sup
This commit is contained in:
Pierre-Francois Loos
parent
c2631e0b54
commit
e58852aff0
@ -140,7 +140,11 @@ Third-order version have been developed but rarely used and accuracy still need
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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}
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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}
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There is also the NEVPT3 method of Angeli and coworkers. \cite{Angeli_2006}
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There is also the NEVPT3 method of Angeli and coworkers. \cite{Angeli_2006}
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\begin{figure}
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\includegraphics[width=\linewidth,viewport=1.cm 10cm 18cm 27cm,clip]{mol.pdf}
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\caption{Various molecular systems considered in this study.
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\label{fig:mol}}
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\end{figure}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Computational details}
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\section{Computational details}
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@ -149,840 +153,6 @@ There is also the NEVPT3 method of Angeli and coworkers. \cite{Angeli_2006}
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All the CASPT2 and CASPT3 calculations have been carried out with MOLPRO within the RS2 and RS3 schemes. \cite{Werner_2020}
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All the CASPT2 and CASPT3 calculations have been carried out with MOLPRO within the RS2 and RS3 schemes. \cite{Werner_2020}
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Both methods have been tested with and without IPEA (labeled as NOIPEA).
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Both methods have been tested with and without IPEA (labeled as NOIPEA).
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\begin{table*}
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\caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of acetaldehyde.}
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\label{tab:acetaldehyde}
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\begin{ruledtabular}
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\begin{tabular}{lcccccccc}
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State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
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& $(a',a'')$ & $(A',A'')$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
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\hline
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$^1A''(n,\pis)$ &(3,2) &(1,1) &4.62$^a$ &4.35$^a$ &4.13$^a$ &4.44$^a$ &4.41$^a$ &4.31\\
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$^3A''(n,\pis)$ &(3,2) &(1,1) &4.28$^a$ &3.94$^a$ &3.71$^a$ &4.06$^a$ &4.03$^a$ &3.97\\
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\end{tabular}
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\end{ruledtabular}
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\flushleft
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$^a$Reference (6e,5o) active space including valence $\nO$, $\piCO$, $\sigCO$, $\pisCO$ and $\sigsCO$ orbitals.
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\end{table*}
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\begin{table*}
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\caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of acetone.}
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\label{tab:acetone}
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\begin{ruledtabular}
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\begin{tabular}{lcccccccc}
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State &Active space &State-average &CASSCF &CASPT2 &CASPT2 &CASPT3 &CASPT3 &TBE \\
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&$(a_1,b_1,b_2,a_2)$ &$(A_1,B_1,B_2,A_2)$ & &IPEA &NOIPEA &IPEA &NOIPEA & \\
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\hline
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$^1A_2(n,\pis)$ &(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\\
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$^1B_2(n,3s)$ &(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\\
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$^1A_2(n,3p_x)$ &(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\\
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$^1A_1(n,3p_y)$ &(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\\
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$^1B_2(n,3p_z)$ &(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\\
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$^3A_2(n,\pis)$ &(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\\
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$^3A_1(\pi,\pis)$ &(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\\
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\end{tabular}
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\end{ruledtabular}
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\flushleft
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$^a$Using reference (6e,6o) active space including valence $\pi$, $\nO$, $\sigCO$, $\sigsCO$ and $3p_x$ orbitals.
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$^b$Using reference (6e,7o) active space including valence $\pi$, $\nO$, $\sigCO$, $\sigsCO$, $3s$ and $3p_z$ orbitals.
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$^c$Using reference (6e,6o) active space including valence $\pi$, $\nO$, $\sigCO$, $\sigsCO$ and $3p_y$ orbitals.
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$^d$Using reference (6e,5o) active space including valence $\pi$, $\nO$, $\sigCO$ and $\sigsCO$ orbitals.
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$^e$Using reference (4e,4o) active space including valence $\pi$, $\sigCO$, $\sigsCO$ orbitals.
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\end{table*}
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\begin{table*}
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\caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of acrolein.}
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\label{tab:acrolein}
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\begin{ruledtabular}
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\begin{tabular}{lcccccccc}
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State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
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& $(a',a'')$ & $(A',A'')$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
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\hline
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$^1A''(n,\pis)$ &(1,5) &(1,3) &3.48$^c$ &3.58$^c$ &3.46$^c$ &3.66$^c$ &3.66$^c$ &3.78\\
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$^1A'(\pi,\pis)$ &(2,4) &(4,0) &8.84$^d$ &6.93$^d$ &6.28$^d$ &7.18$^d$ &7.05$^d$ &6.69\\
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$^1A''(n,\pis)$ &(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\\
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$^1A'(n,3s)$ &(2,4) &(4,0) &7.20$^d$ &7.21$^d$ &6.98$^d$ &7.20$^d$ &7.16$^d$ &7.08\\
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$^1A'(\pi^2,\pis^2)$&(2,4) &(4,0) &7.91$^d$ &8.10$^d$ &7.75$^d$ &8.02$^d$ &7.95$^d$ &7.87\\
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$^3A''(n,\pis)$ &(1,5) &(1,3) &3.25$^c$ &3.28$^c$ &3.15$^c$ &3.39$^c$ &3.40$^c$ &3.51\\
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$^3A'(\pi,\pis)$ &(2,4) &(4,0) &3.89$^d$ &4.01$^d$ &3.78$^d$ &3.96$^d$ &3.91$^d$ &3.94\\
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$^3A'(\pi,\pis)$ &(2,4) &(4,0) &5.89$^d$ &6.20$^d$ &5.93$^d$ &6.10$^d$ &6.02$^d$ &6.18\\
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$^3A''(n,\pis)$ &(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\\
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\end{tabular}
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\end{ruledtabular}
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\flushleft
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$^a$Using reference (12e,12o) active space including valence $\pi$, $\sigCC$, $\sigsCO$, $\sigsCC$, $\sigsCO$, $\nO$ and $3s$ orbitals.
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$^b$Level shift det to \SI{0.4}{\hartree}.
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$^c$Using reference (6e,6o) active space including valence $\pi$, $\nO$ and $3p_z$ orbitals.
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$^d$Using reference (6e,6o) active space including valence $\pi$, $\nO$ and $3s$ orbitals.
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$^e$Substantial Rydberg and doubly-excited character.
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$^f$Substantial doubly-excited character.
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\end{table*}
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\begin{table*}
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\caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of benzene.}
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\label{tab:benzene}
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\begin{ruledtabular}
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\begin{tabular}{lcccccccc}
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State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
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& $(a_g,b_{3u},b_{2u},b_{1g},b_{1u},b_{2g},b_{3g},a_u)$ & $(A_g,B_{3u},B_{2u},B_{1g},B_{1u},B_{2g},B_{3g},A_u)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
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\hline
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$^1B_{2u}(\pi,\pis)$ &(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\\
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$^1B_{1u}(\pi,\pis)$ &(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\\
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$^1E_{1g}(\pi,3s)$ &(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\\
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$^1A_{2u}(\pi,3p_{x,y})$ &(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\\
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$^1E_{2u}(\pi,3p_{x,y})$ &(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\\
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$^1E_{2g}(\pi^2,\pis^2)$ &(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\\
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$^3B_{1u}(\pi,\pis)$ &(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\\
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$^3E_{1u}(\pi,\pis)$ &(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\\
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$^3B_{2u}(\pi,\pis)$ &(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\\
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\end{tabular}
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\end{ruledtabular}
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\flushleft
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$^a$Using reference (6e,6o) active space including valence $\pi$ orbitals.
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$^b$Using reference (6e,9o) active space including valence $\pi$ and three $3p_z$ orbitals.
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$^c$Using reference (6e,7o) active space including valence $\pi$ and $3s$ orbitals.
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$^d$Using reference (6e,8o) active space including valence $\pi$, $3p_x$ and $3p_y$ orbitals.
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$^e$Level shift set to \SI{0.4}{\hartree}.
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\end{table*}
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\begin{table*}
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\caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of butadiene.}
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\label{tab:butadiene}
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\begin{ruledtabular}
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\begin{tabular}{lcccccccc}
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State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
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& $(a_g,a_u,b_u,b_g)$ & $(A_g,A_u,B_u,B_g)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
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\hline
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$^1B_u(\pi,\pis)$ &(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\\
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$^1B_g(\pi,3s)$ &(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\\
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$^1A_g(\pi^2,\pis^2)$ &(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\\
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$^1A_u(\pi,3p_x)$ &(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\\
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$^1A_u(\pi,3p_y)$ &(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\\
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$^1B_u(\pi,3p_z)$ &(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\\
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$^3B_u(\pi,\pis)$ &(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\\
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$^3A_g(\pi,\pis)$ &(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\\
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$^3B_g(\pi,3s)$ &(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\\
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\end{tabular}
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\end{ruledtabular}
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\flushleft
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$^a$Using reference (4e,8o) active space including valence $\pi$ and four $3p_z$.
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$^b$Using reference (10e,11o) active space including valence $\pi$, $\sigCC$, $\sigsCC$ and $3s$ orbitals.
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$^c$Using reference (10e,10o) active space including valence $\pi$, $\sigCC$ and $\sigsCC$ orbitals.
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$^d$Level shift set to \SI{0.4}{\hartree}.
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$^e$Using reference (10e,12o) active space including valence $\pi$, $\sigCC$, $\sigsCC$, $3p_x$ and $3p_y$ orbitals.
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\end{table*}
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\begin{table*}
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\caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of carbon trimer.}
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\label{tab:carbon_trimer}
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\begin{ruledtabular}
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\begin{tabular}{lcccccccc}
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State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
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& $(a_g,b_{3u},b_{2u},b_{1g},b_{1u},b_{2g},b_{3g},a_u)$ & $(A_g,B_{3u},B_{2u},B_{1g},B_{1u},B_{2g},B_{3g},A_u)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
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\hline
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$1\Delta_g(n^2,\pis^2)$ &(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\\
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$1\Sigma_g^+(n^2,\pis^2)$ &(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\\
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\end{tabular}
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\end{ruledtabular}
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\flushleft
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$^a$All calculations using a full valence (12e,12o) active space.
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$^b$Level shift set to \SI{0.4}{\hartree}.
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$^c$Level shift set to \SI{0.5}{\hartree}.
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\end{table*}
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\begin{table*}
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\caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of cyanoacetylene.$^a$}
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\label{tab:cyanoacetylene}
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\begin{ruledtabular}
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\begin{tabular}{lcccccccc}
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State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
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& $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
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\hline
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$^1\Sigma^-(\pi,\pis)$ &(0,4,4,0) &(1,0,0,1) &6.54 &5.85 &5.47 &5.89 &5.81 &5.80\\
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$^1\Delta(\pi,\pis)$ &(0,4,4,0) &(2,0,0,1) &6.80 &6.13 &5.78 &6.17 &6.09 &6.07\\
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$^3\Sigma^+(\pi,\pis)$ &(0,4,4,0) &(2,0,0,0) &4.86 &4.45 &4.04 &4.52 &4.45 &4.44\\
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$^3\Delta(\pi,\pis)$ &(0,4,4,0) &(2,0,0,1) &5.64 &5.21 &4.86 &5.26 &5.19 &5.21\\
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$^1A''[F](\pi,\pis)$ &($a'$:4,$a''$:4) &($A'$:1,$A''$:1) &4.30 &3.67 &3.47 &3.64 &3.58 &3.54\\
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\end{tabular}
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\end{ruledtabular}
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\flushleft
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$^a$All calculations using a full valence $\pi$ active space of (8e,8o).
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\end{table*}
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\begin{table*}
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\caption{CASPT3/aug-cc-pVTZ vertical transition energies (eV) of cyanoformaldehyde.}
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\label{tab:cyanoformaldehyde}
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\begin{ruledtabular}
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\begin{tabular}{lcccccccc}
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State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
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& $(a',a'')$ & $(A',A'')$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
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\hline
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$^1A''(n,\pis)$ &(3,4) &(1,2) &4.02$^a$ &3.98$^a$ &3.67$^a$ &3.94$^a$ &3.89$^a$ &3.81\\
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$^1A''(\pi,\pis)$ &(3,4) &(1,2) &7.61$^a$ &6.79$^a$ &6.43$^a$ &6.77$^a$ &6.67$^a$ &6.46\\
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|
||||||
$^3A''(n,\pis)$ &(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}
|
\section{Results and discussion}
|
||||||
\label{sec:res}
|
\label{sec:res}
|
||||||
|
|||||||
943
Manuscript/sup_CASPT3.tex
Normal file
943
Manuscript/sup_CASPT3.tex
Normal file
@ -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}
|
||||||
|
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|
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|
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|
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|
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|
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|
||||||
|
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|
||||||
|
\newcommand{\SupInf}{\textcolor{blue}{Supporting Information}}
|
||||||
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|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
|
||||||
|
\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\\
|
||||||
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$^3A_2''(n,\pis)$ &(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\\
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$^3E''(n,\pis)$ &(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\\
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$^3A_1''(n,\pis)$ &(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\\
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$^3A_1'(\pi,\pis)$ &(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\\
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$^3E'(\pi,\pis)$ &(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\\
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$^3A_2'(\pi,\pis)$ &(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\\
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\end{tabular}
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\end{ruledtabular}
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\flushleft
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$^a$Using reference (12e,9o) active space including valence $\pi$ and $\nN$ orbitals.
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$^b$Using reference (6e,9o) active space including valence $\pi$ and three $3p_x$ orbitals.
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$^c$Using reference (12e,10o) active space including valence $\pi$, $\nN$ and $3s$ orbitals.
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\end{table*}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\bibliography{CASPT3}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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|
|
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|
\end{document}
|
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Loading…
Reference in New Issue
Block a user