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sup
2022-03-16 17:19:37 +01:00
\documentclass[aip,jcp,reprint,noshowkeys,superscriptaddress,onecolumn]{revtex4-1}
\usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,wrapfig,txfonts,siunitx}
\usepackage[version=4]{mhchem}
%\usepackage{natbib}
%\bibliographystyle{achemso}
\newcommand{\fk}[1]{\textcolor{blue}{#1}}
\newcommand{\ie}{\textit{i.e.}}
\newcommand{\eg}{\textit{e.g.}}
\newcommand{\alert}[1]{\textcolor{black}{#1}}
\usepackage[normalem]{ulem}
\newcommand{\titou}[1]{\textcolor{red}{#1}}
\newcommand{\trashPFL}[1]{\textcolor{red}{\sout{#1}}}
\newcommand{\PFL}[1]{\titou{(\underline{\bf PFL}: #1)}}
\newcommand{\toto}[1]{\textcolor{green}{#1}}
\newcommand{\trashAS}[1]{\textcolor{green}{\sout{#1}}}
\newcommand{\AS}[1]{\toto{(\underline{\bf AS}: #1)}}
\newcommand{\ant}[1]{\textcolor{orange}{#1}}
\newcommand{\SupInf}{\textcolor{blue}{Supporting Information}}
\newcommand{\mc}{\multicolumn}
\newcommand{\fnm}{\footnotemark}
\newcommand{\fnt}{\footnotetext}
\newcommand{\tabc}[1]{\multicolumn{1}{c}{#1}}
\newcommand{\QP}{\textsc{quantum package}}
\newcommand{\sig}{\sigma}
\newcommand{\sigs}{\sigma^*}
\newcommand{\pis}{{\pi^*}}
\newcommand{\nN}{{n_{\ce{N}}}}
\newcommand{\nO}{{n_{\ce{O}}}}
\newcommand{\nS}{{n_{\ce{S}}}}
\newcommand{\sigCC}{\sig_{\ce{CC}}}
\newcommand{\sigsCC}{\sig_{\ce{CC}}^*}
\newcommand{\piCC}{\pi_{\ce{CC}}}
\newcommand{\pisCC}{\pi_{\ce{CC}}^*}
\newcommand{\sigCN}{\sig_{\ce{CN}}}
\newcommand{\sigsCN}{\sig_{\ce{CN}}^*}
\newcommand{\piCN}{\pi_{\ce{CN}}}
\newcommand{\pisCN}{\pi_{\ce{CN}}^*}
\newcommand{\sigNN}{\sig_{\ce{NN}}}
\newcommand{\sigsNN}{\sig_{\ce{NN}}^*}
\newcommand{\piNN}{\pi_{\ce{NN}}}
\newcommand{\pisNN}{\pi_{\ce{NN}}^*}
\newcommand{\sigCO}{\sig_{\ce{CO}}}
\newcommand{\sigsCO}{\sig_{\ce{CO}}^*}
\newcommand{\piCO}{\pi_{\ce{CO}}}
\newcommand{\pisCO}{\pi_{\ce{CO}}^*}
\newcommand{\sigNO}{\sig_{\ce{NO}}}
\newcommand{\sigsNO}{\sig_{\ce{NO}}^*}
\newcommand{\piNO}{\pi_{\ce{NO}}}
\newcommand{\pisNO}{\pi_{\ce{NO}}^*}
\usepackage[
colorlinks=true,
citecolor=blue,
breaklinks=true
]{hyperref}
\urlstyle{same}
\begin{document}
% addresses
\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France}
\newcommand{\CEISAM}{Universit\'e de Nantes, CNRS, CEISAM UMR 6230, F-44000 Nantes, France}
\title{Supporting Information for ``Benchmarking CASPT3 vertical excitation energies''}
\author{Martial \surname{Boggio-Pasqua}}
\email{martial.boggio@irsamc.ups-tlse.fr}
\affiliation{\LCPQ}
\author{Denis \surname{Jacquemin}}
\affiliation{\CEISAM}
\author{Pierre-Fran\c{c}ois \surname{Loos}}
\email{loos@irsamc.ups-tlse.fr}
\affiliation{\LCPQ}
% Abstract
\begin{abstract}
%\bigskip
%\begin{center}
% \boxed{\includegraphics[width=0.4\linewidth]{TOC}}
%\end{center}
%\bigskip
\end{abstract}
% Title
\maketitle
In the following Tables, we report the vertical transition energies (in eV) obtained with the aug-cc-pVTZ basis and computed with state-averaged CASSCF, state-specific CASPT2 and CASPT3 using a level shift of \SI{0.30}{\hartree} with or without an IPEA shift of \SI{0.25}{\hartree}.
The symbol $[F]$ indicates the calculation of emission from the lowest $S_1$ geometry, i.e., a vertical fluorescence.
The composition of the active space is specified in terms of number of active orbitals per irreducible representation.
The state-averaging procedure used is also described in terms of number of states per irreducible representation.
Note that, for all calculations, the ground state is systematically included in the state averaging
procedure even if it does not belong to the same irreducible representation.
first draft of introduction
2022-03-17 18:31:52 +01:00
The cartesian coordinates have been extracted from the QUEST database \cite{Veril_2021} and can be downloaded at \url{https://lcpq.github.io/QUESTDB_website}.
sup
2022-03-16 17:19:37 +01:00
\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
timings
2022-03-20 18:53:38 +01:00
$^a$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.
sup
2022-03-16 17:19:37 +01:00
\end{table*}
\begin{table*}
\caption{Vertical transition energies (eV) of isobutene.}
\label{tab:isobutene}
\begin{ruledtabular}
\begin{tabular}{lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$^1B_1(\pi,3s)$ &(3,2,0,0) &(1,1,0,0) &6.21$^a$ &6.74$^a$ &6.59$^a$ &6.64$^a$ &6.57$^a$ &6.46\\
$^1A_1(\pi,3p_x)$ &(2,3,0,0) &(2,0,0,0) &6.90$^b$ &7.32$^b$ &7.14$^b$ &7.24$^b$ &7.18$^b$ &7.01\\
$^3A_1(\pi,\pis)$ &(2,2,0,0) &(2,0,0,0) &4.66$^c$ &4.59$^c$ &4.41$^c$ &4.58$^c$ &4.53$^c$ &4.53\\
\end{tabular}
\end{ruledtabular}
\flushleft
$^a$Using reference (4e,5o) active space including valence $\pi$, $\sigCC$, $\sigsCC$ and $3s$ orbitals.
$^b$Using reference (4e,5o) active space including valence $\pi$, $\sigCC$, $\sigsCC$ and $3p_x$ orbitals.
$^c$Using reference (4e,4o) active space including valence $\pi$, $\sigCC$ and $\sigsCC$ orbitals.
\end{table*}
\begin{table*}
\caption{Vertical transition energies (eV) of ketene.}
\label{tab:ketene}
\begin{ruledtabular}
\begin{tabular}{lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$^1A2(\pi,\pis)$ &(4,3,2,0) &(1,0,0,1) &3.98$^a$ &3.92$^a$ &3.70$^a$ &3.90$^a$ &3.85$^a$ &3.86\\
$^1B1(\pi,3s)$ &(5,3,2,0) &(1,1,0,0) &5.22$^b$ &5.99$^b$ &5.79$^b$ &6.00$^b$ &5.97$^b$ &6.01\\
$^1A2(\pi,3p)$ &(4,3,3,0) &(1,0,0,2) &6.38$^c$ &7.25$^c$ &7.05$^c$ &7.19$^c$ &7.15$^c$ &7.18\\
$^3A2(\pi,\pis)$ &(4,3,2,0) &(1,0,0,1) &3.92$^a$ &3.81$^a$ &3.59$^a$ &3.79$^a$ &3.74$^a$ &3.77\\
$^3A1(\pi,\pis)$ &(4,3,2,0) &(2,0,0,0) &5.79$^a$ &5.65$^a$ &5.43$^a$ &5.63$^a$ &5.59$^a$ &5.61\\
$^3B1(\pi,3s)$ &(5,3,2,0) &(1,1,0,0) &5.05$^b$ &5.79$^b$ &5.60$^b$ &5.80$^b$ &5.77$^b$ &5.79\\
$^3A2(\pi,3p)$ &(4,3,3,0) &(1,0,0,2) &6.35$^c$ &7.22$^c$ &7.01$^c$ &7.15$^c$ &7.11$^c$ &7.12\\
$^1A''[F](\pi,\pis)$ &($a'$:6,$a''$:3) &($A'$:1,$A''$:1) &0.95$^a$ &1.05$^a$ &0.88$^a$ &1.00$^a$ &0.95$^a$ &1.00\\
\end{tabular}
\end{ruledtabular}
\flushleft
$^a$Reference (10e,9o) active space including valence $\pi$, $\sigCC$, $\sigCO$ and $\sigsCC$, $\sigsCO$ orbitals.
$^b$Reference (10e,10o) active space including valence $\pi$, $\sigCC$, $\sigCO$ and $\sigsCC$, $\sigsCO$, Rydberg $3s$ orbitals.
$^c$Reference (10e,10o) active space including valence $\pi$, $\sigCC$, $\sigCO$ and $\sigsCC$, $\sigsCO$, Rydberg $3p$ orbitals.
\end{table*}
\begin{table*}
\caption{Vertical transition energies (eV) of methylenecyclopropene.}
\label{tab:methylenecyclopropene}
\begin{ruledtabular}
\begin{tabular}{lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$^1B_2(\pi,\pis)$ &(0,3,0,1) &(1,0,1,0) &4.47$^a$ &4.40$^a$ &4.12$^a$ &4.39$^a$ &4.33$^a$ &4.28\\
$^1B_1(\pi,3s)$ &(1,3,0,1) &(1,1,0,0) &4.92$^b$ &5.57$^b$ &5.44$^b$ &5.46$^b$ &5.41$^b$ &5.44\\
$^1A_2(\pi,3p_y)$ &(0,3,1,1) &(1,0,0,1) &5.37$^b$ &6.09$^b$ &5.97$^b$ &5.97$^b$ &5.92$^b$ &5.96\\
$^1A_1(\pi,3p_x)$ &(0,6,0,1) &(5,0,0,0) &5.37$^c$ &6.26$^c$ &6.16$^c$ &6.17$^c$ &6.13$^c$ &6.12\\
$^3B_2(\pi,\pis)$ &(0,3,0,1) &(1,0,1,0) &3.44$^a$ &3.57$^a$ &3.34$^a$ &3.55$^a$ &3.49$^a$ &3.49\\
$^3A_1(\pi,\pis)$ &(0,5,0,1) &(4,0,0,0) &4.60$^d$ &4.82$^d$ &4.58$^d$ &4.77$^d$ &4.72$^d$ &4.74\\
\end{tabular}
\end{ruledtabular}
\flushleft
$^a$Using reference (4e,4o) active space including valence $\pi$.
$^b$Using reference (4e,5o) active space including valence $\pi$ and $3s$.
$^c$Using reference (4e,5o) active space including valence $\pi$ and $3p_y$.
$^d$Using reference (4e,7o) active space including valence $\pi$, two $3p_x$ and one $3d_{xz}$.
$^e$Using reference (4e,6o) active space including valence $\pi$, one $3p_x$ and one $3d_{xz}$.
\end{table*}
\begin{table*}
\caption{Vertical transition energies (eV) of nitrosomethane.}
\label{tab:nitrosomethane}
\begin{ruledtabular}
\begin{tabular}{lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $(a',a'')$ & $(A',A'')$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$^1A''(n,\pis)$ &(4,2) &(1,1) &2.12$^a$ &1.84$^a$ &1.60$^a$ &1.94$^a$ &1.91$^a$ &1.96\\
$^1A'(n^2,\pis^2)$ &(4,2) &(2,0) &4.74$^a$ &4.69$^a$ &4.67$^a$ &4.71$^a$ &4.71$^a$ &4.76\\
$^1A'(n,3s)$ &(5,2) &(3,0) &5.87$^b$ &6.32$^b$ &6.07$^b$ &6.34$^b$ &6.31$^b$ &6.29\\
$^3A''(n,\pis)$ &(4,2) &(1,1) &1.31$^a$ &1.00$^a$ &0.75$^a$ &1.12$^a$ &1.09$^a$ &1.16\\
$^3A'(\pi,\pis)$ &(2,2) &(2,0) &5.52$^c$ &5.52$^c$ &5.37$^c$ &5.54$^c$ &5.50$^c$ &5.60\\
$^1A''[F](n,\pis)$ &(4,2) &(1,1) &1.83$^a$ &1.55$^a$ &1.32$^a$ &1.66$^a$ &1.62$^a$ &1.67\\
\end{tabular}
\end{ruledtabular}
\flushleft
$^a$Reference (8e,6o) active space including valence $\nO$, $\nN$, $\piNO$, $\sigNO$ and $\sigsNO$, $\pisNO$ orbitals.
$^b$Reference (8e,7o) active space including valence $\nO$, $\nN$, $\piNO$, $\sigNO$ and $\sigsNO$, $\pisNO$, Rydberg 3s orbitals.
$^c$Reference (4e,4o) active space including valence $\piNO$, $\sigNO$ and $\sigsNO$, $\pisNO$ orbitals.
\end{table*}
\begin{table*}
\caption{Vertical transition energies (eV) of propynal.}
\label{tab:propynal}
\begin{ruledtabular}
\begin{tabular}{lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $(a',a'')$ & $(A',A'')$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$^1A''(n,\pis)$ &(3,4) &(1,2) &4.00$^a$ &3.92$^a$ &3.64$^a$ &3.90$^a$ &3.86$^a$ &3.80\\
$^1A''(\pi,\pis)$ &(3,4) &(1,2) &6.62$^a$ &5.82$^a$ &5.49$^a$ &5.81$^a$ &5.72$^a$ &5.54\\
$^3A''(n,\pis)$ &(3,4) &(1,1) &3.52$^a$ &3.48$^a$ &3.26$^a$ &3.52$^a$ &3.50$^a$ &3.47\\
$^3A'(\pi,\pis)$ &(2,4) &(2,0) &4.69$^b$ &4.59$^b$ &4.30$^b$ &4.59$^b$ &4.54$^b$ &4.47\\
\end{tabular}
\end{ruledtabular}
\flushleft
$^a$Using reference (8e,7o) active space including valence $\pi$ and $\nO$ orbitals.
$^b$Using reference (6e,6o) active space including valence $\pi$ orbitals.
\end{table*}
\begin{table*}
\caption{Vertical transition energies (eV) of pyrazine.}
\label{tab:pyrazine}
\begin{ruledtabular}
\begin{tabular}{lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $(a_g,b_{3u},b_{2u},b_{1g},b_{1u},b_{2g},b_{3g},a_u)$ & $(A_g,B_{3u},B_{2u},B_{1g},B_{1u},B_{2g},B_{3g},A_u)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$^1B_{3u}(n,\pis)$ &(1,2,0,1,1,2,0,1) &(1,1,0,0,0,0,0,0) &4.76a &4.09a &3.66a &4.31a &4.30a &4.15\\
$^1A_{u}(n,\pis)$ &(1,2,0,1,1,2,0,1) &(1,0,0,0,0,0,0,1) &5.90a &4.76a &4.26a &5.10a &5.10a &4.98\\
$^1B_{2u}(\pi,\pis)$ &(0,2,0,1,0,2,0,1) &(1,0,1,0,0,0,0,0) &4.97b &5.13b &4.65b &5.09b &5.03b &5.02\\
$^1B_{2g}(n,\pis)$ &(1,2,0,1,1,2,0,1) &(1,0,0,0,0,1,0,0) &5.80a &5.68a &5.27a &5.73a &5.70a &5.71\\
$^1A_{g}(n,3s)$ &(2,2,0,1,1,2,0,1) &(2,0,0,0,0,0,0,0) &6.69c &6.66c &6.27c &6.81c &6.80c &6.65\\
$^1B_{1g}(n,\pis)$ &(1,2,0,1,1,2,0,1) &(1,0,0,1,0,0,0,0) &7.16a &6.61a &6.07a &6.78a &6.76a &6.74\\
$^1B_{1u}(\pi,\pis)$ &(0,4,0,1,0,2,0,2) &(1,0,0,0,3,0,0,0) &8.04d &7.14d &6.72d &7.20d &7.12d &6.88\\
$^1B_{1g}(\pi,3s)$ &(1,2,0,1,0,2,0,1) &(1,0,0,1,0,0,0,0) &6.73e &7.41e &7.27e &7.24e &7.18e &7.21\\
$^1B_{2u}(n,3p_y)$ &(1,2,1,1,1,2,0,1) &(1,0,2,0,0,0,0,0) &7.49f &7.34f &6.93f &7.43f &7.40f &7.24\\
$^1B_{1u}(n,3p_z)$ &(1,2,0,1,2,2,0,1) &(1,0,0,0,3,0,0,0) &7.83g &7.55g &7.08g &7.64g &7.59g &7.44\\
$^1B_{1u}(\pi,\pis)$ &(0,4,0,1,0,2,0,2) &(1,0,0,0,3,0,0,0) &9.65d &8.59d &7.96d &8.68d &8.57d &7.98\\
$^3B_{3u}(n,\pis)$ &(1,2,0,1,1,2,0,1) &(1,1,0,0,0,0,0,0) &4.16a &3.49a &3.08a &3.72a &3.71a &3.59\\
$^3B_{1u}(\pi,\pis)$ &(0,4,0,1,0,2,0,2) &(1,0,0,0,2,0,0,0) &3.98d &4.44d &4.15d &4.34d &4.28d &4.35\\
$^3B_{2u}(\pi,\pis)$ &(0,2,0,1,0,2,0,1) &(1,0,1,0,0,0,0,0) &4.62b &4.44b &4.09b &4.47b &4.41b &4.39\\
$^3A_{u}(n,\pis)$ &(1,2,0,1,1,2,0,1) &(1,0,0,0,0,0,0,1) &5.85a &4.73a &4.21a &5.07a &5.07a &4.93\\
$^3B_{2g}(n,\pis)$ &(1,2,0,1,1,2,0,1) &(1,0,0,0,0,1,0,0) &5.25a &5.04a &4.66a &5.14a &5.11a &5.08\\
$^3B_{1u}(\pi,\pis)$ &(0,4,0,1,0,2,0,2) &(1,0,0,0,2,0,0,0) &5.15d &5.29d &4.92d &5.25d &5.19d &5.28\\
\end{tabular}
\end{ruledtabular}
\flushleft
$^a$Using reference (10e,8o) active space including valence $\pi$ and $\nN$ orbitals.
$^b$Using reference (6e,6o) active space including valence $\pi$ orbitals.
$^c$Using reference (10e,9o) active space including valence $\pi$, $\nN$ and $3s$ orbitals.
$^d$Using reference (6e,9o) active space including valence $\pi$ and three $3p_x$ orbitals.
$^e$Using reference (6e,7o) active space including valence $\pi$ and $3s$ orbitals.
$^f$Using reference (10e,9o) active space including valence $\pi$, $\nN$ and $3p_y$ orbitals.
$^g$Using reference (10e,9o) active space including valence $\pi$, $\nN$ and $3p_z$ orbitals.
\end{table*}
\begin{table*}
\caption{Vertical transition energies (eV) of pyridazine.}
\label{tab:pyridazine}
\begin{ruledtabular}
\begin{tabular}{lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$^1B_1(n,\pis)$ &(1,3,1,3) &(1,1,0,0) &4.29$^a$ &3.74$^a$ &3.36$^a$ &3.94$^a$ &3.92$^a$ &3.83\\
$^1A_2(n,\pis)$ &(1,3,1,3) &(1,0,0,1) &4.83$^a$ &4.29$^a$ &3.87$^a$ &4.49$^a$ &4.48$^a$ &4.37\\
$^1A_1(\pi,\pis)$ &(0,3,0,3) &(2,0,0,0) &5.12$^b$ &5.34$^b$ &4.87$^b$ &5.30$^b$ &5.25$^b$ &5.26\\
$^1A_2(n,\pis)$ &(1,3,1,3) &(1,0,0,2) &6.26$^a$ &5.73$^a$ &5.19$^a$ &5.93$^a$ &5.89$^a$ &5.72\\
$^1B_2(n,3s)$ &(2,3,1,3) &(1,0,1,0) &5.99$^c$ &6.18$^c$ &5.90$^c$ &6.28$^c$ &6.27$^c$ &6.17\\
$^1B_1(n,\pis)$ &(1,3,1,3) &(1,2,0,0) &7.16$^a$ &6.50$^a$ &5.94$^a$ &6.72$^a$ &6.67$^a$ &6.37\\
$^1B_2(\pi,\pis)$ &(0,5,0,4) &(1,0,1,0) &7.54$^d$ &7.26$^d$ &6.82$^d$ &7.25$^d$ &7.17$^d$ &6.75\\
$^3B_1(n,\pis)$ &(1,3,1,3) &(1,1,0,0) &3.60$^a$ &3.08$^a$ &2.72$^a$ &3.29$^a$ &3.28$^a$ &3.19\\
$^3A_2(n,\pis)$ &(1,3,1,3) &(1,0,0,1) &4.49$^a$ &4.01$^a$ &3.59$^a$ &4.20$^a$ &4.18$^a$ &4.11\\
$^3B_2(\pi,\pis)$ &(0,3,0,3) &(1,0,1,0) &3.93$^b$ &4.44$^b$ &4.13$^b$ &4.30$^b$ &4.24$^b$ &4.34\\
$^3A_1(\pi,\pis)$ &(0,3,0,3) &(2,0,0,0) &4.93$^b$ &4.87$^b$ &4.48$^b$ &4.89$^b$ &4.83$^b$ &4.82\\
\end{tabular}
\end{ruledtabular}
\flushleft
$^a$Using reference (10e,8o) active space including valence $\pi$ and $\nN$ orbitals.
$^b$Using reference (6e,6o) active space including valence $\pi$ orbitals.
$^c$Using reference (10e,9o) active space including valence $\pi$, $\nN$ and $3s$ orbitals.
$^d$Using reference (6e,9o) active space including valence $\pi$, $\nN$ and three $3p_x$ orbitals.
\end{table*}
\begin{table*}
\caption{Vertical transition energies (eV) of pyridine.}
\label{tab:pyridine}
\begin{ruledtabular}
\begin{tabular}{lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$^1B_1(n,\pis)$ &(1,4,1,2) &(1,2,0,0) &5.43$^a$ &5.15$^a$ &4.81$^a$ &5.18$^a$ &5.13$^a$ &4.95\\
$^1B_2(\pi,\pis)$ &(0,7,0,3) &(1,0,2,0) &5.03$^b$ &5.18$^b$ &4.76$^b$ &5.15$^b$ &5.09$^b$ &5.14\\
$^1A_2(n,\pis)$ &(2,4,0,2) &(1,0,0,2) &6.30$^c$ &5.46$^c$ &5.03$^c$ &5.63$^c$ &5.59$^c$ &5.40\\
$^1A_1(\pi,\pis)$ &(0,4,0,2) &(2,0,0,0) &7.90$^d$ &6.92$^d$ &6.27$^d$ &7.04$^d$ &6.93$^d$ &6.62\\
$^1A_1(n,3s)$ &(2,4,0,2) &(2,0,0,0) &6.40$^c$ &6.90$^c$ &6.67$^c$ &6.97$^c$ &6.96$^c$ &6.76\\
$^1A_2(\pi,3s)$ &(2,4,0,2) &(1,0,0,2) &6.60$^c$ &7.08$^c$ &6.87$^c$ &6.88$^c$ &6.80$^c$ &6.82\\
$^1B_2(\pi,\pis)$ &(0,7,0,3) &(1,0,2,0) &7.45$^b$ &7.92$^b$ &7.67$^b$ &7.80$^b$ &7.73$^b$ &7.40\\
$^1B_1(\pi,3p_y)$ &(1,4,1,2) &(1,2,0,0) &7.12$^a$ &7.70$^a$ &7.51$^a$ &7.48$^a$ &7.40$^a$ &7.38\\
$^1A_1(\pi,\pis)$ &(0,4,0,2) &(4,0,0,0) &9.49$^d$ &7.66$^d$ &6.63$^d$ &7.87$^d$ &7.70$^d$ &7.39\\
$^3A_1(\pi,\pis)$ &(0,4,0,2) &(2,0,0,0) &3.98$^d$ &4.40$^d$ &4.06$^d$ &4.29$^d$ &4.22$^d$ &4.30\\
$^3B_1(n,\pis)$ &(1,4,0,2) &(1,1,0,0) &4.65$^e$ &4.48$^e$ &4.21$^e$ &4.57$^e$ &4.55$^e$ &4.46\\
$^3B_2(\pi,\pis)$ &(0,7,0,3) &(1,0,2,0) &4.83$^b$ &4.86$^b$ &4.53$^b$ &4.81$^b$ &4.74$^b$ &4.79\\
$^3A_1(\pi,\pis)$ &(0,4,0,2) &(3,0,0,0) &5.11$^d$ &5.09$^d$ &4.63$^d$ &5.09$^d$ &5.02$^d$ &5.04\\
$^3A_2(n,\pis)$ &(1,4,0,2) &(1,0,0,1) &5.94$^e$ &5.33$^e$ &4.96$^e$ &5.53$^e$ &5.51$^e$ &5.36\\
$^3B_2(\pi,\pis)$ &(0,7,0,3) &(1,0,2,0) &6.93$^b$ &6.40$^b$ &5.99$^b$ &6.43$^b$ &6.35$^b$ &6.24\\
\end{tabular}
\end{ruledtabular}
\flushleft
$^a$Using reference (8e,8o) active space including valence $\pi$, $\nN$ and $3p_y$ orbitals.
$^b$Using reference (6e,10o) active space including valence $\pi$ and four $3p_x$ orbitals.
$^c$Using reference (8e,8o) active space including valence $\pi$, $\nN$ and $3s$ orbitals.
$^d$Using reference (6e,6o) active space including valence $\pi$ orbitals.
$^e$Using reference (8e,7o) active space including valence $\pi$ and $\nN$ orbitals.
\end{table*}
\begin{table*}
\caption{Vertical transition energies (eV) of pyrimidine.}
\label{tab:pyrimidine}
\begin{ruledtabular}
\begin{tabular}{lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$^1B_1(n,\pis)$ &(1,4,1,2) &(1,1,0,0) &4.85$^a$ &4.44$^a$ &4.07$^a$ &4.58$^a$ &4.55$^a$ &4.44\\
$^1A_2(n,\pis)$ &(1,4,1,2) &(1,0,0,1) &5.52$^a$ &4.80$^a$ &4.36$^a$ &5.02$^a$ &5.00$^a$ &4.85\\
$^1B_2(\pi,\pis)$ &(0,6,0,3) &(1,0,1,0) &5.28$^b$ &5.42$^b$ &4.98$^b$ &5.41$^b$ &5.36$^b$ &5.38\\
$^1A_2(n,\pis)$ &(1,4,1,2) &(1,0,0,2) &6.70$^a$ &5.92$^a$ &5.32$^a$ &6.16$^a$ &6.10$^a$ &5.92\\
$^1B_1(n,\pis)$ &(1,4,1,2) &(1,2,0,0) &7.20$^a$ &6.31$^a$ &5.65$^a$ &6.58$^a$ &6.53$^a$ &6.26\\
$^1B_2(n,3s)$ &(2,4,1,2) &(1,0,2,0) &6.86$^c$ &6.85$^c$ &6.50$^c$ &6.89$^c$ &6.86$^c$ &6.70\\
$^1A_1(\pi,\pis)$ &(0,6,0,3) &(2,0,0,0) &7.69$^b$ &7.31$^b$ &6.94$^b$ &7.29$^b$ &7.22$^b$ &6.88\\
$^3B_1(n,\pis)$ &(1,4,1,2) &(1,1,0,0) &4.45$^a$ &4.05$^a$ &3.67$^a$ &4.20$^a$ &4.18$^a$ &4.09\\
$^3A_1(\pi,\pis)$ &(0,6,0,3) &(2,0,0,0) &4.22$^b$ &4.57$^b$ &4.25$^b$ &4.51$^b$ &4.44$^b$ &4.51\\
$^3A_2(n,\pis)$ &(1,4,1,2) &(1,0,0,1) &5.20$^a$ &4.63$^a$ &4.16$^a$ &4.81$^a$ &4.78$^a$ &4.66\\
$^3B_2(\pi,\pis)$ &(0,4,0,2) &(1,0,1,0) &5.10$^d$ &5.01$^d$ &4.60$^d$ &5.03$^d$ &4.97$^d$ &4.96\\
\end{tabular}
\end{ruledtabular}
\flushleft
$^a$Using reference (10e,8o) active space including valence $\pi$ and $\nN$ orbitals.
$^b$Using reference (6e,9o) active space including valence $\pi$ and three $3p_x$ orbitals.
$^c$Using reference (10e,9o) active space including valence $\pi$, $\nN$ and $3s$ orbitals.
$^d$Using reference (6e,6o) active space including valence $\pi$ orbitals.
\end{table*}
\begin{table*}
\caption{Vertical transition energies (eV) of pyrrole.}
\label{tab:pyrrole}
\begin{ruledtabular}
\begin{tabular}{lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$^1A_2(\pi,3s)$ &(1,3,0,2) &(1,0,0,1) &4.49$^a$ &5.44$^a$ &5.23$^a$ &5.28$^a$ &5.23$^a$ &5.24\\
$^1B_1(\pi,3p_y)$ &(0,3,1,2) &(1,1,0,0) &5.22$^b$ &6.26$^b$ &6.07$^b$ &6.08$^b$ &6.02$^b$ &6.00\\
$^1A_2(\pi,3p_z)$ &(2,3,0,2) &(1,0,0,2) &4.89$^c$ &6.16$^c$ &6.02$^c$ &6.01$^c$ &5.97$^c$ &6.00\\
$^1B_2(\pi,\pis)$ &(0,4,0,2) &(1,0,2,0) &7.73$^d$ &6.62$^d$ &6.36$^d$ &6.45$^d$ &6.38$^d$ &6.26\\
$^1A_1(\pi,\pis)$ &(0,3,0,2) &(3,0,0,0) &6.47$^e$ &6.41$^e$ &5.84$^e$ &6.43$^e$ &6.34$^e$ &6.30\\
$^1B_2(\pi,3p_x)$ &(0,4,0,2) &(1,0,2,0) &5.82$^d$ &6.75$^d$ &6.11$^d$ &6.92$^d$ &6.82$^d$ &6.83\\
$^3B_2(\pi,\pis)$ &(0,3,0,2) &(1,0,1,0) &4.24$^e$ &4.57$^e$ &4.30$^e$ &4.49$^e$ &4.44$^e$ &4.51\\
$^3A_2(\pi,3s)$ &(1,3,0,2) &(1,0,0,1) &4.47$^a$ &5.41$^a$ &5.21$^a$ &5.26$^a$ &5.20$^a$ &5.21\\
$^3A_1(\pi,\pis)$ &(0,3,0,2) &(3,0,0,0) &5.52$^e$ &5.50$^e$ &5.04$^e$ &5.49$^e$ &5.40$^e$ &5.45\\
$^3B_1(\pi,3p_y)$ &(0,3,1,2) &(1,1,0,0) &5.18$^b$ &6.22$^b$ &6.03$^b$ &6.04$^b$ &5.98$^b$ &5.91\\
\end{tabular}
\end{ruledtabular}
\flushleft
$^a$Using reference (6e,6o) active space including valence $\pi$ and $3s$ orbitals.
$^b$Using reference (6e,6o) active space including valence $\pi$ and $3p_y$ orbitals.
$^c$Using reference (6e,7o) active space including valence $\pi$, $3s$ and $3p_z$ orbitals.
$^d$Using reference (6e,6o) active space including valence $\pi$ and $3p_x$ orbitals.
$^e$Using reference (6e,5o) active space including valence $\pi$ orbitals.
\end{table*}
\begin{table*}
\caption{Vertical transition energies (eV) of streptocyanine.}
\label{tab:streptocyanine}
\begin{ruledtabular}
\begin{tabular}{lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$^1B_2(\pi,\pis)$ &(2,2,2,1) &(1,0,1,0) &7.82$^a$ &7.17$^a$ &6.76$^a$ &7.28$^a$ &7.21$^a$ &7.13\\
$^3B_2(\pi,\pis)$ &(2,2,2,1) &(1,0,1,0) &5.86$^a$ &5.49$^a$ &5.22$^a$ &5.54$^a$ &5.49$^a$ &5.52\\
\end{tabular}
\end{ruledtabular}
\flushleft
$^a$Reference (8e,7o) active space including valence $\pi$, two $\sigCN$ and two $\sigsCN$ orbitals.
\end{table*}
\begin{table*}
\caption{Vertical transition energies (eV) of tetrazine.}
\label{tab:tetrazine}
\begin{ruledtabular}
\begin{tabular}{lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $(a_g,b_{3u},b_{2u},b_{1g},b_{1u},b_{2g},b_{3g},a_u)$ & $(A_g,B_{3u},B_{2u},B_{1g},B_{1u},B_{2g},B_{3g},A_u)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$^1B_{3u}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,1,0,0,0,0,0,0) &2.99$^a$ &2.31$^a$ &1.91$^a$ &2.54$^a$ &2.53$^a$ &2.47\\
$^1A_{u}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,0,0,1) &4.37$^a$ &3.49$^a$ &3.00$^a$ &3.77$^a$ &3.78$^a$ &3.69\\
$^1A_{g}(\rm double)$ &(1,2,1,1,1,2,1,1) &(2,0,0,0,0,0,0,0) &5.42$^a$ &4.69$^a$ &4.48$^a$ &4.85$^a$ &4.87$^a$ &---\\
$^1B_{1g}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,1,0,0,0,0) &5.41$^a$ &4.83$^a$ &4.33$^a$ &5.02$^a$ &5.00$^a$ &4.93\\
$^1B_{2u}(\pi,\pis)$ &(0,2,0,1,0,2,0,1) &(1,0,1,0,0,0,0,0) &5.04$^b$ &5.31$^b$ &4.84$^b$ &5.26$^b$ &5.23$^b$ &5.21\\
$^1B_{2g}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,1,0,0) &5.43$^a$ &5.38$^a$ &4.90$^a$ &5.42$^a$ &5.38$^a$ &5.45\\
$^1A_{u}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,0,0,2) &6.37$^a$ &5.51$^a$ &4.92$^a$ &5.80$^a$ &5.80$^a$ &5.53\\
$^1B_{3g}(\rm double)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,0,1,0) &6.59$^a$ &5.85$^a$ &5.22$^a$ &6.20$^a$ &6.22$^a$ &---\\
$^1B_{2g}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,2,0,0) &6.79$^a$ &5.96$^a$ &5.18$^a$ &6.27$^a$ &6.28$^a$ &6.12\\
$^1B_{1g}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,2,0,0,0,0) &7.18$^{a,c}$ &6.59$^{a,c}$ &5.89$^{a,c}$ &6.79$^{a,c}$ &6.72$^{a,c}$ &6.91\\
$^3B_{3u}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,1,0,0,0,0,0,0) &2.38$^a$ &1.70$^a$ &1.31$^a$ &1.94$^a$ &1.93$^a$ &1.85\\
$^3A_{u}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,0,0,1) &4.06$^a$ &3.26$^a$ &2.78$^a$ &3.52$^a$ &3.52$^a$ &3.45\\
$^3B_{1g}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,1,0,0,0,0) &4.66$^a$ &4.10$^a$ &3.62$^a$ &4.32$^a$ &4.30$^a$ &4.20\\
$^3B_{1u}(\pi,\pis)$ &(0,4,0,1,0,2,0,2) &(1,0,0,0,2,0,0,0) &3.90$^d$ &4.55$^d$ &4.29$^d$ &4.39$^d$ &4.34$^d$ &4.49\\
$^3B_{2u}(\pi,\pis)$ &(0,2,0,1,0,2,0,1) &(1,0,1,0,0,0,0,0) &4.68$^b$ &4.55$^b$ &4.20$^b$ &4.60$^b$ &4.55$^b$ &4.52\\
$^3B_{2g}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,1,0,0) &5.17$^a$ &5.02$^a$ &4.53$^a$ &5.10$^a$ &5.07$^a$ &5.04\\
$^3A_{u}(n,\pis)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,0,0,2) &6.12$^a$ &5.07$^a$ &4.44$^a$ &5.41$^a$ &5.41$^a$ &5.11\\
$^3B_{3g}(\rm double)$ &(1,2,1,1,1,2,1,1) &(1,0,0,0,0,0,1,0) &6.56$^a$ &5.39$^a$ &4.86$^a$ &5.83$^a$ &5.85$^a$ &---\\
$^3B1u(\pi,\pis)$ &(0,4,0,1,0,2,0,2) &(1,0,0,0,2,0,0,0) &5.32$^d$ &5.46$^d$ &5.08$^d$ &5.44$^d$ &5.39$^d$ &5.42\\
\end{tabular}
\end{ruledtabular}
\flushleft
$^a$Using reference (14e,10o) active space including valence $\pi$ and $\nN$ orbitals.
$^b$Using reference (6e,6o) active space including valence $\pi$ orbitals.
$^c$Level shift set to \SI{0.4}{\hartree}.
$^d$Using reference (6e,9o) active space including valence $\pi$ and three $3p_x$ orbitals.
\end{table*}
\begin{table*}
\caption{Vertical transition energies (eV) of thioacetone.}
\label{tab:thioacetone}
\begin{ruledtabular}
\begin{tabular}{lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$^1A_2(n,\pis)$ &(2,2,1,0) &(1,0,0,1) &2.72$^a$ &2.58$^a$ &2.33$^a$ &2.60$^a$ &2.53$^a$ &2.53\\
$^1B_2(n,3s)$ &(4,2,1,0) &(1,0,2,0) &4.80$^b$ &5.60$^b$ &5.48$^b$ &5.64$^b$ &5.61$^b$ &5.56\\
$^1A_1(\pi,\pis)$ &(2,2,2,0) &(3,0,0,0) &6.94$^d$ &6.42$^d$ &5.98$^d$ &6.40$^d$ &6.26$^d$ &5.88\\
$^1B_2(n,3p_z)$ &(4,2,1,0) &(1,0,2,0) &5.57$^b$ &6.51$^b$ &6.40$^b$ &6.53$^b$ &6.49$^b$ &6.51\\
$^1A_1(n,3p_y)$ &(2,2,2,0) &(3,0,0,0) &6.24$^d$ &6.66$^d$ &6.41$^d$ &6.59$^d$ &6.50$^d$ &6.61\\
$^3A_2(n,\pis)$ &(2,2,1,0) &(1,0,0,1) &2.52$^a$ &2.34$^a$ &2.09$^a$ &2.38$^a$ &2.31$^a$ &2.33\\
$^3A_1(\pi,\pis)$ &(2,2,0,0) &(2,0,0,0) &3.52$^c$ &3.48$^c$ &3.29$^c$ &3.48$^c$ &3.43$^c$ &3.45\\
\end{tabular}
\end{ruledtabular}
\flushleft
$^a$Using reference (6e,5o) active space including valence $\pi$, $\nO$, $\sigCO$ and $\sigsCO$ orbitals.
$^b$Using reference (6e,7o) active space including valence $\pi$, $\nO$, $\sigCO$, $\sigsCO$, $3s$ and $3p_z$ orbitals.
$^c$Using reference (4e,4o) active space including valence $\pi$, $\sigCO$ and $\sigsCO$ orbitals.
$^d$Using reference (6e,6o) active space including valence $\pi$, $\nO$, $\sigCO$, $\sigsCO$ and $3p_y$ orbitals.
\end{table*}
\begin{table*}
\caption{Vertical transition energies (eV) of thiophene.}
\label{tab:thiophene}
\begin{ruledtabular}
\begin{tabular}{lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$^1A_1(\pi,\pis)$ &(0,3,0,2) &(3,0,0,0) &6.11$^a$ &5.84$^a$ &5.21$^a$ &5.89$^a$ &5.79$^a$ &5.64\\
$^1B_2(\pi,\pis)$ &(0,5,0,2) &(1,0,2,0) &6.94$^b$ &6.35$^b$ &5.89$^b$ &6.44$^b$ &6.35$^b$ &5.98\\
$^1A_2(\pi,3s)$ &(1,3,0,2) &(1,0,0,1) &5.70$^c$ &6.28$^c$ &6.07$^c$ &6.16$^c$ &6.10$^c$ &6.14\\
$^1B_1(\pi,3p_y)$ &(0,3,1,2) &(1,1,0,0) &6.02$^d$ &6.21$^d$ &5.90$^d$ &6.16$^d$ &6.10$^d$ &6.14\\
$^1A_2(\pi,3p_y)$ &(0,3,1,2) &(1,0,0,1) &6.05$^d$ &6.32$^d$ &5.98$^d$ &6.28$^d$ &6.21$^d$ &6.21\\
$^1B_1(\pi,3s)$ &(1,3,1,2) &(1,2,0,0) &5.78$^e$ &6.57$^e$ &6.28$^e$ &6.51$^e$ &6.44$^e$ &6.49\\
$^1B_2(\pi,3p_x)$ &(0,5,0,2) &(1,0,2,0) &6.80$^b$ &7.29$^b$ &7.03$^b$ &7.20$^b$ &7.13$^b$ &7.29\\
$^1A_1(\pi,\pis)$ &(0,3,0,2) &(3,0,0,0) &8.29$^{a,f}$ &7.62$^{a,f}$ &6.85$^{a,f}$ &7.71$^{a,f}$ &7.56$^{a,f}$ &7.31\\
$^3B_2(\pi,\pis)$ &(0,3,0,2) &(1,0,1,0) &3.68$^a$ &3.98$^a$ &3.71$^a$ &3.90$^a$ &3.84$^a$ &3.92\\
$^3A_1(\pi,\pis)$ &(0,3,0,2) &(3,0,0,0) &4.97$^a$ &4.85$^a$ &4.39$^a$ &4.87$^a$ &4.79$^a$ &4.76\\
$^3B_1(\pi,3p_y)$ &(0,3,1,2) &(1,1,0,0) &5.86$^d$ &5.97$^d$ &5.64$^d$ &5.94$^d$ &5.88$^d$ &5.93\\
$^3A_2(\pi,3s)$ &(1,3,0,2) &(1,0,0,1) &5.65$^c$ &6.22$^c$ &6.01$^c$ &6.11$^c$ &6.04$^c$ &6.08\\
\end{tabular}
\end{ruledtabular}
\flushleft
$^a$Using reference (6e,5o) active space including valence $\pi$ orbitals.
$^b$Using reference (6e,7o) active space including valence $\pi$ and two $3p_x$ orbitals.
$^c$Using reference (6e,6o) active space including valence $\pi$ and $3s$ orbitals.
$^d$Using reference (6e,6o) active space including valence $\pi$ and $3p_y$ orbitals.
$^e$Using reference (6e,7o) active space including valence $\pi$, $3s$ and $3p_y$ orbitals.
$^f$Strong double-excitation character.
\end{table*}
\begin{table*}
\caption{Vertical transition energies (eV) of thiopropynal.}
\label{tab:thiopropynal}
\begin{ruledtabular}
\begin{tabular}{lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $(a',a'')$ & $(A',A'')$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$^1A''(n,\pis)$ &(3,4) &(1,1) &2.06$^a$ &2.05$^a$ &1.84$^a$ &2.05$^a$ &2.00$^a$ &2.03\\
$^3A''(n,\pis)$ &(3,4) &(1,1) &1.85$^a$ &1.81$^a$ &1.60$^a$ &1.84$^a$ &1.79$^a$ &1.80\\
\end{tabular}
\end{ruledtabular}
\flushleft
$^a$Using reference (8e,7o) active space including valence $\pi$ and $\nO$ orbitals.
\end{table*}
\begin{table*}
\caption{Vertical transition energies (eV) of triazine.}
\label{tab:triazine}
\begin{ruledtabular}
\begin{tabular}{lcccccccc}
State & Active space & State-average & CASSCF & CASPT2 & CASPT2 & CASPT3 & CASPT3 & TBE \\
& $(a_1,b_1,b_2,a_2)$ & $(A_1,B_1,B_2,A_2)$ & & IPEA & NOIPEA & IPEA & NOIPEA & \\
\hline
$^1A_1''(n,\pis)$ &(2,4,1,2) &(1,2,0,2) &5.88$^a$ &4.62$^a$ &3.90$^a$ &5.00$^a$ &4.99$^a$ &4.72\\
$^1A_2''(n,\pis)$ &(2,4,1,2) &(1,1,0,0) &5.14$^a$ &4.77$^a$ &4.39$^a$ &4.90$^a$ &4.87$^a$ &4.75\\
$^1E''(n,\pis)$ &(2,4,1,2) &(1,2,0,2) &5.51$^a$ &4.76$^a$ &4.14$^a$ &5.01$^a$ &4.98$^a$ &4.78\\
$^1A_2'(\pi,\pis)$ &(0,6,0,3) &(1,0,1,0) &5.55$^b$ &5.76$^b$ &5.32$^b$ &5.75$^b$ &5.72$^b$ &5.75\\
$^1A_1'(\pi,\pis)$ &(0,6,0,3) &(2,0,0,0) &8.20$^b$ &7.43$^b$ &6.89$^b$ &7.50$^b$ &7.41$^b$ &7.24\\
$^1E'(n,3s)$ &(3,4,1,2) &(2,0,2,0) &7.40$^c$ &7.48$^c$ &7.15$^c$ &7.53$^c$ &7.49$^c$ &7.32\\
$^1E''(n,\pis)$ &(2,4,1,2) &(1,1,0,1) &8.26$^a$ &7.75$^a$ &7.04$^a$ &7.92$^a$ &7.90$^a$ &7.78\\
$^1E'(\pi,\pis)$ &(0,6,0,3) &(4,0,3,0) &10.03$^b$ &8.65$^b$ &7.70$^b$ &8.83$^b$ &8.72$^b$ &7.94\\
$^3A_2''(n,\pis)$ &(2,4,1,2) &(1,1,0,0) &4.74$^a$ &4.37$^a$ &3.99$^a$ &4.51$^a$ &4.49$^a$ &4.33\\
$^3E''(n,\pis)$ &(2,4,1,2) &(1,2,0,2) &5.14$^a$ &4.47$^a$ &3.88$^a$ &4.71$^a$ &4.68$^a$ &4.51\\
$^3A_1''(n,\pis)$ &(2,4,1,2) &(1,2,0,2) &5.88$^a$ &4.70$^a$ &3.94$^a$ &5.06$^a$ &5.04$^a$ &4.73\\
$^3A_1'(\pi,\pis)$ &(0,6,0,3) &(2,0,0,0) &4.46$^b$ &4.88$^b$ &4.55$^b$ &4.81$^b$ &4.75$^b$ &4.85\\
$^3E'(\pi,\pis)$ &(0,6,0,3) &(3,0,1,0) &5.57$^b$ &5.62$^b$ &5.20$^b$ &5.62$^b$ &5.57$^b$ &5.59\\
$^3A_2'(\pi,\pis)$ &(0,6,0,3) &(1,0,1,0) &7.70$^b$ &6.62$^b$ &6.12$^b$ &6.76$^b$ &6.68$^b$ &6.62\\
\end{tabular}
\end{ruledtabular}
\flushleft
$^a$Using reference (12e,9o) active space including valence $\pi$ and $\nN$ orbitals.
$^b$Using reference (6e,9o) active space including valence $\pi$ and three $3p_x$ orbitals.
$^c$Using reference (12e,10o) active space including valence $\pi$, $\nN$ and $3s$ orbitals.
\end{table*}
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\bibliography{CASPT3}
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\end{document}
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