference (10e,9o) active space including valence $\pi$, $\nN$ and $3s$ orbitals. + $^d$Using reference (6e,9o) active space including valence $\pi$ and three $3p_x$ orbitals. + $^e$Using reference (6e,7o) active space including valence $\pi$ and $3s$ orbitals. + $^f$Using reference (10e,9o) active space including valence $\pi$, $\nN$ and $3p_y$ orbitals. + $^g$Using reference (10e,9o) active space including valence $\pi$, $\nN$ and $3p_z$ orbitals. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of pyridazine.} + \label{tab:pyridazine} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1B_1(n,\pis)$ &(1,3,1,3) &(1,1,0,0) &4.29$^a$ &3.74$^a$ &3.36$^a$ &3.94$^a$ &3.92$^a$ &3.83\\ + $^1A_2(n,\pis)$ &(1,3,1,3) &(1,0,0,1) &4.83$^a$ &4.29$^a$ &3.87$^a$ &4.49$^a$ &4.48$^a$ &4.37\\ + $^1A_1(\pi,\pis)$ &(0,3,0,3) &(2,0,0,0) &5.12$^b$ &5.34$^b$ &4.87$^b$ &5.30$^b$ &5.25$^b$ &5.26\\ + $^1A_2(n,\pis)$ &(1,3,1,3) &(1,0,0,2) &6.26$^a$ &5.73$^a$ &5.19$^a$ &5.93$^a$ &5.89$^a$ &5.72\\ + $^1B_2(n,3s)$ &(2,3,1,3) &(1,0,1,0) &5.99$^c$ &6.18$^c$ &5.90$^c$ &6.28$^c$ &6.27$^c$ &6.17\\ + $^1B_1(n,\pis)$ &(1,3,1,3) &(1,2,0,0) &7.16$^a$ &6.50$^a$ &5.94$^a$ &6.72$^a$ &6.67$^a$ &6.37\\ + $^1B_2(\pi,\pis)$ &(0,5,0,4) &(1,0,1,0) &7.54$^d$ &7.26$^d$ &6.82$^d$ &7.25$^d$ &7.17$^d$ &6.75\\ + $^3B_1(n,\pis)$ &(1,3,1,3) &(1,1,0,0) &3.60$^a$ &3.08$^a$ &2.72$^a$ &3.29$^a$ &3.28$^a$ &3.19\\ + $^3A_2(n,\pis)$ &(1,3,1,3) &(1,0,0,1) &4.49$^a$ &4.01$^a$ &3.59$^a$ &4.20$^a$ &4.18$^a$ &4.11\\ + $^3B_2(\pi,\pis)$ &(0,3,0,3) &(1,0,1,0) &3.93$^b$ &4.44$^b$ &4.13$^b$ &4.30$^b$ &4.24$^b$ &4.34\\ + $^3A_1(\pi,\pis)$ &(0,3,0,3) &(2,0,0,0) &4.93$^b$ &4.87$^b$ &4.48$^b$ &4.89$^b$ &4.83$^b$ &4.82\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Using reference (10e,8o) active space including valence $\pi$ and $\nN$ orbitals. + $^b$Using reference (6e,6o) active space including valence $\pi$ orbitals. + $^c$Using reference (10e,9o) active space including valence $\pi$, $\nN$ and $3s$ orbitals. + $^d$Using reference (6e,9o) active space including valence $\pi$, $\nN$ and three $3p_x$ orbitals. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of pyridine.} + \label{tab:pyridine} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1B_1(n,\pis)$ &(1,4,1,2) &(1,2,0,0) &5.43$^a$ &5.15$^a$ &4.81$^a$ &5.18$^a$ &5.13$^a$ &4.95\\ + $^1B_2(\pi,\pis)$ &(0,7,0,3) &(1,0,2,0) &5.03$^b$ &5.18$^b$ &4.76$^b$ &5.15$^b$ &5.09$^b$ &5.14\\ + $^1A_2(n,\pis)$ &(2,4,0,2) &(1,0,0,2) &6.30$^c$ &5.46$^c$ &5.03$^c$ &5.63$^c$ &5.59$^c$ &5.40\\ + $^1A_1(\pi,\pis)$ &(0,4,0,2) &(2,0,0,0) &7.90$^d$ &6.92$^d$ &6.27$^d$ &7.04$^d$ &6.93$^d$ &6.62\\ + $^1A_1(n,3s)$ &(2,4,0,2) &(2,0,0,0) &6.40$^c$ &6.90$^c$ &6.67$^c$ &6.97$^c$ &6.96$^c$ &6.76\\ + $^1A_2(\pi,3s)$ &(2,4,0,2) &(1,0,0,2) &6.60$^c$ &7.08$^c$ &6.87$^c$ &6.88$^c$ &6.80$^c$ &6.82\\ + $^1B_2(\pi,\pis)$ &(0,7,0,3) &(1,0,2,0) &7.45$^b$ &7.92$^b$ &7.67$^b$ &7.80$^b$ &7.73$^b$ &7.40\\ + $^1B_1(\pi,3p_y)$ &(1,4,1,2) &(1,2,0,0) &7.12$^a$ &7.70$^a$ &7.51$^a$ &7.48$^a$ &7.40$^a$ &7.38\\ + $^1A_1(\pi,\pis)$ &(0,4,0,2) &(4,0,0,0) &9.49$^d$ &7.66$^d$ &6.63$^d$ &7.87$^d$ &7.70$^d$ &7.39\\ + $^3A_1(\pi,\pis)$ &(0,4,0,2) &(2,0,0,0) &3.98$^d$ &4.40$^d$ &4.06$^d$ &4.29$^d$ &4.22$^d$ &4.30\\ + $^3B_1(n,\pis)$ &(1,4,0,2) &(1,1,0,0) &4.65$^e$ &4.48$^e$ &4.21$^e$ &4.57$^e$ &4.55$^e$ &4.46\\ + $^3B_2(\pi,\pis)$ &(0,7,0,3) &(1,0,2,0) &4.83$^b$ &4.86$^b$ &4.53$^b$ &4.81$^b$ &4.74$^b$ &4.79\\ + $^3A_1(\pi,\pis)$ &(0,4,0,2) &(3,0,0,0) &5.11$^d$ &5.09$^d$ &4.63$^d$ &5.09$^d$ &5.02$^d$ &5.04\\ + $^3A_2(n,\pis)$ &(1,4,0,2) &(1,0,0,1) &5.94$^e$ &5.33$^e$ &4.96$^e$ &5.53$^e$ &5.51$^e$ &5.36\\ + $^3B_2(\pi,\pis)$ &(0,7,0,3) &(1,0,2,0) &6.93$^b$ &6.40$^b$ &5.99$^b$ &6.43$^b$ &6.35$^b$ &6.24\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Using reference (8e,8o) active space including valence $\pi$, $\nN$ and $3p_y$ orbitals. + $^b$Using reference (6e,10o) active space including valence $\pi$ and four $3p_x$ orbitals. + $^c$Using reference (8e,8o) active space including valence $\pi$, $\nN$ and $3s$ orbitals. + $^d$Using reference (6e,6o) active space including valence $\pi$ orbitals. + $^e$Using reference (8e,7o) active space including valence $\pi$ and $\nN$ orbitals. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of pyrimidine.} + \label{tab:pyrimidine} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1B_1(n,\pis)$ &(1,4,1,2) &(1,1,0,0) &4.85$^a$ &4.44$^a$ &4.07$^a$ &4.58$^a$ &4.55$^a$ &4.44\\ + $^1A_2(n,\pis)$ &(1,4,1,2) &(1,0,0,1) &5.52$^a$ &4.80$^a$ &4.36$^a$ &5.02$^a$ &5.00$^a$ &4.85\\ + $^1B_2(\pi,\pis)$ &(0,6,0,3) &(1,0,1,0) &5.28$^b$ &5.42$^b$ &4.98$^b$ &5.41$^b$ &5.36$^b$ &5.38\\ + $^1A_2(n,\pis)$ &(1,4,1,2) &(1,0,0,2) &6.70$^a$ &5.92$^a$ &5.32$^a$ &6.16$^a$ &6.10$^a$ &5.92\\ + $^1B_1(n,\pis)$ &(1,4,1,2) &(1,2,0,0) &7.20$^a$ &6.31$^a$ &5.65$^a$ &6.58$^a$ &6.53$^a$ &6.26\\ + $^1B_2(n,3s)$ &(2,4,1,2) &(1,0,2,0) &6.86$^c$ &6.85$^c$ &6.50$^c$ &6.89$^c$ &6.86$^c$ &6.70\\ + $^1A_1(\pi,\pis)$ &(0,6,0,3) &(2,0,0,0) &7.69$^b$ &7.31$^b$ &6.94$^b$ &7.29$^b$ &7.22$^b$ &6.88\\ + $^3B_1(n,\pis)$ &(1,4,1,2) &(1,1,0,0) &4.45$^a$ &4.05$^a$ &3.67$^a$ &4.20$^a$ &4.18$^a$ &4.09\\ + $^3A_1(\pi,\pis)$ &(0,6,0,3) &(2,0,0,0) &4.22$^b$ &4.57$^b$ &4.25$^b$ &4.51$^b$ &4.44$^b$ &4.51\\ + $^3A_2(n,\pis)$ &(1,4,1,2) &(1,0,0,1) &5.20$^a$ &4.63$^a$ &4.16$^a$ &4.81$^a$ &4.78$^a$ &4.66\\ + $^3B_2(\pi,\pis)$ &(0,4,0,2) &(1,0,1,0) &5.10$^d$ &5.01$^d$ &4.60$^d$ &5.03$^d$ &4.97$^d$ &4.96\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Using reference (10e,8o) active space including valence $\pi$ and $\nN$ orbitals. + $^b$Using reference (6e,9o) active space including valence $\pi$ and three $3p_x$ orbitals. + $^c$Using reference (10e,9o) active space including valence $\pi$, $\nN$ and $3s$ orbitals. + $^d$Using reference (6e,6o) active space including valence $\pi$ orbitals. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of pyrrole.} + \label{tab:pyrrole} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1A_2(\pi,3s)$ &(1,3,0,2) &(1,0,0,1) &4.49$^a$ &5.44$^a$ &5.23$^a$ &5.28$^a$ &5.23$^a$ &5.24\\ + $^1B_1(\pi,3p_y)$ &(0,3,1,2) &(1,1,0,0) &5.22$^b$ &6.26$^b$ &6.07$^b$ &6.08$^b$ &6.02$^b$ &6.00\\ + $^1A_2(\pi,3p_z)$ &(2,3,0,2) &(1,0,0,2) &4.89$^c$ &6.16$^c$ &6.02$^c$ &6.01$^c$ &5.97$^c$ &6.00\\ + $^1B_2(\pi,\pis)$ &(0,4,0,2) &(1,0,2,0) &7.73$^d$ &6.62$^d$ &6.36$^d$ &6.45$^d$ &6.38$^d$ &6.26\\ + $^1A_1(\pi,\pis)$ &(0,3,0,2) &(3,0,0,0) &6.47$^e$ &6.41$^e$ &5.84$^e$ &6.43$^e$ &6.34$^e$ &6.30\\ + $^1B_2(\pi,3p_x)$ &(0,4,0,2) &(1,0,2,0) &5.82$^d$ &6.75$^d$ &6.11$^d$ &6.92$^d$ &6.82$^d$ &6.83\\ + $^3B_2(\pi,\pis)$ &(0,3,0,2) &(1,0,1,0) &4.24$^e$ &4.57$^e$ &4.30$^e$ &4.49$^e$ &4.44$^e$ &4.51\\ + $^3A_2(\pi,3s)$ &(1,3,0,2) &(1,0,0,1) &4.47$^a$ &5.41$^a$ &5.21$^a$ &5.26$^a$ &5.20$^a$ &5.21\\ + $^3A_1(\pi,\pis)$ &(0,3,0,2) &(3,0,0,0) &5.52$^e$ &5.50$^e$ &5.04$^e$ &5.49$^e$ &5.40$^e$ &5.45\\ + $^3B_1(\pi,3p_y)$ &(0,3,1,2) &(1,1,0,0) &5.18$^b$ &6.22$^b$ &6.03$^b$ &6.04$^b$ &5.98$^b$ &5.91\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Using reference (6e,6o) active space including valence $\pi$ and $3s$ orbitals. + $^b$Using reference (6e,6o) active space including valence $\pi$ and $3p_y$ orbitals. + $^c$Using reference (6e,7o) active space including valence $\pi$, $3s$ and $3p_z$ orbitals. + $^d$Using reference (6e,6o) active space including valence $\pi$ and $3p_x$ orbitals. + $^e$Using reference (6e,5o) active space including valence $\pi$ orbitals. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of streptocyanine.} + \label{tab:streptocyanine} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1B_2(\pi,\pis)$ &(2,2,2,1) &(1,0,1,0) &7.82$^a$ &7.17$^a$ &6.76$^a$ &7.28$^a$ &7.21$^a$ &7.13\\ + $^3B_2(\pi,\pis)$ &(2,2,2,1) &(1,0,1,0) &5.86$^a$ &5.49$^a$ &5.22$^a$ &5.54$^a$ &5.49$^a$ &5.52\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Reference (8e,7o) active space including valence $\pi$, two $\sigCN$ and two $\sigsCN$ orbitals. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of tetrazine.} + \label{tab:tetrazine} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_g,b_{3u},b_{2u},b_{1g},b_{1u},b_{2g},b_{3g},a_u)$ & $(A_g,B_{3u},B_{2u},B_{1g},B_{1u},B_{2g},B_{3g},A_u)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1B_{3u}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,1,0,0,0,0,0,0) &2.99$^a$ &2.31$^a$ &1.91$^a$ &2.54$^a$ &2.53$^a$ &2.47\\ + $^1A_{u}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,0,0,1) &4.37$^a$ &3.49$^a$ &3.00$^a$ &3.77$^a$ &3.78$^a$ &3.69\\ + $^1A_{g}(\rm double)$ &(1,2,1,1,1,2,1,1) &(2,0,0,0,0,0,0,0) &5.42$^a$ &4.69$^a$ &4.48$^a$ &4.85$^a$ &4.87$^a$ &---\\ + $^1B_{1g}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,1,0,0,0,0) &5.41$^a$ &4.83$^a$ &4.33$^a$ &5.02$^a$ &5.00$^a$ &4.93\\ + $^1B_{2u}(\pi,\pis)$ &(0,2,0,1,0,2,0,1) &(1,0,1,0,0,0,0,0) &5.04$^b$ &5.31$^b$ &4.84$^b$ &5.26$^b$ &5.23$^b$ &5.21\\ + $^1B_{2g}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,1,0,0) &5.43$^a$ &5.38$^a$ &4.90$^a$ &5.42$^a$ &5.38$^a$ &5.45\\ + $^1A_{u}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,0,0,2) &6.37$^a$ &5.51$^a$ &4.92$^a$ &5.80$^a$ &5.80$^a$ &5.53\\ + $^1B_{3g}(\rm double)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,0,1,0) &6.59$^a$ &5.85$^a$ &5.22$^a$ &6.20$^a$ &6.22$^a$ &---\\ + $^1B_{2g}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,2,0,0) &6.79$^a$ &5.96$^a$ &5.18$^a$ &6.27$^a$ &6.28$^a$ &6.12\\ + $^1B_{1g}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,2,0,0,0,0) &7.18$^{a,c}$ &6.59$^{a,c}$ &5.89$^{a,c}$ &6.79$^{a,c}$ &6.72$^{a,c}$ &6.91\\ + $^3B_{3u}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,1,0,0,0,0,0,0) &2.38$^a$ &1.70$^a$ &1.31$^a$ &1.94$^a$ &1.93$^a$ &1.85\\ + $^3A_{u}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,0,0,1) &4.06$^a$ &3.26$^a$ &2.78$^a$ &3.52$^a$ &3.52$^a$ &3.45\\ + $^3B_{1g}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,1,0,0,0,0) &4.66$^a$ &4.10$^a$ &3.62$^a$ &4.32$^a$ &4.30$^a$ &4.20\\ + $^3B_{1u}(\pi,\pis)$ &(0,4,0,1,0,2,0,2) &(1,0,0,0,2,0,0,0) &3.90$^d$ &4.55$^d$ &4.29$^d$ &4.39$^d$ &4.34$^d$ &4.49\\ + $^3B_{2u}(\pi,\pis)$ &(0,2,0,1,0,2,0,1) &(1,0,1,0,0,0,0,0) &4.68$^b$ &4.55$^b$ &4.20$^b$ &4.60$^b$ &4.55$^b$ &4.52\\ + $^3B_{2g}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,1,0,0) &5.17$^a$ &5.02$^a$ &4.53$^a$ &5.10$^a$ &5.07$^a$ &5.04\\ + $^3A_{u}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,0,0,2) &6.12$^a$ &5.07$^a$ &4.44$^a$ &5.41$^a$ &5.41$^a$ &5.11\\ + $^3B_{3g}(\rm double)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,0,1,0) &6.56$^a$ &5.39$^a$ &4.86$^a$ &5.83$^a$ &5.85$^a$ &---\\ + $^3B1u(\pi,\pis)$ &(0,4,0,1,0,2,0,2) &(1,0,0,0,2,0,0,0) &5.32$^d$ &5.46$^d$ &5.08$^d$ &5.44$^d$ &5.39$^d$ &5.42\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Using reference (14e,10o) active space including valence $\pi$ and $\nN$ orbitals. + $^b$Using reference (6e,6o) active space including valence $\pi$ orbitals. + $^c$Level shift set to \SI{0.4}{\hartree}. + $^d$Using reference (6e,9o) active space including valence $\pi$ and three $3p_x$ orbitals. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of thioacetone.} + \label{tab:thioacetone} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1A_2(n,\pis)$ &(2,2,1,0) &(1,0,0,1) &2.72$^a$ &2.58$^a$ &2.33$^a$ &2.60$^a$ &2.53$^a$ &2.53\\ + $^1B_2(n,3s)$ &(4,2,1,0) &(1,0,2,0) &4.80$^b$ &5.60$^b$ &5.48$^b$ &5.64$^b$ &5.61$^b$ &5.56\\ + $^1A_1(\pi,\pis)$ &(2,2,2,0) &(3,0,0,0) &6.94$^d$ &6.42$^d$ &5.98$^d$ &6.40$^d$ &6.26$^d$ &5.88\\ + $^1B_2(n,3p_z)$ &(4,2,1,0) &(1,0,2,0) &5.57$^b$ &6.51$^b$ &6.40$^b$ &6.53$^b$ &6.49$^b$ &6.51\\ + $^1A_1(n,3p_y)$ &(2,2,2,0) &(3,0,0,0) &6.24$^d$ &6.66$^d$ &6.41$^d$ &6.59$^d$ &6.50$^d$ &6.61\\ + $^3A_2(n,\pis)$ &(2,2,1,0) &(1,0,0,1) &2.52$^a$ &2.34$^a$ &2.09$^a$ &2.38$^a$ &2.31$^a$ &2.33\\ + $^3A_1(\pi,\pis)$ &(2,2,0,0) &(2,0,0,0) &3.52$^c$ &3.48$^c$ &3.29$^c$ &3.48$^c$ &3.43$^c$ &3.45\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Using reference (6e,5o) active space including valence $\pi$, $\nO$, $\sigCO$ and $\sigsCO$ orbitals. + $^b$Using reference (6e,7o) active space including valence $\pi$, $\nO$, $\sigCO$, $\sigsCO$, $3s$ and $3p_z$ orbitals. + $^c$Using reference (4e,4o) active space including valence $\pi$, $\sigCO$ and $\sigsCO$ orbitals. + $^d$Using reference (6e,6o) active space including valence $\pi$, $\nO$, $\sigCO$, $\sigsCO$ and $3p_y$ orbitals. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of thiophene.} + \label{tab:thiophene} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1A_1(\pi,\pis)$ &(0,3,0,2) &(3,0,0,0) &6.11$^a$ &5.84$^a$ &5.21$^a$ &5.89$^a$ &5.79$^a$ &5.64\\ + $^1B_2(\pi,\pis)$ &(0,5,0,2) &(1,0,2,0) &6.94$^b$ &6.35$^b$ &5.89$^b$ &6.44$^b$ &6.35$^b$ &5.98\\ + $^1A_2(\pi,3s)$ &(1,3,0,2) &(1,0,0,1) &5.70$^c$ &6.28$^c$ &6.07$^c$ &6.16$^c$ &6.10$^c$ &6.14\\ + $^1B_1(\pi,3p_y)$ &(0,3,1,2) &(1,1,0,0) &6.02$^d$ &6.21$^d$ &5.90$^d$ &6.16$^d$ &6.10$^d$ &6.14\\ + $^1A_2(\pi,3p_y)$ &(0,3,1,2) &(1,0,0,1) &6.05$^d$ &6.32$^d$ &5.98$^d$ &6.28$^d$ &6.21$^d$ &6.21\\ + $^1B_1(\pi,3s)$ &(1,3,1,2) &(1,2,0,0) &5.78$^e$ &6.57$^e$ &6.28$^e$ &6.51$^e$ &6.44$^e$ &6.49\\ + $^1B_2(\pi,3p_x)$ &(0,5,0,2) &(1,0,2,0) &6.80$^b$ &7.29$^b$ &7.03$^b$ &7.20$^b$ &7.13$^b$ &7.29\\ + $^1A_1(\pi,\pis)$ &(0,3,0,2) &(3,0,0,0) &8.29$^{a,f}$ &7.62$^{a,f}$ &6.85$^{a,f}$ &7.71$^{a,f}$ &7.56$^{a,f}$ &7.31\\ + $^3B_2(\pi,\pis)$ &(0,3,0,2) &(1,0,1,0) &3.68$^a$ &3.98$^a$ &3.71$^a$ &3.90$^a$ &3.84$^a$ &3.92\\ + $^3A_1(\pi,\pis)$ &(0,3,0,2) &(3,0,0,0) &4.97$^a$ &4.85$^a$ &4.39$^a$ &4.87$^a$ &4.79$^a$ &4.76\\ + $^3B_1(\pi,3p_y)$ &(0,3,1,2) &(1,1,0,0) &5.86$^d$ &5.97$^d$ &5.64$^d$ &5.94$^d$ &5.88$^d$ &5.93\\ + $^3A_2(\pi,3s)$ &(1,3,0,2) &(1,0,0,1) &5.65$^c$ &6.22$^c$ &6.01$^c$ &6.11$^c$ &6.04$^c$ &6.08\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Using reference (6e,5o) active space including valence $\pi$ orbitals. + $^b$Using reference (6e,7o) active space including valence $\pi$ and two $3p_x$ orbitals. + $^c$Using reference (6e,6o) active space including valence $\pi$ and $3s$ orbitals. + $^d$Using reference (6e,6o) active space including valence $\pi$ and $3p_y$ orbitals. + $^e$Using reference (6e,7o) active space including valence $\pi$, $3s$ and $3p_y$ orbitals. + $^f$Strong double-excitation character. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of thiopropynal.} + \label{tab:thiopropynal} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a',a'')$ & $(A',A'')$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1A''(n,\pis)$ &(3,4) &(1,1) &2.06$^a$ &2.05$^a$ &1.84$^a$ &2.05$^a$ &2.00$^a$ &2.03\\ + $^3A''(n,\pis)$ &(3,4) &(1,1) &1.85$^a$ &1.81$^a$ &1.60$^a$ &1.84$^a$ &1.79$^a$ &1.80\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Using reference (8e,7o) active space including valence $\pi$ and $\nO$ orbitals. +\end{table*} + +\begin{table*} + \caption{Vertical transition energies (eV) of triazine.} + \label{tab:triazine} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\ + & $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\ + \hline + $^1A_1''(n,\pis)$ &(2,4,1,2) &(1,2,0,2) &5.88$^a$ &4.62$^a$ &3.90$^a$ &5.00$^a$ &4.99$^a$ &4.72\\ + $^1A_2''(n,\pis)$ &(2,4,1,2) &(1,1,0,0) &5.14$^a$ &4.77$^a$ &4.39$^a$ &4.90$^a$ &4.87$^a$ &4.75\\ + $^1E''(n,\pis)$ &(2,4,1,2) &(1,2,0,2) &5.51$^a$ &4.76$^a$ &4.14$^a$ &5.01$^a$ &4.98$^a$ &4.78\\ + $^1A_2'(\pi,\pis)$ &(0,6,0,3) &(1,0,1,0) &5.55$^b$ &5.76$^b$ &5.32$^b$ &5.75$^b$ &5.72$^b$ &5.75\\ + $^1A_1'(\pi,\pis)$ &(0,6,0,3) &(2,0,0,0) &8.20$^b$ &7.43$^b$ &6.89$^b$ &7.50$^b$ &7.41$^b$ &7.24\\ + $^1E'(n,3s)$ &(3,4,1,2) &(2,0,2,0) &7.40$^c$ &7.48$^c$ &7.15$^c$ &7.53$^c$ &7.49$^c$ &7.32\\ + $^1E''(n,\pis)$ &(2,4,1,2) &(1,1,0,1) &8.26$^a$ &7.75$^a$ &7.04$^a$ &7.92$^a$ &7.90$^a$ &7.78\\ + $^1E'(\pi,\pis)$ &(0,6,0,3) &(4,0,3,0) &10.03$^b$ &8.65$^b$ &7.70$^b$ &8.83$^b$ &8.72$^b$ &7.94\\ + $^3A_2''(n,\pis)$ &(2,4,1,2) &(1,1,0,0) &4.74$^a$ &4.37$^a$ &3.99$^a$ &4.51$^a$ &4.49$^a$ &4.33\\ + $^3E''(n,\pis)$ &(2,4,1,2) &(1,2,0,2) &5.14$^a$ &4.47$^a$ &3.88$^a$ &4.71$^a$ &4.68$^a$ &4.51\\ + $^3A_1''(n,\pis)$ &(2,4,1,2) &(1,2,0,2) &5.88$^a$ &4.70$^a$ &3.94$^a$ &5.06$^a$ &5.04$^a$ &4.73\\ + $^3A_1'(\pi,\pis)$ &(0,6,0,3) &(2,0,0,0) &4.46$^b$ &4.88$^b$ &4.55$^b$ &4.81$^b$ &4.75$^b$ &4.85\\ + $^3E'(\pi,\pis)$ &(0,6,0,3) &(3,0,1,0) &5.57$^b$ &5.62$^b$ &5.20$^b$ &5.62$^b$ &5.57$^b$ &5.59\\ + $^3A_2'(\pi,\pis)$ &(0,6,0,3) &(1,0,1,0) &7.70$^b$ &6.62$^b$ &6.12$^b$ &6.76$^b$ &6.68$^b$ &6.62\\ + \end{tabular} + \end{ruledtabular} + \flushleft + $^a$Using reference (12e,9o) active space including valence $\pi$ and $\nN$ orbitals. + $^b$Using reference (6e,9o) active space including valence $\pi$ and three $3p_x$ orbitals. + $^c$Using reference (12e,10o) active space including valence $\pi$, $\nN$ and $3s$ orbitals. +\end{table*} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\bibliography{CASPT3} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\end{document}