From e5763c26b55e5f38422413a06e66d383d51ade52 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Wed, 4 Dec 2019 15:41:30 +0100 Subject: [PATCH] SI MC --- Manuscript/FCI2-MC.tex | 870 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 870 insertions(+) create mode 100644 Manuscript/FCI2-MC.tex diff --git a/Manuscript/FCI2-MC.tex b/Manuscript/FCI2-MC.tex new file mode 100644 index 0000000..de5603c --- /dev/null +++ b/Manuscript/FCI2-MC.tex @@ -0,0 +1,870 @@ +\documentclass[journal=jctcce,manuscript=article,layout=traditional]{achemso} +\usepackage{graphicx,dcolumn,bm,xcolor,microtype,hyperref,multirow,amsmath,amssymb,amsfonts,physics,float,lscape,soul,rotating,longtable,tabularx} +\usepackage[version=4]{mhchem} + + +\newcommand{\alert}[1]{\textcolor{red}{#1}} +\newcommand{\mc}{\multicolumn} +\newcommand{\mcc}[1]{\multicolumn{1}{c}{#1}} +\newcommand{\mr}{\multirow} + +\newcommand{\EFCI}{E_\text{FCI}} +\newcommand{\EexCI}{E_\text{exCI}} +\newcommand{\EsCI}{E_\text{sCI}} +\newcommand{\EPT}{E_\text{PT2}} +\newcommand{\PsisCI}{\Psi_\text{sCI}} +\newcommand{\Ndet}{N_\text{det}} + +\newcommand{\ex}[6]{$^{#1}#2_{#3}^{#4}(#5 \rightarrow #6)$} +\newcommand{\pis}{\pi^\star} +\newcommand{\si}{\sigma} +\newcommand{\sis}{\sigma^\star} + +% methods +\newcommand{\TDDFT}{TD-DFT} +\newcommand{\CASSCF}{CASSCF} +\newcommand{\CASPT}{CASPT2} +\newcommand{\ADC}[1]{ADC(#1)} +\newcommand{\AD}{ADC(2)} +\newcommand{\CCD}{CC2} +\newcommand{\CCT}{CC3} +\newcommand{\STEOM}{STEOM-CCSD} +\newcommand{\AT}{ADC(3)} +\newcommand{\CC}[1]{CC#1} +\newcommand{\CCSD}{CCSD} +\newcommand{\EOMCCSD}{EOM-CCSD} +\newcommand{\CCSDT}{CCSDT} +\newcommand{\CCSDTQ}{CCSDTQ} +\newcommand{\CI}{CI} +\newcommand{\sCI}{sCI} +\newcommand{\exCI}{exFCI} +\newcommand{\FCI}{FCI} + +% basis +\newcommand{\Pop}{6-31+G(d)} +\newcommand{\AVDZ}{\emph{aug}-cc-pVDZ} +\newcommand{\AVTZ}{\emph{aug}-cc-pVTZ} +\newcommand{\DAVTZ}{d-\emph{aug}-cc-pVTZ} +\newcommand{\AVQZ}{\emph{aug}-cc-pVQZ} +\newcommand{\DAVQZ}{d-\emph{aug}-cc-pVQZ} +\newcommand{\TAVQZ}{t-\emph{aug}-cc-pVQZ} +\newcommand{\AVFZ}{\emph{aug}-cc-pV5Z} +\newcommand{\DAVFZ}{d-\emph{aug}-cc-pV5Z} + +% units +\newcommand{\IneV}[1]{#1 eV} +\newcommand{\InAU}[1]{#1 a.u.} +\newcommand{\Ryd}{\mathrm{R}} +\newcommand{\Val}{\mathrm{V}} +\newcommand{\Fl}{\mathrm{F}} +\newcommand{\ra}{\rightarrow} + +\newcommand{\SI}{Supporting Information} + +\setcounter{table}{0} +\setcounter{figure}{0} +\setcounter{page}{1} +\setcounter{equation}{0} +\renewcommand{\thepage}{S\arabic{page}} +\renewcommand{\thefigure}{S\arabic{figure}} +\renewcommand{\theequation}{S\arabic{equation}} +\renewcommand{\thetable}{S\arabic{table}} +\renewcommand{\thesection}{S\arabic{section}} + +\renewcommand\floatpagefraction{.99} +\renewcommand\topfraction{.99} +\renewcommand\bottomfraction{.99} +\renewcommand\textfraction{.01} + +% addresses +\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques, Universit\'e de Toulouse, CNRS, UPS, France} +\newcommand{\CEISAM}{Laboratoire CEISAM - UMR CNRS 6230, Universit\'e de Nantes, 2 Rue de la Houssini\`ere, BP 92208, 44322 Nantes Cedex 3, France} +\newcommand{\Pisa}{Dipartimento di Chimica e Chimica Industriale, University of Pisa, Via Moruzzi 3, 56124 Pisa, Italy} + +\title{Highly-Accurate Reference Excitation Energies and Benchmarks: Medium Size Molecules\\Supporting Information} + +\author{Pierre-Fran{\c c}ois Loos} + \email{loos@irsamc.ups-tlse.fr} + \affiliation[LCPQ, Toulouse]{\LCPQ} +\author{Filippo Lipparini} + \affiliation[DC, Pisa]{\Pisa} + \email{filippo.lipparini@unipi.it} +\author{Martial Boggio-Pasqua} + \affiliation[LCPQ, Toulouse]{\LCPQ} +\author{Anthony Scemama} + \affiliation[LCPQ, Toulouse]{\LCPQ} +\author{Denis Jacquemin} + \email{Denis.Jacquemin@univ-nantes.fr} + \affiliation[UN, Nantes]{\CEISAM} + +\begin{document} + +\clearpage + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of acetone.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Acetone &$^1A_2 (\Val; n \ra \pis)$ &4.57$^a$,4.48$^b$ \\ + &$^1B_2 (\Ryd; n \ra 3s)$ &6.81$^c$ \\ + &$^1A_2 (\Ryd; n \ra 3p)$ &7.65$^b$ \\ + &$^1A_1 (\Ryd; n \ra 3p)$ &7.75$^d$ \\ + &$^1B_2 (\Ryd; n \ra 3p)$ &7.91$^c$ \\ + &$^3A_2 (\Val; n \ra \pis)$ &4.20$^a$ \\ + &$^3A_1 (\Val; \pi \ra \pis)$ &6.28$^e$ \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$Using reference (6e,5o) active space including valence $\pi$, $n_\text{O}$, $\si_\text{CO}$ and $\si^*_\text{CO}$ orbitals. +$^b$Using reference (6e,6o) active space including valence $\pi$, $n_\text{O}$, $\si_\text{CO}$, $\si^*_\text{CO}$ and $3p_x$ orbitals. +$^c$Using reference (6e,7o) active space including valence $\pi$, $n_\text{O}$, $\si_\text{CO}$, $\si^*_\text{CO}$, 3s and $3p_z$ orbitals. +$^d$Using reference (6e,6o) active space including valence $\pi$, $n_\text{O}$, $\si_\text{CO}$, $\si^*_\text{CO}$ and $3p_y$ orbitals. +$^e$Using reference (4e,4o) active space including valence $\pi$, $\si_\text{CO}$ and $\si^*_\text{CO}$ orbitals. +\end{footnotesize} +\end{flushleft} +\end{table} + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of acrolein.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Acrolein &$^1A'' (\Val; n \ra \pis)$ &3.76$^a$,3.73$^b$ \\ + &$^1A' (\Val; \pi \ra \pis)$ &6.67$^a$ \\ + &$^1A'' (\Val; n \ra \pis)$ &7.16$^{a,c}$,7.57$^{b,c}$ \\ + &$^1A' (\Ryd; n \ra 3s)$ &7.05$^a$ \\ + &$^3A'' (\Val; n \ra \pis)$ &3.46$^a$,3.44$^b$ \\ + &$^3A' (\Val; \pi \ra \pis)$ &3.95$^a$ \\ + &$^3A' (\Val; \pi \ra \pis)$ &6.23$^a$ \\ + &$^3A'' (\Val; n \ra \pis)$ &6.83$^{a,d}$,7.06$^{b,d}$ \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$Using reference (12e,12o) active space including valence $\pi$, $\si_\text{CC}$, $\si_\text{CO}$, $\si^*_\text{CC}$, $\si^*_\text{CO}$, $n_\text{O}$ and 3s orbitals. +$^b$Using reference (12e,13o) active space including valence $\pi$, $\si_\text{CC}$, $\si_\text{CO}$, $\si^*_\text{CC}$, $\si^*_\text{CO}$, $n_\text{O}$, 3s and $3p_z$ orbitals. +$^c$Substantial Rydberg and doubly-excited character. +$^d$Substantial doubly-excited character. +\end{footnotesize} +\end{flushleft} +\end{table} + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of benzene.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Benzene &$^1B_{2u} (\Val; \pi \ra \pis)$ &5.32$^a$,5.32$^b$ \\ + &$^1B_{1u} (\Val; \pi \ra \pis)$ &6.01$^a$,6.43$^b$ \\ + &$^1E_{1g} (\Ryd; \pi \ra 3s)$ &6.75$^c$ \\ + &$^1A_{2u} (\Ryd; \pi \ra 3p)$ &7.40$^d$\\ + &$^1E_{2u} (\Ryd; \pi \ra 3p)$ &7.45$^d$ \\ + &$^3B_{1u} (\Val; \pi \ra \pis)$ &4.44$^a$,4.32$^b$\\ + &$^3E_{1u}(\Val; \pi \ra \pis)$ &4.99$^a$,4.92$^b$\\ + &$^3B_{2u} (\Val; \pi \ra \pis)$ &5.30$^a$,5.51$^b$\\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$Using reference (6e,6o) active space including valence $\pis$ orbitals. +$^b$Using reference (6e,9o) active space including valence $\pis$ and three $3p_z$ orbitals. +$^c$Using reference (6e,7o) active space including valence $\pis$ and 3s orbitals. +$^d$Using reference (6e,8o) active space including valence $\pis$, $3p_x$ and $3p_y$ orbitals. +\end{footnotesize} +\end{flushleft} +\end{table} + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of butadiene.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Butadiene &$^1B_u (\Val; \pi \ra \pis)$ &6.04$^a$,6.73$^b$,6.68$^c$ \\ + &$^1B_g (\Ryd; \pi \ra 3s)$ &6.44$^d$ \\ + &$^1A_g (\Val; \pi \ra \pis)$ &6.70$^a$ \\ + &$^1A_u (\Ryd; \pi \ra 3p)$ &6.84$^e$ \\ + &$^1A_u (\Ryd; \pi \ra 3p)$ &7.01$^e$ \\ + &$^1B_u (\Ryd; \pi \ra 3p)$ &6.99$^b$,7.45$^c$ \\ + &$^3B_u (\Val; \pi \ra \pis)$ &3.40$^a$ \\ + &$^3A_g (\Val; \pi \ra \pis)$ &5.30$^a$ \\ + &$^3B_g (\Ryd; \pi \ra 3s)$ &6.38$^d$ \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$Using reference (10e,10o) active space including valence $\pi$, $\si_\text{CC}$ and $\si^*_\text{CC}$ orbitals. +$^b$Using reference (10e,11o) active space including valence $\pi$, $\si_\text{CC}$, $\si^*_\text{CC}$ and $3p_z$ orbitals. +$^c$Using reference (4e,8o) active space including valence $\pi$ and four $3p_z$. +$^d$Using reference (10e,11o) active space including valence $\pi$, $\si_\text{CC}$, $\si^*_\text{CC}$ and 3s orbitals. +$^e$Using reference (10e,12o) active space including valence $\pi$, $\si_\text{CC}$, $\si^*_\text{CC}$, $3p_x$ and $3p_y$ orbitals. +\end{footnotesize} +\end{flushleft} +\end{table} + + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of cyanoacetylene.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Cyanoacetylene &$^1\Sigma^- (\Val; \pi \ra \pis)$ & \\ + &$^1\Delta (\Val; \pi \ra \pis)$ & \\ + &$^3\Sigma^+ (\Val; \pi \ra \pis)$ & \\ + &$^3\Delta (\Val; \pi \ra \pis)$ & \\ + &$^1A'' [\mathrm{F}] (\Val; \pi \ra \pis)$ & \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} + +\end{footnotesize} +\end{flushleft} +\end{table} + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of cyanoformaldehyde.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Cyanoformaldehyde &$^1A'' (\Val; n \ra \pis)$ &3.98$^a$ \\ + &$^1A'' (\Val; \pi \ra \pis)$ & 6.44$^a$ \\ + &$^3A'' (\Val; n \ra \pis)$ & 3.58$^a$ \\ + &$^3A' (\Val; \pi \ra \pis)$ & 5.35$^b$ \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$ Using reference (8e,7o) active space including valence $\pi$ and $n_\text{O}$ orbitals. +$^b$ Using reference (6e,6o) active space including valence $\pi$ orbitals. +\end{footnotesize} +\end{flushleft} +\end{table} + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of cyanogen.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Cyanogen & $^1\Sigma_u^- (\Val; \pi \ra \pis)$ & \\ + & $^1\Delta_u (\Val; \pi \ra \pis)$ & \\ + & $^3\Sigma_u^+ (\Val; \pi \ra \pis)$ & \\ + & $^1\Sigma_u^- [\mathrm{F}] (\Val; \pi \ra \pis)$ & \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} + +\end{footnotesize} +\end{flushleft} +\end{table} + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of cyclopentadiene.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Cyclopentadiene &$^1B_2 (\Val; \pi \ra \pis)$ &4.96$^a$,4.92$^b$,5.65$^c$ \\ + &$^1A_2 (\Ryd; \pi \ra 3s)$ &5.92$^d$ \\ + &$^1B_1 (\Ryd; \pi \ra 3p)$ &6.42$^e$ \\ + &$^1A_2 (\Ryd; \pi \ra 3p)$ &6.59$^d$ \\ + &$^1B_2 (\Ryd; \pi \ra 3p)$ &6.58$^c$ \\ + &$^1A_1 (\Val; \pi \ra \pis)$ &6.75$^{a,f}$ \\ + &$^3B_2 (\Val; \pi \ra \pis)$ &3.41$^a$ \\ + &$^3A_1 (\Val; \pi \ra \pis)$ &5.36$^a$ \\ + &$^3A_2 (\Ryd; \pi \ra 3s)$ &5.73$^g$ \\ + &$^3B_1 (\Ryd; \pi \ra 3p)$ &6.40$^e$ \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$Using reference (4e,4o) active space including valence $\pi$ orbitals. +$^b$Using reference (4e,5o) active space including valence $\pi$ and $3p_x$ orbitals. +$^c$Using reference (4e,8o) active space including valence $\pi$ and four $3p_x$ orbitals. +$^d$Using reference (4e,6o) active space including valence $\pi$, 3s and $3p_z$ orbitals. +$^e$Using reference (4e,5o) active space including valence $\pi$ and $3p_y$ orbitals. +$^f$Strong double-excitation character. +$^g$Using reference (4e,5o) active space including valence $\pi$ and 3s orbitals. +\end{footnotesize} +\end{flushleft} +\end{table} + + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of cyclopropenone.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Cyclopropenone &$^1B_1 (\Val; n \ra \pis)$ & 4.04$^a$,4.20$^b$,4.21$^c$ \\ + &$^1A_2 (\Val; n \ra \pis)$ & 5.85$^a$,5.86$^b$,5.94$^c$ \\ + &$^1B_2 (\Ryd; n \ra 3s)$ & 6.51$^a$,6.64$^b$,6.75$^c$ \\ + &$^1B_2 (\Val; \pi \ra \pis$) & 6.82$^a$,6.93$^b$,7.06$^c$ \\ + &$^1B_2 (\Ryd; n \ra 3p)$ & 7.07$^a$,7.25$^b$,7.38$^c$ \\ + &$^1A_1 (\Ryd; n \ra 3p)$ & 7.28$^a$,7.08$^b$,7.28$^c$ \\ + &$^1A_1 (\Val; \pi \ra \pis)$ & 8.19$^a$,8.19$^c$ \\ + &$^3B_1 (\Val; n \ra \pis)$ & 3.51$^a$,3.68$^b$,3.67$^c$ \\ + &$^3B_2 (\Val; \pi \ra \pis)$ & 5.10$^a$,5.09$^b$,5.29$^c$ \\ + &$^3A_2 (\Val; n \ra \pis)$ & 5.60$^a$,5.60$^b$,5.69$^c$ \\ + &$^3A_1 (\Val; \pi \ra \pis)$ & 7.16$^a$,7.21$^b$,7.16$^c$ \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$Using reference (6e,7o) active space averaging with the ground state for each irreducible representation. +$^b$Using reference (6e,7o) active space averaging between three states of the same irreducible representation. +$^c$Using reference (6e,7o) active space averaging between four states of the same irreducible representation. +\end{footnotesize} +\end{flushleft} +\end{table} + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of cyclopropenethione.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Cyclopropenethione &$^1A_2 (\Val; n \ra \pis)$ &3.52$^a$ \\ + &$^1B_1 (\Val; n \ra \pis)$ &3.50$^a$ \\ + &$^1B_2 (\Val; \pi \ra \pis)$ &4.77$^b$ \\ + &$^1B_2 (\Ryd; n \ra 3s)$ &5.35$^b$ \\ + &$^1A_1 (\Val; \pi \ra \pis)$ &5.54$^c$ \\ + &$^1B_2 (\Ryd; n \ra 3p)$ &5.99$^b$ \\ + &$^3A_2 (\Val; n \ra \pis)$ &3.38$^a$ \\ + &$^3B_1 (\Val; n \ra \pis)$ &3.40$^a$ \\ + &$^3B_2 (\Val; \pi \ra \pis)$ &4.21$^c$,4.17$^b$ \\ + &$^3A_1 (\Val; \pi \ra \pis)$ &4.13$^c$ \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$Using reference (6e,5o) active space. +$^b$Using reference (6e,7o) active space. +$^c$Using reference (4e,4o) active space. +\end{footnotesize} +\end{flushleft} +\end{table} + + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of diacetylene.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Diacetylene &$^1\Sigma_u^- (\Val; \pi \ra \pis)$ & \\ + &$^1\Delta_u (\Val; \pi \ra \pis)$ & \\ + &$^3\Sigma_u^+ (\Val; \pi \ra \pis)$ & \\ + &$^3\Delta_u (\Val; \pi \ra \pis)$ & \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} + +\end{footnotesize} +\end{flushleft} +\end{table} + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of furan.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Furan &$^1A_2 (\Ryd; \pi \ra 3s)$ & 6.28$^a$ \\ + &$^1B_2 (\Val; \pi \ra \pis)$ & 5.92$^b$,6.20$^{c,d}$ \\ + &$^1A_1 (\Val; \pi \ra \pis)$ & 6.77$^{b,e}$ \\ + &$^1B_1 (\Ryd; \pi \ra 3p)$ & 6.71$^f$ \\ + &$^1A_2 (\Ryd; \pi \ra 3p)$ & 6.99$^a$ \\ + &$^1B_2 (\Ryd; \pi \ra 3p)$ & 7.01$^{c,d}$ \\ + &$^3B_2 (\Val; \pi \ra \pis)$ & 4.42$^b$ \\ + &$^3A_1 (\Val; \pi \ra \pis)$ & 5.60$^b$ \\ + &$^3A_2 (\Ryd; \pi \ra 3s)$ & 6.08$^g$ \\ + &$^3B_1 (\Ryd; \pi \ra 3p)$ & 6.68$^f$ \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$Using reference (6e,7o) active space including valence $\pi$, 3s and $3p_z$ orbitals. +$^b$Using reference (6e,5o) active space including valence $\pi$ orbitals. +$^c$Using reference (6e,6o) active space including valence $\pi$ and $3p_x$ orbitals. +$^d$Increasing the $\pi$ $3p_x$ active space leads to strong mixing in the zeroth-order wavefunction requiring QD-NEVPT2 (see Pastore et al., Chem. Phys. Lett. 2006, 426, 445--451). +$^e$Strong double-excitation character. +$^f$Using reference (6e,6o) active space including valence $\pi$ and $3p_y$ orbitals. +$^g$Using reference (4e,5o) active space including valence $\pi$ and 3s orbitals. +\end{footnotesize} +\end{flushleft} +\end{table} + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of glyoxal.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Glyoxal &$^1A_u (\Val; n \ra \pis)$ & 2.90$^a$ \\ + &$^1B_g (\Val; n \ra \pis)$ & 4.31$^a$,4.30$^b$ \\ + &$^1A_g (\Val; n,n \ra \pis,\pis)$ & 5.52$^a$ \\ + &$^1B_g (\Val; n \ra \pis)$ & 6.91$^{a,c}$,6.64$^{b,c}$ \\ + &$^1B_u (\Ryd; n \ra 3p)$ & 7.84$^d$ \\ + &$^3A_u (\Val; n \ra \pis)$ & 2.49$^a$ \\ + &$^3B_g (\Val; n \ra \pis)$ & 3.99$^a$ \\ + &$^3B_u (\Val; \pi \ra \pis)$ & 5.17$^a$ \\ + &$^3A_g (\Val; \pi \ra \pis)$ & 6.33$^a$ \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$Using reference (14e,12o) active space including valence $\pi$, two nO, $\si_\text{CC}$, $\si_\text{CO}$, $\si^*_\text{CC}$ and $\si^*_\text{CO}$ orbitals. +$^b$Using reference (14e,13o) active space including valence $\pi$, two nO, $\si_\text{CC}$, $\si_\text{CO}$, $\si^*_\text{CC}$, $\si^*_\text{CO}$ and $3p_z$ orbitals. +$^c$Non-negligible doubly-excited and Rydberg character. +$^d$Using reference (14e,13o) active space including valence $\pi$, two nO, $\si_\text{CC}$, $\si_\text{CO}$, $\si^*_\text{CC}$, $\si^*_\text{CO}$ and $3p_x$ orbitals. +\end{footnotesize} +\end{flushleft} +\end{table} + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of imidazole.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Imidazole &$^1A'' (\Ryd; \pi \ra 3s)$ &5.97$^a$,5.93$^b$ \\ + &$^1A' (\Val; \pi \ra \pis)$ &6.86$^c$,6.81$^d$,6.73$^e$ \\ + &$^1A'' (\Val; n \ra \pis)$ &6.97$^f$,6.96$^b$ \\ + &$^1A' (\Ryd; \pi \ra 3p)$ &7.08$^d$,7.00$^e$ \\ + &$^3A' (\Val; \pi \ra \pis)$ &4.98$^c$,4.86$^e$ \\ + &$^3A'' (\Ryd; \pi \ra 3s)$ &5.93$^a$,5.91$^b$ \\ + &$^3A' (\Val; \pi \ra \pis)$ &6.09$^c$,5.91$^e$ \\ + &$^3A'' (\Val; n \ra \pis)$ &6.49$^f$,6.48$^b$ \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$Using reference (6e,6o) active space including valence $\pi$ and 3s orbitals. +$^b$Using reference (8e,7o) active space including valence $\pi$, $n_\text{N}$ and 3s orbitals. +$^c$Using reference (6e,5o) active space including valence $\pi$ orbitals. +$^d$Using reference (6e,6o) active space including valence $\pi$ and one $3p_z$ orbitals. +$^e$Using reference (6e,9o) active space including valence $\pi$ and four $3p_z$ orbitals. +$^f$Using reference (8e,6o) active space including valence $\pi$ and $n_\text{N}$ orbitals. +$^g$Using reference (8e,9o) active space including valence $\pi$, $n_\text{N}$, two $3p_z$ and 3s orbitals. +\end{footnotesize} +\end{flushleft} +\end{table} + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of isobutene.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Isobutene &$^1B_1 (\Ryd; \pi \ra 3s)$ &6.63$^a$ \\ + &$^1A_1 (\Ryd; \pi \ra 3p)$ &7.20$^b$ \\ + &$^3A_1 (\Val; (\pi \ra \pis)$ &4.61$^c$ \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$Using reference (4e,5o) active space including valence $\pi$, $\si_\text{CC}$, $\si^*_\text{CC}$ and 3s orbitals. +$^b$Using reference (4e,5o) active space including valence $\pi$, $\si_\text{CC}$, $\si^*_\text{CC}$ and $3p_x$ orbitals. +$^c$Using reference (4e,4o) active space including valence $\pi$, $\si_\text{CC}$ and $\si^*_\text{CC}$ orbitals. +\end{footnotesize} +\end{flushleft} +\end{table} + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of methylenecyclopropene.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Methylenecyclopropene& $^1B_2 (\Val; \pi \ra \pis)$ &4.37$^a$ \\ + &$^1B_1 (\Ryd; \pi \ra 3s)$ &5.51$^b$,5.49$^c$ \\ + &$^1A_2 (\Ryd; \pi \ra 3p)$ &6.00$^c$ \\ + &$^1A_1(\Val; \pi \ra \pis)$ &7.55$^d$,7.95$^e$ \\ + &$^3B_2 (\Val; \pi \ra \pis)$ &3.66$^a$ \\ + &$^3A_1 (\Val; \pi \ra \pis)$ &4.87$^d$ \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$Using reference (4e,4o) active space. +$^b$Using reference (6e,6o) active space. +$^c$Using reference (4e,5o) active space. +$^d$Using reference (4e,6o) active space. +$^e$Using reference (4e,7o) active space. +$^f$The $\pi^*$ orbital has some diffuse character, even in the case of natural orbitals. +$^g$Heavily mixed states. +\end{footnotesize} +\end{flushleft} +\end{table} + + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of propynal.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Propynal & $^1A'' (\Val; n \ra \pis)$ &3.95$^a$ \\ + &$^1A'' (\Val; \pi \ra \pis)$ & 5.50$^a$ \\ + &$^3A'' (\Val; n \ra \pis)$ & 3.59$^a$ \\ + &$^3A' (\Val; \pi \ra \pis)$ & 4.63$^b$ \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$Using reference (8e,7o) active space including valence $\pi$ and $n_\text{O}$ orbitals. +$^b$Using reference (6e,6o) active space including valence $\pi$ orbitals. +\end{footnotesize} +\end{flushleft} +\end{table} + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of pyrazine.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Pyrazine &$^1B_{3u} (\Val; n \ra \pis)$ & 4.17$^a$ \\ + &$^1A_{u} (\Val; n \ra \pis)$ & 4.77$^a$ \\ + &$^1B_{2u} (\Val; \pi \ra \pis)$ & 5.32$^b$,5.37$^c$ \\ + &$^1B_{2g} (\Val; n \ra \pis)$ & 5.88$^a$ \\ + &$^1A_{g} (\Ryd; n \ra 3s)$ & 6.70$^d$\\ + &$^1B_{1g} (\Val; n \ra \pis)$ & 6.75$^a$ \\ + &$^1B_{1u} (\Val; \pi \ra \pis)$ & 6.38$^b$,6.31$^e$,6.81$^f$ \\ + &$^1B_{1g} (\Ryd; \pi \ra 3s)$ & 7.33$^g$ \\ + &$^1B_{2u} (\Ryd; n \ra 3p)$ & 7.25$^c$ \\ + &$^1B_{1u} (\Ryd; n \ra 3p)$ & 7.42$^e$ \\ + &$^1B_{1u} (\Val; \pi \ra \pis)$ & 7.29$^b$,6.96$^e$,8.25$^f$\\ + &$^3B_{3u} (\Val; n \ra \pis)$ & 3.56$^a$ \\ + &$^3B_{1u} (\Val; \pi \ra \pis)$ & 4.68$^b$,4.57$^f$ \\ + &$^3B_{2u} (\Val; (\pi \ra \pis)$ & 4.42$^b$ \\ + &$^3A_{u} (\Val; n \ra \pis)$ & 4.75$^a$ \\ + &$^3B_{2g} (\Val; n \ra \pis)$ & 5.21$^a$ \\ + &$^3B_{1u} (\Val; \pi \ra \pis)$ & 5.43$^b$,5.35$^f$ \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$Using reference (10e,8o) active space including valence $\pi$ and $n_\text{N}$ orbitals. +$^b$Using reference (6e,6o) active space including valence $\pi$ orbitals. +$^c$Using reference (10e,9o) active space including valence $\pi$, $n_\text{N}$ and $3p_y$ orbitals. +$^d$Using reference (10e,9o) active space including valence $\pi$, $n_\text{N}$ and 3s orbitals. +$^e$Using reference (10e,9o) active space including valence $\pi$, $n_\text{N}$ and $3p_z$ orbitals. +$^f$Using reference (6e,9o) active space including valence $\pi$ and three $3p_x$ orbitals. +\end{footnotesize} +\end{flushleft} +\end{table} + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of pyridazine.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Pyridazine &$^1B_1 (\Val; n \ra \pis)$ & 3.80$^a$ \\ + &$^1A_2 (\Val; n \ra \pis)$ & 4.40$^a$ \\ + &$^1A_1 (\Val; \pi \ra \pis)$ & 5.58b \\ + &$^1A_2 (\Val; n \ra \pis)$ & 5.88$^a$ \\ + &$^1B_2 (\Ryd; n \ra 3s)$ & 6.21c \\ + &$^1B_1 (\Val; n \ra \pis)$ & 6.64$^a$ \\ + &$^1B_2 (\Val; \pi \ra \pis)$ & 7.82b,7.19d,7.10e \\ + &$^3B_1 (\Val; n \ra \pis)$ & 3.13$^a$ \\ + &$^3A_2 (\Val; n \ra \pis)$ & 4.14$^a$ \\ + &$^3B_2 (\Val; \pi \ra \pis)$ & 4.65b,4.55d,4.49e \\ + &$^3A_1 (\Val; \pi \ra \pis)$ & 4.94$^a$ \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$Using reference (10e,8o) active space including valence $\pi$ and $n_\text{N}$ orbitals. +$^b$Using reference (6e,6o) active space including valence $\pi$ orbitals. +$^c$Using reference (10e,9o) active space including valence $\pi$, $n_\text{N}$ and 3s orbitals. +$^d$Using reference (6e,9o) active space including valence $\pi$, $n_\text{N}$ and three $3p_X$ orbitals. +$^e$Using reference (6e,12o) active space including valence $\pi$, $n_\text{N}$ and six $3p_x$ orbitals. +\end{footnotesize} +\end{flushleft} +\end{table} + + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of pyridine.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Pyridine &$^1B_1 (\Val; n \ra \pis)$ & 5.17$^a$,5.15b \\ + &$^1B_2 (\Val; \pi \ra \pis)$ & 5.44c,5.31d \\ + &$^1A_2 (\Val; n \ra \pis)$ & 5.32$^a$,5.29e \\ + &$^1A_1 (\Val; \pi \ra \pis)$ & 6.69c \\ + &$^1A_1 (\Ryd; n \ra 3s)$ & 6.99e \\ + &$^1A_2 (\Ryd; \pi \ra 3s)$ & 6.96f,6.86e\\ + &$^1B_2 (\Val; \pi \ra \pis)$ & 8.61$^a$,7.83d \\ + &$^1B_1 (\Ryd; \pi \ra 3p)$ & 7.57g,7.45b \\ + &$^1A_1 (\Val; \pi \ra \pis)$ & 6.97c \\ + &$^3A_1 (\Val; \pi \ra \pis)$ & 4.60c \\ + &$^3B_1 (\Val; n \ra \pis)$ & 4.58$^a$ \\ + &$^3B_2 (\Val; \pi \ra \pis)$ & 4.90c,4.88d \\ + &$^3A_1 (\Val; \pi \ra \pis)$ & 5.19c \\ + &$^3A_2 (\Val; n \ra \pis)$ & 5.33$^a$ \\ + &$^3B_2 (\Val; \pi \ra \pis)$ & 7.00c,6.29d \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$Using reference (8e,7o) active space including valence $\pi$ and $n_\text{N}$ orbitals. +$^b$Using reference (8e,8o) active space including valence $\pi$, $n_\text{N}$ and $3p_y$ orbitals. +$^c$Using reference (6e,6o) active space including valence $\pi$ orbitals. +$^d$Using reference (6e,10o) active space including valence $\pi$and four $3p_x$ orbitals. +$^e$Using reference (8e,8o) active space including valence $\pi$, $n_\text{N}$ and 3s orbitals. +$^d$Using reference (6e,8o) active space including valence $\pi$ and 3s orbitals. +$^g$Using reference (6e,7o) active space including valence $\pi$ and $3p_y$ orbitals. +\end{footnotesize} +\end{flushleft} +\end{table} + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of pyrimidine.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Pyrimidine &$^1B_1 (\Val; n \ra \pis)$ & 4.55$^a$ \\ + &$^1A_2 (\Val; n \ra \pis)$ & 4.84$^a$ \\ + &$^1B_2 (\Val; \pi \ra \pis)$ & 5.71$^b$,5.57$^d$,5.53$^e$ \\ + &$^1A_2 (\Val; n \ra \pis)$ & 6.02$^a$ \\ + &$^1B_1 (\Val; n \ra \pis)$ & 6.40$^a$ \\ + &$^1B_2 (\Ryd; n \ra 3s)$ & 6.77$^c$ \\ + &$^1A_1 (\Val; \pi \ra \pis)$ & 7.47$^b$,7.11$^e$ \\ + &$^3B_1 (\Val; n \ra \pis)$ & 4.17$^a$ \\ + &$^3A_1 (\Val; \pi \ra \pis)$ & 4.84$^b$,4.67$^e$ \\ + &$^3A_2 (\Val; n \ra \pis)$ & 4.72$^a$ \\ + &$^3B_2 (\Val; \pi \ra \pis)$ & 5.08$^b$,5.01$^e$ \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$Using reference (10e,8o) active space including valence $\pi$ and $n_\text{N}$ orbitals +$^b$Using reference (6e,6o) active space including valence $\pi$ orbitals. +$^c$Using reference (10e,9o) active space including valence $\pi$, $n_\text{N}$ and 3s orbitals. +$^d$Using reference (6e,9o) active space including valence $\pi$ and three $3p_x$ orbitals. +$^e$Using reference (6e,11o) active space including valence $\pi$ and five $3p_x$ orbitals. +\end{footnotesize} +\end{flushleft} +\end{table} + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of pyrrole.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Pyrrole &$^1A_2 (\Ryd; \pi \ra 3s)$ & 5.51$^a$ \\ + &$^1B_1 (\Ryd; \pi \ra 3p)$ & 6.32$^b$ \\ + &$^1A_2 (\Ryd; \pi \ra 3p)$ & 6.44$^c$ \\ + &$^1B_2 (\Val; (\pi \ra \pis)$ & 6.48$^{e,f}$ \\ + &$^1A_1 (\Val; \pi \ra \pis)$ & 6.53$^d$ \\ + &$^1B_2 (\Ryd; \pi \ra 3p)$ & 6.50$^d$,6.62$^e$ \\ + &$^3B_2 (\Val; \pi \ra \pis)$ & 4.74$^d$ \\ + &$^3A_2 (\Ryd; \pi \ra 3s)$ & 5.49$^a$ \\ + &$^3A_1 (\Val; \pi \ra \pis)$ & 5.56$^d$ \\ + &$^3B_1 (\Ryd; \pi \ra 3p)$ & 6.28$^b$ \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$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,5o) active space including valence $\pi$ orbitals. +$^e$Using reference (6e,6o) active space including valence $\pi$ and $3p_x$ orbitals. +$^f$Increasing the $\pi$ $3p_x$ active space leads to strong mixing in the zeroth-order wavefunction requiring a multi-state treatment (see Roos et al., J. Chem. Phys. 2002, 116, 7526--7536). +\end{footnotesize} +\end{flushleft} +\end{table} + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of tetrazine.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Tetrazine &$^1B_{3u} (\Val; n \ra \pis)$ & 2.35$^a$ \\ + &$^1A_{u} (\Val; n \ra \pis)$ & 3.58$^a$ \\ + &$^1A_{g} (\Val; n,n \ra \pis, \pis)$ & 4.61$^a$ \\ + &$^1B_{1g} (\Val; n \ra \pis)$ & 4.95$^a$ \\ + &$^1B_{2u} (\Val; \pi \ra \pis)$ & 5.56$^b$ \\ + &$^1B_{2g} (\Val; n \ra \pis)$ & 5.63$^a$ \\ + &$^1A_{u} (\Val; n \ra \pis)$ & 5.62$^a$ \\ + &$^1B_{3g} (\Val; n,n \ra \pis, \pis)$ & 6.15$^a$ \\ + &$^1B_{2g} (\Val; n \ra \pis)$ & 6.13$^a$ \\ + &$^1B_{1g} (\Val; n \ra \pis)$ & 6.76$^a$ \\ + &$^3B_{3u} (\Val; n \ra \pis)$ & 1.73$^a$ \\ + &$^3A_{u} (\Val; n \ra \pis)$ & 3.36$^a$ \\ + &$^3B_{1g} (\Val; n \ra \pis)$ & 4.24$^a$ \\ + &$^3B_{1u} (\Val; \pi \ra \pis)$ & 4.80$^b$,4.70$^a$ \\ + &$^3B_{2u} (\Val; \pi \ra \pis)$ & 4.58$^b$ \\ + &$^3B_{2g} (\Val; n \ra \pis)$ & 5.27$^a$ \\ + &$^3A_{u} (\Val; n \ra \pis)$ & 5.13$^a$ \\ + &$^3B_{3g} (\Val; n,n \ra \pis, \pis)$ & 5.51$^a$ \\ + &$^3B_{1u} (\Val; \pi \ra \pis)$ & 5.64$^b$,5.56$^c$ \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$Using reference (14e,10o) active space including valence $\pi$ and $n_\text{N}$ orbitals. +$^b$Using reference (6e,6o) active space including valence $\pi$ orbitals. +$^c$Using reference (6e,9o) active space including valence $\pi$ and three $3p_x$ orbitals. +\end{footnotesize} +\end{flushleft} +\end{table} + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of thioacetone.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Thioacetone &$^1A_2 (\Val; n \ra \pis)$ & 2.55$^a$ \\ + &$^1B_2 (\Ryd; n \ra 4s)$ & 5.72$^b$ \\ + &$^1A_1 (\Val; \pi \ra \pis)$ & 6.09$^c$,6.24$^d$ \\ + &$^1B_2 (\Ryd; n \ra 4p)$ & 6.62$^b$ \\ + &$^1A_1 (\Ryd; n \ra 4p)$ & 6.52$^d$ \\ + &$^3A_2 (\Val; n \ra \pis)$ & 2.32$^a$ \\ + &$^3A_1 (\Val; \pi \ra \pis)$ & 3.48$^c$ \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$Using reference (6e,5o) active space including valence $\pi$, $n_\text{O}$, $\si_\text{CO}$ and $\si^*_\text{CO}$ orbitals. +$^b$Using reference (6e,7o) active space including valence $\pi$, $n_\text{O}$, $\si_\text{CO}$, $\si^*_\text{CO}$, 4s and $4p_z$ orbitals. +$^c$Using reference (4e,4o) active space including valence $\pi$, $\si_\text{CO}$ and $\si^*_\text{CO}$ orbitals. +$^d$Using reference (6e,6o) active space including valence $\pi$, $n_\text{O}$, $\si_\text{CO}$, $\si^*_\text{CO}$ and $4p_y$ orbitals. +\end{footnotesize} +\end{flushleft} +\end{table} + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of thiophene.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Thiophene &$^1A_1 (\Val; \pi \ra \pis)$ & 5.84$^a$ \\ + &$^1B_2 (\Val; \pi \ra \pis)$ & 5.64$^a$,5.54$^b$,6.10$^c$ \\ + &$^1A_2 (\Ryd; \pi \ra 3s)$ & 6.20$^d$ \\ + &$^1B_1 (\Ryd; \pi \ra 3p)$ & 6.19$^e$ \\ + &$^1A_2 (\Ryd; \pi \ra 3p)$ & 6.40$^e$,6.52$^f$ \\ + &$^1B_1 (\Ryd; \pi \ra 3s)$ & 6.73$^d$, 6.71$^f$ \\ + &$^1B_2 (\Ryd; \pi \ra 3p)$ & 77.42$^b$,7.25$^c$ \\ + &$^1A_1 (\Val; \pi \ra \pis)$ & 7.39$^{a,h}$ \\ + &$^3B_2 (\Val; \pi \ra \pis)$ & 4.13$^a$ \\ + &$^3A_1 (\Val; \pi \ra \pis)$ & 4.84$^a$ \\ + &$^3B_1 (\Ryd; \pi \ra 3p)$ & 5.98$^e$ \\ + &$^3A_2 (\Ryd; \pi \ra 3s)$ & 6.14$^d$ \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$Using reference (6e,5o) active space including valence $\pi$ orbitals. +$^b$Using reference (6e,6o) active space including valence $\pi$ and $3p_x$ orbitals. +$^c$Using reference (6e,7o) active space including valence $\pi$ and two $3p_x$ orbitals. +$^d$Using reference (6e,6o) active space including valence $\pi$ and 3s orbitals. +$^e$Using reference (6e,6o) active space including valence $\pi$ and $3p_y$ orbitals. +$^f$Using reference (6e,7o) active space including valence $\pi$, 3s and $3p_y$ orbitals. +$^g$Using reference (6e,8o) active space including valence $\pi$, 3s, $3p_y$ and $3p_z$ orbitals. +$^h$Strong double-excitation character. +\end{footnotesize} +\end{flushleft} +\end{table} + + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of thiopropynal.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Thiopropynal &$^1A'' (\Val; n \ra \pis)$ & 2.05$^a$ \\ + &$^3A'' (\Val; n \ra \pis)$ & 1.81$^a$ \\ + +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$Using reference (8e,7o) active space including valence $\pi$ and $n_\text{O}$ orbitals. +\end{footnotesize} +\end{flushleft} +\end{table} + + +\begin{table} +\caption{NEVPT2/aug-cc-pVTZ vertical transition energies (in eV) of triazine.} +\begin{tabularx}{\textwidth}{XXX} +\hline +Molecule & State & NEVPT2 \\ +\hline +Triazine &$^1A_1'' (\Val; n \ra \pis)$ & 4.61$^a$ \\ + &$^1A_2'' (\Val; n \ra \pis)$ & 4.89$^a$ \\ + &$^1E'' (\Val; n \ra \pis)$ & 4.88$^a$ \\ + &$^1A_2' (\Val; \pi \ra \pis)$ & 6.10$^v$,6.15$^c$,5.95$^d$ \\ + &$^1A_1' (\Val; \pi \ra \pis)$ & 7.06$^b$,7.30$^d$ \\ + &$^1E' (\Ryd; n \ra 3s)$ & 7.45$^c$ \\ + &$^1E'' (\Val; n \ra \pis)$ & 7.98$^a$ \\ + &$^1E' (\Val; \pi \ra \pis)$ & 7.74$^b$,8.34$^d$ \\ + &$^3A_2'' (\Val; n \ra \pis)$ & 4.51$^a$ \\ + &$^3E'' (\Val; n \ra \pis)$ & 4.61$^a$ \\ + &$^3A_1'' (\Val; n \ra \pis)$ & 4.71$^a$ \\ + &$^3A_1' (\Val; \pi \ra \pis)$ & 5.20$^b$,5.05$^d$ \\ + &$^3E' (\Val; \pi \ra \pis)$ & 5.83$^b$,5.73$^d$ \\ + &$^3A_2' (\Val; (\pi \ra \pis)$ & 5.83$^b$,6.36$^d$ \\ +\hline +\end{tabularx} +\begin{flushleft} +\begin{footnotesize} +$^a$Using reference (12e,9o) active space including valence $\pi$ and $n_\text{N}$ orbitals. +$^b$Using reference (6e,6o) active space including valence $\pi$ orbitals. +$^c$Using reference (12e,10o) active space including valence $\pi$, $n_\text{N}$ and 3s orbitals. +$^d$Using reference (6e,9o) active space including valence $\pi$ and three $3p_x$ orbitals. +\end{footnotesize} +\end{flushleft} +\end{table} + + +\end{document} +