From 34954a094a070267bcbea3aeebdfb9f97fa65e88 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Thu, 7 Nov 2019 23:25:24 +0100 Subject: [PATCH] starting working on manuscript --- Data/cyclopropenone_13_PopleDZ_2.dat | 98 +- Data/thioacetone_1_PopleDZ.dat | 15 +- Data/thiopropynal_13_PopleDZ.dat | 88 +- Manuscript/FCI2-SI.tex | 1999 +- Manuscript/FCI2.tex | 2283 +- Manuscript/Figure-1.pdf | Bin 0 -> 1636925 bytes Manuscript/biblio-new.bib | 1096 +- Mountain2.nb | 218008 ++++++++++++++++-------- 8 files changed, 152264 insertions(+), 71323 deletions(-) create mode 100644 Manuscript/Figure-1.pdf mode change 100644 => 100755 Manuscript/biblio-new.bib diff --git a/Data/cyclopropenone_13_PopleDZ_2.dat b/Data/cyclopropenone_13_PopleDZ_2.dat index b102628..25d4976 100644 --- a/Data/cyclopropenone_13_PopleDZ_2.dat +++ b/Data/cyclopropenone_13_PopleDZ_2.dat @@ -1,46 +1,54 @@ - 3 -11 + 2 +13 1241 - 3406 - 9322 - 25485 - 69640 - 190276 - 519868 - 1407606 - 3842348 - 10470441 - 28401042 - -189.54650026 -189.37243002 -189.36794564 - 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- -\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{\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{\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 - -\section{Basis set and frozen-core effects} - -\subsection{CC3} - -\subsubsection{Cyanoacetylene, cyanogen, and diacetylene} - -\begin{table}[htp] -\caption{\small CC3 vertical transition energies of cyanoacetylene, cyanogen, and diacetylene using various atomic basis sets. -FC stands for frozen core. All values are in eV.} -\label{Table-S1} - \begin{small} -\begin{tabular}{l|cccccccc} -\hline - & {\Pop} & {\AVDZ} & {\AVTZ} & \multicolumn{2}{c}{\AVQZ} & \multicolumn{2}{c}{\DAVQZ} & {\AVFZ} \\ - & FC & FC &FC & FC & Full & FC & Full & FC \\ -\hline - & \multicolumn{8}{c}{Cyanoacetylene} \\ -\hline -$^1\Sigma^-$ &6.02 &5.92 &5.80 &5.79 &5.79 &5.79 &5.79 &5.79 \\ -$^1\Delta$ &6.29 &6.17 &6.08 &6.06 &6.07 &6.06 &6.07 &6.06 \\ -$^3\Sigma^+$ &4.44 &4.43 &4.45 &4.46 &4.46 &4.46 &4.46 &4.47 \\ -$^3\Delta$ &5.35 &5.28 &5.22 &5.22 &5.21 &5.22 &5.21 &5.22 \\ -\hline - & \multicolumn{8}{c}{Cyanogen} \\ -\hline -$^1\Sigma_u^-$ &6.62 &6.52 &6.39 &6.38 &6.38 &6.38 &6.38 &6.38 \\ -$^1\Delta_u$ &6.88 &6.77 &6.66 &6.64 &6.65 &6.64 &6.65 &6.64 \\ -$^3\Sigma_u^+$ &4.92 &4.89 &4.90 &4.91 &4.91 &4.91 &4.91 &4.92 \\ -$^1\Sigma_u^-$[F] &5.27 &5.19 &5.06 &5.05 &5.05 &5.05 &5.05 &5.04 \\ -\hline - & \multicolumn{8}{c}{Diacetylene} \\ -\hline -$^1\Sigma_u^-$ &5.57 &5.44 &5.34 &5.33 &5.34 &5.33 &5.34 &5.33 \\ -$^1\Delta_u$ &5.83 &5.69 &5.61 &5.60 &5.60 &5.60 &5.60 &5.60 \\ -$^3\Sigma_u^+$ &4.07 &4.06 &4.08 &4.10 &4.09 &4.10 &4.09 &4.11 \\ -$^3\Delta_u$ &4.93 &4.86 &4.80 &4.80 &4.80 &4.80 &4.80 &4.80 \\ -\hline - \end{tabular} - \end{small} -\end{table} -\clearpage - -\subsubsection{Cyclopropenone, cyclopropenethione, and methylenecyclopropene} - -\begin{table}[htp] -\caption{\small CC3 vertical transition energies of cyclopropenone, cyclopropenethione, and methylenecyclopropene using various atomic basis sets. -FC stands for frozen core. All values are in eV.} -\label{Table-S2} - \begin{small} -\begin{tabular}{l|ccccccc} -\hline - & {\Pop} & {\AVDZ} & {\AVTZ} & \multicolumn{2}{c}{\AVQZ} &{\DAVQZ} & {\AVFZ} \ \\ - & FC & FC &FC & FC & Full & FC & FC \\ -\hline - & \multicolumn{7}{c}{Cyclopropenone} \\ -\hline -$^1B_1 (n \rightarrow \pi^\star)$ &4.32 &4.22 &4.21 &4.23 &4.22& 4.23 & 4.23\\% 4.23 en 5Z -$^1A_2 (n \rightarrow \pi^\star)$ &5.68 &5.59 &5.57 &5.58 &5.57& 5.58 & 5.58\\% 5.58 en 5Z -$^1B_2 (n \rightarrow 3s)$ &6.39 &6.21 &6.32 &6.37 &6.38& 6.36 & \hl{xxx}\\% -$^1B_2 (\pi \rightarrow \pi^\star)$ &6.70 &6.56 &6.54 &6.56 &6.56& 6.56 & \hl{xxx}\\% -$^1B_2 (n \rightarrow 3p)$ &6.92 &6.88 &6.96 &6.99 &7.00& 6.96 & \hl{xxx}\\% -$^1A_1 (n \rightarrow 3p)$ &7.00 &6.88 &7.00 &7.05 &7.06& 7.03 & 7.06\\%To be looked at 7.06 en 5Z -$^1A_1 (\pi \rightarrow \pi^\star)$ &8.51 &8.32 &8.28 &8.28 &8.28& 8.22 & 8.26\\%To be looked at 8.26 en 5Z -$^3B_1 (n \rightarrow \pi^\star)$ &4.02 &3.90 &3.91 &3.93 &3.92& 3.93 & \hl{xxx}\\% N043, ~3.94, proche -$^3B_2 (\pi \rightarrow \pi^\star)$ &4.92 &4.90 &4.89 &4.91 &4.90& 4.91 & \hl{xxx} \\% -$^3A_2 (n \rightarrow \pi^\star)$ &5.48 &5.38 &5.37 &5.39 &5.37& 5.39 & \hl{xxx}\\% -$^3A_1 (\pi \rightarrow \pi^\star)$ &6.89 &6.79 &6.83 &6.84 &6.83& 6.84 & 6.85\\% 6.85 en 57 -\hline - & \multicolumn{7}{c}{Cyclopropenethione} \\ -\hline -$^1A_2 (n \rightarrow \pi^\star)$ &3.46 &3.47 &3.43 &3.44 &3.42& 3.44 \\ -$^1B_1 (n \rightarrow \pi^\star)$ &3.45 &3.42 &3.43 &3.45 &3.43& 3.45 \\ -$^1B_2 (\pi \rightarrow \pi^\star)$ &4.67 &4.66 &4.64 &4.66 &4.64& 4.66 \\ -$^1B_2 (n \rightarrow 3s)$ &5.26 &5.23 &5.34 &5.39 &5.39& 5.38 \\ -$^1A_1 (\pi \rightarrow \pi^\star)$ &5.53 &5.52 &5.49 &5.49 &5.48& 5.49 \\ -$^1B_2 (n \rightarrow 3p)$ &5.83 &5.86 &5.93 &5.95 &5.95& 5.91 \\%$^a$, mais les autres aussi !! -$^3A_2 (n \rightarrow \pi^\star)$ &3.33 &3.34 &3.31 &3.31 &3.29& 3.31 \\ -$^3B_1 (n \rightarrow \pi^\star)$ &3.34 &3.30 &3.31 &3.34 &3.32& 3.34 \\ -$^3B_2 (\pi \rightarrow \pi^\star)$ &4.01 &4.03 &4.02 &4.04 &4.03& 4.04 \\ -$^3A_1 (\pi \rightarrow \pi^\star)$ &4.06 &4.09 &4.03 &4.04 &4.02& 4.04 \\ -\hline - & \multicolumn{7}{c}{Methylenecyclopropene} \\ -\hline -$^1B_2 (\pi \rightarrow \pi^\star)$ &4.38 &4.32 &4.31 &4.31 &4.31& 4.31 \\ -$^1B_1 (\pi \rightarrow \sigma^\star)$ &5.65 &5.35 &5.44 &5.47 &5.48& 5.46\\ -$^1A_2 (\pi \rightarrow 3p)$ &5.97 &5.86 &5.95 &5.98 &5.99& 5.96\\ -$^1A_1 (\pi \rightarrow \pi^\star)$ &6.17 &6.15 &6.13 &6.09 &6.10& 5.98\\%<= Stong mixing -$^3B_2 (\pi \rightarrow \pi^\star)$ &3.50 &3.49 &3.50 &3.50 &3.50& 3.50\\ -$^3A_1 (\pi \rightarrow \pi^\star)$ &4.74 &4.74 &4.74 &4.75 &4.74& 4.74\\ -\hline - \end{tabular} -\begin{flushleft} -%$^a${Significant mixing.} -\end{flushleft} - \end{small} - -\end{table} - -\clearpage - - -\subsubsection{Acrolein, butadiene, and glyoxal} - -\begin{table}[htp] -\caption{\small CC3 vertical transition energies of acrolein, butadiene, and glyoxal using various atomic basis sets. -FC stands for frozen core. All values are in eV.} -\label{Table-S3} - \begin{small} -\begin{tabular}{l|cccccc} -\hline - & {\Pop} & {\AVDZ} & {\AVTZ} & \multicolumn{2}{c}{\AVQZ} &{\DAVQZ} \\ - & FC & FC &FC & FC & Full & FC \\ -\hline - & \multicolumn{6}{c}{Acrolein} \\ -\hline -$^1A'' (n \rightarrow \pi^\star)$ &3.83 &3.77 &3.74 &3.75 &3.74\\ -$^1A' (\pi \rightarrow \pi^\star)$ &6.83 &6.67 &6.65 &6.65 &6.65\\ -$^1A'' (n \rightarrow \pi^\star)$ &6.94 &6.75 &6.75 &6.77 &6.76\\ -$^1A' (n \rightarrow 3s)$ &7.22 &6.99 &7.07 &7.11 &7.11\\ -$^3A'' (n \rightarrow \pi^\star)$ &3.55 &3.47 &3.46 &3.47 &3.46\\ -$^3A' (\pi \rightarrow \pi^\star)$ &3.94 &3.95 &3.94 &3.95 &3.94\\ -$^3A' (\pi \rightarrow \pi^\star)$ &6.25 &6.22 &6.19 &6.20 &6.19\\ -$^3A'' (\pi \rightarrow 3s)$ &6.81 &6.60 &6.61 &6.63 &6.62\\ -\hline - & \multicolumn{6}{c}{Butadiene} \\ -\hline -$^1B_u (\pi \rightarrow \pi^\star)$ &6.41 &6.25 &6.22 &6.21 &6.22\\ -$^1B_g (\pi \rightarrow 3s)$ &6.53 &6.26 &6.33 &6.35 &6.36\\ -$^1A_g (\pi \rightarrow \pi^\star)$ &6.73 &6.68 &6.67 &6.67 &6.67& 6.67\\ -$^1A_u (\pi \rightarrow 3p)$ &6.87 &6.57 &6.64 &6.66 &6.67\\ -$^1A_u (\pi \rightarrow 3p)$ &6.93 &6.73 &6.80 &6.82 &6.83\\ -$^1B_u (\pi \rightarrow 3p)$ &7.98 &7.86 &7.68 &7.54 &7.55\\ -$^3B_u (\pi \rightarrow \pi^\star)$ &3.35 &3.36 &3.36 &3.37 &3.36\\ -$^3A_g (\pi \rightarrow \pi^\star)$ &5.22 &5.21 &5.20 &5.21 &5.20\\ -$^3B_g (\pi \rightarrow 3s)$ &6.46 &6.20 &6.28 &6.30 &6.31\\ -\hline - & \multicolumn{6}{c}{Glyoxal} \\ -\hline -$^1A_u (n \rightarrow \pi^\star)$ &2.94 &2.90 &2.88 &2.88 &2.87& 2.88\\ -$^1B_g (n \rightarrow \pi^\star)$ &4.34 &4.30 &4.27 &4.27 &4.27& 4.27\\ -$^1A_g (n,n \rightarrow \pi^\star,\pi^\star)$&6.74 &6.70 &6.76 &6.76 &6.74& 6.76\\ -$^1B_g (n \rightarrow \pi^\star)$ &6.81 &6.59 &6.58 &6.59 &6.58& 6.58\\ -$^1B_u (n \rightarrow3p)$ &7.72 &7.55 &7.67 &7.72 &7.73& 7.72\\ -$^3A_u (n \rightarrow \pi^\star)$ &2.55 &2.49 &2.49 &2.49 &2.49& 2.49\\ -$^3B_g (n \rightarrow \pi^\star)$ &3.97 &3.91 &3.90 &3.91 &3.90& 3.91\\ -$^3B_u (\pi \rightarrow \pi^\star)$ &5.22 &5.20 &5.17 &5.18 &5.17& 5.18\\ -$^3A_g (\pi \rightarrow \pi^\star)$ &6.35 &6.34 &6.30 &6.31 &6.30& 6.31\\ -\hline - \end{tabular} - \end{small} -\end{table} - -\clearpage - - -\subsubsection{Acetone, cyanoformaldehyde, isobutene, propynal, thioacetone, and thiopropynal} - -\begin{table}[htp] -\caption{\small CC3 vertical transition energies of acetone, cyanoformaldehyde, isobutene, propynal, thioacetone, and thiopropynal using various atomic basis sets. -FC stands for frozen core. All values are in eV.} -\label{Table-S4} - \begin{small} -\begin{tabular}{l|cccccc} -\hline - & {\Pop} & {\AVDZ} & {\AVTZ} & \multicolumn{2}{c}{\AVQZ} &{\DAVQZ} \\ - & FC & FC &FC & FC & Full & FC\\ -\hline - & \multicolumn{5}{c}{Acetone} \\ -\hline -$^1A_2 (n \rightarrow \pi^\star)$ &4.55 &4.50 &4.48 &4.49 &4.48\\ -$^1B_2 (n \rightarrow 3s)$ &6.65 &6.31 &6.43 &6.48 &6.49\\ -$^1A_2 (n \rightarrow 3p)$ &7.83 &7.37 &7.45 &7.48 &7.49\\ -$^1A_1 (n \rightarrow 3p)$ &7.81 &7.39 &7.48 &7.52 &7.53\\ -$^1B_2 (n \rightarrow 3p)$ &7.87 &7.56 &7.59 &7.60 &7.61\\ -$^3A_2 (n \rightarrow \pi^\star)$ &4.21 &4.16 &4.15 &4.17 &4.16\\ -$^3A_1 (\pi \rightarrow \pi^\star)$ &6.32 &6.31 &6.28 &6.30 &6.28\\ -\hline - & \multicolumn{5}{c}{Cyanoformaldehyde} \\ -\hline -$^1A'' (n \rightarrow \pi^\star)$ &3.91 &3.86 &3.83 &3.84 &3.83 &3.84\\ -$^1A'' (\pi \rightarrow \pi^\star)$ &6.64 &6.51 &6.42 &6.41 &6.41 &6.41\\ -$^3A'' (n \rightarrow \pi^\star)$ &3.53 &3.47 &3.46 &3.47 &3.46 &3.47\\ -$^3A' (\pi \rightarrow \pi^\star)$ &5.07 &5.03 &5.01 &5.02 &5.01 &5.02\\ -\hline - & \multicolumn{5}{c}{Isobutene} \\ -\hline -$^1B_1 (\pi \rightarrow 3s)$ &6.77 &6.39 &6.45 &6.47 &\\ -$^1A_1 (\pi \rightarrow 3p)$ &7.16 &7.00 &7.00 &6.99 &\\ -$^3A_1 (\pi \rightarrow \pi^\star)$ &4.52 &4.54 &4.53 &4.54 &\\ -\hline - & \multicolumn{5}{c}{Propynal} \\ -\hline -$^1A'' (n \rightarrow \pi^\star)$ &3.90 &3.85 &3.82 &3.83 &3.82 &3.83\\ -$^1A'' (\pi \rightarrow \pi^\star)$ &5.69 &5.59 &5.51 &5.50 &5.50 &5.50\\ -$^3A'' (n \rightarrow \pi^\star)$ &3.56 &3.50 &3.49 &3.50 &3.49 &\hl{xxx}\\ -$^3A' (\pi \rightarrow \pi^\star)$ &4.46 &4.40 &4.43 &4.44 &4.43 &4.44\\ -\hline - & \multicolumn{5}{c}{Thioacetone} \\ -\hline -$^1A_2 (n \rightarrow \pi^\star)$ &2.58 &2.59 &2.55 &2.56 &\\ -$^1B_2 (n \rightarrow 4s)$ &5.65 &5.44 &5.55 &5.60 &\\ -$^1A_1 (\pi \rightarrow \pi^\star)$ &6.09 &5.97 &5.90 &5.88 &\\ -$^1A_1 (n \rightarrow 4p)$ &6.95 &6.54 &6.61 &6.64 &\\ -$^1B_2 (n \rightarrow 4p)$ &6.59 &6.45 &6.51 &6.52 &\\ -$^3A_2 (n \rightarrow \pi^\star)$ &2.36 &2.36 &2.34 &2.35 &\\ -$^3A_1 (\pi \rightarrow \pi^\star)$ s&3.45 &3.51 &3.46 &3.47 &\\ -\hline - & \multicolumn{5}{c}{Thiopropynal} \\ -\hline -$^1A'' (n \rightarrow \pi^\star)$ &2.09 &2.09 &2.05 &2.06 &2.04\\ -$^3A'' (n \rightarrow \pi^\star)$ &1.84 &1.83 &1.81 &1.82 &\hl{xxx}\\ -\hline -\end{tabular} -\end{small} -\end{table} - - -\clearpage - -\subsection{Multi-reference results} - -\subsubsection{Cyanoacetylene, cyanogen, and diacetylene} - -\begin{table}[htp] -\caption{\small Vertical transition energies of cyanoacetylene, cyanogen, and diacetylene using various atomic basis sets and -multi-reference methods. All values are in eV and have been obtained with within the FC approximation. The CASPT2 calculations -are performed with a level shift of 0.3 and a IPEA of 0.25. Pop, AVDZ, AVTZ, and AVQZ respectively stand for {\Pop}, {\AVDZ}, -{\AVTZ}, and {\AVQZ}. } -\label{Table-S1b} - \begin{footnotesize} -\begin{tabular}{l|cccccccccccc} -\hline - & \multicolumn{4}{c}{CASPT2(8,8)} & \multicolumn{4}{c}{PC-NEVPT2(8,8)} & \multicolumn{4}{c}{SC-NEVPT2(8,8)} \\ - & Pop &AVDZ & AVTZ & AVQZ & Pop &AVDZ & AVTZ & AVQZ& Pop &AVDZ & AVTZ & AVQZ \\ -\hline - & \multicolumn{12}{c}{Cyanoacetylene} \\ -\hline -$^1\Sigma^-$ & & 6.00 & 5.86 & & & 5.93 & 5.78 & & & 5.98 & 5.83 & \\ -$^1\Delta$ & & 6.26 & 6.13 & & & 6.22 & 6.10 & & & 6.27 & 6.14 & \\ -$^3\Sigma^+$ & & 4.47 & 4.45 & & & 4.46 & 4.45 & & & 4.51 & 4.49 & \\ -$^3\Delta$ & & 5.30 & 5.21 & & & 5.28 & 5.19 & & & 5.31 & 5.23 & \\ -\hline - & \multicolumn{12}{c}{Cyanogen} \\ -\hline -$^1\Sigma_u^-$ & 6.63 & 6.56 & 6.40 & 6.37 & 6.56 & 6.49 & 6.32 & 6.29 & 6.61 & 6.54 & 6.37 & 6.34 \\ -$^1\Delta_u$ & 6.93 & 6.84 & 6.70 & 6.66 & 6.91 & 6.81 & 6.66 & 6.63 & 6.95 & 6.86 & 6.71 & 6.68 \\ -$^3\Sigma_u^+$ & 4.91 & 4.89 & 4.86 & 4.86 & 4.92 & 4.91 & 4.88 & 4.89 & 4.96 & 4.95 & 4.92 & 4.93 \\ -$^1\Sigma_u^-$[F] & & 5.23 & 5.07 & & & 5.14 & 4.97 & & & 5.17 & 5.01 & \\ -\hline - & \multicolumn{12}{c}{Diacetylene} \\ -\hline -$^1\Sigma_u^-$ & & 5.56 & 5.43 & & & 5.47 & 5.33 & & & 5.53 & 5.39 & \\ -$^1\Delta_u$ & & 5.80 & 5.68 & & & 5.73 & 5.61 & & & 5.78 & 5.67 & \\ -$^3\Sigma_u^+$ & & 4.12 & 4.11 & & & 4.09 & 4.08 & & & 4.14 & 4.13 & \\ -$^3\Delta_u$ & & 4.89 & 4.81 & & & 4.86 & 4.78 & & & 4.90 & 4.82 & \\ -\hline - \end{tabular} - \end{footnotesize} -\end{table} - -\clearpage - -\section{Geometries} - -Below are given the cartesian coordinates of the compounds investigated in this study. -These are provided in atomic units (bohr) and they have been obtained at the \CC{3}(full)/{\AVTZ} level of theory. - -\subsection{Acetone} - -\begin{singlespace} -\begin{verbatim} -C 0.00000000 0.00000000 0.18807702 -C 0.00000000 2.42007545 -1.31764698 -C 0.00000000 -2.42007545 -1.31764698 -O 0.00000000 0.00000000 2.48269094 -H 0.00000000 4.03690733 -0.05185132 -H 0.00000000 -4.03690733 -0.05185132 -H 1.66061256 2.48420530 -2.53995285 -H -1.66061256 2.48420530 -2.53995285 -H 1.66061256 -2.48420530 -2.53995285 -H -1.66061256 -2.48420530 -2.53995285 -\end{verbatim} -\end{singlespace} - - -\subsection{Acrolein} - -\begin{singlespace} -\begin{verbatim} -C -1.11645072 -0.68348783 0.00000000 -C 1.20647847 0.83714564 0.00000000 -C 3.46831059 -0.28872636 0.00000000 -O -3.23666415 0.19187203 0.00000000 -H -0.80613858 -2.74747338 0.00000000 -H 0.98699813 2.86613511 0.00000000 -H 5.20930864 0.77443560 0.00000000 -H 3.60951559 -2.33000749 0.00000000 -\end{verbatim} -\end{singlespace} - - -\subsection{Butadiene} - -\begin{singlespace} -\begin{verbatim} -C 1.14656244 0.00000000 0.75468820 -C -1.14656244 0.00000000 -0.75468820 -C 3.48132647 0.00000000 -0.22482805 -C -3.48132647 0.00000000 0.22482805 -H 0.90770978 0.00000000 2.78883925 -H -0.90770978 0.00000000 -2.78883925 -H 3.77525814 0.00000000 -2.24895470 -H -3.77525814 0.00000000 2.24895470 -H 5.13664967 0.00000000 0.96861890 -H -5.13664967 0.00000000 -0.96861890 -\end{verbatim} -\end{singlespace} - -\subsection{Cyanoacetylene} - -\begin{singlespace} -\begin{verbatim} -C 0.00000000 0.00000000 -3.59120182 -C 0.00000000 0.00000000 -1.30693904 -C 0.00000000 0.00000000 1.28880240 -N 0.00000000 0.00000000 3.48692211 -H 0.00000000 0.00000000 -5.59619886 -\end{verbatim} -\end{singlespace} - -\subsection{Cyanoformaldehyde} - -\begin{singlespace} -\begin{verbatim} -C -0.91561483 0.00000000 -1.22522833 -C -0.01092219 0.00000000 1.39523175 -N 0.64170259 0.00000000 3.48820325 -O 0.50833684 0.00000000 -3.00337867 -H -2.97202213 0.00000000 -1.42565674 -\end{verbatim} -\end{singlespace} - - -\subsection{Cyanogen} - -\begin{singlespace} -Ground state -\begin{verbatim} -C 0.00000000 0.00000000 1.30401924 -C 0.00000000 0.00000000 -1.30401924 -N 0.00000000 0.00000000 3.49784121 -N 0.00000000 0.00000000 -3.49784121 -\end{verbatim} -\end{singlespace} - -\begin{singlespace} -\noindent Lowest excited state -\begin{verbatim} -C 0.00000000 0.00000000 1.22784115 -C 0.00000000 0.00000000 -1.22784115 -N 0.00000000 0.00000000 3.56462559 -N 0.00000000 0.00000000 -3.56462559 - -\end{verbatim} -\end{singlespace} - -\subsection{Cyclopentadiene} - -\begin{singlespace} -\begin{verbatim} -C 0.00000000 0.00000000 -2.33113051 -C 0.00000000 2.22209092 -0.56871188 -C 0.00000000 -2.22209092 -0.56871188 -C 0.00000000 1.38514451 1.83772922 -C 0.00000000 -1.38514451 1.83772922 -H 1.66130504 0.00000000 -3.56414299 -H -1.66130504 0.00000000 -3.56414299 -H 0.00000000 4.16550405 -1.18116624 -H 0.00000000 -4.16550405 -1.18116624 -H 0.00000000 2.54514584 3.51352303 -H 0.00000000 -2.54514584 3.51352303 -\end{verbatim} -\end{singlespace} - -\subsection{Cyclopropenone} - -\begin{singlespace} -\begin{verbatim} -C 0.00000000 1.27491826 -1.86930519 -C 0.00000000 -1.27491826 -1.86930519 -C 0.00000000 0.00000000 0.51814554 -O 0.00000000 0.00000000 2.79326776 -H 0.00000000 2.92791371 -3.05679837 -H 0.00000000 -2.92791371 -3.05679837 -\end{verbatim} -\end{singlespace} - -\subsection{Cyclopropenethione} - -\begin{singlespace} -\begin{verbatim} -C 0.00000000 1.26230744 -2.86571925 -C 0.00000000 -1.26230744 -2.86571925 -C 0.00000000 0.00000000 -0.49233236 -S 0.00000000 0.00000000 2.57821680 -H 0.00000000 2.97773331 -3.95114059 -H 0.00000000 -2.97773331 -3.95114059 -\end{verbatim} -\end{singlespace} - -\subsection{Diacetylene} - -\begin{singlespace} -\begin{verbatim} -C 0.00000000 0.00000000 1.29447700 -C 0.00000000 0.00000000 -1.29447700 -C 0.00000000 0.00000000 3.58448429 -C 0.00000000 0.00000000 -3.58448429 -H 0.00000000 0.00000000 5.58943003 -H 0.00000000 0.00000000 -5.58943003 -\end{verbatim} -\end{singlespace} - -\subsection{Furan} - -\begin{singlespace} -\begin{verbatim} -C 0.00000000 2.06365826 -0.60051250 -C 0.00000000 -2.06365826 -0.60051250 -C 0.00000000 1.35348578 1.86336416 -C 0.00000000 -1.35348578 1.86336416 -O 0.00000000 0.00000000 -2.13945332 -H 0.00000000 3.86337287 -1.53765695 -H 0.00000000 -3.86337287 -1.53765695 -H 0.00000000 2.59168789 3.47168051 -H 0.00000000 -2.59168789 3.47168051 -\end{verbatim} -\end{singlespace} - - -\subsection{Glyoxal} - -\begin{singlespace} -\begin{verbatim} -C 1.21360282 0.75840215 0.00000000 -C -1.21360282 -0.75840215 0.00000000 -O 3.25581408 -0.26453186 0.00000000 -O -3.25581408 0.26453186 0.00000000 -H 0.96135276 2.81883243 0.00000000 -H -0.96135276 -2.81883243 0.00000000 -\end{verbatim} -\end{singlespace} - -\subsection{Imidazole} - -\begin{singlespace} -\begin{verbatim} -C 0.41662795 2.06006259 0.00000000 -C -1.52618386 -1.62343163 0.00000000 -C 1.04160471 -1.93007427 0.00000000 -N -1.90345764 0.94914956 0.00000000 -N 2.24215443 0.38083431 0.00000000 -H 0.65501634 4.07748278 0.00000000 -H -3.57500545 1.84103166 0.00000000 -H -3.06363894 -2.94559167 0.00000000 -H 2.08673940 -3.67001102 0.00000000 -\end{verbatim} -\end{singlespace} - - -\subsection{Isobutene} - -\begin{singlespace} -\begin{verbatim} -C 0.00000000 0.00000000 2.70790758 -C 0.00000000 0.00000000 0.18431282 -C 0.00000000 2.39894572 -1.32482735 -C 0.00000000 -2.39894572 -1.32482735 -H 0.00000000 1.74848405 3.76691310 -H 0.00000000 -1.74848405 3.76691310 -H 0.00000000 4.05897160 -0.10582007 -H 0.00000000 -4.05897160 -0.10582007 -H 1.66026992 2.48337908 -2.55086178 -H -1.66026992 2.48337908 -2.55086178 -H 1.66026992 -2.48337908 -2.55086178 -H -1.66026992 -2.48337908 -2.55086178 -\end{verbatim} -\end{singlespace} - - -\subsection{Methylenecyclopropene} - -\begin{singlespace} -\begin{verbatim} -C 0.00000000 0.00000000 0.53512883 -C 0.00000000 0.00000000 3.04739824 -C 0.00000000 1.25042956 -1.88571561 -C 0.00000000 -1.25042956 -1.88571561 -H 0.00000000 2.96887531 -2.96270271 -H 0.00000000 -2.96887531 -2.96270271 -H 0.00000000 1.75335023 4.08608382 -H 0.00000000 -1.75335023 4.08608382 -\end{verbatim} -\end{singlespace} - - -\subsection{Propynal} - -\begin{singlespace} -\begin{verbatim} -C -0.78051115 0.00000000 -1.38900384 -C -0.17873562 0.00000000 1.27825868 -C 0.23763714 0.00000000 3.52644798 -O 0.80143996 0.00000000 -3.04628328 -H -2.80713069 0.00000000 -1.82768750 -H 0.64026209 0.00000000 5.48853193 -\end{verbatim} -\end{singlespace} - - -\subsection{Pyrrole} - -\begin{singlespace} -\begin{verbatim} -C 0.00000000 2.11924634 0.62676569 -C 0.00000000 -2.11924634 0.62676569 -C 0.00000000 1.34568862 -1.85506908 -C 0.00000000 -1.34568862 -1.85506908 -N 0.00000000 0.00000000 2.10934391 -H 0.00000000 0.00000000 4.00257355 -H 0.00000000 3.97648410 1.44830201 -H 0.00000000 -3.97648410 1.44830201 -H 0.00000000 2.56726559 -3.47837232 -H 0.00000000 -2.56726559 -3.47837232 -\end{verbatim} -\end{singlespace} - - -\subsection{Thioacetone} - -\begin{singlespace} -\begin{verbatim} -C 0.00000000 0.00000000 0.68476030 -C 0.00000000 2.38541696 2.20685096 -C 0.00000000 -2.38541696 2.20685096 -S 0.00000000 0.00000000 -2.39920303 -H 0.00000000 4.04609254 1.00090614 -H 0.00000000 -4.04609254 1.00090614 -H 1.65894780 2.42602225 3.43712000 -H -1.65894780 2.42602225 3.43712000 -H 1.65894780 -2.42602225 3.43712000 -H -1.65894780 -2.42602225 3.43712000 -\end{verbatim} -\end{singlespace} - -\subsection{Thiophene} - -\begin{singlespace} -\begin{verbatim} -C 0.00000000 2.33342542 -0.09858421 -C 0.00000000 -2.33342542 -0.09858421 -C 0.00000000 1.34371718 -2.48297725 -C 0.00000000 -1.34371718 -2.48297725 -S 0.00000000 0.00000000 2.17250692 -H 0.00000000 4.29028016 0.44577296 -H 0.00000000 -4.29028016 0.44577296 -H 0.00000000 2.48760051 -4.16768392 -H 0.00000000 -2.48760051 -4.16768392 -\end{verbatim} -\end{singlespace} - -\subsection{Thiopropynal} - -\begin{singlespace} -\begin{verbatim} -C -0.00382924 0.00000000 -1.25249909 -C -2.27832423 0.00000000 0.15152736 -C -4.26309583 0.00000000 1.29548793 -S 2.81920288 0.00000000 -0.00828974 -H -0.23056990 0.00000000 -3.28862183 -H -5.97712967 0.00000000 2.33206931 -\end{verbatim} -\end{singlespace} - - - -\clearpage - -\section{Benchmark} - - -\end{document} - +\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} +\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 + +\section{Basis set and frozen-core effects} + +\subsection{Cyanoacetylene, cyanogen, and diacetylene} + +\begin{table}[htp] +\caption{\small CC3 vertical transition energies of cyanoacetylene, cyanogen, and diacetylene using various atomic basis sets. +FC stands for frozen core. All values are in eV.} +\label{Table-S1} + \begin{small} +\begin{tabular}{l|cccccccc} +\hline + & {\Pop} & {\AVDZ} & {\AVTZ} & \multicolumn{2}{c}{\AVQZ} & \multicolumn{2}{c}{\DAVQZ} & {\AVFZ} \\ + & FC & FC &FC & FC & Full & FC & Full & FC \\ +\hline + & \multicolumn{8}{c}{Cyanoacetylene} \\ +\hline +$^1\Sigma^-$ &6.02 &5.92 &5.80 &5.79 &5.79 &5.79 &5.79 &5.79 \\ +$^1\Delta$ &6.29 &6.17 &6.08 &6.06 &6.07 &6.06 &6.07 &6.06 \\ +$^3\Sigma^+$ &4.44 &4.43 &4.45 &4.46 &4.46 &4.46 &4.46 &4.47 \\ +$^3\Delta$ &5.35 &5.28 &5.22 &5.22 &5.21 &5.22 &5.21 &5.22 \\ +$^1A''$[F] &3.70 &3.60 &3.54 &3.54 &3.54 & & & \\ +\hline + & \multicolumn{8}{c}{Cyanogen} \\ +\hline +$^1\Sigma_u^-$ &6.62 &6.52 &6.39 &6.38 &6.38 &6.38 &6.38 &6.38 \\ +$^1\Delta_u$ &6.88 &6.77 &6.66 &6.64 &6.65 &6.64 &6.65 &6.64 \\ +$^3\Sigma_u^+$ &4.92 &4.89 &4.90 &4.91 &4.91 &4.91 &4.91 &4.92 \\ +$^1\Sigma_u^-$[F] &5.27 &5.19 &5.06 &5.05 &5.05 &5.05 &5.05 &5.04 \\ +\hline + & \multicolumn{8}{c}{Diacetylene} \\ +\hline +$^1\Sigma_u^-$ &5.57 &5.44 &5.34 &5.33 &5.34 &5.33 &5.34 &5.33 \\ +$^1\Delta_u$ &5.83 &5.69 &5.61 &5.60 &5.60 &5.60 &5.60 &5.60 \\ +$^3\Sigma_u^+$ &4.07 &4.06 &4.08 &4.10 &4.09 &4.10 &4.09 &4.11 \\ +$^3\Delta_u$ &4.93 &4.86 &4.80 &4.80 &4.80 &4.80 &4.80 &4.80 \\ +\hline + \end{tabular} + \end{small} +\end{table} +\clearpage + +\subsection{Cyclopropenone, cyclopropenethione, and methylenecyclopropene} + +\begin{table}[htp] +\caption{\small CC3 vertical transition energies of cyclopropenone, cyclopropenethione, and methylenecyclopropene using various atomic basis sets. +FC stands for frozen core. All values are in eV.} +\label{Table-S2} + \begin{small} +\begin{tabular}{l|ccccccc} +\hline + & {\Pop} & {\AVDZ} & {\AVTZ} & \multicolumn{2}{c}{\AVQZ} &{\DAVQZ} & {\AVFZ} \ \\ + & FC & FC &FC & FC & Full & FC & FC \\ +\hline + & \multicolumn{7}{c}{Cyclopropenone} \\ +\hline +$^1B_1 (n \rightarrow \pi^\star)$ &4.32 &4.22 &4.21 &4.23 &4.22& 4.23 & 4.23\\ +$^1A_2 (n \rightarrow \pi^\star)$ &5.68 &5.59 &5.57 &5.58 &5.57& 5.58 & 5.58\\ +$^1B_2 (n \rightarrow 3s)$ &6.39 &6.21 &6.32 &6.37 &6.38& 6.36 & 6.38\\% +$^1B_2 (\pi \rightarrow \pi^\star)$ &6.70 &6.56 &6.54 &6.56 &6.56& 6.56 & 6.56\\ +$^1B_2 (n \rightarrow 3p)$ &6.92 &6.88 &6.96 &6.99 &7.00& 6.96 & 6.99\\ +$^1A_1 (n \rightarrow 3p)$ &7.00 &6.88 &7.00 &7.05 &7.06& 7.03 & 7.06\\ +$^1A_1 (\pi \rightarrow \pi^\star)$ &8.51 &8.32 &8.28 &8.28 &8.28& 8.22 & 8.26\\ +$^3B_1 (n \rightarrow \pi^\star)$ &4.02 &3.90 &3.91 &3.93 &3.92& 3.93 & 3.94\\ +$^3B_2 (\pi \rightarrow \pi^\star)$ &4.92 &4.90 &4.89 &4.91 &4.90& 4.91 & 4.92\\ +$^3A_2 (n \rightarrow \pi^\star)$ &5.48 &5.38 &5.37 &5.39 &5.37& 5.39 & 5.39\\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &6.89 &6.79 &6.83 &6.84 &6.83& 6.84 & 6.85\\ +\hline + & \multicolumn{7}{c}{Cyclopropenethione} \\ +\hline +$^1A_2 (n \rightarrow \pi^\star)$ &3.46 &3.47 &3.43 &3.44 &3.42& 3.44 & 3.43 \\ +$^1B_1 (n \rightarrow \pi^\star)$ &3.45 &3.42 &3.43 &3.45 &3.43& 3.45 & 3.46\\ +$^1B_2 (\pi \rightarrow \pi^\star)$ &4.67 &4.66 &4.64 &4.66 &4.64& 4.66 & 4.66 \\ +$^1B_2 (n \rightarrow 3s)$ &5.26 &5.23 &5.34 &5.39 &5.39& 5.38 & 5.40 \\ +$^1A_1 (\pi \rightarrow \pi^\star)$ &5.53 &5.52 &5.49 &5.49 &5.48& 5.49 & 5.49\\ +$^1B_2 (n \rightarrow 3p)$ &5.83 &5.86 &5.93 &5.95 &5.95& 5.91 & 5.95 \\%$^a$, mais les autres aussi !! +$^3A_2 (n \rightarrow \pi^\star)$ &3.33 &3.34 &3.31 &3.31 &3.29& 3.31 & 3.31 \\ +$^3B_1 (n \rightarrow \pi^\star)$ &3.34 &3.30 &3.31 &3.34 &3.32& 3.34 & 3.35\\ +$^3B_2 (\pi \rightarrow \pi^\star)$ &4.01 &4.03 &4.02 &4.04 &4.03& 4.04 & 4.05 \\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &4.06 &4.09 &4.03 &4.04 &4.02& 4.04& 4.03 \\ +\hline + & \multicolumn{7}{c}{Methylenecyclopropene} \\ +\hline +$^1B_2 (\pi \rightarrow \pi^\star)$ &4.38 &4.32 &4.31 &4.31 &4.31& 4.31& 4.32 \\% 5Z: 4.32 +$^1B_1 (\pi \rightarrow 3s)$ &5.65 &5.35 &5.44 &5.47 &5.48& 5.46& 5.47\\% 5Z: 5.47 +$^1A_2 (\pi \rightarrow 3p)$ &5.97 &5.86 &5.95 &5.98 &5.99& 5.96& \hl{xxx}\\ %N122 +$^1A_1 (\pi \rightarrow \pi^\star)$ &6.17 &6.15 &6.13 &6.09 &6.10& 5.98& 6.04\\%<= Stong mixing 5Z: 6.04 <= A italusˇ dans la liste des TBE ? +$^3B_2 (\pi \rightarrow \pi^\star)$ &3.50 &3.49 &3.50 &3.50 &3.50& 3.50& \hl{xxx}\\ %N122 +$^3A_1 (\pi \rightarrow \pi^\star)$ &4.74 &4.74 &4.74 &4.75 &4.74& 4.74& 4.75\\% 5Z: 4.75 +\hline + \end{tabular} +\begin{flushleft} +%$^a${Significant mixing.} +\end{flushleft} + \end{small} + +\end{table} + +\clearpage + + +\subsection{Acrolein, butadiene, and glyoxal} + +\begin{sidewaystable}[htp] +\caption{\small CC3 vertical transition energies of acrolein, butadiene, and glyoxal using various atomic basis sets. +FC stands for frozen core. All values are in eV.} +\label{Table-S3} + \begin{small} +\begin{tabular}{l|ccccccc} +\hline + & {\Pop} & {\AVDZ} & {\AVTZ} & \multicolumn{2}{c}{\AVQZ} &{\DAVQZ} &{\AVFZ}\\ + & FC & FC &FC & FC & Full & FC & FC \\ +\hline + & \multicolumn{6}{c}{Acrolein} \\ +\hline +$^1A'' (n \rightarrow \pi^\star)$ &3.83 &3.77 &3.74 &3.75 &3.74\\ +$^1A' (\pi \rightarrow \pi^\star)$ &6.83 &6.67 &6.65 &6.65 &6.65\\ +$^1A'' (n \rightarrow \pi^\star)$ &6.94 &6.75 &6.75 &6.77 &6.76\\ +$^1A' (n \rightarrow 3s)$ &7.22 &6.99 &7.07 &7.11 &7.11\\ +$^3A'' (n \rightarrow \pi^\star)$ &3.55 &3.47 &3.46 &3.47 &3.46\\ +$^3A' (\pi \rightarrow \pi^\star)$ &3.94 &3.95 &3.94 &3.95 &3.94\\ +$^3A' (\pi \rightarrow \pi^\star)$ &6.25 &6.22 &6.19 &6.20 &6.19\\ +$^3A'' (n \rightarrow \pi^\star)$ &6.81 &6.60 &6.61 &6.63 &6.62\\ +\hline + & \multicolumn{6}{c}{Butadiene} \\ +\hline +$^1B_u (\pi \rightarrow \pi^\star)$ &6.41 &6.25 &6.22 &6.21 &6.22\\ +$^1B_g (\pi \rightarrow 3s)$ &6.53 &6.26 &6.33 &6.35 &6.36\\ +$^1A_g (\pi \rightarrow \pi^\star)$ &6.73 &6.68 &6.67 &6.67 &6.67& 6.67\\ +$^1A_u (\pi \rightarrow 3p)$ &6.87 &6.57 &6.64 &6.66 &6.67\\ +$^1A_u (\pi \rightarrow 3p)$ &6.93 &6.73 &6.80 &6.82 &6.83\\ +$^1B_u (\pi \rightarrow 3p)$ &7.98 &7.86 &7.68 &7.54 &7.55\\ +$^3B_u (\pi \rightarrow \pi^\star)$ &3.35 &3.36 &3.36 &3.37 &3.36\\ +$^3A_g (\pi \rightarrow \pi^\star)$ &5.22 &5.21 &5.20 &5.21 &5.20\\ +$^3B_g (\pi \rightarrow 3s)$ &6.46 &6.20 &6.28 &6.30 &6.31\\ +\hline + & \multicolumn{6}{c}{Glyoxal} \\ +\hline +$^1A_u (n \rightarrow \pi^\star)$ &2.94 &2.90 &2.88 &2.88 &2.87& 2.88& 2.88\\ +$^1B_g (n \rightarrow \pi^\star)$ &4.34 &4.30 &4.27 &4.27 &4.27& 4.27& \\ +$^1A_g (n,n \rightarrow \pi^\star,\pi^\star)$&6.74 &6.70 &6.76 &6.76 &6.74& 6.76& 6.75 \\ +$^1B_g (n \rightarrow \pi^\star)$ &6.81 &6.59 &6.58 &6.59 &6.58& 6.58& \\ +$^1B_u (n \rightarrow3p)$ &7.72 &7.55 &7.67 &7.72 &7.73& 7.72& 7.74\\ +$^3A_u (n \rightarrow \pi^\star)$ &2.55 &2.49 &2.49 &2.49 &2.49& 2.49& 2.50\\ +$^3B_g (n \rightarrow \pi^\star)$ &3.97 &3.91 &3.90 &3.91 &3.90& 3.91& \\ +$^3B_u (\pi \rightarrow \pi^\star)$ &5.22 &5.20 &5.17 &5.18 &5.17& 5.18& 5.19\\ +$^3A_g (\pi \rightarrow \pi^\star)$ &6.35 &6.34 &6.30 &6.31 &6.30& 6.31& 6.31\\ +\hline + \end{tabular} + \end{small} +\end{sidewaystable} + +\clearpage + + +\subsection{Acetone, cyanoformaldehyde, isobutene, propynal, thioacetone, and thiopropynal} + +\begin{table}[htp] +\caption{\small CC3 vertical transition energies of acetone, cyanoformaldehyde, isobutene, propynal, thioacetone, and thiopropynal using various atomic basis sets. +FC stands for frozen core. All values are in eV.} +\label{Table-S4} + \begin{small} +\begin{tabular}{l|cccccc} +\hline + & {\Pop} & {\AVDZ} & {\AVTZ} & \multicolumn{2}{c}{\AVQZ} &{\DAVQZ} \\ + & FC & FC &FC & FC & Full & FC\\ +\hline + & \multicolumn{6}{c}{Acetone} \\ +\hline +$^1A_2 (n \rightarrow \pi^\star)$ &4.55 &4.50 &4.48 &4.49 &4.48\\ +$^1B_2 (n \rightarrow 3s)$ &6.65 &6.31 &6.43 &6.48 &6.49\\ +$^1A_2 (n \rightarrow 3p)$ &7.83 &7.37 &7.45 &7.48 &7.49\\ +$^1A_1 (n \rightarrow 3p)$ &7.81 &7.39 &7.48 &7.52 &7.53\\ +$^1B_2 (n \rightarrow 3p)$ &7.87 &7.56 &7.59 &7.60 &7.61\\ +$^3A_2 (n \rightarrow \pi^\star)$ &4.21 &4.16 &4.15 &4.17 &4.16\\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &6.32 &6.31 &6.28 &6.30 &6.28\\ +\hline + & \multicolumn{6}{c}{Cyanoformaldehyde} \\ +\hline +$^1A'' (n \rightarrow \pi^\star)$ &3.91 &3.86 &3.83 &3.84 &3.83 &3.84\\ +$^1A'' (\pi \rightarrow \pi^\star)$ &6.64 &6.51 &6.42 &6.41 &6.41 &6.41\\ +$^3A'' (n \rightarrow \pi^\star)$ &3.53 &3.47 &3.46 &3.47 &3.46 &3.47\\ +$^3A' (\pi \rightarrow \pi^\star)$ &5.07 &5.03 &5.01 &5.02 &5.01 &5.02\\ +\hline + & \multicolumn{6}{c}{Isobutene} \\ +\hline +$^1B_1 (\pi \rightarrow 3s)$ &6.77 &6.39 &6.45 &6.47 &6.49\\ +$^1A_1 (\pi \rightarrow 3p)$ &7.16 &7.00 &7.00 &6.99 &7.00\\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &4.52 &4.54 &4.53 &4.54 &4.54\\ +\hline + & \multicolumn{6}{c}{Propynal} \\ +\hline +$^1A'' (n \rightarrow \pi^\star)$ &3.90 &3.85 &3.82 &3.83 &3.82 &3.83\\ +$^1A'' (\pi \rightarrow \pi^\star)$ &5.69 &5.59 &5.51 &5.50 &5.50 &5.50\\ +$^3A'' (n \rightarrow \pi^\star)$ &3.56 &3.50 &3.49 &3.50 &3.49 &3.50\\ +$^3A' (\pi \rightarrow \pi^\star)$ &4.46 &4.40 &4.43 &4.44 &4.43 &4.44\\ +\hline + & \multicolumn{6}{c}{Thioacetone} \\ +\hline +$^1A_2 (n \rightarrow \pi^\star)$ &2.58 &2.59 &2.55 &2.56 &\\ +$^1B_2 (n \rightarrow 4s)$ &5.65 &5.44 &5.55 &5.60 &\\ +$^1A_1 (\pi \rightarrow \pi^\star)$ &6.09 &5.97 &5.90 &5.88 &\\ +$^1B_2 (n \rightarrow 4p)$ &6.59 &6.45 &6.51 &6.52 &\\ +$^1A_1 (n \rightarrow 4p)$ &6.95 &6.54 &6.61 &6.64 &6.64\\ +$^3A_2 (n \rightarrow \pi^\star)$ &2.36 &2.36 &2.34 &2.35 &\\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &3.45 &3.51 &3.46 &3.47 &\\ +\hline + & \multicolumn{5}{c}{Thiopropynal} \\ +\hline +$^1A'' (n \rightarrow \pi^\star)$ &2.09 &2.09 &2.05 &2.06 &2.04\\ +$^3A'' (n \rightarrow \pi^\star)$ &1.84 &1.83 &1.81 &1.82 &1.81\\ +\hline +\end{tabular} +\end{small} +\end{table} + +\clearpage + + +\subsection{Cyclopentadiene, furan, imidazole, pyrrole, and thiophene} + + +\begin{table}[htp] +\caption{\small CC3 vertical transition energies of furan and pyrrole using various atomic basis sets. +FC stands for frozen core. All values are in eV.} +\label{Table-S5} + \begin{small} +\begin{tabular}{l|ccccc} +\hline + & {\Pop} & {\AVDZ} & {\AVTZ} & \multicolumn{2}{c}{{\AVQZ}} \\ + & FC & FC &FC & FC & Full \\ +\hline + & \multicolumn{5}{c}{Furan} \\ +\hline +$^1A_2 (\pi \rightarrow 3s)$ &6.26 &6.00 &6.08 &6.10 &6.12\\ +$^1B_2 (\pi \rightarrow \pi^\star)$ &6.50 &6.37 &6.34 &6.34 &6.34\\ +$^1A_1 (\pi \rightarrow \pi^\star)$ &6.71 &6.62 &6.58 &6.58 &6.58\\ +$^1B_1 (\pi \rightarrow 3p)$ &6.76 &6.55 &6.63 &6.65 &6.67\\ +$^1A_2 (\pi \rightarrow 3p)$ &6.97 &6.73 &6.80 &6.82 &6.83\\ +$^1B_2 (\pi \rightarrow 3p)$ &7.53 &7.39 &7.23 &7.13 &7.14\\ +$^3B_2 (\pi \rightarrow \pi^\star)$ &4.28 &4.25 &4.22 &4.22 &4.22\\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &5.56 &5.51 &5.48 &5.49 &5.48\\ +$^3A_2 (\pi \rightarrow 3s)$ &6.18 &5.94 &6.02 &6.05 &6.07\\ +$^3B_1 (\pi \rightarrow 3p)$ &6.69 &6.51 &6.59 &6.61 &6.63\\ +\hline + & \multicolumn{5}{c}{Pyrrole} \\ +\hline +$^1A_2 (\pi \rightarrow 3s)$ &5.25 &5.15 &5.24 &5.27 &\hl{XXX} \\ +$^1B_1 (\pi \rightarrow 3p)$ &5.99 &5.89 &5.98 &6.01 &6.02 \\ +$^1A_2 (\pi \rightarrow 3p)$ &6.27 &5.94 &6.01 &6.03 &\hl{XXX} \\ +$^1B_2 (\pi \rightarrow \pi^\star)$ &6.33 &6.28 &6.25 &6.22 &6.23 \\ +$^1A_1 (\pi \rightarrow \pi^\star)$ &6.43 &6.35 &6.32 &6.31 &6.31 \\ +$^1B_2 (\pi \rightarrow 3p)$ &7.20 &7.00 &6.83 &6.74 &6.75 \\ +$^3B_2 (\pi \rightarrow \pi^\star)$ &4.59 &4.56 &4.53 &4.53 &4.52 \\ +$^3A_2 (\pi \rightarrow 3s)$ &5.22 &5.12 &5.21 &5.24 &\hl{XXX} \\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &5.54 &5.49 &5.46 &5.47 &5.46 \\ +$^3B_1 (\pi \rightarrow 3p)$ &5.91 &5.82 &5.92 &5.95 &5.97 \\ +\hline +\end{tabular} +\end{small} +\end{table} + + + +\begin{table}[htp] +\caption{\small CC3 vertical transition energies of cyclopentadiene, imidazole, and thiophene using various atomic basis sets. +FC stands for frozen core. All values are in eV.} +\label{Table-S6} + \begin{small} +\begin{tabular}{l|cccc} +\hline + & {\Pop} & {\AVDZ} & {\AVTZ} & {{\AVQZ}} \\ + & FC & FC &FC & FC \\ +\hline + & \multicolumn{4}{c}{Cyclopentadiene} \\ +\hline +$^1B_2 (\pi \rightarrow \pi^\star)$ &5.79 &5.59 &5.54 &5.53 \\ +$^1A_2 (\pi \rightarrow 3s)$ &6.08 &5.70 &5.77 &5.79 \\ +$^1B_1 (\pi \rightarrow 3p)$ &6.57 &6.34 &6.40 &6.42 \\ +$^1A_2 (\pi \rightarrow 3p)$ &6.67 &6.39 &6.45 &6.46 \\ +$^1B_2 (\pi \rightarrow 3p)$ &7.06 &6.55 &6.56 &6.55 \\ +$^1A_1 (\pi \rightarrow \pi^\star)$ &6.67 &6.59 &6.57 &6.57 \\ +$^3B_2 (\pi \rightarrow \pi^\star)$ &3.33 &3.32 &3.32 &3.32 \\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &5.16 &5.14 &5.12 &5.13 \\ +$^3A_2 (\pi \rightarrow 3s)$ &6.01 &5.65 &5.73 &5.75 \\ +$^3B_1 (\pi \rightarrow 3p)$ &6.51 &6.30 &6.36 &6.38 \\ +\hline + & \multicolumn{4}{c}{Imidazole} \\ +\hline +$^1A'' (\pi \rightarrow 3s)$ &5.77 &5.60 &5.71 &5.73 \\ +$^1A' (\pi \rightarrow \pi^\star)$ &6.51 &6.43 &6.41 &6.41 \\ +$^1A'' (n \rightarrow \pi^\star)$ &6.66 &6.42 &6.50 &6.53 \\ +$^1A' (\pi \rightarrow 3p)$ &7.04 &6.93 &6.87 &6.86 \\ +$^3A' (\pi \rightarrow \pi^\star)$ &4.83 &4.78 &4.75 &4.76 \\ +$^3A'' (\pi \rightarrow 3s)$ &5.72 &5.57 &5.67 &5.70 \\ +$^3A' (\pi \rightarrow \pi^\star)$ &5.88 &5.78 &5.74 &5.75 \\ +$^3A'' (n \rightarrow \pi^\star)$ &6.48 &6.37 &6.33 &6.33 \\ +\hline + & \multicolumn{4}{c}{Thiophene} \\ +\hline +$^1A_1 (\pi \rightarrow \pi^\star)$ &5.79 &5.70 &5.65 &5.64\\ +$^1B_2 (\pi \rightarrow \pi^\star)$ &6.23 &6.05 &5.96 &5.94\\ +$^1A_2 (\pi \rightarrow 3s)$ &6.26 &6.07 &6.14 &6.16\\ +$^1B_1 (\pi \rightarrow 3p)$ &6.18 &6.19 &6.14 &6.11\\ +$^1A_2 (\pi \rightarrow 3p)$ &6.32 &6.33 &6.25 &6.22\\ +$^1B_1 (\pi \rightarrow 3s)$ &6.62 &6.42 &6.50 &6.53\\ +$^1B_2 (\pi \rightarrow 3p)$ &7.45 &7.45 &7.29 &7.18\\ +$^1A_1 (\pi \rightarrow \pi^\star)$ &7.50 &7.41 &7.35 &7.33\\ +$^3B_2 (\pi \rightarrow \pi^\star)$ &3.95 &3.96 &3.94 &3.93\\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &4.90 &4.82 &4.77 &4.77\\ +$^3B_1 (\pi \rightarrow 3p)$ &6.00 &6.01 &5.95 &5.92\\ +$^3A_2 (\pi \rightarrow 3s)$ &6.20 &6.01 &6.09 &5.99\\ +\hline +\end{tabular} +\end{small} +\end{table} + + +\clearpage + +\subsection{Benzene, pyrazine, and tetrazine} + +\begin{table}[htp] +\caption{\small CC3 vertical transition energies of benzene using various atomic basis sets. +FC stands for frozen core. All values are in eV.} +\label{Table-S7} + \begin{small} +\begin{tabular}{l|cccc} +\hline + & {\Pop} & {\AVDZ} & {\AVTZ} & {\AVQZ} \\ + & FC & FC &FC & FC \\ +\hline + & \multicolumn{4}{c}{Benzene} \\ +\hline +$^1B_{2u} (\pi \rightarrow \pi^\star)$ &5.13 &5.11 &5.09 &5.09\\ +$^1B_{1u} (\pi \rightarrow \pi^\star)$ &6.68 &6.50 &6.44 &6.43\\ +$^1E_{1g} (\pi \rightarrow 3s)$ &6.75 &6.46 &6.52 &6.54\\ +$^1A_{2u} (\pi \rightarrow 3p)$ &7.24 &7.02 &7.08 &7.10\\ +$^1E_{2u} (\pi \rightarrow 3p)$ &7.34 &7.09 &7.15 &7.16\\ +$^3B_{1u} (\pi \rightarrow \pi^\star)$ &4.18 &4.19 &4.18 &4.19\\ +$^3E_{1u}(\pi \rightarrow \pi^\star)$ &4.95 &4.89 &4.86 &4.87\\ +$^3B_{2u} (\pi \rightarrow \pi^\star)$ &6.06 &5.86 &5.81 &5.81\\ +\hline +\end{tabular} +\end{small} +\end{table} + +\clearpage + +\begin{table}[htp] +\caption{\small CC3 vertical transition energies of tetrazine using various atomic basis sets. +FC stands for frozen core. All values are in eV.} +\label{Table-S8} + \begin{small} +\begin{tabular}{l|ccccc} +\hline + & {\Pop} & {\AVDZ} & {\AVTZ} & \multicolumn{2}{c}{{\AVQZ}} \\ + & FC & FC &FC & FC & Full \\ +\hline + & \multicolumn{5}{c}{Pyrazine} \\ +\hline +$^1B_{3u} (n \rightarrow \pi^\star)$ & 4.28 &4.19 &4.14 &4.14\\ +$^1A_{u} (n \rightarrow \pi^\star)$ & 5.08 &4.98 &4.97 &4.98\\ +$^1B_{2u} (\pi \rightarrow \pi^\star)$ & 5.10 &5.07 &5.03 &5.02\\ +$^1B_{2g} (n \rightarrow \pi^\star)$ & 5.86 &5.78 &5.71 &5.71\\ +$^1A_{g} (n \rightarrow 3s)$ & 6.74 &6.54 &6.66 &6.70& 6.71\\ +$^1B_{1g} (n \rightarrow \pi^\star)$ & 6.87 &6.75 &6.73 &6.73\\ +$^1B_{1u} (\pi \rightarrow \pi^\star)$ & 7.10 &6.92 &6.86 &6.85& 6.85\\ +$^1B_{1g} (n \rightarrow 3p)$ & 7.36 &7.13 &7.20 &7.23\\ +$^1B_{2u} (n \rightarrow 3p)$ & 7.39 &7.14 &7.25 &7.29\\ +$^1B_{1u} (\pi \rightarrow 3s)$ & 7.56 &7.38 &7.45 &7.48& 7.49\\ +$^1B_{1u} (\pi \rightarrow \pi^\star)$ & 8.19 &7.99 &7.94 &7.93& 7.93\\ +$^3B_{3u} (n \rightarrow \pi^\star)$ & 3.68 &3.60 &3.59 &3.59\\ +$^3B_{1u} (\pi \rightarrow \pi^\star)$ & 4.39 &4.40 &4.39 &4.40& 4.39\\ +$^3B_{2u} (\pi \rightarrow \pi^\star)$ & 4.56 &4.46 &4.40 &4.40\\ +$^3A_{u} (n \rightarrow \pi^\star)$ & 5.05 &4.93 &4.93 &4.94\\ +$^3B_{2g} (n \rightarrow \pi^\star)$ & 5.18 &5.11 &5.08 &5.09\\ +$^3B_{1u} (\pi \rightarrow \pi^\star)$ & 5.38 &5.32 &5.29 &5.29& 5.28\\ +\hline + & \multicolumn{5}{c}{Tetrazine} \\ +\hline +$^1B_{3u} (n \rightarrow \pi^\star)$ & 2.53 &2.49 &2.46 &2.45 &2.45\\ +$^1A_{u} (n \rightarrow \pi^\star)$ & 3.75 &3.69 &3.67 &3.68 &3.67\\ +$^1A_{g} (n,n \rightarrow \pi^\star, \pi^\star)$ & 6.22 &6.22 &6.21 &6.19 &6.17\\ +$^1B_{1g} (n \rightarrow \pi^\star)$ & 5.01 &4.97 &4.91 &4.90 &4.88\\ +$^1B_{2u} (\pi \rightarrow \pi^\star)$ & 5.29 &5.27 &5.23 &5.22 &5.21\\ +$^1B_{2g} (n \rightarrow \pi^\star)$ & 5.56 &5.53 &5.46 &5.46 &5.45\\ +$^1A_{u} (n \rightarrow \pi^\star)$ & 5.61 &5.59 &5.52 &5.52 &5.50\\ +$^1B_{3g} (n,n \rightarrow \pi^\star, \pi^\star)$ & 7.64 &7.62 &7.62 &7.60 &7.58\\ +$^1B_{2g} (n \rightarrow \pi^\star)$ & 6.24 &6.17 &6.13 &6.13 &6.10\\ +$^1B_{1g} (n \rightarrow \pi^\star)$ & 7.04 &6.98 &6.92 &6.92 &6.91\\ +$^3B_{3u} (n \rightarrow \pi^\star)$ & 1.87 &1.86 &1.85 &1.86 &1.85\\ +$^3A_{u} (n \rightarrow \pi^\star)$ & 3.48 &3.43 &3.44 &3.45 &3.43\\ +$^3B_{1g} (n \rightarrow \pi^\star)$ & 4.25 &4.23 &4.20 &4.21 &4.18\\ +$^3B_{1u} (\pi \rightarrow \pi^\star)$ & 4.54 &4.54 &4.54 &4.54 &4.53\\ +$^3B_{2u} (\pi \rightarrow \pi^\star)$ & 4.65 &4.58 &4.52 &4.52 &4.51\\ +$^3B_{2g} (n \rightarrow \pi^\star)$ & 5.11 &5.09 &5.05 &5.05 &5.04\\ +$^3A_{u} (n \rightarrow \pi^\star)$ & 5.17 &5.15 &5.11 &5.11 &5.10\\ +$^3B_{3g} (n,n \rightarrow \pi^\star, \pi^\star)$ & 7.35 &7.33 &7.35 &7.34 &7.32\\ +$^3B_{1u} (\pi \rightarrow \pi^\star)$ & 5.51 &5.46 &5.42 &5.43 &5.42\\ +\hline +\end{tabular} +\end{small} +\end{table} + +\clearpage + +\subsubsection{Pyridazine, pyridine, pyrimidine and triazine} + +\begin{table}[htp] +\caption{\small CC3 vertical transition energies of pyridazine and pyridine using various atomic basis sets. +FC stands for frozen core. All values are in eV.} +\label{Table-S9} + \begin{small} +\begin{tabular}{l|cccc} +\hline + & {\Pop} & {\AVDZ} & {\AVTZ} & {\AVQZ} \\ + & FC & FC &FC & FC \\ +\hline + & \multicolumn{4}{c}{Pyridazine} \\ +\hline +$^1B_1 (n \rightarrow \pi^\star)$ &3.95 &3.86 &3.83 &\\ +$^1A_2 (n \rightarrow \pi^\star)$ &4.49 &4.39 &4.37 &\\ +$^1A_1 (\pi \rightarrow \pi^\star)$ &5.36 &5.33 &5.29 &5.29\\ +$^1A_2 (n \rightarrow \pi^\star)$ &5.88 &5.80 &5.74 &\\ +$^1B_2 (n \rightarrow 3s)$ &6.26 &6.06 &6.17 &\\ +$^1B_1 (n \rightarrow \pi^\star)$ &6.51 &6.41 &6.37 &\\ +$^1B_2 (\pi \rightarrow \pi^\star)$ &6.96 &6.79 &6.74 &\\ +$^3B_1 (n \rightarrow \pi^\star)$ &3.27 &3.20 &3.19 &3.20\\ +$^3A_2 (n \rightarrow \pi^\star)$ &4.19 &4.11 &4.11 &\\ +$^3B_2 (\pi \rightarrow \pi^\star)$ &4.39 &4.39 &4.38 &\\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &4.93 &4.87 &4.83 &4.82\\ +\hline + & \multicolumn{4}{c}{Pyridine} \\ +\hline +$^1B_1 (n \rightarrow \pi^\star)$ &5.12 &5.01 &4.96\\ +$^1B_2 (\pi \rightarrow \pi^\star)$ &5.23 &5.21 &5.17\\ +$^1A_2 (n \rightarrow \pi^\star)$ &5.55 &5.41 &5.40\\ +$^1A_1 (\pi \rightarrow \pi^\star)$ &6.84 &6.64 &6.63\\ +$^1A_1 (n \rightarrow 3s)$ &6.92 &6.71 &6.76\\ +$^1A_2 (\pi \rightarrow 3s)$ &6.98 &6.74 &6.81\\ +$^1B_2 (\pi \rightarrow \pi^\star)$ &7.50 &7.40 &7.35/7.38\\ +$^1B_1 (\pi \rightarrow 3p)$ &7.54 &7.32 &7.38\\ +$^1A_1 (\pi \rightarrow \pi^\star)$ &7.56 &7.34 &7.39\\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &4.33 &4.34 &4.33\\ +$^3B_1 (n \rightarrow \pi^\star)$ &4.57 &4.47 &4.46& 4.47\\ +$^3B_2 (\pi \rightarrow \pi^\star)$ &4.92 &4.83 &4.79\\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &5.14 &5.08 &5.05\\ +$^3A_2 (n \rightarrow \pi^\star)$ &5.51 &5.37 &5.35\\ +$^3B_2 (\pi \rightarrow \pi^\star)$ &6.46 &6.30 &6.25\\ +\hline +\end{tabular} +\end{small} +\end{table} + +\clearpage + + +\begin{table}[htp] +\caption{\small CC3 vertical transition energies of pyrimidine and triazine using various atomic basis sets. +FC stands for frozen core. All values are in eV.} +\label{Table-S10} + \begin{small} +\begin{tabular}{l|cccc} +\hline + & {\Pop} & {\AVDZ} & {\AVTZ} & {\AVQZ} \\ + & FC & FC &FC & FC \\ +\hline + & \multicolumn{4}{c}{Pyrimidine} \\ +\hline +$^1B_1 (n \rightarrow \pi^\star)$ & 4.58 &4.48 &4.44 &\\ +$^1A_2 (n \rightarrow \pi^\star)$ & 4.99 &4.89 &4.86 &\\ +$^1B_2 (\pi \rightarrow \pi^\star)$ & 5.47 &5.44 &5.41 &\\ +$^1A_2 (n \rightarrow \pi^\star)$ & 6.07 &5.98 &5.93 &\\ +$^1B_1 (n \rightarrow \pi^\star)$ & 6.39 &6.29 &6.26 &\\ +$^1B_2 (n \rightarrow 3s)$ & 6.81 &6.61 &6.72 &6.76\\ +$^1A_1 (\pi \rightarrow \pi^\star)$ & 7.08 &6.93 &6.87 &6.86\\ +$^3B_1 (n \rightarrow \pi^\star)$ & 4.20 &4.12 &4.10 &4.11\\ +$^3A_1 (\pi \rightarrow \pi^\star)$ & 4.55 &4.56 &4.55 &4.56\\ +$^3A_2 (n \rightarrow \pi^\star)$ & 4.77 &4.67 &4.66 &4.67\\ +$^3B_2 (\pi \rightarrow \pi^\star)$ & 5.08 &5.00 &4.96 &4.96\\ +\hline + & \multicolumn{4}{c}{Triazine} \\ +\hline +$^1A_1'' (n \rightarrow \pi^\star)$ & 4.85 &4.76 &4.73 &4.74\\ +$^1A_2'' (n \rightarrow \pi^\star)$ & 4.84 &4.78 &4.74 &4.74\\ +$^1E'' (n \rightarrow \pi^\star)$ & 4.89 &4.82 &4.78 &4.79\\ +$^1A_2' (\pi \rightarrow \pi^\star)$ & 5.84 &5.81 &5.78 &5.78\\ +$^1A_1' (\pi \rightarrow \pi^\star)$ & 7.45 &7.31 &7.24 &7.23\\ +$^1E' (n \rightarrow 3s)$ & 7.44 &7.24 &7.35 &7.39\\ +$^1E'' (n \rightarrow \pi^\star)$ & 7.89 &7.82 &7.79 &7.78\\ +$^1E' (\pi \rightarrow \pi^\star)$ & 8.12 &7.97 &7.92 &7.92\\ +$^3A_2'' (n \rightarrow \pi^\star)$ & 4.40 &4.35 &4.33 &4.34\\ +$^3E'' (n \rightarrow \pi^\star)$ & 4.59 &4.52 &4.51 &4.51\\ +$^3A_1'' (n \rightarrow \pi^\star)$ & 4.87 &4.78 &4.75 &4.76\\ +$^3A_1' (\pi \rightarrow \pi^\star)$ & 4.88 &4.88 &4.88 &4.89\\ +$^3E' (\pi \rightarrow \pi^\star)$ & 5.70 &5.64 &5.61 &5.61\\ +$^3A_2' (\pi \rightarrow \pi^\star)$ & 6.85 &6.69 &6.63 &6.62\\ +\hline +\end{tabular} +\end{small} +\end{table} + +\clearpage + + + +\clearpage + +\section{Multi-reference results} + +\subsection{Basis set effects} + +\begin{table}[htp] +\caption{\small Vertical transition energies of cyanoacetylene, cyanogen, and diacetylene using various atomic basis sets and +multi-reference methods. All values are in eV and have been obtained with within the FC approximation. The CASPT2 calculations +are performed with a level shift of 0.3 and a IPEA of 0.25. Pop, AVDZ, AVTZ, and AVQZ respectively stand for {\Pop}, {\AVDZ}, +{\AVTZ}, and {\AVQZ}. } +\label{Table-S1b} + \begin{footnotesize} +\begin{tabular}{l|cccccccccccc} +\hline + & \multicolumn{4}{c}{CASPT2(8,8)} & \multicolumn{4}{c}{PC-NEVPT2(8,8)} & \multicolumn{4}{c}{SC-NEVPT2(8,8)} \\ + & Pop &AVDZ & AVTZ & AVQZ & Pop &AVDZ & AVTZ & AVQZ& Pop &AVDZ & AVTZ & AVQZ \\ +\hline + & \multicolumn{12}{c}{Cyanoacetylene} \\ +\hline +$^1\Sigma^-$ & & 6.00 & 5.86 & & & 5.93 & 5.78 & & & 5.98 & 5.83 & \\ +$^1\Delta$ & & 6.26 & 6.13 & & & 6.22 & 6.10 & & & 6.27 & 6.14 & \\ +$^3\Sigma^+$ & & 4.47 & 4.45 & & & 4.46 & 4.45 & & & 4.51 & 4.49 & \\ +$^3\Delta$ & & 5.30 & 5.21 & & & 5.28 & 5.19 & & & 5.31 & 5.23 & \\ +\hline + & \multicolumn{12}{c}{Cyanogen} \\ +\hline +$^1\Sigma_u^-$ & 6.63 & 6.56 & 6.40 & 6.37 & 6.56 & 6.49 & 6.32 & 6.29 & 6.61 & 6.54 & 6.37 & 6.34 \\ +$^1\Delta_u$ & 6.93 & 6.84 & 6.70 & 6.66 & 6.91 & 6.81 & 6.66 & 6.63 & 6.95 & 6.86 & 6.71 & 6.68 \\ +$^3\Sigma_u^+$ & 4.91 & 4.89 & 4.86 & 4.86 & 4.92 & 4.91 & 4.88 & 4.89 & 4.96 & 4.95 & 4.92 & 4.93 \\ +$^1\Sigma_u^-$[F] & & 5.23 & 5.07 & & & 5.14 & 4.97 & & & 5.17 & 5.01 & \\ +\hline + & \multicolumn{12}{c}{Diacetylene} \\ +\hline +$^1\Sigma_u^-$ & & 5.56 & 5.43 & & & 5.47 & 5.33 & & & 5.53 & 5.39 & \\ +$^1\Delta_u$ & & 5.80 & 5.68 & & & 5.73 & 5.61 & & & 5.78 & 5.67 & \\ +$^3\Sigma_u^+$ & & 4.12 & 4.11 & & & 4.09 & 4.08 & & & 4.14 & 4.13 & \\ +$^3\Delta_u$ & & 4.89 & 4.81 & & & 4.86 & 4.78 & & & 4.90 & 4.82 & \\ +\hline + \end{tabular} + \end{footnotesize} +\end{table} +\clearpage + +\subsection{Active Spaces} + +\clearpage + +\section{sCI results} + +\begin{landscape} +\begin{footnotesize} +\begin{longtable}{p{3.5cm}p{3.5cm}p{2cm}p{1.2cm}p{2.8cm}p{2cm}p{1.2cm}p{2.8cm}} +\caption{ +Vertical excitations (in eV) for various states of the studied molecules computed with an extrapolated sCI method (exFCI). +The number of determinants $N_\text{det}$ of the largest sCI wave functions and their corresponding excitation energies are also reported. +The extrapolation error is estimated as the difference in excitation energy between the largest sCI wave function and its corresponding extrapolated value. +\label{tab:sCI}} +\\ +\hline +Molecule & Transition & \mc{3}{c}{\Pop} & \mc{3}{c}{\AVDZ} \\ + \cline{3-5} \cline{6-8} + & & $\Ndet$ & sCI & exFCI & $\Ndet$ & sCI & exFCI \\ +\hline +\endfirsthead +\hline +Molecule & Transition & \mc{3}{c}{\Pop} & \mc{3}{c}{\AVDZ} \\ + \cline{3-5} \cline{6-8} + & & $\Ndet$ & sCI & exFCI & $\Ndet$ & sCI & exFCI \\ +\hline +\endhead +\hline \multicolumn{8}{r}{{Continued on next page}} \\ +\endfoot +\hline +\endlastfoot +Acetone & $^1A_2 (\Val; n \ra \pis)$ & $26\,526\,782$ & $4.55$ & $4.60\pm0.05$ \\ +% & $^1B_2 (\Ryd; n \ra 3s)$ & $25\,1675\,94$ & $6.91$ & $6.83\pm0.08$ \\ %TO BE CHECKED !!!!! +% & $^1A_2 (\Ryd; n \ra 3p)$ & $$ & $$ & $$ \\ +% & $^1A_1 (\Ryd; n \ra 3p)$ & $$ & $$ & $$ \\ +% & $^1B_2 (\Ryd; n \ra 3p)$ & $$ & $$ & $$ \\ + & $^3A_2 (\Val; n \ra \pis)$ & $26\,553\,941$ & $4.22$ & $4.18\pm0.04$ \\ +% & $^3A_1 (\Val; \pi \ra \pis)$ & $$ & $$ & $$ \\ +Acrolein & $^1A'' (\Val; n \ra \pis)$ & $23\,273\,572$ & $3.84$ & $3.85\pm0.01$ \\ +% & $^1A' (\Val; \pi \ra \pis)$ & $$ & $$ & $$ \\ +% & $^1A'' (\Val; n \ra \pis)$ & $$ & $$ & $$ \\ +% & $^1A' (\Ryd; n \ra 3s)$ & $$ & $$ & $$ \\ + & $^3A'' (\Val; n \ra \pis)$ & $26\,531\,491$ & $3.59$ & $3.60\pm0.01$ + & $15\,827\,189$ & $3.58$ & $3.51\pm0.07$ \\ + & $^3A' (\Val; \pi \ra \pis)$ & $37\,480\,261$ & $4.01$ & $3.98\pm0.03$ + & $15\,827\,189$ & $4.05$ & $3.96\pm0.09$ \\ +% & $^3A' (\Val; \pi \ra \pis)$ & $$ & $$ & $$ \\ +% & $^3A'' (\Ryd; \pi \ra 3s)$ & $$ & $$ & $$ \\ +Butadiene & $^1B_u (\Val; \pi \ra \pis)$ & $20\,552\,493$ & $6.43$ & $6.41\pm0.02$ \\ +% & $^1B_g (\Ryd; \pi \ra 3s)$ & $$ & $$ & $$ \\ +% & $^1A_g (\Val; \pi \ra \pis)$ & $92\,506\,300$ & $6.59$ & $6.55\pm0.04$ +% & $59\,594\,588$ & $6.58$ & $6.51\pm0.07$ \\ +% & $^1A_u (\Ryd; \pi \ra 3p)$ & $$ & $$ & $$ \\ + & $^1A_u (\Ryd; \pi \ra 3p)$ & $20\,552\,493$ & $6.96$ & $6.95\pm0.01$ + & $12\,521\,242$ & $6.72$ & $6.72\pm0.00$ \\ +% & $^1B_u (\Ryd; \pi \ra 3p)$ & $$ & $$ & $$ \\ + & $^3B_u (\Val; \pi \ra \pis)$ & $49\,847\,526$ & $3.40$ & $3.37\pm0.03$ \\ + & $^3A_g (\Val; \pi \ra \pis)$ & & & + & $17\,235\,280$ & $6.29$ & $6.21\pm0.08$ \\ + & $^3B_g (\Val; \pi \ra 3s)$ & $49\,847\,526$ & $6.43$ & $6.40\pm0.03$ \\ +Cyanoacetylene & $^1\Sigma^- (\Val; \pi \ra \pis)$ & $21\,269\,249$ & $6.01$ & $6.02\pm0.01$ + & $11\,023\,351$ & $5.93$ & $5.84\pm0.09$ \\ + & $^1\Delta (\Val; \pi \ra \pis)$ & $21\,269\,249$ & $6.29$ & $6.28\pm0.01$ + & $11\,023\,351$ & $6.19$ & $6.14\pm0.05$ \\ + & $^3\Sigma^+ (\Val; \pi \ra \pis)$ & $18\,198\,954$ & $4.48$ & $4.45\pm0.03$ + & $25\,646\,703$ & $4.47$ & $4.41\pm0.06$ \\ + & $^3\Delta (\Val; \pi \ra \pis)$ & $18\,198\,954$ & $5.35$ & $5.32\pm0.03$ + & $25\,646\,703$ & $5.28$ & $5.20\pm0.08$ \\ + & $^1A'' [\Fl] (\Val; \pi \ra \pis)$ & $104\,485\,975$ & $3.70$ & $3.67\pm0.03$ + & $62\,248\,690$ & $3.61$ & $3.50\pm0.02$ \\ +Cyanoformaldehyde & $^1A'' (\Val; n \ra \pis)$ & $17\,778\,047$ & $3.94$ & $3.92\pm0.02$ + & $19\,020\,785$ & $3.93$ & $3.98\pm0.05$ \\ + & $^1A'' (\Val; \pi \ra \pis)$ & $17\,778\,047$ & $6.67$ & $6.60\pm0.07$ + & $19\,020\,785$ & $6.57$ & $6.58\pm0.01$ \\ + & $^3A'' (\Val; n \ra \pis)$ & $21\,011\,221$ & $3.54$ & $3.48\pm0.06$ + & $48\,532\,729$ & $3.51$ & $3.52\pm0.01$ \\ + & $^3A' (\Val; \pi \ra \pis)$ & & & + & $48\,5327\,29$ & $5.10$ & $5.07\pm0.03$ \\ +Cyanogen & $^1\Sigma_u^- (\Val; \pi \ra \pis)$ & $12\,1991\,55$ & $6.61$ & $6.58\pm0.03$ + & $20\,9495\,13$ & $6.52$ & $6.44\pm0.08$ \\ + & $^1\Delta_u (\Val; \pi \ra \pis)$ & $12\,1991\,55$ & $6.89$ & $6.87\pm0.02$ + & $20\,9495\,13$ & $6.78$ & $6.74\pm0.04$ \\ + & $^3\Sigma_u^+ (\Val; \pi \ra \pis)$ & $34\,1277\,36$ & $4.97$ & $4.91\pm0.06$ + & $25\,7606\,68$ & $4.94$ & $4.87\pm0.07$ \\ + & $^1\Sigma_u^- [\Fl] (\Val; \pi \ra \pis)$ & $21\,4163\,04$ & $5.36$ & $5.31\pm0.05$ + & $28\,8841\,38$ & $5.17$ & $5.26\pm0.09$ \\ +Cyclopropenone & $^1B_1 (\Val; n \ra \pis)$ & $48\,8976\,96$ & $4.40$ & $4.38\pm0.02$ \\ + & $^1A_2 (\Val; n \ra \pis)$ & $24\,5411\,16$ & $5.70$ & $5.64\pm0.06$ \\ +% & $^1B_2 (\Ryd; n \ra 3s)$ & $$ & $$ & $$ \\ +% & $^1B_2 (\Val; \pi \ra \pis$) & $$ & $$ & $$ \\ +% & $^1B_2 (\Ryd; n \ra 3p)$ & $$ & $$ & $$ \\ +% & $^1A_1 (\Ryd; n \ra 3p)$ & $$ & $$ & $$ \\ +% & $^1A_1 (\Val; \pi \ra \pis)$ & $$ & $$ & $$ \\ + & $^3B_1 (\Val; n \ra \pis)$ & $24\,008\,328$ & $4.07$ & $4.00\pm0.07$ \\ + & $^3B_2 (\Val; \pi \ra \pis)$ & $48\,311\,362$ & $4.95$ & $4.95\pm0.00$ \\ +% & $^3A_2 (\Val; n \ra \pis)$ & $$ & $$ & $$ \\ +% & $^3A_1 (\Val; \pi \ra \pis)$ & $$ & $$ & $$ \\ +Cyclopropenethione & $^1A_2 (\Val; n \ra \pis)$ & $39\,385\,657$ & $3.46$ & $3.45\pm0.01$ \\ + & $^1B_1 (\Val; n \ra \pis)$ & $39\,385\,657$ & $3.50$ & $3.44\pm0.05$ \\ + & $^1B_2 (\Val; \pi \ra \pis)$ & $39\,385\,657$ & $4.68$ & $4.59\pm0.09$ \\ +% & $^1B_2 (\Ryd; n \ra 3s)$ & $$ & $$ & $$ \\ +% & $^1A_1 (\Val; \pi \ra \pis)$ & $$ & $$ & $$ \\ +% & $^1B_2 (\Ryd; n \ra 3p)$ & $$ & $$ & $$ \\ + & $^3A_2 (\Val; n \ra \pis)$ & $23\,904\,962$ & $3.32$ & $3.29\pm0.03$ \\ +% & $^3B_1 (\Val; n \ra \pis)$ & $$ & $$ & $$ \\ + & $^3B_2 (\Val; \pi \ra \pis)$ & $23\,904\,962$ & $4.06$ & $4.03\pm0.03$ \\ +% & $^3A_1 (\Val; \pi \ra \pis)$ & $$ & $$ & $$ \\ +Diacetylene & $^1\Sigma_u^- (\Val; \pi \ra \pis)$ & $18\,955\,451$ & $5.58$ & $5.52\pm0.06$ + & $19\,192\,556$ & $5.45$ & $5.47\pm0.02$ \\ + & $^1\Delta_u (\Val; \pi \ra \pis)$ & $18\,955\,451$ & $5.85$ & $5.84\pm0.01$ + & $19\,192\,556$ & $5.45$ & $5.69\pm0.02$ \\ + & $^3\Sigma_u^+ (\Val; \pi \ra \pis)$ & $13\,777\,757$ & $4.11$ & $4.04\pm0.07$ + & $26\,668\,471$ & $4.11$ & $4.07\pm0.04$ \\ + & $^3\Delta_u (\Val; \pi \ra \pis)$ & $13\,777\,757$ & $4.93$ & $4.94\pm0.01$ + & $26\,668\,471$ & $4.87$ & $4.85\pm0.02$ \\ +Glyoxal & $^1A_u (\Val; n \ra \pis)$ & $51\,656\,090$ & $2.96$ & $2.93\pm0.03$ + & $34\,125\,394$ & $2.94$ & $2.93\pm0.01$ \\ + & $^1B_g (\Val; n \ra \pis)$ & $24\,394\,242$ & $4.34$ & $4.28\pm0.06$ \\ +% & $^1A_g (\Val; n,n \ra \pis,\pis)$ & $118\,275\,835$ & $5.69$ & $5.60\pm0.09$ \\ +% & $^1B_g (\Val; n \ra \pis)$ & $$ & $$ & $$ \\ +% & $^1B_u (\Ryd; n \ra 3p)$ & $$ & $$ & $$ \\ + & $^3A_u (\Val; n \ra \pis)$ & $47\,693\,908$ & $2.58$ & $2.54\pm0.04$ \\ +% & $^3B_g (\Val; n \ra \pis)$ & $$ & $$ & $$ \\ +% & $^3B_u (\Val; \pi \ra \pis)$ & $$ & $$ & $$ \\ +% & $^3A_g (\Val; \pi \ra \pis)$ & $$ & $$ & $$ \\ +Isobutene & $^1B_1 (\Ryd; \pi \ra 3s)$ & $28\,095\,377$ & $6.86$ & $6.78\pm0.08$ \\ + & $^1A_1 (\Ryd; \pi \ra 3p)$ & $59\,728\,169$ & $7.22$ & $7.16\pm0.02$ \\ + & $^3A_1 \Val; (\pi \ra \pis)$ & $32\,440\,621$ & $4.54$ & $4.56\pm0.02$ \\ +Methylenecyclopropene & $^1B_2 (\Val; \pi \ra \pis)$ & $51\,918\,524$ & $4.35$ & $4.32\pm0.03$ \\ +% & $^1B_1 (\Ryd; \pi \ra \sigma^\star)$ & $$ & $$ & $$ \\ + & $^1A_2 (\Ryd; \pi \ra 3p)$ & $25\,146\,911$ & $6.02$ & $5.92\pm0.10$ \\ + & $^1A_1(\Val; \pi \ra \pis)$ & $31\,721\,213$ & $6.21$ & $6.20\pm0.01$ \\ + & $^3B_2 (\Val; \pi \ra \pis)$ & $24\,379\,551$ & $3.50$ & $3.44\pm0.06$ + & $43\,090\,114$ & $3.49$ & $3.45\pm0.04$ \\ + & $^3A_1 (\Val; \pi \ra \pis)$ & $24\,379\,551$ & $4.77$ & $4.67\pm0.10$ + & $43\,090\,114$ & $4.77$ & $4.79\pm0.02$ \\ +Propynal & $^1A'' (\Val; n \ra \pis)$ & $48\,945\,252$ & $3.90$ & $3.84\pm0.06$ + & $28\,249\,344$ & $3.92$ & $3.89\pm0.03$ \\ + & $^1A'' (\Val; \pi \ra \pis)$ & $26\,554\,616$ & $5.72$ & $5.64\pm0.08$ + & $28\,249\,344$ & $5.72$ & $5.63\pm0.09$ \\ + & $^3A'' (\Val; n \ra \pis)$ & $23\,182\,284$ & $3.58$ & $3.54\pm0.04$ \\ + & $^3A' (\Val; \pi \ra \pis)$ & $39\,375\,360$ & $4.52$ & $4.44\pm0.08$ \\ +Thioacetone & $^1A_2 (\Val; n \ra \pis)$ & $26\,515\,070$ & $2.56$ & $2.61\pm0.05$ \\ +% & $^1B_2 (\Ryd; n \ra 4s)$ & $??$ & $??$ & $5.60\pm0.04$ \\ +% & $^1A_1 (\Val; \pi \ra \pis)$ & $$ & $$ & $$ \\ +% & $^1A_1 (\Ryd; n \ra 4p)$ & $$ & $$ & $$ \\ +% & $^1B_2 (\Ryd; n \ra 4p)$ & $$ & $$ & $$ \\ + & $^3A_2 (\Val; n \ra \pis)$ & $63\,669\,401$ & $2.36$ & $2.36\pm0.00$ \\ +% & $^3A_1 (\Val; \pi \ra \pis)$ & $$ & $$ & $$ \\ +Thiopropynal & $^1A'' (\Val; n \ra \pis)$ & $15\,782\,429$ & $2.07$ & $2.08\pm0.01$ \\ +% & $^3A'' (\Val; n \ra \pis)$ & $$ & $$ & $$ \\ +\end{longtable} +\end{footnotesize} +\begin{flushleft}\begin{footnotesize} +%$^a${CI convergence too slow to provide reliable estimate.} +\end{footnotesize}\end{flushleft} + +\end{landscape} + +\clearpage + +\section{Benchmarks} + +\subsection{Raw data} + +\subsection{MSE determined for the subsets} + +\begin{table}[htp] +\caption{MSE in eV obtained for various subsets of transition energies.} +\label{Table-SI-b2} +\begin{tabular}{lcccccc} +\hline +Method & Singlet & Triplet & Valence & Rydberg & $n\rightarrow\pi^\star$ & $\pi\rightarrow\pi^\star$ \\ +\hline +CIS(D) &0.10 &0.25 &0.24 &-0.05 &0.19 &0.28 \\ +{\AD} &-0.04 &0.08 &0.06 &-0.13 &-0.04 &0.14 \\ +{\CCD} &-0.03 &0.11 &0.10 &-0.17 &0.01 &0.17 \\ +{\STEOM} &0.06 &-0.07 &-0.04 &0.12 &-0.02 &-0.07 \\ + {\CCSD} &0.15 &0.04 &0.12 &0.09 &0.19 &0.06 \\ +CCSDR(3) &0.05 & &0.07 &0.02 &0.08 &0.06 \\ +CCSDT-3 &0.05 & &0.06 &0.03 &0.08 &0.04 \\ +{\CCT} &0.00 &0.01 &0.01 &0.00 &0.00 &0.01 \\ +\hline + \end{tabular} + \end{table} + + +\clearpage + +\section{Geometries} + +Below are given the cartesian coordinates of the compounds investigated in this study. +These are provided in atomic units (bohr) and they have been obtained at the \CC{3}(full)/{\AVTZ} level of theory. + +\subsection{Acetone} + +\begin{singlespace} +\begin{verbatim} +C 0.00000000 0.00000000 0.18807702 +C 0.00000000 2.42007545 -1.31764698 +C 0.00000000 -2.42007545 -1.31764698 +O 0.00000000 0.00000000 2.48269094 +H 0.00000000 4.03690733 -0.05185132 +H 0.00000000 -4.03690733 -0.05185132 +H 1.66061256 2.48420530 -2.53995285 +H -1.66061256 2.48420530 -2.53995285 +H 1.66061256 -2.48420530 -2.53995285 +H -1.66061256 -2.48420530 -2.53995285 +\end{verbatim} +\end{singlespace} + + +\subsection{Acrolein} + +\begin{singlespace} +\begin{verbatim} +C -1.11645072 -0.68348783 0.00000000 +C 1.20647847 0.83714564 0.00000000 +C 3.46831059 -0.28872636 0.00000000 +O -3.23666415 0.19187203 0.00000000 +H -0.80613858 -2.74747338 0.00000000 +H 0.98699813 2.86613511 0.00000000 +H 5.20930864 0.77443560 0.00000000 +H 3.60951559 -2.33000749 0.00000000 +\end{verbatim} +\end{singlespace} + +\clearpage + +\subsection{Benzene} + +\begin{singlespace} +\begin{verbatim} +C 0.00000000 2.63144965 0.00000000 +C -2.27890225 1.31572483 0.00000000 +C -2.27890225 -1.31572483 0.00000000 +C 0.00000000 -2.63144965 0.00000000 +C 2.27890225 -1.31572483 0.00000000 +C 2.27890225 1.31572483 0.00000000 +H -4.04725813 2.33668557 0.00000000 +H -4.04725813 -2.33668557 0.00000000 +H -0.00000000 -4.67337115 0.00000000 +H 4.04725813 -2.33668557 0.00000000 +H 4.04725813 2.33668557 0.00000000 +H 0.00000000 4.67337115 0.00000000 +\end{verbatim} +\end{singlespace} + +\subsection{Butadiene} + +\begin{singlespace} +\begin{verbatim} +C 1.14656244 0.00000000 0.75468820 +C -1.14656244 0.00000000 -0.75468820 +C 3.48132647 0.00000000 -0.22482805 +C -3.48132647 0.00000000 0.22482805 +H 0.90770978 0.00000000 2.78883925 +H -0.90770978 0.00000000 -2.78883925 +H 3.77525814 0.00000000 -2.24895470 +H -3.77525814 0.00000000 2.24895470 +H 5.13664967 0.00000000 0.96861890 +H -5.13664967 0.00000000 -0.96861890 +\end{verbatim} +\end{singlespace} + +\subsection{Cyanoacetylene} + +\begin{singlespace} +\begin{verbatim} +C 0.00000000 0.00000000 -3.59120182 +C 0.00000000 0.00000000 -1.30693904 +C 0.00000000 0.00000000 1.28880240 +N 0.00000000 0.00000000 3.48692211 +H 0.00000000 0.00000000 -5.59619886 +\end{verbatim} +\end{singlespace} + +\clearpage + +\begin{singlespace} +\noindent Lowest excited state +\begin{verbatim} +C 1.99411175 0.00000000 2.81781077 +C -0.07304269 0.00000000 1.33125774 +C -0.63630126 0.00000000 -1.14556678 +N -1.39755756 0.00000000 -3.26154643 +H 1.90749857 0.00000000 4.87279180 +\end{verbatim} +\end{singlespace} + +\subsection{Cyanoformaldehyde} + +\begin{singlespace} +\begin{verbatim} +C -0.91561483 0.00000000 -1.22522833 +C -0.01092219 0.00000000 1.39523175 +N 0.64170259 0.00000000 3.48820325 +O 0.50833684 0.00000000 -3.00337867 +H -2.97202213 0.00000000 -1.42565674 +\end{verbatim} +\end{singlespace} + + +\subsection{Cyanogen} + +\begin{singlespace} +Ground state +\begin{verbatim} +C 0.00000000 0.00000000 1.30401924 +C 0.00000000 0.00000000 -1.30401924 +N 0.00000000 0.00000000 3.49784121 +N 0.00000000 0.00000000 -3.49784121 +\end{verbatim} +\end{singlespace} + +\begin{singlespace} +\noindent Lowest excited state +\begin{verbatim} +C 0.00000000 0.00000000 1.22784115 +C 0.00000000 0.00000000 -1.22784115 +N 0.00000000 0.00000000 3.56462559 +N 0.00000000 0.00000000 -3.56462559 +\end{verbatim} +\end{singlespace} + +\clearpage + + +\subsection{Cyclopentadiene} + +\begin{singlespace} +\begin{verbatim} +C 0.00000000 0.00000000 -2.33113051 +C 0.00000000 2.22209092 -0.56871188 +C 0.00000000 -2.22209092 -0.56871188 +C 0.00000000 1.38514451 1.83772922 +C 0.00000000 -1.38514451 1.83772922 +H 1.66130504 0.00000000 -3.56414299 +H -1.66130504 0.00000000 -3.56414299 +H 0.00000000 4.16550405 -1.18116624 +H 0.00000000 -4.16550405 -1.18116624 +H 0.00000000 2.54514584 3.51352303 +H 0.00000000 -2.54514584 3.51352303 +\end{verbatim} +\end{singlespace} + +\subsection{Cyclopropenone} + +\begin{singlespace} +\begin{verbatim} +C 0.00000000 1.27491826 -1.86930519 +C 0.00000000 -1.27491826 -1.86930519 +C 0.00000000 0.00000000 0.51814554 +O 0.00000000 0.00000000 2.79326776 +H 0.00000000 2.92791371 -3.05679837 +H 0.00000000 -2.92791371 -3.05679837 +\end{verbatim} +\end{singlespace} + +\subsection{Cyclopropenethione} + +\begin{singlespace} +\begin{verbatim} +C 0.00000000 1.26230744 -2.86571925 +C 0.00000000 -1.26230744 -2.86571925 +C 0.00000000 0.00000000 -0.49233236 +S 0.00000000 0.00000000 2.57821680 +H 0.00000000 2.97773331 -3.95114059 +H 0.00000000 -2.97773331 -3.95114059 +\end{verbatim} +\end{singlespace} + +\clearpage + +\subsection{Diacetylene} + +\begin{singlespace} +\begin{verbatim} +C 0.00000000 0.00000000 1.29447700 +C 0.00000000 0.00000000 -1.29447700 +C 0.00000000 0.00000000 3.58448429 +C 0.00000000 0.00000000 -3.58448429 +H 0.00000000 0.00000000 5.58943003 +H 0.00000000 0.00000000 -5.58943003 +\end{verbatim} +\end{singlespace} + +\subsection{Furan} + +\begin{singlespace} +\begin{verbatim} +C 0.00000000 2.06365826 -0.60051250 +C 0.00000000 -2.06365826 -0.60051250 +C 0.00000000 1.35348578 1.86336416 +C 0.00000000 -1.35348578 1.86336416 +O 0.00000000 0.00000000 -2.13945332 +H 0.00000000 3.86337287 -1.53765695 +H 0.00000000 -3.86337287 -1.53765695 +H 0.00000000 2.59168789 3.47168051 +H 0.00000000 -2.59168789 3.47168051 +\end{verbatim} +\end{singlespace} + + +\subsection{Glyoxal} + +\begin{singlespace} +\begin{verbatim} +C 1.21360282 0.75840215 0.00000000 +C -1.21360282 -0.75840215 0.00000000 +O 3.25581408 -0.26453186 0.00000000 +O -3.25581408 0.26453186 0.00000000 +H 0.96135276 2.81883243 0.00000000 +H -0.96135276 -2.81883243 0.00000000 +\end{verbatim} +\end{singlespace} + +\clearpage + + +\subsection{Imidazole} + +\begin{singlespace} +\begin{verbatim} +C 0.41662795 2.06006259 0.00000000 +C -1.52618386 -1.62343163 0.00000000 +C 1.04160471 -1.93007427 0.00000000 +N -1.90345764 0.94914956 0.00000000 +N 2.24215443 0.38083431 0.00000000 +H 0.65501634 4.07748278 0.00000000 +H -3.57500545 1.84103166 0.00000000 +H -3.06363894 -2.94559167 0.00000000 +H 2.08673940 -3.67001102 0.00000000 +\end{verbatim} +\end{singlespace} + + +\subsection{Isobutene} + +\begin{singlespace} +\begin{verbatim} +C 0.00000000 0.00000000 2.70790758 +C 0.00000000 0.00000000 0.18431282 +C 0.00000000 2.39894572 -1.32482735 +C 0.00000000 -2.39894572 -1.32482735 +H 0.00000000 1.74848405 3.76691310 +H 0.00000000 -1.74848405 3.76691310 +H 0.00000000 4.05897160 -0.10582007 +H 0.00000000 -4.05897160 -0.10582007 +H 1.66026992 2.48337908 -2.55086178 +H -1.66026992 2.48337908 -2.55086178 +H 1.66026992 -2.48337908 -2.55086178 +H -1.66026992 -2.48337908 -2.55086178 +\end{verbatim} +\end{singlespace} + + +\subsection{Methylenecyclopropene} + +\begin{singlespace} +\begin{verbatim} +C 0.00000000 0.00000000 0.53512883 +C 0.00000000 0.00000000 3.04739824 +C 0.00000000 1.25042956 -1.88571561 +C 0.00000000 -1.25042956 -1.88571561 +H 0.00000000 2.96887531 -2.96270271 +H 0.00000000 -2.96887531 -2.96270271 +H 0.00000000 1.75335023 4.08608382 +H 0.00000000 -1.75335023 4.08608382 +\end{verbatim} +\end{singlespace} + + +\subsection{Propynal} + +\begin{singlespace} +\begin{verbatim} +C -0.78051115 0.00000000 -1.38900384 +C -0.17873562 0.00000000 1.27825868 +C 0.23763714 0.00000000 3.52644798 +O 0.80143996 0.00000000 -3.04628328 +H -2.80713069 0.00000000 -1.82768750 +H 0.64026209 0.00000000 5.48853193 +\end{verbatim} +\end{singlespace} + +\subsection{Pyrazine} + +\begin{singlespace} +\begin{verbatim} +C 1.31510863 2.13188686 0.00000000 +C 1.31510863 -2.13188686 0.00000000 +C -1.31510863 2.13188686 0.00000000 +C -1.31510863 -2.13188686 0.00000000 +N 2.66620111 0.00000000 0.00000000 +N -2.66620111 0.00000000 0.00000000 +H 2.35234226 3.88751412 0.00000000 +H 2.35234226 -3.88751412 0.00000000 +H -2.35234226 3.88751412 0.00000000 +H -2.35234226 -3.88751412 0.00000000 +\end{verbatim} +\end{singlespace} + +\subsection{Pyridazine} + +\begin{singlespace} +\begin{verbatim} +C 0.00000000 1.30150855 -2.31552865 +C 0.00000000 -1.30150855 -2.31552865 +C 0.00000000 2.49271907 0.03513416 +C 0.00000000 -2.49271907 0.03513416 +N 0.00000000 1.26228251 2.23104685 +N 0.00000000 -1.26228251 2.23104685 +H 0.00000000 4.52804172 0.19299731 +H 0.00000000 -4.52804172 0.19299731 +H 0.00000000 2.39011496 -4.03967703 +H 0.00000000 -2.39011496 -4.03967703 +\end{verbatim} +\end{singlespace} + +\subsection{Pyridine} + +\begin{singlespace} +\begin{verbatim} +C 0.00000000 0.00000000 -2.66451139 +C 2.25494985 0.00000000 -1.32069889 +C -2.25494985 0.00000000 -1.32069889 +C 2.15398594 0.00000000 1.30669632 +C -2.15398594 0.00000000 1.30669632 +N 0.00000000 0.00000000 2.62778932 +H 0.00000000 0.00000000 -4.70641516 +H 4.05768507 0.00000000 -2.27625442 +H -4.05768507 0.00000000 -2.27625442 +H 3.88059079 0.00000000 2.40341581 +H -3.88059079 0.00000000 2.40341581 +\end{verbatim} +\end{singlespace} + +\subsection{Pyrimidine} + +\begin{singlespace} +\begin{verbatim} +C 0.00000000 0.00000000 2.41518350 +C 0.00000000 -0.00000000 -2.60410885 +C 0.00000000 2.23272561 -1.22869402 +C 0.00000000 -2.23272561 -1.22869402 +N 0.00000000 2.26214196 1.29619742 +N 0.00000000 -2.26214196 1.29619742 +H 0.00000000 0.00000000 4.45780256 +H 0.00000000 0.00000000 -4.64120942 +H 0.00000000 4.05149341 -2.16351748 +H 0.00000000 -4.05149341 -2.16351748 +\end{verbatim} +\end{singlespace} + +\subsection{Pyrrole} + +\begin{singlespace} +\begin{verbatim} +C 0.00000000 2.11924634 0.62676569 +C 0.00000000 -2.11924634 0.62676569 +C 0.00000000 1.34568862 -1.85506908 +C 0.00000000 -1.34568862 -1.85506908 +N 0.00000000 0.00000000 2.10934391 +H 0.00000000 0.00000000 4.00257355 +H 0.00000000 3.97648410 1.44830201 +H 0.00000000 -3.97648410 1.44830201 +H 0.00000000 2.56726559 -3.47837232 +H 0.00000000 -2.56726559 -3.47837232 +\end{verbatim} +\end{singlespace} + +\subsection{Tetrazine} + +\begin{singlespace} +\begin{verbatim} +C 0.00000000 0.00000000 2.38208164 +C 0.00000000 0.00000000 -2.38208164 +N 2.25673244 0.00000000 1.24973261 +N -2.25673244 0.00000000 1.24973261 +N 2.25673244 0.00000000 -1.24973261 +N -2.25673244 0.00000000 -1.24973261 +H 0.00000000 0.00000000 4.41850901 +H 0.00000000 0.00000000 -4.41850901 +\end{verbatim} +\end{singlespace} + + +\subsection{Thioacetone} + +\begin{singlespace} +\begin{verbatim} +C 0.00000000 0.00000000 0.68476030 +C 0.00000000 2.38541696 2.20685096 +C 0.00000000 -2.38541696 2.20685096 +S 0.00000000 0.00000000 -2.39920303 +H 0.00000000 4.04609254 1.00090614 +H 0.00000000 -4.04609254 1.00090614 +H 1.65894780 2.42602225 3.43712000 +H -1.65894780 2.42602225 3.43712000 +H 1.65894780 -2.42602225 3.43712000 +H -1.65894780 -2.42602225 3.43712000 +\end{verbatim} +\end{singlespace} + +\subsection{Thiophene} + +\begin{singlespace} +\begin{verbatim} +C 0.00000000 2.33342542 -0.09858421 +C 0.00000000 -2.33342542 -0.09858421 +C 0.00000000 1.34371718 -2.48297725 +C 0.00000000 -1.34371718 -2.48297725 +S 0.00000000 0.00000000 2.17250692 +H 0.00000000 4.29028016 0.44577296 +H 0.00000000 -4.29028016 0.44577296 +H 0.00000000 2.48760051 -4.16768392 +H 0.00000000 -2.48760051 -4.16768392 +\end{verbatim} +\end{singlespace} + +\subsection{Thiopropynal} + +\begin{singlespace} +\begin{verbatim} +C -0.00382924 0.00000000 -1.25249909 +C -2.27832423 0.00000000 0.15152736 +C -4.26309583 0.00000000 1.29548793 +S 2.81920288 0.00000000 -0.00828974 +H -0.23056990 0.00000000 -3.28862183 +H -5.97712967 0.00000000 2.33206931 +\end{verbatim} +\end{singlespace} + + +\subsection{Triazine} + +\begin{singlespace} +\begin{verbatim} +C 0.00000000 -2.11414732 -1.22060353 +C 0.00000000 0.00000000 2.44120705 +C 0.00000000 2.11414732 -1.22060353 +N 0.00000000 -2.24624733 1.29687150 +N 0.00000000 2.24624733 1.29687150 +N 0.00000000 0.00000000 -2.59374300 +H 0.00000000 3.88296710 -2.24183210 +H 0.00000000 -3.88296710 -2.24183210 +H 0.00000000 0.00000000 4.48366420 +\end{verbatim} +\end{singlespace} + + +\clearpage + +\section{Benchmark} + + +\end{document} + diff --git a/Manuscript/FCI2.tex b/Manuscript/FCI2.tex index 52e8223..c9c22d1 100644 --- a/Manuscript/FCI2.tex +++ b/Manuscript/FCI2.tex @@ -1,765 +1,1518 @@ -\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} -\usepackage[version=4]{mhchem} - -\usepackage[normalem]{ulem} - -\definecolor{darkgreen}{RGB}{0, 180, 0} -\newcommand{\titou}[1]{\textcolor{purple}{#1}} -\newcommand{\beurk}[1]{\textcolor{darkgreen}{#1}} -\newcommand{\trash}[1]{\textcolor{purple}{\sout{#1}}} - - -\newcommand{\mc}{\multicolumn} -\newcommand{\mr}{\multirow} - -% energies -\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)$} - -% methods -\newcommand{\TDDFT}{TD-DFT} -\newcommand{\CASSCF}{CASSCF} -\newcommand{\CASPT}{CASPT2} -\newcommand{\NEV}{NEVPT2} -\newcommand{\PNEV}{PC-NEVPT2} -\newcommand{\SNEV}{SC-NEVPT2} -\newcommand{\AD}{ADC(2)} -\newcommand{\AT}{ADC(3)} -\newcommand{\CCD}{CC2} -\newcommand{\CCSD}{CCSD} -\newcommand{\CCT}{CC3} -\newcommand{\EOMCCSD}{EOM-CCSD} -\newcommand{\CCSDT}{CCSDT} -\newcommand{\CCSDTQ}{CCSDTQ} -\newcommand{\CCSDTQP}{CCSDTQP} -\newcommand{\CI}{CI} -\newcommand{\sCI}{sCI} -\newcommand{\exCI}{exCI} -\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{\AVFZ}{\emph{aug}-cc-pV5Z} -\newcommand{\DAVQZ}{d-\emph{aug}-cc-pVQZ} -\newcommand{\TAVQZ}{t-\emph{aug}-cc-pVQZ} -\newcommand{\AVPZ}{\emph{aug}-cc-pV5Z} -\newcommand{\DAVPZ}{d-\emph{aug}-cc-pV5Z} - -% units -\newcommand{\IneV}[1]{#1 eV} -\newcommand{\InAU}[1]{#1 a.u.} -\newcommand{\InAA}[1]{#1 \AA} - -% greek shortcut -\newcommand{\pis}{\pi^\star} -\newcommand{\Ryd}{\mathrm{R}} - -\newcommand{\SI}{Supporting Information} - -\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} - -\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} -\begin{abstract} -Following our previous work focussed on compounds containing 1--3 non-hydrogen atoms [\emph{J. Chem. Theory Comput.} {\bfseries 14} (2018) 4360--4379], we present highly-accurate vertical transition energies -obtained for molecules encompassing 4, 5, and 6 non-hydrogen atoms, namely: \hl{complete alphabetic list here}. -To obtain these energies, we use both Coupled-Cluster approaches up to the highest possible order ({\CCT}, {\CCSDT}, and {\CCSDTQ}), the selected Configuration Interaction approach up to several millions determinants, -and the $N$-Electron Valence State Perturbation Theory (NEVPT2), all approaches being combined with a diffuse-containing atomic basis sets. For all states, we report at least {\CCT}/{\AVQZ} transition -energies and as well as {\CCT}/{\AVTZ} oscillator strengths for all dipole-allowed transitions. \hl{xxx nb and nature of states xxx}. We show that {\CCT} almost systematically delivers transition energies -very close to the theoretical best estimates ($\pm$ 0.04 eV) but for transitions presenting a dominant double excitation character. We use a series of \hl{xxxx} theoretical best estimates to benchmark a series of popular -methods for excited state calculations [CIS(D), {\CCD}, STEOM-CCSD, {\CCSD}, CCSDR(3), {\AD}, and {\AT})] \hl{xxxxx}. The results of these benchmarks are compared to available literature data. -\end{abstract} -\clearpage - -% -% I. Introduction -% -\section{Introduction} - -Accurately describing transition energies between the electronic ground state (GS) and excited states (ES) remains an important challenge in quantum chemistry. When dealing with large compounds in complex environments, -one is typically limited to the use of Time-Dependent Density Functional Theory (TD-DFT), \cite{Cas95,Ulr12b,Ada13a} which is a successful, yet far from flawless, theory. In particular, to perform TD-DFT calculations, one needs -to choose an ``appropriate'' exchange-correlation functional (XCF), which is difficultas the impact of the XCF on the results is exacerbated in TD-DFT as compared to DFT. \cite{Lau13} Such selection can of course rely -on the intrinsic features of each XCF, e.g., it is well-known that range-separated hybrids provide a more physically-sound description of long-range charge-transfer (CT) transitions than semi-local XCF. \cite{Dre04,Pea08} -However, to obtain a quantitative assessment of the accuracy that can be expected from TD-DFT calculations, benchmarks are needed. This is why many assessment of TD-DFT performances for various properties are -available. \cite{Lau13} While several of these benchmarks use experimental data as reference, typically band shapes \cite{Die04,Die04b,Avi13,Cha13,Lat15b,Mun15,Vaz15,San16b} or 0-0 energies, -\cite{Die04b,Goe10a,Jac12d,Chi13b,Win13,Fan14b,Jac14a,Jac15b,Loo19b} using theoretical best estimates (TBE) obtained with a more refined level of theory as references, \cite{Sch08,Sau09,Sil10b,Sil10c,Sch17,Loo18a} -is advantageous as it allows comparisons on a perfectly equal footing (same geometry, vertical transitions, no environmental effects...). However, obtaining accurate TBE is not an easy task as high-level theories -generally come with a dreadful scaling with system size and, additionally, typically require large atomic basis sets to deliver transition energies close to the basis set limit. - -More than 20 years ago, Serrano-Andr\`es, Roos, and their coworkers proposed an impressive series of reference transition energies for several typical conjugated organic molecules (butadiene, furan, pyrrole, tetrazine...). -\cite{Ser93,Ser93b,Ser93c,Mer96,Mer96b,Roo96,Ser96b} To this end, they relied on the Complete Active Space Second-Order Perturbation Theory ({\CASPT}) approach with the largest active spaces and basis sets -they could offer at that time, and they typically used experimental GS geometries. Beyond comparisons with experiments, which are always challenging when computing vertical transition energies, \cite{San16b} there was no approach -available at that time to ascertain the accuracy of the obtained transition energies. These {\CASPT} values were latter used to assess the performances of TD-DFT combined with various XCF, \cite{Toz99b,Bur02} and remained for a long -time the best references available. A decade ago, Thiel and coworkers defined TBE for 104 singlet and 63 triplet valence ES in 28 small and medium conjugated CNOH organic molecules. \cite{Sch08,Sil10b,Sil10c} These TBE -were computed on MP2/6-31G(d) structures with various levels of theories, notably {\CASPT} and various Coupled-Cluster levels ({\CCD}, {\CCSD}, and {\CCT}). Interestingly, while the default reference approach used by Thiel for his -first series of TBE was {\CASPT}, \cite{Sch08} the majority of the most recent TBE (so-called ``TBE-2'' in Ref. \citenum{Sil10c}) were determined at the {\CCT}/{\AVTZ} level, often using a basis set extrapolation technique to obtain these -estimates. In more details, CC3/TZVP values were typically corrected for basis set effects by the difference between {\CCD}/{\AVTZ} and {\CCD}/TZVP results. \cite{Sil10b,Sil10c} Many works used Thiel's TBE for -assessing low-order methods, \cite{Sil08,Goe09,Jac09c,Roh09,Sau09,Jac10c,Jac10g,Sil10,Mar11,Jac11a,Hui11,Del11,Tra11,Pev12,Dom13,Dem13,Sch13b,Voi14,Har14,Yan14b,Sau15,Pie15,Taj16,Mai16,Ris17,Dut18} highlighting -their value for the community. In contrast, the number of extensions of this original set remains quite limited, e.g., {\CCSDT}/TZVP reference energies computed for 17 singlet states of six molecules appeared in 2014, \cite{Kan14} -and 46 {\CCSDT}/{\AVTZ} transition energies in small compounds containing two or three non-hydrogen atoms (ethylene, acetylene, formaldehyde, formaldimine, and formamide) have been described in 2017. \cite{Kan17} -This has motivated us to propose in 2018 a set of 106 transition energies for which it was technically possible to reach the Full Configuration Interaction (FCI) limit by combining high-order Coupled-Cluster (up to {\CCSDTQP}) and selected -CI (sCI) transition energy calculations on {\CCT} GS structures. \cite{Loo18a} We used these TBE to benchmark many ES theories. \cite{Loo18a} Amongst our conclusions, we found that {\CCSDTQ} was on the {\FCI} spot, whereas we could not -detect significant differences of accuracies between {\CCT} and {\CCSDT}, both being very accurate with mean absolute errors (MAE) as small as 0.03 eV compared to {\FCI} for ES with a single excitation character. These conclusions -agree well with earlier studies. \cite{Wat13,Kan14,Kan17} We also recently proposed a set of 20 TBE for transitions presenting a large double excitation character. \cite{Loo19c} For such transitions, one can distinguish the ES -as a function of $\%T_1$, the percentage of single excitation calculated at the {\CCT} level. For ES with a significant yet not dominant double excitation character, such as the famous $A_g$ ES of butadiene ($\%T_1$=75\%), -CC methods including triples in the GS treatment deliver rather accurate estimates (MAE of 0.11 eV with {\CCT} and 0.06 eV with {\CCSDT}), surprisingly outperforming second-order multi-reference schemes such as {\CASPT} or -the generally robust $N$-Electron Valence State Perturbation Theory ({\NEV}). In contrast, for ES with a dominant double excitation character, e.g., the low-lying $n,n \rightarrow \pi^\star,\pi^\star$ excitation in nitrosomethane ($\%T_1$=2\%), -single-reference methods are not suited (MAE of 0.86 eV with {\CCT} and 0.42 eV with {\CCSDT} and multi-reference methods are in practice required to obtain accurate results. \cite{Loo19c} In Ref. \citenum{Loo18a} we also reported a relatively -limited accuracy of the third-order Algebraic Diagrammatic Construction scheme [{\AT}] and larger errors with {\CCD} than with {\CCSD} for the set of 106 single-excitation TBE, both results being in par with previously published -conclusions. \cite{Sch08,Sau09,Har14} Obviously, a possible origin of these discrepancies is that we treated only compounds containing 1--3 non-hydrogen atoms, hence introducing a significant chemical bias. Therefore we have decided to -go for larger molecules and we consider in the present contribution organic compounds encompassing 4, 5, and 6 non-hydrogen atoms. For such systems, performing {\CCSDTQ} calculations with large bases remains a dream, and, -the convergence of {\sCI} with the number of determinants is slower, so that extrapolating to the {\FCI} limit with a ca. 0.01 eV error bar is also rarely doable in practice. Consequently, the ``brute-force'' determination of {\FCI}/CBS estimates, -as in our earlier work,\cite{Loo18a} is beyond reach. Anticipating this problem, we have previously demonstrated that one can very accurately estimate such limit by correcting values obtained with a high-level of theory and a double-$\zeta$ -basis set by {\CCT} results obtained with a larger basis, \cite{Loo18a} and we follow such strategy here. In addition, we also performed {\NEV} calculations in an effort to check the consistency of our estimates, especially for ES with -intermediate $\%T_1$ values. Using this protocol, we define a set of \hl{xxxxxxxx} {\AVTZ} reference transition energies, most being within $\pm$ 0.03 eV for the {\FCI} limit. These reference energies are obtained on {\CCT} geometries and -further basis set corrections at least up to quadruple-$\zeta$, are also provided with {\CCT}. Together with the results obtained in our two earlier works, \cite{Loo18a,Loo19c} the present TBE will hopefully contribute to reach a further step -on the accuracy staircase. - -% -% II. Computational Details -% -\section{Computational Details} -\label{sec-met} - -All our transition energies are computed in the frozen-core approximation (large cores for S), except when noted, and we globally follow the same procedure as in Ref. \citenum{Loo18a}, so that we only briefly outline the models used below. - -\subsection{Geometries} - -Consistently with our previous work, \cite{Loo18a} we systematically use {\CCT}/{\AVTZ} GS geometries (obtained without applying the frozen core approximation). Cartesian coordinates for all compounds can be found in the Supporting -Information (SI). Some structures have been taken from previous contributions, \cite{Bud17,Jac18a,Bre18a} whereas we performed additional optimizations using Dalton \cite{dalton} and/or CFOUR, \cite{cfour} applying default parameters -in both cases, to obtain the missing structures. - -\subsection{Selected Configuration Interaction methods} - -All the sCI calculations have been performed in the frozen-core approximation with a new version of Quantum Package \cite{Gar19} using the Configuration Interaction using a Perturbative Selection made Iteratively (CIPSI) algorithm to select the -most important determinants in the FCI space. Instead of generating all possible excited determinants like a conventional CI calculation, the iterative CIPSI algorithm performs a sparse exploration of the FCI space via a selection of the most relevant -determinants using a second-order perturbative criterion. At each iteration, the variational (or reference) space is enlarged with new determinants. CIPSI can be seen as a deterministic version of the FCIQMC algorithm developed by Alavi and -coworkers. \cite{Alavi} We refer the interested reader to Ref.~\citenum{Gar19} where our implementation of the CIPSI algorithm is detailed. - -Excited-state calculations are performed within a state-averaged formalism which means that the CIPSI algorithm select determinants simultaneously for the GS and ES. Therefore, all electronic states share the same set of determinants with different CI coefficients. -Our implementation of the CIPSI algorithm for ES is detailed in Ref.~\citenum{Sce19}. For each system, a preliminary sCI calculation is performed using Hartree-Fock orbitals in order to generate sCI wave functions with at least 5,000,000 determinants. -State-averaged natural orbitals are then computed based on this wave function, and a new, larger sCI calculation is performed with this new set of orbitals. This has the advantage to produce a smoother and faster convergence of the sCI energy to the FCI limit. -For the largest systems (5 and 6-membered rings), an additional iteration is sometimes required in order to obtain better quality natural orbitals and hence well-converged calculations. - -The total sCI energy is defined as the sum of the (zeroth-order) variational energy (computed via diagonalization of the CI matrix in the reference space) and a second-order perturbative correction which takes into account the external determinants, i.e., -the determinants which do not belong to the variational space but are linked to the reference space via a non-zero matrix element. The magnitude of this second-order correction $E^{(2)}$ provides a qualitative idea of the "distance" to the FCI limit. -For maximum efficiency, the total sCI energy is linearly extrapolated to $E^{(2)} = 0$ (which effectively corresponds to the FCI limit) using the two largest sCI wave functions. These extrapolated total energies (labeled as exFCI in the remaining of the paper) -are then used to computed vertical excitation energies. Although it is not possible to provide a theoretically-sound error bar, we estimate the extrapolation error by the difference in excitation energy between the largest sCI wave function and its corresponding -extrapolated value. More theoretical and technical details about our extrapolation procedure can be found in Ref.~\citenum{Gar19}. Additional information about the sCI wave functions and excitation energies as well as their extrapolated values can be found in the SI. - - -\subsection{NEVPT2} - - -\hl{Martial: you to play} - -In the following, {\NEV} stands systematically for {\PNEV}. + active space in the SI ? - - -\subsection{Other Wavefunction calculations} - -For the other levels of theory, we apply a variety of programs, namely, CFOUR,\cite{cfour} Dalton,\cite{dalton} Gaussian,\cite{Gaussian16} Orca,\cite{Nee12} MRCC,\cite{Rol13,mrcc} and Q-Chem. \cite{Sha15} CFOUR is used for - {\CCT}, \cite{Chr95b,Koc97} CCSDT-3, \cite{Wat96,Pro10} {\CCSDT} \cite{Nog87} and {\CCSDTQ}\cite{Kuc91}; Dalton for {\CCD}, \cite{Chr95,Hat00} {\CCSD},\cite{Pur82} CCSDR(3), \cite{Chr96b} and {\CCT} \cite{Chr95b,Koc97}; Gaussian -for CIS(D); \cite{Hea94,Hea95} Orca for the similarity-transformed EOM-CCSD (STEOM-CCSD)\cite{Noo97,Dut18}; MRCC for {\CCSDT} \cite{Nog87} and {\CCSDTQ}; \cite{Kuc91} and Q-Chem for {\AD} and {\AT}. \cite{Dre15} -Default program setting are applied. We underline that for the STEOM-CCSD we report only states that are characterized by an active character percentage of 98\%\ or larger. For all calculations, we use Pople's {\Pop} as well as -the well-known Dunning's \emph{aug}-cc-pVXZ (X $=$ D, T, Q, and 5) atomic basis sets. - -% -% III. Results & Discussion -% -\section{Results} -\label{sec-res} - -In the following, we present the results obtained for molecules containing four, five, and six (non-hydrogen) atoms. In all cases, we test several atomic basis sets and push the CC expansion as far as technically doable. -Given that the {\sCI} results converges rather slowly for these rather large systems, we provide an error bar for these extrapolated {\FCI} values. In most cases, the latter are used as a safety net to demonstrate the -consistency of the approaches rather than as definitive TBE (see next Section). We also show the results {\NEV}/{\AVTZ} calculations for all relevant states to have a further consistency check. We underline that, except -when specifically discussed, all ES present a dominant single-excitation character (see also next Section), so that we do not expect serious CC breakdowns. This is especially true for the triplet ES that are known to show -an ultra-large \%$T_1$, \cite{Sch08} and we consequently put our maximal computational effort on determining accurate transition energies for singlet states. To assign the different ES, we used literature data, as well as -usual criteria, i.e., relative energies, symmetries and compositions of the underlying MOs, as well as oscillator strengths. This allowed clear-cut assignment for the vast majority of the cases. There are however some -state/method combination for which strong mixing between ES of the same symmetry makes unambiguous assignments beyond reach, which is a typical problem in such calculation. Such cases are however not statistically -relevant and are therefore unlikely to change our conclusions. - -\subsection{Four-atom molecules} - -\subsubsection{Cyanoacetylene, cyanogen, and diacetylene} - -The ES of these three closely-related linear molecules containing two triple bonds have been quite rarely investigated with theory, \cite{Fis03,Pat06,Luo08,Loo18b,Loo19a} though (rather old) measurements of their -0-0 energies are available for several excited states. \cite{Cal63,Job66a,Job66b,Bel69,Fis72,Har77,Hai79,All84} Our main results are collected in Tables \ref{Table-1} and S1 in the SI. We consider only low-lying -valence $\pi \rightarrow \pi^\star$ transitions, and, all have a strongly dominant single excitation character (\%$T_1 > 90$, \emph{vide infra}). For cyanoacetylene, the {\FCI} estimates come with small error bars -with {\Pop} and one notes an excellent agreement between these values and their {\CCSDTQ} counterparts, a statement holding for the Dunning's double-$\zeta$ basis for which the {\FCI} errors bars are however -larger. Using the {\CCSDTQ} values as references, it appears that the previously obtained {\CASPT} estimates\cite{Luo08} are too low and that the {\CCT} transition energies are slightly more accurate than -their CCSDT counterparts, although all CC estimates of Table \ref{Table-1} come in a very tight energetic window for a given basis set . There is also a superb agreement between the CC and {\NEV} values with the -{\AVTZ} basis set. All these facts give high confidence that the CC estimates can be trusted. The basis set effects are quite significant for the valence excited-states of cyanoacetylene with successive drops of the transitions -energies by ca. -0.10 eV, when going from {\Pop} to {\AVDZ} and from {\AVDZ} to {\AVTZ}, but for the lowest triplet state that appears less sensitive to the selected basis. As expected, the changes when further -extending the basis set to quadruple and quintuple-$\zeta$ are trifling, and the same holds when adding a second set of diffuse functions in the basis, or when correlating the core electrons (see the SI). Obviously, -both cyanogen and diacetylene yield very similar trends, with limited methodological effects and quite large basis set effects, but for the transitions to the $^3\Sigma_u^+$ ES. We note that all CC values are, at worst, -within $\pm$ 0.02 eV of the {\exCI} window, i.e., all methods presented in Table \ref{Table-1} provide very consistent estimates. Across all states reported in that Table with {\AVTZ}, the average deviations between {\NEV} and {\CCT} -(or {\CCSDT}) is as small as 0.03 eV, the lowest absorption and emission of cyanogen being the only two cases showing significant deviations. As a final note, all our vertical transition energies are significantly bigger -than the experimentally measured 0-0 energies, as it should. We refer the interested reader to previous works, \cite{Fis03,Loo19a} for comparisons of {\CASPT} and {\CCT} values with measured 0-0 energies -for these linear compounds. - -\begin{sidewaystable}[htp] -\caption{\small Vertical transition energies determined in cyanoacetylene, cyanogen, and diaectylene. All states have a valence $\pi \rightarrow \pi^\star$ character. All values are in eV.} -\label{Table-1} - \begin{footnotesize} -\begin{tabular}{l|p{.5cm}p{1.0cm}p{1.2cm}p{1.4cm}|p{.5cm}p{1.0cm}p{1.2cm}p{1.4cm}|p{.5cm}p{1.0cm}p{1.2cm}|p{.5cm}|p{.5cm}|p{.6cm}p{.6cm}} -\hline - \multicolumn{14}{c}{Cyanoacetylene}\\ - & \multicolumn{4}{c}{\Pop} & \multicolumn{4}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{1}{c}{\AVQZ} & \multicolumn{1}{c}{\AVFZ} & \multicolumn{2}{c}{Litt.}\\ -State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI}& {\CCT} & {\CCSDT} & {\NEV} & {\CCT} & {\CCT}& Th.$^a$ & Exp.$^b$ \\ -\hline -$^1\Sigma^-$ &6.02&6.04&6.02&6.02$\pm$0.01 &5.92&5.92&5.91&5.84$\pm$0.09 &5.80&5.81&5.78& 5.79 &5.79 &5.46&4.77\\ -$^1\Delta$ &6.29&6.31&6.29&6.28$\pm$0.01 &6.17&6.19&6.17&6.14$\pm$0.05 &6.08&6.09&6.10& 6.06 &6.06 &5.81&5.48\\ -$^3\Sigma^+$ &4.44&4.45& &4.45$\pm$0.03 &4.43&4.43& &4.41$\pm$0.06 &4.45&4.44&4.45& 4.46 &4.47 &&\\ -$^3\Delta$ &5.35&5.34& &5.32$\pm$0.03 &5.28&5.27& &5.29$\pm$0.08 &5.22&5.21&5.19& 5.22 &5.22 &&\\ -\hline - \multicolumn{14}{c}{Cyanogen}\\ - & \multicolumn{4}{c}{\Pop} & \multicolumn{4}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{1}{c}{\AVQZ} & \multicolumn{1}{c}{\AVFZ} & \multicolumn{1}{c}{Litt.}\\ -State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI}& {\CCT} & {\CCSDT} & {\NEV}& {\CCT} & {\CCT}& Exp.$^c$ \\ -\hline -$^1\Sigma_u^-$ &6.62&6.63&6.62&6.58$\pm$0.03 &6.52&6.52&6.51&6.44$\pm$0.08 &6.39&6.40&6.32& 6.38 &6.38 &5.63\\ -$^1\Delta_u$ &6.88&6.89&6.88&6.87$\pm$0.02 &6.77&6.78&6.77&6.74$\pm$0.04 &6.66&6.67&6.66& 6.64 &6.64 &5.99\\ -$^3\Sigma_u^+$ &4.92&4.92&4.94&4.91$\pm$0.06 &4.89&4.89& &4.87$\pm$0.07 &4.90&4.89&4.88& 4.91 &4.91 &4.13\\ -$^1\Sigma_u^-$[F]$^d$ &5.27&5.28&5.26&5.21$\pm$0.05 &5.19&5.20&5.18&5.26$\pm$0.09 &5.06&5.07&4.97& 5.05 &5.05 & \\ -\hline - \multicolumn{14}{c}{Diacetylene}\\ - & \multicolumn{4}{c}{\Pop} & \multicolumn{4}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{1}{c}{\AVQZ} & \multicolumn{1}{c}{\AVFZ} & \multicolumn{1}{c}{Litt.}\\ -State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI}& {\CCT} & {\CCSDT} & {\NEV}& {\CCT} & {\CCT}& Exp.$^e$ \\ -\hline -$^1\Sigma_u^-$ &5.57&5.58&5.56&5.52$\pm$0.06 &5.44&5.45&5.43&5.47$\pm$0.02 &5.34&5.35&5.33& 5.33 &5.33 &4.81\\ -$^1\Delta_u$ &5.83&5.85& &5.84$\pm$0.01 &5.69&5.70&5.69&5.69$\pm$0.02 &5.61&5.62&5.61& 5.60 &5.60 &5.06\\ -$^3\Sigma_u^+$ &4.07&4.08&4.09&4.04$\pm$0.07 &4.06&4.06& &4.07$\pm$0.04 &4.08& &4.08& 4.10 &4.11 &2.7 \\ -$^3\Delta_u$ &4.93&4.93&4.92&4.94$\pm$0.01 &4.86&4.85& &4.85$\pm$0.02 &4.80&4.79&4.78& 4.80 &4.80 &3.21\\ -\hline - \end{tabular} - \end{footnotesize} -\begin{flushleft} -\begin{footnotesize} -$^a${{\CASPT} values from Ref. \citenum{Luo08};} -$^b${Experimental 0-0 energies from Refs. \citenum{Job66a} and \citenum{Job66b} (vacuum UV experiments);} -$^c${Experimental 0-0 energies from Refs. \citenum{Cal63} ($^3\Sigma_u^+$), \citenum{Bel69} ($^1\Sigma_u^-$), and \citenum{Fis72} ($^1\Delta_u$), all analyzing vacuum electronic spectra;} -$^d${Vertical fluorescence energy from the lowest excited-state;} -$^e${Experimental 0-0 energies from Ref. \citenum{Hai79} (singlet ES, vacuum UV experiment) and Ref. \citenum{All84} (triplet ES, EELS). In the latter paper, the 2.7 eV value for the $^3\Sigma_u^+$ -state is the onset, whereas an estimate of the vertical energy of 4.2$\pm$0.2 eV is given for the $^3\Delta_u$ state.} -\end{footnotesize} -\end{flushleft} -\end{sidewaystable} - -% -\clearpage -% - -\subsubsection{Cyclopropenone, cyclopropenethione, and methylenecyclopropene} - -These three related compounds present a three-member $sp^2$ carbon cycle conjugated to an external $\pi$ bond. While the ES of methylenecyclopropene has regularly been investigated with theoretical tools in the past, -\cite{Mer96,Roo96,Car10b,Lea12,Gua13,Dad14,Gua14,Sch17,Bud17} the only investigations of vertical transitions we could find for the two other derivatives are the 2002 detailed {\CASPT} study of Serrano-Andr\'es and -coworkers on both compounds, \cite{Ser02} and a more recent work reporting three low-lying singlet states of cyclopropenone at the {\CASPT}/6-31G level.\cite{Liu14b} - -Our results are listed in Tables \ref{Table-2} and S2. As above, considering the Pople's basis set, we note very small differences between {\CCT}, {\CCSDT}, and {\CCSDTQ} results, the latter method giving transition energies -systematically falling within the {\FCI} extrapolation incertitude. Depending on the state, it is either {\CCT} or {\CCSDT} that is the closest to {\CCSDTQ}. In fact, considering all {\CCSDTQ}/{\Pop} data listed in Table \ref{Table-2}, -the mean absolute deviation of {\CCT} and {\CCSDT} are 0.019 and 0.016 eV, respectively, hinting that the improvements brought by the latter more computationally intensive method are limited. For the lowest $B_2$ state of n -methylenecyclopropene, one of the most challenging cases (\%$T_1 = 85$), it is clear from the {\exCI} value that only {\CCSDTQ} is really close to the spot, the {\CCT} and {\CCSDT} results being slightly too large. It seems -likely that the same trends appears for the same state in cyclopropenethione. Interestingly, the quite small Pople basis set provides data within ca. 0.10 eV of basis set convergence at {\CCT} level for 80\%\ of the transitions. -There are of course exceptions to this rule, e.g., the strongly dipole-allowed $^1A_1\ \pi \rightarrow \pi^\star$ ES of cyclopropenone and the $^1B_1\ \pi \rightarrow \sigma^\star$ ES of methylenecyclopropene are significantly too -blueshifted with the Pople's basis set (Table S2). For cyclopropenone, our {\CCSDT}/{\AVTZ} estimates do agree reasonably well with the data of Serrano-Andr\'es, but for the $^1B_2\ \pi \rightarrow \pi^\star$ state that we locate -significantly higher in energy and the three Rydberg states that CC foresees at significantly smaller energies. The current {\NEV} results are globally in better agreement with the CC values, though some non-negligible deviations -pertain. Although comparisons with experiments should be made very cautiously, we note that the CC data are clearly more coherent with the electron impact measurements\cite{Har74} for the Rydberg states. For cyclopropenethione, -we obtain transition energies typically in agreement or larger than those obtained with {\CASPT}, \cite{Ser02} though there is no obvious relationship between the valence/Rydberg nature of the considered ES and the relative -{\CASPT} error. \hl{commenter les NEV} Eventually methylenecyclopropene, our values logically agree very well with the recent estimates of Schwabe and Goerigk, \cite{Sch17} obtained at the {\CCT}/{\AVTZ} level on a different geometry, -whereas the available {\CASPT} values \cite{Mer96,Roo96} appear comparatively too low. For this compound, the available experimental data being wavelength of maximal absorption determined in condensed phase, \cite{Sta84} -only a qualitative match is logically reached between theory and experiment. - -\begin{table}[htp] -\caption{\small Vertical transition energies determined in cyclopropenone, cyclopropenethione, and methylenecyclopropene. All values are in eV.} -\label{Table-2} - \begin{footnotesize} -\begin{tabular}{l|p{.5cm}p{.9cm}p{1.1cm}p{1.4cm}|p{.5cm}p{.9cm}|p{.5cm}p{.9cm}p{1.2cm}|p{.6cm}p{.6cm}p{.6cm}} -\hline - \multicolumn{12}{c}{Cyclopropenone}\\ - & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{2}{c}{Litt.}\\ -State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV} & Th.$^a$ & Exp.$^b$ \\ -\hline -$^1B_1 (n \rightarrow \pi^\star)$ &4.32&4.34&4.36& 4.38$\pm$0.02 &4.22&4.23 &4.21&4.24&4.04 &4.25&4.13 \\%4.50 in Liu14b MS-CASPT2/6-31G -$^1A_2 (n \rightarrow \pi^\star)$ &5.68&5.65&5.65& 5.64$\pm$0.06 &5.59&5.56 &5.57&5.55&5.85 &5.59&5.5 \\%5.18 in Liu14b -$^1B_2 (n \rightarrow 3s)$ &6.39&6.38&6.41& &6.21&6.19 &6.32&6.31&6.51 &6.90&6.22 \\%6.44 in Liu14b -$^1B_2 (\pi \rightarrow \pi^\star$) &6.70&6.67&6.68& &6.56&6.54 &6.54&6.53&6.82 &5.96&6.1 \\ -$^1B_2 (n \rightarrow 3p)$ &6.92&6.91&6.94& &6.88&6.86 &6.96&6.95&7.04 &7.24&6.88 \\ -$^1A_1 (n \rightarrow 3p)$ &7.00&7.00&7.03& &6.88&6.87 &7.00&6.99&7.28 &7.28& \\ -$^1A_1 (\pi \rightarrow \pi^\star)$ &8.51&8.49&8.51& &8.32&8.29 &8.28&8.26&8.19 &7.80&$\sim$8.1 \\ -$^3B_1 (n \rightarrow \pi^\star)$ &4.02&4.03& & 4.00$\pm$0.07 &3.90&3.92 &3.91&3.93& &4.05& \\ -$^3B_2 (\pi \rightarrow \pi^\star)$ &4.92&4.92& & 4.92$\pm$0.03 &4.90&4.89 &4.89&4.88& &4.81& \\ -$^3A_2 (n \rightarrow \pi^\star)$ &5.48&5.44& & &5.38&5.35 &5.37&5.35& &5.56& \\ -$^3A_1 (\pi \rightarrow \pi^\star)$ &6.89&6.88& & &6.79&6.78 &6.83&6.79& &6.98& \\ -\hline - \multicolumn{12}{c}{Cyclopropenethione}\\ - & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{2}{c}{Litt.}\\ -State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV} & Th.$^a$ \\ -\hline -$^1A_2 (n \rightarrow \pi^\star)$ &3.46&3.44&3.44& 3.45$\pm$0.01 &3.47&3.45 &3.43&3.41& &3.23 & \\ -$^1B_1 (n \rightarrow \pi^\star)$ &3.45&3.44&3.45& 3.44$\pm$0.05 &3.42&3.42 &3.43&3.44& &3.47 & \\ -$^1B_2 (\pi \rightarrow \pi^\star)$ &4.67&4.64&4.62& 4.59$\pm$0.09 &4.66&4.64 &4.64&4.62& &4.34 & \\ -$^1B_2 (n \rightarrow 3s)$ &5.26&5.24&5.27& &5.23&5.21 &5.34&5.31& &4.98 & \\ -$^1A_1 (\pi \rightarrow \pi^\star)$ &5.53&5.52&5.51& &5.52&5.50 &5.49&5.47& &5.52 & \\ -$^1B_2 (n \rightarrow 3p)$ &5.83&5.81&5.83& &5.86&5.84 &5.93&5.90& &5.88 & \\ -$^3A_2 (n \rightarrow \pi^\star)$ &3.33&3.31& & 3.29$\pm$0.03 &3.34&3.32 &3.30&\hl{?} & &3.20 & \\ -$^3B_1 (n \rightarrow \pi^\star)$ &3.34&3.33& & &3.30&3.30 &3.31&3.32& &3.30 & \\ -$^3B_2 (\pi \rightarrow \pi^\star)$ &4.01&4.00& & 4.03$\pm$0.03 &4.03&4.02 &4.02&\hl{?} & &3.86 & \\ -$^3A_1 (\pi \rightarrow \pi^\star)$ &4.06&4.04& & &4.09&4.07 &4.03&\hl{?} & &3.99 & \\ -\hline - \multicolumn{12}{c}{Methylenecyclopropene}\\ - & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{3}{c}{Litt.}\\ -State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV}& Th.$^c$ & Th.$^d$ & Exp.$^e$\\ -\hline -$^1B_2 (\pi \rightarrow \pi^\star)$ &4.38&4.37&4.34& 4.32$\pm$0.03 &4.32&4.31 &4.31&4.31& &4.13&4.36 &4.01\\ -$^1B_1 (\pi \rightarrow \sigma^\star)$ &5.65&5.66&5.66& &5.35&5.35 &5.44&5.44& &5.32&5.44 &5.12\\ -$^1A_2 (\pi \rightarrow 3p)$ &5.97&5.98&5.98& 5.92$\pm$0.10 &5.86&5.88 &5.95&5.96& &5.83& &\\ -$^1A_1(\pi \rightarrow \pi^\star)$ &6.17&6.18&6.17& &6.15&6.15 &6.13&6.13& & &6.13 &6.02\\ -$^3B_2 (\pi \rightarrow \pi^\star)$ &3.50&3.50& & 3.44$\pm$0.06 &3.49&3.49 &3.50&\hl{?} & &3.24& &\\ -$^3A_1 (\pi \rightarrow \pi^\star)$ &4.74&4.74& & 4.67$\pm$0.10 &4.74&4.74 &4.74&\hl{?} & &4.52& &\\ -\hline -\end{tabular} - \end{footnotesize} -\begin{flushleft} -\begin{footnotesize} -$^a${{\CASPT} values of Ref. \citenum{Ser02};} -$^b${Electron impact experiment of Ref. \citenum{Har74}, note that the 5.5 eV peak was assigned differently in the original paper, and we follow here the analysis of Serrano-Andr\'es\cite{Ser02} -whereas the 6.1 eV assignment was "supposed" in the original paper; experimental $\lambda_{\mathrm{max}}$ have been measured at at 3.62 eV and 6.52 eV for the $^1B_1 (n \rightarrow \pi^\star)$ and -$^1B_2 (\pi \rightarrow \pi^\star$) transitions, respectively; \cite{Bre72}} -$^c${{\CASPT} values of Refs. \citenum{Mer96} and \citenum{Roo96};} -$^d${ {\CCT} values of Ref. \citenum{Sch17};} -$^e${$\lambda_{\mathrm{max}}$ in pentane at -78$^o$C from Ref. \citenum{Sta84}.} -\end{footnotesize} -\end{flushleft} -\end{table} - -\clearpage -% - -\subsubsection{Acrolein, butadiene, and glyoxal} - -Let us now turn to three pseudo-linear $\pi$-conjugated systems that have been the subject to several ES investigations before, namely, acrolein, \cite{Aqu03,Sah06,Car10b,Lea12,Gua13,Mai14,Aza17b,Sch17,Bat17} -butadiene, \cite{Dal04,Sah06,Sch08,Sil10c,Li11,Wat12,Dad12,Lea12,Ise12,Ise13,Sch17,Shu17,Sok17,Chi18,Cop18,Tra19,Loo19c} and glyoxal, \cite{Sta97b,Koh03,Hat05c,Sah06,Lea12,Poo14,Sch17,Aza17b,Loo18b} -that we all consider in their most stable \emph{trans} conformation in the following. Amongst these works, it is worth highlighting the detailed theoretical investigation by Saha, Ehara, and Nakatsuji, who reported a huge -number of ES in these three systems using a coherent theoretical Symmetry-Adapted-Cluster Configuration-Interaction (SAC-CI) protocol. \cite{Sah06} Our results are listed in Tables \ref{Table-3} and S3. - -\hl{All below to be completed with NEV} - -Acrolein, due to its lower symmetry and high density of ES with mixed characters, is challenging for theory and {\CCSDTQ} calculations were technically impossible despite our efforts. For the lowest $n \rightarrow \pi^\star$ -transitions of both spin symmetries, the {\FCI} estimates come with a tiny error bar, and it is obvious that the CC estimates are too slightly low, especially with {\CCSDT}. Nevertheless, at the exception the second singlet -and triplet $A''$ ES, the {\CCT} and {\CCSDT} estimates are within $\pm$ 0.03 eV of each other, hinting at a reasonable accuracy. Additionally, the CC values are nearly systematically bracketed by the {\CASPT} -(lower bound)\cite{Aqu03} and SAC-CI (higher bound)\cite{Sah06} results, consistently with the typical error signs of these two models. For the two lowest triplet states, the present {\CCT}/{\AVTZ} values are also -within $\pm$0.05 eV of recent MR-CI estimates (3.50 and 3.89 eV). \cite{Mai14} As can be seen in Table S3, {\AVTZ} is sufficient to be very close from basis set convergence, the largest variation when going to {\AVQZ} -being +0.04 eV for the second $^1A'$ ES of Rydberg nature. As the experimental data are limited to measured UV spectra, \cite{Wal45,Bec70} one has therefore to be cautious in establishing TBE for acrolein -(\emph{vide infra}). - -The nature and relative energies of the lowest bright $B_u$ and dark $A_g$ ES of butadiene have been puzzling theoretical chemists for many years. It is beyond our scope to provide an exhaustive -list of previous calculations and experimental estimates for these two hallmark ES, and we refer the reader to Refs. \citenum{Wat12} and \citenum{Shu17} for overviews and references. For the $B_u$ transition -the best previous TBE we are aware of is the 6.21 eV value obtained by Watson and Chan using a computational strategy similar to ours. \cite{Wat12} Our {\CCSDT}/{\AVTZ} value of 6.24 eV is obviously compatible -with this reference value, and our TBE value is actually 6.21 eV as well (\emph{vide infra}). For the $A_g$ state, we believe that our previous basis-corrected exCI estimate of 6.50 eV \cite{Loo19c} remains -the most accurate available to date. These two values are slightly smaller than the heath-bath CI data obtained by Chien \emph{et al.} with a double-$\zeta$ basis and a slightly different geometry: 6.45 and 6.58 eV for $B_u$ and $A_g$, -respectively. \cite{Chi18} One can of course find many other estimates, e.g., at the SAC-CI, \cite{Sah06} {\CCT}, \cite{Sil10c,Sch17} {\CASPT}, \cite{Sil10c} and {\NEV} levels, \cite{Sok17} for these two states. -More globally, in butadiene, we find an excellent coherence between the {\CCT}, {\CCSDT}, and {\CCSDTQ} estimates, that all fall in a $\pm$0.02 eV window. Unsurprisingly, this rule does not apply for the -already mentioned $^A_g$ ES that is 0.2 and 0.1 eV too high with the two former methods, consistent with the large electronic reorganization taking place in that state. For all the other butadiene ES listed in -Table \ref{Table-3}, both {\CCT} and {\CCSDT} can be trusted. Finally, as can be seen in Table S3, {\AVTZ} is sufficient for most ES, but one notes a significant basis set effect for the Rydberg $^1B_u\ \pi \rightarrow 3p$ ES -with an energy decrease as large as -0.12 eV when going from {\AVTZ} to {\AVQZ}. For the records, we note that the available electron impact data \cite{Mos73,Fli78,Doe81} provide the same ES ordering value as -our calculations. - -Globally, the conclusions obtained for acrolein and butadiene pertain for glyoxal, i.e., highly consistent CC estimates and limited basis set effects beyond {\AVTZ} but for the Rydberg state (see Tables -\ref{Table-3} and S3). This state shows also a comparatively large deviation between {\CCT} and {\CCSDTQ}, that is 0.04 eV. More interestingly, glyoxal presents a low-lying ``true'' double ES, -$^1A_g\ n,n \rightarrow \pi^\star,\pi^\star$, a state that is totally unseen by approaches that do not explicitly include double excitations during the calculation of transition energies, e.g., TD-DFT, {\CCSD}, -and {\AD}. Compared to the {\exCI} values, the {\CCT} and {\CCSDT} estimates for this transition are too large by ca. 1.0 and 0.5 eV, respectively, whereas {\CCSDTQ} is close to the spot, as already -mentioned in our previous work. \cite{Loo19c} For the other transitions, the present {\CCT} estimates are logically coherent with the values of Ref. \citenum{Sch17} obtained with the same approach on a different -geometry and remain slightly lower than the SAC-CI estimates of Ref. \citenum{Sah06}. Again experimental data \cite{Ver80,Rob85b} make an unhelpful guide in view of the targeted accuracy. - -Finally, considering the {\CCSDTQ}/{\Pop} values of Table \ref{Table-3} as reference, we obtain mean absolute errors of 0.012 and 0.017 eV with {\CCT} and {\CCSDT}, respectively for the ES with $\%T_1 > 80$\%. - -\begin{table}[htp] -\caption{\small Vertical transition energies determined in acrolein, butadiene, and glyoxal. All values are in eV.} -\label{Table-3} - \begin{footnotesize} -\begin{tabular}{l|p{.5cm}p{.9cm}p{1.1cm}p{1.5cm}|p{.5cm}p{.9cm}|p{.5cm}p{.9cm}p{1.2cm}|p{.6cm}p{.6cm}p{.6cm}} -\hline - \multicolumn{12}{c}{Acrolein}\\ - & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{3}{c}{Litt.}\\ -State & {\CCT} & {\CCSDT} & & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV} & Th.$^a$ & Th.$^b$ & Exp.$^c$ \\ -\hline -$^1A'' (n \rightarrow \pi^\star)$ &3.83&3.80& &3.85$\pm$0.01&3.77&3.74& 3.74&3.73& &3.63&3.83&3.71 \\ -$^1A' (\pi \rightarrow \pi^\star)$ &6.83&6.86& & &6.67&6.70& 6.65&6.69& &6.10&6.92&6.41 \\ -$^1A'' (n \rightarrow \pi^\star)$ &6.94&6.89& & &6.75&6.72& 6.75& & &6.26&7.40& \\ -$^1A' (n \rightarrow 3s)$ &7.22&7.23& & &6.99&7.00& 7.07& & &6.97&7.19&7.08 \\ -$^3A'' (n \rightarrow \pi^\star)$ &3.55&3.53& &3.60$\pm$0.01&3.47&3.45& 3.46& & &3.39&3.61& \\ -$^3A' (\pi \rightarrow \pi^\star)$ &3.94&3.95& &3.97$\pm$0.03&3.95&3.95& 3.94& & &3.81&3.87& \\ -$^3A' (\pi \rightarrow \pi^\star)$ &6.25&6.23& & &6.22&\hl{?}& 6.19& & & &6.21& \\ -$^3A'' (\pi \rightarrow 3s)$ &6.81&6.74& & &6.60&\hl{?}& 6.61& & & &7.36& \\ -\hline - \multicolumn{12}{c}{Butadiene}\\ - & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{3}{c}{Litt.}\\ -State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV} & Th.$^b$ & Th.$^d$ & Exp$^e$ \\ -\hline -$^1B_u (\pi \rightarrow \pi^\star)$ &6.41&6.43&6.41&6.41$\pm$0.02 &6.25&6.27& 6.22&6.24 & &6.33&6.36&5.92\\ -$^1B_g (\pi \rightarrow 3s)$ &6.53&6.55&6.54& &6.26&6.27& 6.33&6.34 & &6.18&6.32&6.21\\ -$^1A_g (\pi \rightarrow \pi^\star)$ &6.73&6.63&6.56&6.55$\pm$0.03$^f$ &6.68&6.59& 6.67&6.60 & &6.56&6.60& \\ -$^1A_u (\pi \rightarrow 3p)$ &6.87&6.89&6.87& &6.57&6.59& 6.64&6.66 & &6.45&6.56&6.64\\ -$^1A_u (\pi \rightarrow 3p)$ &6.93&6.95&6.94&6.95$\pm$0.01 &6.73&6.74& 6.80&6.81 & &6.65&6.74&6.80\\ -$^1B_u (\pi \rightarrow 3p)$ &7.98&8.00&7.98& &7.86&7.87& 7.68& & &7.08&7.02&7.07\\ -$^3B_u (\pi \rightarrow \pi^\star)$ &3.35&3.36& &3.37$\pm$0.03 &3.36&3.36& 3.36& & &3.20& &3.22\\ -$^3A_g (\pi \rightarrow \pi^\star)$ &5.22&5.22& & &5.21&5.21& 5.20& & &5.08& &4.91\\ -$^3B_g (\pi \rightarrow 3s)$ &6.46&6.47& & &6.20&6.21& 6.28& & &6.14& &\\ -\hline - \multicolumn{12}{c}{Glyoxal}\\ - & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{3}{c}{Litt.}\\ -State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV} & Th.$^b$ & Th.$^g$ & Exp.$^h$\\ -\hline -$^1A_u (n \rightarrow \pi^\star)$ &2.94&2.94&2.94& 2.93$\pm$0.03 &2.90&2.90& 2.88&2.88 & &3.10&2.93 &2.8 \\ -$^1B_g (n \rightarrow \pi^\star)$ &4.34&4.32&4.31&4.28$\pm$0.06 &4.30&4.28& 4.27&4.25 & &4.68&4.39 &$\sim$4.4\\ -$^1A_g (n,n \rightarrow \pi^\star,\pi^\star)$&6.74&6.24&5.67&5.60$\pm$0.01$^f$ &6.70&6.22& 6.76&6.35 & &5.66& &\\ -$^1B_g (n \rightarrow \pi^\star)$ &6.81&6.83&6.79& &6.59&6.61& 6.58&6.61 & &7.54&6.63 &7.45\\ -$^1B_u (n \rightarrow 3p)$ &7.72&7.74&7.76& &7.55&7.56& 7.67&7.69 & &7.83&7.61 &$\sim$7.7\\ -$^3A_u (n \rightarrow \pi^\star)$ &2.55&2.55& &2.54$\pm$0.04 &2.49&2.49& 2.49&2.49 & &2.63& &2.5\\ -$^3B_g (n \rightarrow \pi^\star)$ &3.97&3.95& & &3.91&3.90& 3.90&3.89 & &4.12& &$\sim$3.8\\ -$^3B_u (\pi \rightarrow \pi^\star)$ &5.22&5.20& & &5.20&5.19& 5.17&5.15 & &5.35& &$\sim$5.2\\ -$^3A_g (\pi \rightarrow \pi^\star)$ &6.35&6.35& & &6.34&6.34& 6.30&6.30 & & & &\\ -\hline -\end{tabular} - \end{footnotesize} -\begin{flushleft} -\begin{footnotesize} -$^a${{\CASPT} values of Ref. \citenum{Aqu03};} -$^b${SAC-CI values of Ref. \citenum{Sah06};} -$^c${Vacuum UV spectra from Ref. \citenum{Wal45}. For the lowest state, the same 3.71 eV value is reported in Ref. \citenum{Bec70}.} -$^d${MR-AQCC values of Ref. \citenum{Dal04}, theoretical best estimates listed for the lowest $B_u$ and $A_g$ states;} -$^e${Electron impact experiment from Refs. \citenum{Fli78} and \citenum{Doe81} for the singlet states and from Ref. \citenum{Mos73} for the two lowest triplet transitions; -Note that for the lowest $B_u$ state, there is a vibrational structure with peaks at 5.76, 5.92, and 6.05 eV;} -$^f${From Ref. \citenum{Loo19c};} -$^g${{\CCT} values of Ref. \citenum{Sch17};} -$^h${Electron impact experiment from Ref. \citenum{Ver80} but for the second $^1B_g$ ES for which the value is from another work; \cite{Rob85b} note that -for the lowest $^1B_g$ ($^1B_u$) ES, a range of 4.2--4.5 (7.4--7.9) eV is given Ref. \citenum{Ver80}. } -\end{footnotesize} -\end{flushleft} -\end{table} - -\clearpage - -\subsubsection{Acetone, cyanoformaldehyde, isobutene, propynal, thioacetone, and thiopropynal} - -There are earlier estimates of vertical transition energies for both acetone \cite{Gwa95,Mer96b,Roo96,Wib98,Toz99b,Wib02,Sch08,Sil10c,Car10,Pas12,Ise12,Gua13,Sch17} and isobutene. \cite{Wib02,Car10,Ise12} -To the best of our knowledge, the previous computational efforts were mainly focussed on 0-0 energies of the lowest-lying states for the four other compounds. \cite{Koh03,Hat05c,Sen11b,Loo18b,Loo19a} -There are also a few experimental values available for these six derivatives. \cite{Bir73,Jud83,Bra74,Sta75,Joh79,Jud83,Jud84c,Rob85,Pal87,Kar91b,Xin93} Our main data are reported in Tables \ref{Table-4} -and S4. - -For acetone, one should clearly distinguish the valence ES, for which both methodological and basis set effects are small \hl{T2: please check the lowest S transition}, and the Rydberg transitions that, not only are very -sensitive to the basis set, but are upshifted by ca. 0.04 eV with {\CCSDTQ} as compared to {\CCT} and {\CCSDT}. For this compound, the 1996 {\CASPT} estimates of Merch\'an and coworkers listed on the -r.h.s. of Table \ref{Table-4} are quite clearly too low, especially for the three valence ES. \cite{Mer96b} As expected, this error can be partially ascribed to the details of the calculations, as the Urban group obtained {\CASPT} -excitation energies of 4.40, 4.09 and 6.22 eV for the $^1A_2$, $^3A_2$, and $^3A_1$ ES, \cite{Pas12} in much better agreement with ours. Their estimates for the three $n \rightarrow 3p$ transitions of 7.52, 7.57, and 7.53 eV -for the $^1A_2$, $^1A_1$, and $^1B_2$ ES also systematically fall within 0.10 eV of our current CC values. \hl{NEVPT ?} - -\hl{Thioacetone: en attente des CCSDTQ} - -For the isoleectronic isobutene, we considered two singlet Rydberg and one triplet valence ES. For all three cases, we note very nice agreement between {\CCT} and {\CCSDT} results for all considered basis sets, these -CC results being also within or very close to the {\FCI} estimates with Pople's basis set. The match with the {\CCSD} results of Caricato and coworkers, \cite{Car10} is also very satisfying. \hl{CCSDTQ doable ?} - -For the three remaining compounds, namely, cyanoformaldehyde, propynal, and thiopropynal, we have considered low-lying valence transitions all showing a largely dominant single excitation character. The basis set -effects are clearly under control (they are only significant for the second $^1A''$ ES of cyanoformaldehyde) and we could not detect any variation larger than 0.03 eV between the {\CCT} and {\CCSDT} values for -a given basis, hinting that the CC values should be close to the spot, as confirmed by the extrapolated {\FCI} data listed in Table \ref{Table-4}. - - -\begin{table}[htp] -\caption{\small Vertical transition energies determined in acetone, cyanonformaldehyde, isobutene, propynal, thioacetone, and thiopropynal. All values are in eV.} -\label{Table-4} - \begin{footnotesize} -\begin{tabular}{l|p{.5cm}p{.9cm}p{1.1cm}p{1.4cm}|p{.5cm}p{.9cm}|p{.5cm}p{.9cm}p{1.2cm}|p{.6cm}p{.6cm}p{.6cm}} -\hline - \multicolumn{12}{c}{Acetone}\\ - & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{3}{c}{Litt.}\\ -State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV} & Th.$^a$ & Th.$^b$ & Exp.$^c$ \\ -\hline -$^1A_2 (n \rightarrow \pi^\star)$ &4.55&4.52&4.53&4.60$\pm$0.05 &4.50&4.48& 4.48&4.46& &4.18&4.18&4.48\\ -$^1B_2 (n \rightarrow 3s)$ &6.65&6.64&6.68& &6.31&6.30& 6.43&6.42& &6.58&6.58&6.36\\ -$^1A_2 (n \rightarrow 3p)$ &7.83&7.83&7.87& &7.37&7.36& 7.45& & &7.34&7.34&7.36\\ -$^1A_1 (n \rightarrow 3p)$ &7.81&7.81&7.84& &7.39&7.38& 7.48&7.48& &7.26&7.26&7.41\\ -$^1B_2 (n \rightarrow 3p)$ &7.87&7.87&7.91& &7.56&7.55& 7.59& & &7.48&7.48&7.45\\ -$^3A_2 (n \rightarrow \pi^\star)$ &4.21&4.19& &4.18$\pm$0.04 &4.16&4.14& 4.15& & &3.90&3.90&4.15\\ -$^3A_1 (\pi \rightarrow \pi^\star)$ &6.32&6.30& & &6.31&6.28& 6.28& & &5.98&5.98&\\ -\hline - \multicolumn{12}{c}{Cyanoformaldehyde}\\ - & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{1}{c}{Litt.}\\\ -State & {\CCT} & {\CCSDT} & & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV} & Exp$^d$ \\ -\hline -$^1A'' (n \rightarrow \pi^\star)$ &3.91&3.89& &3.92$\pm$0.02 &3.86&3.84& 3.83&3.81 && 3.26\\ -$^1A'' (\pi \rightarrow \pi^\star)$ &6.64&6.67& &6.60$\pm$0.07 &6.51&6.54& 6.42&6.46&& \\ -$^3A'' (n \rightarrow \pi^\star)$ &3.53&3.51& &3.48$\pm$0.06 &3.47&3.45& 3.46& && \\ -$^3A' (\pi \rightarrow \pi^\star)$ &5.07&5.07& & &5.03&5.03& 5.01& && \\ -\hline - \multicolumn{12}{c}{Isobutene}\\ - & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{3}{c}{Litt.}\\\ -State & {\CCT} & {\CCSDT} & & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV} & Th.$^e$ & Exp.$^f$ & Exp.$^g$ \\ -\hline -$^1B_1 (\pi \rightarrow 3s)$ &6.77&6.77& &6.78$\pm$0.08 &6.39&6.39& 6.45&6.46&&6.40&6.15&6.17 \\ -$^1A_1 (\pi \rightarrow 3p)$ &7.16&7.17& &7.16$\pm$0.02 &7.00&7.00& 7.00&7.01&&6.96& &6.71 \\ -$^3A_1 (\pi \rightarrow \pi^\star)$ &4.52&4.53& &4.56$\pm$0.02 &4.54&4.54& 4.53& && &4.21 &4.3 \\ -\hline - \multicolumn{12}{c}{Propynal}\\ - & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{1}{c}{Litt.} \\ -State & {\CCT} & {\CCSDT} & & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV} & Exp$^h$ \\ -\hline -$^1A'' (n \rightarrow \pi^\star)$ &3.90&3.87& &3.84$\pm$0.06 &3.85&3.82& 3.82&3.80&& 3.24\\ -$^1A'' (\pi \rightarrow \pi^\star)$ &5.69&5.73& &5.63$\pm$0.09 &5.59&5.62& 5.51&5.54&& \\ -$^3A'' (n \rightarrow \pi^\star)$ &3.56&3.54& &3.54$\pm$0.04 &3.50&3.48& 3.49& && 2.99\\ -$^3A' (\pi \rightarrow \pi^\star)$ &4.46&4.47& &4.44$\pm$0.08 &4.40&4.44& 4.43& && \\ -\hline - \multicolumn{12}{c}{Thioacetone}\\ - & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{1}{c}{Litt.}\\ -State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV} & Exp$^i$ \\ -\hline -$^1A_2 (n \rightarrow \pi^\star)$ &2.58&2.56& &2.61$\pm$0.05 &2.59&2.57& 2.55&2.53 & &2.33\\ -$^1B_2 (n \rightarrow 4s)$ &5.65&5.64& &5.60$\pm$0.04 &5.44&5.43& 5.55&5.54 & &5.49\\ -$^1A_1 (\pi \rightarrow \pi^\star)$ &6.09&6.10& & &5.97&5.98& 5.90&5.91 & &5.64\\ -$^1A_1 (n \rightarrow 4p)$ &6.95&6.95& & &6.54&6.53& 6.61& & &6.52\\ -$^1B_2 (n \rightarrow 4p)$ &6.59&6.59& & &6.45&6.44& 6.51& & &6.40\\ -$^3A_2 (n \rightarrow \pi^\star)$ &2.36&2.34& &2.36$\pm$0.00 &2.36&2.35& 2.34& & &2.14\\ -$^3A_1 (\pi \rightarrow \pi^\star)$ &3.45&3.45& & &3.51&3.50& 3.46& & &\\ -\hline - \multicolumn{12}{c}{Thiopropynal}\\ - & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{1}{c}{Litt.}\\ -State & {\CCT} & {\CCSDT} & & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV} & Exp$^j$ \\ -\hline -$^1A'' (n \rightarrow \pi^\star)$ &2.09&2.06& &2.07$\pm$0.02 &2.09&2.06& 2.05&2.03 & &1.82\\ -$^3A'' (n \rightarrow \pi^\star)$ &1.84&1.82& & &1.83&1.82& 1.81& & &1.64\\ -\hline -\end{tabular} - \end{footnotesize} -\begin{flushleft} -\begin{footnotesize} -$^a${{\CASPT} values of Ref. \citenum{Mer96b};} -$^b${EOM-CCSD values of Ref. \citenum{Gwa95};} -$^c${Two lowest singlet states: various experiments summarized in Ref. \citenum{Rob85}; three next singlet states: REMPI experiments from Ref. \citenum{Xin93}; lowest triplet: trapped electron measurements from Ref. \citenum{Sta75};} -$^d${0-0 energy reported in Ref. \citenum{Kar91b};} -$^e${EOM-CCSD values from Ref. \citenum{Car10};} -$^f${Energy loss experiment from Ref. \citenum{Joh79};} -$^g${VUV experiment from Ref. \citenum{Pal87} (we report the lowest of the $\pi \rightarrow 3p$ state for the $^1A_1$ state)}; -$^h${0-0 energies reported in Ref. \citenum{Bra74} (singlet) and \citenum{Bir73} (triplet);} -$^i${0-0 energies reported in Ref. \citenum{Jud83};} -$^i${0-0 energies reported in Ref. \citenum{Jud84c}.} -\end{footnotesize} -\end{flushleft} -\end{table} - -\clearpage - -\subsection{Five-atom molecules} - - -Thiophene: - For instance, this problem occurs for the second $B_2$ state of thiophene for which mixing with the third -$B_2$ state renders the assignment of the valence ($\pi \rightarrow \pi^\star$) or Rydberg ($\pi \rightarrow 3p$) nature uneasy at the CC3 level. The same problems occurs with other levels of theory. \cite{Ser93c,Wan01} - -\clearpage - -\section{Theoretical Best Estimates} - -In Table \ref{Table-tbe}, we present our theoretical best estimates obtained with the {\AVTZ} basis set and further corrected for basis set effects. The details of the approaches used are given in Table \ref{Table-tbe}. -For all states with a dominant single-excitation character, that is when $\%T_1 > 85$\%, we relied on CC results, using the incremental strategy to obtain the our TBE. For the other transitions, we relied either -on the current or previous FCI \cite{Loo19c} or the {\NEV} values shown here as references \hl{correct ?}. In a few cases, e.g., the second singlet and triplet $A''$ ES of acrolein, the affordable CC expansion -yields quite large changes from one level of theory to the other, and we believe such estimates are not robust enough. \hl{que faire: italique ? enlever ?} -To determine the basis set corrections above triple-$\zeta$, we mainly used the {\CCT}/{\AVQZ} data. -For several of the smallest compounds, we also provide in the {\SI}, {\CCT}/{\DAVQZ} transition energies. However, we did not used these values as reference. This is because, the use of second set of -diffuse orbitals tends to modify the computed transition energies significantly only when it induces a more complex orbital mixture as well. This indicates that state mixing takes place, even if we use the -{\CCT} approach. We also stick to the frozen-core approximation for two reasons: i) the corrections brought by ``full-correlation'' are generally trifling (typically $\pm$ 0.02 eV) for the compounds under study -(see the {\SI}); and ii) it would probably be in principle necessary to add core polarization functions for such calculations. - -\hl{On ferait une erreur totale CC3 versus CCSDTQ et CCSDT versus CCSDTQ pour choisir la meilleure approche ? Pas clair si CC3 ou CCSDTQ avec les donnees qu'on a jusqu'ici...Au moins discuter -de cela} - -\hl{Decrire le set} - -It should also be recalled that all our data are obtained on {\CCT){\AVTZ} geometries, consistently with our previous work, \cite{Loo18a} and therefore offer a consistent set of transition energies. -\hl{in total} - -\renewcommand*{\arraystretch}{.55} -\LTcapwidth=\textwidth - -\begin{footnotesize} -\begin{longtable}{llcccccc} -\caption{\small TBE values determined for all considered states. For each state, we provide the oscillator strength and percentage of single excitations obtained at the \CCT/{\AVTZ} level, -as well TBE obtained with the same basis set together with the method used to obtain that TBE. In the right-most columns, we list the values obtained by including further basis set corrections, -that have always been obtained at the \CCT level. All values are in the FC approximation.} \label{Table-tbe}\\ -\hline - & & & & \multicolumn{2}{l}{TBE/{\AVTZ}} & \multicolumn{2}{l}{TBE/CBS} \\ - & State & $f$ & $\%T_1$ & Value & Method$^a$ & Value & Corr. \\ -\hline -\endfirsthead -\hline - & & & & \multicolumn{2}{l}{TBE/{\AVTZ}} & \multicolumn{2}{l}{TBE/CBS} \\ - & State & $f$ & $\%T_1$ & Value & Method $^a$ & Value & Corr. \\ -\hline -\endhead -\hline \multicolumn{7}{r}{{Continued on next page}} \\ -\endfoot -\hline -\endlastfoot -Acetone &$^1A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 91.1 & 4.47 & B & 4.48 & {\AVQZ} \\ - &$^1B_2 (\mathrm{R}; n \rightarrow 3s)$ &0.000 & 90.5 & 6.46 & B & 6.51 & {\AVQZ} \\ - &$^1A_2 (\mathrm{R}; n \rightarrow 3p)$ & & 90.9 & 7.45 & C & 7.48 & {\AVQZ} \\ - &$^1A_1 (\mathrm{R}; n \rightarrow 3p)$ &0.004 & 90.6 & 7.51 & B & 7.44 & {\AVQZ} \\ - &$^1B_2 (\mathrm{R}; n \rightarrow 3p)$ &0.029 & 91.2 & 7.63 & C & 7.64 & {\AVQZ} \\ - &$^3A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.8 & 4.13 & D & 4.15 & {\AVQZ} \\ - &$^3A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.7 & 6.25 & D & 6.27 & {\AVQZ} \\ -Acrolein &$^1A'' (\mathrm{V}; n \rightarrow \pi^\star)$ &0.000 & 87.6 & 3.76 & G & 3.77 & {\AVQZ} \\ - &$^1A' (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.344 & 91.2 & 6.69 & {\CCSDT}/{\AVTZ} & 6.69 & {\AVQZ} \\ - &$^1A'' (\mathrm{V}; n \rightarrow \pi^\star)$ &0.000 & 79.4 & \hl{6.72} & \hl{xxxx} &\hl{ 6.74} & {\AVQZ} \\ - &$^1A' (\mathrm{R}; n \rightarrow 3s)$ &0.109 & 89.4 & 7.08 & D & 7.12 & {\AVQZ} \\ - &$^3A'' (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.0 & 3.51 & G & 3.52 & {\AVQZ} \\ - &$^3A' (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.6 & 3.94 & D & 3.95 & {\AVQZ} \\ - &$^3A' (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.4 & 6.17 & E & 6.18 & {\AVQZ} \\ - &$^3A'' (\mathrm{R}; \pi \rightarrow 3s)$ & & 92.7 & \hl{6.61} & \hl{xxxxx} & \hl{6.62} & {\AVQZ} \\ -Butadiene &$^1B_u (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.664 & 93.3 & 6.22 & B & 6.21 & {\AVQZ} \\ - &$^1B_g (\mathrm{R}; \pi \rightarrow 3s)$ & & 94.1 & 6.33 & B & 6.35 & {\AVQZ} \\ - &$^1A_g (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 75.1 & 6.50 & F & 6.50 & {\AVQZ} \\ - &$^1A_u (\mathrm{R}; \pi \rightarrow 3p)$ &0.001 & 94.1 & 6.64 & B & 6.66 & {\AVQZ} \\ - &$^1A_u (\mathrm{R}; \pi \rightarrow 3p)$ &0.049 & 94.1 & 6.80 & B & 6.82 & {\AVQZ} \\ - &$^1B_u (\mathrm{R}; \pi \rightarrow 3p)$ &0.055 & 93.8 & 7.68 & C & 7.54 & {\AVQZ} \\ - &$^3B_u (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.4 & 3.36 & D & 3.37 & {\AVQZ} \\ - &$^3A_g (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.7 & 5.20 & D & 5.21 & {\AVQZ} \\ - &$^3B_g (\mathrm{V}; \pi \rightarrow 3s)$ & & 97.9 & 6.29 & D & 6.31 & {\AVQZ} \\ -Cyanoacetylene &$^1\Sigma^- (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 94.3 & 5.80 & A & 5.79 & {\AVFZ} \\ - &$^1\Delta (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 94.0 & 6.07 & A & 6.05 & {\AVFZ} \\ - &$^3\Sigma^+ (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.5 & 4.44 & {\CCSDT}/{\AVTZ} & 4.46 & {\AVFZ} \\ - &$^3\Delta (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.2 & 5.21 & {\CCSDT}/{\AVTZ} & 5.21 & {\AVFZ} \\ -Cyanoformaldehyde &$^1A'' (\mathrm{V}; n \rightarrow \pi^\star)$ & 0.001 & 89.8 & 3.81 & {\CCSDT}/{\AVTZ} & 3.82 & {\AVQZ} \\ - &$^1A'' (\mathrm{V}; \pi \rightarrow \pi^\star)$ & 0.000 & 91.9 & 6.46 & {\CCSDT}/{\AVTZ} & 6.45 & {\AVQZ} \\ - &$^3A'' (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.6 & 3.44 & D & 3.45 & {\AVQZ} \\ - &$^3A' (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.4 & 5.01 & D & 5.00 & {\AVQZ} \\ -Cyanogen & $^1\Sigma_u^- (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 94.1 & 6.39 & A & 6.38 & {\AVFZ} \\ - & $^1\Delta_u (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 93.4 & 6.66 & A & 6.64 & {\AVFZ} \\ - & $^3\Sigma_u^+ (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.5 & 4.91 & B & 4.89 & {\AVFZ} \\ - & $^1\Sigma_u^- [\mathrm{F}] (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 93.4 & 5.05 & A & 5.03 & {\AVFZ} \\ -Cyclopropenone &$^1B_1 (\mathrm{V}; n \rightarrow \pi^\star)$ &0.000 & 87.7 & 4.26 & B & 4.28 & {\AVFZ} \\ - &$^1A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 91.0 & 5.55 & B & 5.56 & {\AVFZ} \\ - &$^1B_2 (\mathrm{R}; n \rightarrow 3s)$ &0.003 & 90.8 & 6.34 & B & 6.39 & {\AVQZ} \\ - &$^1B_2 (\mathrm{V}; \pi \rightarrow \pi^\star$) &0.047 & 86.5 & 6.54 & B & 6.56 & {\AVQZ} \\ - &$^1B_2 (\mathrm{R}; n \rightarrow 3p)$ &0.018 & 91.1 & 6.98 & B & 7.01 & {\AVQZ} \\ - &$^1A_1 (\mathrm{R}; n \rightarrow 3p)$ &0.003 & 91.2 & 7.02 & B & 7.08 & {\AVFZ} \\ - &$^1A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.320 & 90.8 & 8.28 & B & 8.26 & {\AVFZ} \\ - &$^3B_1 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 96.0 & 3.93 & {\CCSDT}/{\AVTZ} & 3.95 & {\AVQZ} \\ - &$^3B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 97.9 & 4.88 & {\CCSDT}/{\AVTZ} & 4.90 & {\AVQZ} \\ - &$^3A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.5 & 5.35 & {\CCSDT}/{\AVTZ} & 5.37 & {\AVQZ} \\ - &$^3A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.1 & 6.79 & {\CCSDT}/{\AVTZ} & 6.81 & {\AVFZ} \\ -Cyclopropenethione &$^1A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 89.6 & 3.41 & B & 3.42 & {\AVQZ} \\ - &$^1B_1 (\mathrm{V}; n \rightarrow \pi^\star)$ &0.000 & 84.8 & 3.45 & B & 3.47 & {\AVQZ} \\ - &$^1B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.007 & 83.0 & 4.60 & B & 4.62 & {\AVQZ} \\ - &$^1B_2 (\mathrm{R}; n \rightarrow 3s)$ &0.048 & 91.8 & 5.34 & B & 5.39 & {\AVQZ} \\ - &$^1A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.228 & 89.0 & 5.46 & B & 5.46 & {\AVQZ} \\ - &$^1B_2 (\mathrm{R}; n \rightarrow 3p)$ &0.084 & 91.3 & 5.92 & B & 5.94 & {\AVQZ} \\ - &$^3A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.2 & 3.28 & D & 3.29 & {\AVQZ} \\ - &$^3B_1 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 94.5 & 3.32 & {\CCSDT}/{\AVTZ} & 3.35 & {\AVQZ} \\ - &$^3B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 96.5 & 4.01 & D & 4.03 & {\AVQZ} \\ - &$^3A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.2 & 4.01 & D & 4.02 & {\AVQZ} \\ -Diacetylene &$^1\Sigma_u^- (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 94.4 & 5.33 & A & 5.32 & {\AVFZ} \\ - &$^1\Delta_u (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 94.1 & 5.61 & A & 5.60 & {\AVFZ} \\ - &$^3\Sigma_u^+ (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.5 & 4.10 & C & 4.07 & {\AVFZ} \\ - &$^3\Delta_u (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.2 & 4.78 & B & 4.78 & {\AVFZ} \\ -Glyoxal &$^1A_u (\mathrm{V}; n \rightarrow \pi^\star)$ & 0.000 & 91.0 & 2.88 & B & 2.88 & {\AVQZ} \\ - &$^1B_g (\mathrm{V}; n \rightarrow \pi^\star)$ & & 88.3 & 4.24 & B & 4.24 & {\AVQZ} \\ - &$^1A_g (\mathrm{V}; n,n \rightarrow \pi^\star,\pi^\star)$ & & 0.5 & 5.61 & F & 5.61 & {\AVQZ} \\ - &$^1B_g (\mathrm{V}; n \rightarrow \pi^\star)$ & & 83.9 & 6.57 & B & 6.58 & {\AVQZ} \\ - &$^1B_u (\mathrm{R}; n \rightarrow 3p)$ & 0.095 & 91.7 & 7.71 & B & 7.75 & {\AVQZ} \\ - &$^3A_u (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.6 & 2.49 & {\CCSDT}/{\AVTZ} & 2.49 & {\AVQZ} \\ - &$^3B_g (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.4 & 3.89 & {\CCSDT}/{\AVTZ} & 3.90 & {\AVQZ} \\ - &$^3B_u (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.5 & 5.15 & {\CCSDT}/{\AVTZ} & 5.16 & {\AVQZ} \\ - &$^3A_g (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.8 & 6.30 & {\CCSDT}/{\AVTZ} & 6.31 & {\AVQZ} \\ -Isobutene &$^1B_1 (\mathrm{R}; \pi \rightarrow 3s)$ & 0.006 & 94.1 & 6.46 & {\CCSDT}/{\AVTZ} & 6.48 & {\AVQZ} \\ - &$^1A_1 (\mathrm{R}; \pi \rightarrow 3p)$ & 0.228 & 94.2 & 7.01 & {\CCSDT}/{\AVTZ} & 7.00 & {\AVQZ} \\ - &$^3A_1 \mathrm{V}; (\pi \rightarrow \pi^\star)$ & & 98.9 & 4.53 & D & 4.54 & {\AVQZ} \\ -Methylenecyclopropene& $^1B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & 0.011 & 85.4 & 4.28 & B & 4.28 & {\AVQZ} \\ - &$^1B_1 (\mathrm{R}; \pi \rightarrow \sigma^\star)$ & 0.005 & 93.6 & 5.44 & B & 5.47 & {\AVQZ} \\ - &$^1A_2 (\mathrm{R}; \pi \rightarrow 3p)$ & & 93.3 & 5.96 & B & 5.99 & {\AVQZ} \\ - &$^1A_1(\mathrm{V}; \pi \rightarrow \pi^\star)$ & 0.224 & 92.8 & 6.12 & B & 6.08 & {\AVQZ} \\ - &$^3B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 97.2 & 3.50 & D & 3.50 & {\AVQZ} \\ - &$^3A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.6 & 4.74 & D & 4.75 & {\AVQZ} \\ -Propynal & $^1A'' (\mathrm{V}; n \rightarrow \pi^\star)$ & 0.000 & 89.0 & 3.80 & {\CCSDT}/{\AVTZ} & 3.81 & {\AVQZ} \\ - &$^1A'' (\mathrm{V}; \pi \rightarrow \pi^\star)$ & 0.000 & 92.9 & \hl{5.54} & {\CCSDT}/{\AVTZ} & \hl{5.53} & {\AVQZ} \\ - &$^3A'' (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.4 & 3.47 & D & 3.48 & {\AVQZ} \\ - &$^3A' (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.3 & 4.47 & D & 4.48 & {\AVQZ} \\ -Thioacetone &$^1A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 88.9 & \hl{xxx} & \hl{xxx} & \hl{xxx} & {\AVQZ} \\ - &$^1B_2 (\mathrm{R}; n \rightarrow 4s)$ & 0.052 & 91.3 & \hl{xxx} & \hl{xxx} & \hl{xxx} & {\AVQZ} \\ - &$^1A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & 0.242 & 90.6 & \hl{xxx} & \hl{xxx} & \hl{xxx} & {\AVQZ} \\ - &$^1A_1 (\mathrm{R}; n \rightarrow 4p)$ & 0.023 & 91.6 & \hl{xxx} & \hl{xxx} & \hl{xxx} & {\AVQZ} \\ - &$^1B_2 (\mathrm{R}; n \rightarrow 4p)$ & 0.028 & 92.4 & \hl{xxx} & \hl{xxx} & \hl{xxx} & {\AVQZ} \\ - &$^3A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.4 & 2.33 & D & 2.34 & {\AVQZ} \\ - &$^3A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.7 & 3.45 & D & 3.46 & {\AVQZ} \\ -Thiopropynal &$^1A'' (\mathrm{V}; n \rightarrow \pi^\star)$ & 0.000 & 87.5 & \hl{xxx} & \hl{xxx} & \hl{xxx} & {\AVQZ} \\ - &$^3A'' (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.2 & \hl{xxx} & \hl{xxx} & \hl{xxx} & {\AVQZ} \\ - \end{longtable} - \end{footnotesize} -\begin{flushleft}\begin{footnotesize}\begin{singlespace} -$^a${ -Method A: {\CCSDT}/{\AVTZ} value corrected by the difference between {\CCSDTQ}/{\AVDZ} and {\CCSDT}/{\AVDZ} results; -Method B: {\CCSDT}/{\AVTZ} value corrected by the difference between {\CCSDTQ}/{\Pop} and {\CCSDT}/{\Pop} results; -Method C: {\CCT}/{\AVTZ} value corrected by the difference between {\CCSDTQ}/{\Pop} and {\CCT}/{\Pop} results; -Method D: {\CCT}/{\AVTZ} value corrected by the difference between {\CCSDT}/{\AVDZ} and {\CCT}/{\AVDZ} results; -Method E: {\CCT}/{\AVTZ} value corrected by the difference between {\CCSDT}/{\Pop} and {\CCT}/{\Pop} results; -Method F: {exCI}/{\AVDZ} value (from Ref. \citenum{Loo19c}) corrected by the difference between {\CCSDT}/{\AVTZ} and {\CCSDT}/{\AVDZ} results; -Method G: {exCI}/{\Pop} value (this work) corrected by the difference between {\CCT}/{\AVTZ} and {\CCT}/{\Pop} results; -} -\end{singlespace}\end{footnotesize}\end{flushleft} - - -\section{Benchmarks} - -\section{Conclusions and outlook} - - -\begin{suppinfo} -\end{suppinfo} - -\begin{acknowledgement} -D.J.~acknowledges the \emph{R\'egion des Pays de la Loire} for financial support. This research used resources of i) the GENCI-CINES/IDRIS (Grant 2016-08s015); ii) CCIPL (\emph{Centre de Calcul Intensif des Pays de Loire}); -iii) the Troy cluster installed in Nantes; and iv) CALMIP under allocations 2018-0510 and 2018-18005 (Toulouse). -\end{acknowledgement} - -\bibliography{biblio-new} -\clearpage - -\begin{tocentry} -\begin{center} -%\includegraphics[scale=.17]{TOC.png} -\end{center} -\end{tocentry} - - -\end{document} +\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} +\usepackage[version=4]{mhchem} + +\usepackage[normalem]{ulem} + +\definecolor{darkgreen}{RGB}{0, 180, 0} +\newcommand{\titou}[1]{\textcolor{purple}{#1}} +\newcommand{\beurk}[1]{\textcolor{darkgreen}{#1}} +\newcommand{\trash}[1]{\textcolor{purple}{\sout{#1}}} + + +\newcommand{\mc}{\multicolumn} +\newcommand{\mr}{\multirow} +\newcommand{\ra}{\rightarrow} +\newcommand{\eg}{\textit{e.g.}} +\newcommand{\ie}{\textit{i.e.}} + +% energies +\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)$} + +% methods +\newcommand{\TDDFT}{TD-DFT} +\newcommand{\CASSCF}{CASSCF} +\newcommand{\CASPT}{CASPT2} +\newcommand{\NEV}{NEVPT2} +\newcommand{\PNEV}{PC-NEVPT2} +\newcommand{\SNEV}{SC-NEVPT2} +\newcommand{\AD}{ADC(2)} +\newcommand{\AT}{ADC(3)} +\newcommand{\CCD}{CC2} +\newcommand{\CCSD}{CCSD} +\newcommand{\STEOM}{STEOM-CCSD} +\newcommand{\CCT}{CC3} +\newcommand{\EOMCCSD}{EOM-CCSD} +\newcommand{\CCSDT}{CCSDT} +\newcommand{\CCSDTQ}{CCSDTQ} +\newcommand{\CCSDTQP}{CCSDTQP} +\newcommand{\CI}{CI} +\newcommand{\sCI}{sCI} +\newcommand{\exCI}{exCI} +\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{\AVFZ}{\emph{aug}-cc-pV5Z} +\newcommand{\DAVQZ}{d-\emph{aug}-cc-pVQZ} +\newcommand{\TAVQZ}{t-\emph{aug}-cc-pVQZ} +\newcommand{\AVPZ}{\emph{aug}-cc-pV5Z} +\newcommand{\DAVPZ}{d-\emph{aug}-cc-pV5Z} + +% units +\newcommand{\IneV}[1]{#1 eV} +\newcommand{\InAU}[1]{#1 a.u.} +\newcommand{\InAA}[1]{#1 \AA} +\newcommand{\MaxP}{Max($+$)} +\newcommand{\MaxN}{Max($-$)} + +% greek shortcut +\newcommand{\pis}{\pi^\star} +\newcommand{\Ryd}{\mathrm{R}} + +\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} + +\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} +\begin{abstract} +Following our previous work focussing on compounds containing up to 3 non-hydrogen atoms [\emph{J. Chem. Theory Comput.} {\bfseries 14} (2018) 4360--4379], we present here highly-accurate vertical transition energies +obtained for 27 molecules encompassing 4, 5, and 6 non-hydrogen atoms: acetone, acrolein, benzene, butadiene, cyanoacetylene, cyanoformaldehyde, cyanogen, cyclopentadiene, cyclopropenone, cyclopropenethione, +diacetylene, furan, glyoxal, imidazole, isobutene, methylenecyclopropene, propynal, pyrazine, pyridazine, pyridine, pyrimidine, pyrrole, tetrazine, thioacetone, thiophene, thiopropynal, and triazine. +To obtain these energies, we use equation-of-motion coupled cluster theory up to the highest technically possible excitation order ({\CCT}, {\CCSDT}, and {\CCSDTQ}), selected configuration interaction ({\sCI}) calculations (with tens of millions of determinants in the reference space), +as well as the $n$-electron valence state perturbation theory (NEVPT2). +All these approaches were applied in combination with diffuse-containing atomic basis sets. For all transitions, we report at least {\CCT}/{\AVQZ} vertical excitation +energies as well as {\CCT}/{\AVTZ} oscillator strengths for each dipole-allowed transition. We show that {\CCT} almost systematically delivers transition energies in agreement with higher-level theoretical methods with a typically deviation of $\pm 0.04$ eV, except for transitions presenting a dominant double excitation character where the error is much larger. +This contribution gathers a large, diverse and accurate set of more than 200 highly-accurate transition energies for states of various natures +(valence, Rydberg, singlet, triplet, $n \ra \pi^\star$, $\pi \ra \pi^\star$, \ldots). +We use this series of theoretical best estimates to benchmark a series of popular methods for excited state calculations: CIS(D), {\AD}, +{\CCD}, {\STEOM}, {\CCSD}, CCSDR(3), CCSDT-3, and {\CCT}. The results of these benchmarks are compared to the available literature data. +\end{abstract} +\clearpage + +% +% I. Introduction +% +\section{Introduction} + +Accurately describing transition energies between the electronic ground state (GS) and excited states (ES) remains an important challenge in quantum chemistry. When dealing with large compounds in complex environments, +one is typically limited to the use of time-dependent density-functional theory (TD-DFT), \cite{Cas95,Ulr12b,Ada13a} a successful yet far from flawless approach. In particular, to perform TD-DFT calculations, one must +choose an ``appropriate'' exchange-correlation functional, which is difficult yet primordial as the impact of the exchange-correlation functional is exacerbated in TD-DFT as compared to DFT. \cite{Lau13} Such selection can, of course, rely +on the intrinsic features of each exchange-correlation functional, \eg, it is well-known that range-separated hybrids provide a more physically-sound description of long-range charge-transfer transitions than semi-local exchange-correlation functionals. \cite{Dre04,Pea08} +However, to obtain a quantitative assessment of the accuracy that can be expected from TD-DFT calculations, benchmarks are needed. This is why many assessment of TD-DFT performances for various properties are +available. \cite{Lau13} While several of these benchmarks use experimental data as reference, typically band shapes \cite{Die04,Die04b,Avi13,Cha13,Lat15b,Mun15,Vaz15,San16b} or 0-0 energies, +\cite{Die04b,Goe10a,Jac12d,Chi13b,Win13,Fan14b,Jac14a,Jac15b,Loo19b} using theoretical best estimates (TBE) obtained with more refined levels of theory as references, \cite{Sch08,Sau09,Sil10b,Sil10c,Sch17,Loo18a} +is advantageous as it allows comparisons on a perfectly equal footing (same geometry, vertical transitions, no environmental effects...). For such works, the challenge is in fact to obtain accurate TBE, as high-level theories +generally come with a dreadful scaling with system size and, in addition, typically require large atomic basis sets to deliver transition energies close to the basis set limit. + +More than 20 years ago, Serrano-Andr\`es, Roos, and their coworkers proposed an impressive series of reference transition energies for several typical conjugated organic molecules (butadiene, furan, pyrrole, tetrazine...). +\cite{Ful92,Ser93,Ser93b,Ser93c,Lor95b,Mer96,Mer96b,Roo96,Ser96b} To this end, they relied on the Complete Active Space Second-Order Perturbation Theory ({\CASPT}) approach with the largest active spaces and basis sets +they could offer at that time, typically using experimental GS geometries. Beyond comparisons with experiments, which are always challenging when computing vertical transition energies, \cite{San16b} there was no approach +available at that time to ascertain the accuracy of the obtained transition energies. These {\CASPT} values were latter used to assess the performances of TD-DFT combined with various exchange-correlation functionals, \cite{Toz99b,Bur02} and remained for a long +time the best references available. A decade ago, Thiel and coworkers defined TBE for 104 singlet and 63 triplet valence ES in 28 small and medium conjugated CNOH organic molecules. \cite{Sch08,Sil10b,Sil10c} These TBE +were computed on MP2/6-31G(d) structures with several levels of theories, notably {\CASPT} and various Coupled-Cluster levels ({\CCD}, {\CCSD}, and {\CCT}). Interestingly, while the default reference approach used by Thiel to define his +first series of TBE was {\CASPT}, \cite{Sch08} the majority of the most recent TBE (so-called ``TBE-2'' in Ref. \citenum{Sil10c}) were determined at the {\CCT}/{\AVTZ} level, often using a basis set extrapolation technique. +In more details, CC3/TZVP values were typically corrected for basis set effects by the difference between {\CCD}/{\AVTZ} and {\CCD}/TZVP results. \cite{Sil10b,Sil10c} Many works used Thiel's TBE for +assessing low-order methods, \cite{Sil08,Goe09,Jac09c,Roh09,Sau09,Jac10c,Jac10g,Sil10,Mar11,Jac11a,Hui11,Del11,Tra11,Pev12,Dom13,Dem13,Sch13b,Voi14,Har14,Yan14b,Sau15,Pie15,Taj16,Mai16,Ris17,Dut18,Hel19} highlighting +their value for the community. In contrast, the number of extensions of this original set remains quite limited, i.e., {\CCSDT}/TZVP reference energies computed for 17 singlet states of six molecules appeared in 2014, \cite{Kan14} +and 46 {\CCSDT}/{\AVTZ} transition energies in small compounds containing two or three non-hydrogen atoms (ethylene, acetylene, formaldehyde, formaldimine, and formamide) have been described in 2017. \cite{Kan17} +This has motivated us to propose two years ago a set of 106 transition energies for which it was technically possible to reach the Full Configuration Interaction (FCI) limit by performing high-order Coupled-Cluster (up to {\CCSDTQP}) and selected +CI (sCI) transition energy calculations on {\CCT} GS structures. \cite{Loo18a} We used these TBE to benchmark many ES theories. \cite{Loo18a} Amongst our conclusions, we found that {\CCSDTQ} was on the {\FCI} spot, whereas we could not +detect significant differences of accuracies between {\CCT} and {\CCSDT}, both being very accurate with mean absolute errors (MAE) as small as 0.03 eV compared to {\FCI} for ES with a single excitation character. These conclusions +agree well with earlier studies. \cite{Wat13,Kan14,Kan17} We also recently proposed a set of 20 TBE for transitions presenting a large double excitation character. \cite{Loo19c} For such transitions, one can distinguish the ES +as a function of $\%T_1$, the percentage of single excitation calculated at the {\CCT} level. For ES with a significant yet not dominant double excitation character, such as the famous $A_g$ ES of butadiene ($\%T_1$=75\%), +CC methods including triples in the GS treatment deliver rather accurate estimates (MAE of 0.11 eV with {\CCT} and 0.06 eV with {\CCSDT}), surprisingly outperforming second-order multi-reference schemes such as {\CASPT} or +the generally robust $N$-Electron Valence State Perturbation Theory ({\NEV}). In contrast, for ES with a dominant double excitation character, e.g., the low-lying $n,n \rightarrow \pi^\star,\pi^\star$ excitation in nitrosomethane ($\%T_1$=2\%), +single-reference methods are not suited (MAE of 0.86 eV with {\CCT} and 0.42 eV with {\CCSDT}) and multi-reference methods are, in practice, required to obtain accurate results. \cite{Loo19c} Obviously, a clear limit of our 2018 work\cite{Loo18a} +is that we treated only compounds containing 1--3 non-hydrogen atoms, hence introducing a significant chemical bias. Therefore we have decided to go for larger molecules and we consider in the present contribution organic +compounds encompassing 4, 5, and 6 non-hydrogen atoms. For such systems, performing {\CCSDTQ} calculations with large bases remains a dream, and, the convergence of {\sCI} with the number of determinants is slower +as well, so that extrapolating to the {\FCI} limit with a ca. 0.01 eV error bar is rarely doable in practice. Consequently, the ``brute-force'' determination of {\FCI}/CBS estimates, as in our earlier work,\cite{Loo18a} is beyond reach. +Anticipating this problem, we have previously demonstrated that one can very accurately estimate such limit by correcting values obtained with a high-level of theory and a double-$\zeta$ basis set by {\CCT} results obtained with a +larger basis, \cite{Loo18a} and we glibally follow such strategy here. In addition, we also performed {\NEV} calculations in an effort to check the consistency of our estimates, especially for ES with intermediate $\%T_1$ values. +Using this protocol, we define a set of more than 200 {\AVTZ} reference transition energies, most being within $\pm$ 0.03 eV for the {\FCI} limit. These reference energies are obtained on {\CCT} geometries and further basis set +corrections up to at least quadruple-$\zeta$, are also provided with {\CCT}. Together with the results obtained in our two earlier works, \cite{Loo18a,Loo19c} the present TBE will hopefully contribute to climb a further step +on the ES accuracy staircase. + +% +% II. Computational Details +% +\section{Computational Details} +\label{sec-met} + +Except otherwise stated, all the transition energies are computed in the frozen-core approximation (with a large core for the sulfur atom). +Pople's {\Pop} and Dunning's \emph{aug}-cc-pVXZ (X $=$ D, T, Q, and 5) atomic basis sets are systematically employed in our excited-state calculations. +Here, we globally follow the same procedure as in Ref.~\citenum{Loo18a}, so that we only briefly outline the models used below. + + +\subsection{Geometries} + +Consistently with our previous work, \cite{Loo18a} we systematically use {\CCT}/{\AVTZ} GS geometries obtained without applying the frozen core approximation. +The cartesian coordinates (in bohr) of each compound can be found in the Supporting Information (SI). +Several structures have been extracted from previous contributions, \cite{Bud17,Jac18a,Bre18a} whereas the missing structures were optimized using Dalton \cite{dalton} and/or CFOUR, \cite{cfour} applying default parameters in both cases. + +\subsection{Selected Configuration Interaction methods} + +All the sCI calculations have been performed in the frozen-core approximation with the latest version of Quantum Package \cite{Gar19} using the Configuration Interaction using a Perturbative Selection made Iteratively (CIPSI) algorithm to select the +most important determinants in the FCI space. Instead of generating all possible excited determinants like a conventional CI calculation, the iterative CIPSI algorithm performs a sparse exploration of the FCI space via a selection of the most relevant +determinants using a second-order perturbative criterion. At each iteration, the variational (or reference) space is enlarged with new determinants. CIPSI can be seen as a deterministic version of the FCIQMC algorithm developed by Alavi and +coworkers. \cite{Boo09} We refer the interested reader to Ref.~\citenum{Gar19} where our implementation of the CIPSI algorithm is detailed. + +Excited-state calculations are performed within a state-averaged formalism which means that the CIPSI algorithm select determinants simultaneously for the GS and ES. Therefore, all electronic states share the same set of determinants with different CI coefficients. +Our implementation of the CIPSI algorithm for ES is detailed in Ref.~\citenum{Sce19}. For each system, a preliminary sCI calculation is performed using Hartree-Fock orbitals in order to generate sCI wavefunctions with at least 5,000,000 determinants. +State-averaged natural orbitals are then computed based on this wavefunction, and a new, larger sCI calculation is performed with this new set of orbitals. This has the advantage to produce a smoother and faster convergence of the sCI energy to the FCI limit. +For the largest systems, an additional iteration is sometimes required in order to obtain better quality natural orbitals and hence well-converged calculations. + +The total sCI energy is defined as the sum of the (zeroth-order) variational energy (computed via diagonalization of the CI matrix in the reference space) and a second-order perturbative correction which takes into account the external determinants, \ie, +the determinants which do not belong to the variational space but are linked to the reference space via a non-zero matrix element. The magnitude of this second-order correction, $E^{(2)}$, provides a qualitative idea of the ``distance" to the FCI limit. +For maximum efficiency, the total sCI energy is linearly extrapolated to $E^{(2)} = 0$ (which effectively corresponds to the FCI limit) using the two largest sCI wavefunctions. These extrapolated total energies simply (labeled as FCI in the remaining of the paper) +are then used to computed vertical excitation energies. Although it is not possible to provide a theoretically-sound error bar, we estimate the extrapolation error by the difference in excitation energy between the largest sCI wavefunction and its corresponding +extrapolated value. We believe that it provides a very safe estimate of the extrapolation error. Additional information about the sCI wavefunctions and excitation energies as well as their extrapolated values can be found in the SI. + + +\subsection{NEVPT2} + +The {\NEV} calculations have been performed with MOLPRO \cite{molpro} within the partially-contracted scheme ({\PNEV}), which is theoretically superior to its strongly-contracted version due to the larger number of perturbers and greater flexibility. \cite{Ang01,Ang01b,Ang02} +These {\NEV} calculations are performed on top of a state-averaged CASSCF calculation. + + +\hl{Martial: you to play} + +\hl{xxxxx} + +\hl{xxxxx} + +\hl{xxxxx} + +\hl{xxxxx} + +In the following, {\NEV} stands systematically for {\PNEV}. + active space in the SI ? + + +\subsection{Other wavefunction calculations} + +For the other levels of theory, we apply a variety of programs, namely, CFOUR,\cite{cfour} Dalton,\cite{dalton} Gaussian,\cite{Gaussian16} Orca,\cite{Nee12} MRCC,\cite{Rol13,mrcc} and Q-Chem. \cite{Sha15} CFOUR is used for + {\CCT}, \cite{Chr95b,Koc97} CCSDT-3, \cite{Wat96,Pro10} {\CCSDT} \cite{Nog87} and {\CCSDTQ}\cite{Kuc91}; Dalton for {\CCD}, \cite{Chr95,Hat00} {\CCSD},\cite{Pur82} CCSDR(3), \cite{Chr96b} and {\CCT} \cite{Chr95b,Koc97}; Gaussian +for CIS(D); \cite{Hea94,Hea95} Orca for the similarity-transformed EOM-CCSD ({\STEOM})\cite{Noo97,Dut18}; MRCC for {\CCSDT} \cite{Nog87} and {\CCSDTQ}; \cite{Kuc91} and Q-Chem for {\AD}. \cite{Dre15} +Default program setting are applied. We underline that for the {\STEOM} we report only states that are characterized by an active character percentage of 98\%\ or larger. +% +% III. Results & Discussion +% +\section{Main results} +\label{sec-res} + +In the following, we present the results obtained for molecules containing four, five, and six (non-hydrogen) atoms. In all cases, we test several atomic basis sets and push the CC expansion as far as technically doable. +Given that the {\sCI} results converges rather slowly for these rather large systems, we provide an estimated error bar for these extrapolated {\FCI} values (\emph{vide supra}). In most cases, the latter are used as a safety net to demonstrate the +consistency of the approaches rather than as definitive TBE (see next Section). We also show the results of {\NEV}/{\AVTZ} calculations for all relevant states to have a further consistency check. We underline that, except +when specifically discussed, all ES present a dominant single-excitation character (see also next Section), so that we do not expect serious CC breakdowns. This is especially true for the triplet ES that are known to show +very large \%$T_1$ for the vast majority of states, \cite{Sch08} and we consequently put our maximal computational effort on determining accurate transition energies for singlet states. To assign the different ES, we use literature data, as well as +usual criteria, i.e., relative energies, symmetries and compositions of the underlying MOs, as well as oscillator strengths. This allows clear-cut assignment for the vast majority of the cases. There are however some +state/method combination for which strong mixing between ES of the same symmetry makes unambiguous assignments beyond reach, which is a typical problem in such works. Such cases are however not statistically +relevant and are therefore unlikely to change any of our main conclusions. + +\subsection{Four-atom molecules} + +\subsubsection{Cyanoacetylene, cyanogen, and diacetylene} + +\begin{sidewaystable}[htp] +\caption{\small Vertical transition energies determined in cyanoacetylene, cyanogen, and diaectylene. All states have a valence $\pi \rightarrow \pi^\star$ character. All values are in eV.} +\label{Table-1} + \begin{footnotesize} +\begin{tabular}{l|p{.5cm}p{1.0cm}p{1.2cm}p{1.4cm}|p{.5cm}p{1.0cm}p{1.2cm}p{1.4cm}|p{.5cm}p{1.0cm}p{1.2cm}|p{.5cm}|p{.5cm}|p{.6cm}p{.6cm}} +\hline + \multicolumn{14}{c}{Cyanoacetylene}\\ + & \multicolumn{4}{c}{\Pop} & \multicolumn{4}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{1}{c}{\AVQZ} & \multicolumn{1}{c}{\AVFZ} & \multicolumn{2}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI}& {\CCT} & {\CCSDT} & {\NEV} & {\CCT} & {\CCT}& Th.$^a$ & Exp.$^b$ \\ +\hline +$^1\Sigma^-$ &6.02&6.04&6.02&6.02$\pm$0.01 &5.92&5.92&5.91&5.84$\pm$0.09 &5.80&5.81&5.78& 5.79 &5.79 &5.46&4.77\\ +$^1\Delta$ &6.29&6.31&6.29&6.28$\pm$0.01 &6.17&6.19&6.17&6.14$\pm$0.05 &6.08&6.09&6.10& 6.06 &6.06 &5.81&5.48\\ +$^3\Sigma^+$ &4.44&4.45& &4.45$\pm$0.03 &4.43&4.43& &4.41$\pm$0.06 &4.45&4.44&4.45& 4.46 &4.47 &&\\ +$^3\Delta$ &5.35&5.34& &5.32$\pm$0.03 &5.28&5.27& &5.20$\pm$0.08 &5.22&5.21&5.19& 5.22 &5.22 &&\\ +$^1A''$[F]$^c$ &3.70&3.72&3.70&3.67$\pm$0.03 &3.60&3.62&3.60&3.59$\pm$0.02 &3.54&3.56&3.50& 3.54 & &&\\ +\hline + \multicolumn{14}{c}{Cyanogen}\\ + & \multicolumn{4}{c}{\Pop} & \multicolumn{4}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{1}{c}{\AVQZ} & \multicolumn{1}{c}{\AVFZ} & \multicolumn{1}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI}& {\CCT} & {\CCSDT} & {\NEV}& {\CCT} & {\CCT}& Exp.$^d$ \\ +\hline +$^1\Sigma_u^-$ &6.62&6.63&6.62&6.58$\pm$0.03 &6.52&6.52&6.51&6.44$\pm$0.08 &6.39&6.40&6.32& 6.38 &6.38 &5.63\\ +$^1\Delta_u$ &6.88&6.89&6.88&6.87$\pm$0.02 &6.77&6.78&6.77&6.74$\pm$0.04 &6.66&6.67&6.66& 6.64 &6.64 &5.99\\ +$^3\Sigma_u^+$ &4.92&4.92&4.94&4.91$\pm$0.06 &4.89&4.89& &4.87$\pm$0.07 &4.90&4.89&4.88& 4.91 &4.91 &4.13\\ +$^1\Sigma_u^-$[F]$^c$ &5.27&5.28&5.26&5.31$\pm$0.05 &5.19&5.20&5.18&5.26$\pm$0.09 &5.06&5.07&4.97& 5.05 &5.05 & \\ +\hline + \multicolumn{14}{c}{Diacetylene}\\ + & \multicolumn{4}{c}{\Pop} & \multicolumn{4}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{1}{c}{\AVQZ} & \multicolumn{1}{c}{\AVFZ} & \multicolumn{1}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI}& {\CCT} & {\CCSDT} & {\NEV}& {\CCT} & {\CCT}& Exp.$^e$ \\ +\hline +$^1\Sigma_u^-$ &5.57&5.58&5.56&5.52$\pm$0.06 &5.44&5.45&5.43&5.47$\pm$0.02 &5.34&5.35&5.33& 5.33 &5.33 &4.81\\ +$^1\Delta_u$ &5.83&5.85& &5.84$\pm$0.01 &5.69&5.70&5.69&5.69$\pm$0.02 &5.61&5.62&5.61& 5.60 &5.60 &5.06\\ +$^3\Sigma_u^+$ &4.07&4.08&4.09&4.04$\pm$0.07 &4.06&4.06& &4.07$\pm$0.04 &4.08& &4.08& 4.10 &4.11 &2.7 \\ +$^3\Delta_u$ &4.93&4.93&4.92&4.94$\pm$0.01 &4.86&4.85& &4.85$\pm$0.02 &4.80&4.79&4.78& 4.80 &4.80 &3.21\\ +\hline + \end{tabular} + \end{footnotesize} +\vspace{-0.5 cm} +\begin{flushleft} +\begin{footnotesize} +$^a${{\CASPT} from Ref. \citenum{Luo08};} +$^b${Experimental 0-0 energies from Refs. \citenum{Job66a} and \citenum{Job66b} (vacuum UV experiments);} +$^c${Vertical fluorescence energy from the lowest excited-state;} +$^d${Experimental 0-0 energies from Refs. \citenum{Cal63} ($^3\Sigma_u^+$), \citenum{Bel69} ($^1\Sigma_u^-$), and \citenum{Fis72} ($^1\Delta_u$), all analyzing vacuum electronic spectra;} +$^e${Experimental 0-0 energies from Ref. \citenum{Hai79} (singlet ES, vacuum UV experiment) and Ref. \citenum{All84} (triplet ES, EELS). In the latter contribution, the 2.7 eV value for the $^3\Sigma_u^+$ +state is the onset, whereas an estimate of the vertical energy of 4.2$\pm$0.2 eV is given for the $^3\Delta_u$ state.} +\end{footnotesize} +\end{flushleft} +\end{sidewaystable} + +The ES of these three closely-related linear molecules containing two triple bonds have been quite rarely investigated with theory, \cite{Fis03,Pat06,Luo08,Loo18b,Loo19a} though (rather old) measurements of their +0-0 energies are available for several ES. \cite{Cal63,Job66a,Job66b,Bel69,Fis72,Har77,Hai79,All84} Our main results are collected in Tables \ref{Table-1} and S1. We consider only low-lying +valence $\pi \rightarrow \pi^\star$ transitions, and, all have a strongly dominant single excitation character (\%$T_1 > 90$, \emph{vide infra}). For cyanoacetylene, the {\FCI} estimates come with small error bars +with {\Pop} and one notes an excellent agreement between these values and their {\CCSDTQ} counterparts, a statement holding for the Dunning's double-$\zeta$ basis for which the {\FCI} uncertainities are however +larger. Using the {\CCSDTQ} values as references, it appears that the previously obtained {\CASPT} estimates\cite{Luo08} are too low and that the {\CCT} transition energies are slightly more accurate than +their CCSDT counterparts, although all CC estimates of Table \ref{Table-1} come in a very tight energetic window for a given basis set. There is also a superb agreement between the CC and {\NEV} values with the +{\AVTZ} basis set. All these facts give high confidence that the CC estimates can be trusted. The basis set effects are quite significant for the valence excited-states of cyanoacetylene with successive drops of the transitions +energies by ca. -0.10 eV, when going from {\Pop} to {\AVDZ} and from {\AVDZ} to {\AVTZ}, but for the lowest triplet state that appears less sensitive to the selected basis. As expected, the changes when further +extending the basis set to quadruple and quintuple-$\zeta$ are trifling, and the same holds when adding a second set of diffuse functions in the basis, or when correlating the core electrons (see the SI). Obviously, +both cyanogen and diacetylene yield very similar trends, with limited methodological effects and quite large basis set effects, but for the transition to the $^3\Sigma_u^+$ ES. We note that all CC3 and CCSDT values are, at worst, +within $\pm$ 0.02 eV of the {\FCI} window, i.e., all methods presented in Table \ref{Table-1} provide very consistent estimates. Across all states reported in that Table with {\AVTZ}, the average absolute deviation between {\NEV} and {\CCT} +({\CCSDT}) is as small as 0.02 (0.03) eV, the lowest absorption and emission energies of cyanogen being the only two cases showing significant deviations. As a final note, all our vertical absorption (emission) energies are significantly bigger +(smaller) than the experimentally measured 0-0 energies, as it should. We refer the interested reader to previous works, \cite{Fis03,Loo19a} for comparisons of {\CASPT} and {\CCT} values with measured 0-0 energies +for these three compounds. + + +\subsubsection{Cyclopropenone, cyclopropenethione, and methylenecyclopropene} + +These three related compounds present a three-member $sp^2$ carbon cycle conjugated to an external $\pi$ bond. While the ES of methylenecyclopropene has regularly been investigated with theoretical tools in the past, +\cite{Mer96,Roo96,Car10b,Lea12,Gua13,Dad14,Gua14,Sch17,Bud17} the only investigations of vertical transitions we could find for the two other derivatives are the detailed 2002 {\CASPT} study of Serrano-Andr\'es and +coworkers on both compounds, \cite{Ser02} and a more recent work reporting the three lowest-lying singlet states of cyclopropenone at the {\CASPT}/6-31G level.\cite{Liu14b} + + +\begin{table}[htp] +\caption{\small Vertical transition energies determined in cyclopropenone, cyclopropenethione, and methylenecyclopropene. All values are in eV.} +\label{Table-2} + \begin{footnotesize} +\begin{tabular}{l|p{.5cm}p{.9cm}p{1.1cm}p{1.4cm}|p{.5cm}p{.9cm}|p{.5cm}p{.9cm}p{1.2cm}|p{.6cm}p{.6cm}p{.6cm}} +\hline + \multicolumn{12}{c}{Cyclopropenone}\\ + & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{2}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV} & Th.$^a$ & Exp.$^b$ \\ +\hline +$^1B_1 (n \rightarrow \pi^\star)$ &4.32&4.34&4.36& 4.38$\pm$0.02 &4.22&4.23 &4.21&4.24&4.04 &4.25&4.13 \\%4.50 in Liu14b MS-CASPT2/6-31G +$^1A_2 (n \rightarrow \pi^\star)$ &5.68&5.65&5.65& 5.64$\pm$0.06 &5.59&5.56 &5.57&5.55&5.85 &5.59&5.5 \\%5.18 in Liu14b +$^1B_2 (n \rightarrow 3s)$ &6.39&6.38&6.41& &6.21&6.19 &6.32&6.31&6.51 &6.90&6.22 \\%6.44 in Liu14b +$^1B_2 (\pi \rightarrow \pi^\star$) &6.70&6.67&6.68& &6.56&6.54 &6.54&6.53&6.82 &5.96&6.1 \\ +$^1B_2 (n \rightarrow 3p)$ &6.92&6.91&6.94& &6.88&6.86 &6.96&6.95&7.07 &7.24&6.88 \\ +$^1A_1 (n \rightarrow 3p)$ &7.00&7.00&7.03& &6.88&6.87 &7.00&6.99&7.28 &7.28& \\ +$^1A_1 (\pi \rightarrow \pi^\star)$ &8.51&8.49&8.51& &8.32&8.29 &8.28&8.26&8.19 &7.80&$\sim$8.1 \\ +$^3B_1 (n \rightarrow \pi^\star)$ &4.02&4.03& & 4.00$\pm$0.07 &3.90&3.92 &3.91&3.93&3.51 &4.05& \\ +$^3B_2 (\pi \rightarrow \pi^\star)$ &4.92&4.92& & 4.95$\pm$0.00 &4.90&4.89 &4.89&4.88&5.10 &4.81& \\ +$^3A_2 (n \rightarrow \pi^\star)$ &5.48&5.44& & &5.38&5.35 &5.37&5.35&5.60 &5.56& \\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &6.89&6.88& & &6.79&6.78 &6.83&6.79&7.16 &6.98& \\ +\hline + \multicolumn{12}{c}{Cyclopropenethione}\\ + & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{2}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV} & Th.$^a$ \\ +\hline +$^1A_2 (n \rightarrow \pi^\star)$ &3.46&3.44&3.44& 3.45$\pm$0.01 &3.47&3.45 &3.43&3.41&3.52 &3.23 & \\ +$^1B_1 (n \rightarrow \pi^\star)$ &3.45&3.44&3.45& 3.44$\pm$0.05 &3.42&3.42 &3.43&3.44&3.50 &3.47 & \\ +$^1B_2 (\pi \rightarrow \pi^\star)$ &4.67&4.64&4.62& 4.59$\pm$0.09 &4.66&4.64 &4.64&4.62&4.77 &4.34 & \\ +$^1B_2 (n \rightarrow 3s)$ &5.26&5.24&5.27& &5.23&5.21 &5.34&5.31&5.35 &4.98 & \\ +$^1A_1 (\pi \rightarrow \pi^\star)$ &5.53&5.52&5.51& &5.52&5.50 &5.49&5.47&5.54 &5.52 & \\ +$^1B_2 (n \rightarrow 3p)$ &5.83&5.81&5.83& &5.86&5.84 &5.93&5.90&5.99 &5.88 & \\ +$^3A_2 (n \rightarrow \pi^\star)$ &3.33&3.31& & 3.29$\pm$0.03 &3.34&3.32 &3.30& &3.38 &3.20 & \\ +$^3B_1 (n \rightarrow \pi^\star)$ &3.34&3.33& & &3.30&3.30 &3.31&3.32&3.40 &3.30 & \\ +$^3B_2 (\pi \rightarrow \pi^\star)$ &4.01&4.00& & 4.03$\pm$0.03 &4.03&4.02 &4.02& &4.17 &3.86 & \\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &4.06&4.04& & &4.09&4.07 &4.03& &4.13 &3.99 & \\ +\hline + \multicolumn{12}{c}{Methylenecyclopropene}\\ + & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{3}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV}& Th.$^c$ & Th.$^d$ & Exp.$^e$\\ +\hline +$^1B_2 (\pi \rightarrow \pi^\star)$ &4.38&4.37&4.34& 4.32$\pm$0.03 &4.32&4.31 &4.31&4.31&4.37 &4.13&4.36 &4.01\\ +$^1B_1 (\pi \rightarrow 3s)$ &5.65&5.66&5.66& &5.35&5.35 &5.44&5.44&5.49 &5.32&5.44 &5.12\\ +$^1A_2 (\pi \rightarrow 3p)$ &5.97&5.98&5.98& 5.92$\pm$0.10 &5.86&5.88 &5.95&5.96&6.00 &5.83& &\\ +$^1A_1(\pi \rightarrow \pi^\star)$$^f$ &6.17&6.18&6.17& 6.20$\pm$0.01 &6.15&6.15 &6.13&6.13&6.36 & &6.13 &6.02\\ +$^3B_2 (\pi \rightarrow \pi^\star)$ &3.50&3.50& & 3.44$\pm$0.06 &3.49&3.49$^g$&3.50&3.49&3.66 &3.24& &\\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &4.74&4.74& & 4.67$\pm$0.10 &4.74&4.74$^g$&4.74& &4.87 &4.52& &\\ +\hline +\end{tabular} + \end{footnotesize} +\vspace{-0.5 cm} +\begin{flushleft} +\begin{footnotesize} +$^a${{\CASPT} of Ref. \citenum{Ser02};} +$^b${Electron impact experiment of Ref. \citenum{Har74}, note that the 5.5 eV peak was assigned differently in the original paper, and we follow here the analysis of Serrano-Andr\'es\cite{Ser02} +whereas the 6.1 eV assignment was ``supposed'' in the original paper; experimental $\lambda_{\mathrm{max}}$ have been measured at at 3.62 eV and 6.52 eV for the $^1B_1 (n \rightarrow \pi^\star)$ and +$^1B_2 (\pi \rightarrow \pi^\star$) transitions, respectively; \cite{Bre72}} +$^c${{\CASPT} of Refs. \citenum{Mer96} and \citenum{Roo96};} +$^d${ {\CCT} of Ref. \citenum{Sch17};} +$^e${$\lambda_{\mathrm{max}}$ in pentane at -78$^o$C from Ref. \citenum{Sta84};} +$^f${Significant state mixing with the $^1A_1(\pi \rightarrow 3p)$ transition, rendering unambiguous attribution difficult;} +$^g${As can be seen in the SI, our {\FCI} estimates are 3.45$\pm$0.04 and 4.79$\pm$0.02 for the two lowest triplet states of methylenecyclopropene with {\AVDZ} hinting that the CC3 and CCSDT +results might be slightly too low for the second transition. } +\end{footnotesize} +\end{flushleft} +\end{table} + + +Our results are listed in Tables \ref{Table-2} and S2. As above, considering the Pople's basis set, we note very small differences between {\CCT}, {\CCSDT}, and {\CCSDTQ} results, the latter method giving transition energies +systematically falling within the {\FCI} extrapolation incertitude, but in one case, the lowest totally symmetric state of methylenecyclopropene for which the {\CCSDTQ} value is ``off'' by 0.02 eV only. Depending on the state, it is +either {\CCT} or {\CCSDT} that is the closest to {\CCSDTQ}. In fact, considering all {\CCSDTQ}/{\Pop} data listed in Table \ref{Table-2} as benchmark, the mean absolute deviation of {\CCT} and {\CCSDT} are 0.019 and 0.016 eV, respectively, +hinting that the improvements brought by the latter more computationally intensive method are limited for these compounds. For the lowest $B_2$ state of methylenecyclopropene, one of the most challenging cases (\%$T_1 = 85\%$), +it is clear from the {\exCI} value that only {\CCSDTQ} is really close to the spot, the {\CCT} and {\CCSDT} results being slightly too large by ca. 0.05 eV. It seems likely that the same pattern appears for the corresponding state in +cyclopropenethione, although in that case the FCI error bar is large, preventing definitive conclusions. Interestingly, the quite small Pople basis set provides data within ca. 0.10 eV of basis set convergence at {\CCT} level for 80\%\ of +the transitions. There are of course exceptions to this rule, e.g., the strongly dipole-allowed $^1A_1 (\pi \rightarrow \pi^\star)$ ES of cyclopropenone and the $^1B_1(\pi \rightarrow 3s)$ ES of methylenecyclopropene are significantly +too blueshifted with the Pople's basis set (Table S2). For cyclopropenone, our {\CCSDT}/{\AVTZ} estimates do agree reasonably well with the {\CASPT} data of Serrano-Andr\'es, but for the $^1B_2 (\pi \rightarrow \pi^\star)$ state +that we locate significantly higher in energy and the three Rydberg states that CC foresees at significantly smaller energies. The current {\NEV} results are globally in better agreement with the CC values than the older {\CASPT} estimates, +though some non-negligible deviations pertain. Even if comparisons with experiments should be made very cautiously, we note that the CC data are clearly more coherent with the electron impact measurements\cite{Har74} for the Rydberg +states than the original {\CASPT} values. For cyclopropenethione, we obtain transition energies typically in agreement or larger than those obtained with {\CASPT}, \cite{Ser02} though there is no obvious relationship between the +valence/Rydberg nature of the considered ES and the relative {\CASPT} error. The average absolute deviation between our {\NEV} and {\CCT} results is 0.08 eV only. Eventually for methylenecyclopropene, our values logically agree +very well with the recent estimates of Schwabe and Goerigk, \cite{Sch17} obtained at the {\CCT}/{\AVTZ} level on a different geometry, whereas the available {\CASPT} values \cite{Mer96,Roo96} appear too low as compared to the +current {\NEV} and {\CCSDT} values. For this compound, the available experimental data being wavelength of maximal absorption determined in condensed phase, \cite{Sta84} only a qualitative match is logically reached between theory and experiment. + +\subsubsection{Acrolein, butadiene, and glyoxal} + +Let us now turn to three pseudo-linear $\pi$-conjugated systems that have been the subject to several ES investigations before, namely, acrolein, \cite{Aqu03,Sah06,Car10b,Lea12,Gua13,Mai14,Aza17b,Sch17,Bat17} +butadiene, \cite{Dal04,Sah06,Sch08,Sil10c,Li11,Wat12,Dad12,Lea12,Ise12,Ise13,Sch17,Shu17,Sok17,Chi18,Cop18,Tra19,Loo19c} and glyoxal, \cite{Sta97b,Koh03,Hat05c,Sah06,Lea12,Poo14,Sch17,Aza17b,Loo18b} +that we all consider in their most stable \emph{trans} conformation in the following. Amongst these works, it is worth highlighting the detailed theoretical investigation by Saha, Ehara, and Nakatsuji, who reported a huge +number of ES in these three systems using a coherent theoretical Symmetry-Adapted-Cluster Configuration-Interaction (SAC-CI) protocol. \cite{Sah06} Our results are listed in Tables \ref{Table-3} and S3. + +\begin{table}[htp] +\caption{\small Vertical transition energies determined in acrolein, butadiene, and glyoxal. All values are in eV.} +\label{Table-3} + \begin{footnotesize} +\begin{tabular}{p{2.9cm}|p{.5cm}p{.9cm}p{1.1cm}p{1.45cm}|p{.5cm}p{.9cm}|p{.5cm}p{.9cm}p{1.2cm}|p{.6cm}p{.6cm}p{.6cm}} +\hline + \multicolumn{12}{c}{Acrolein}\\ + & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{3}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV} & Th.$^a$ & Th.$^b$ & Exp.$^c$ \\ +\hline +$^1A'' (n \rightarrow \pi^\star)$ &3.83&3.80& &3.85$\pm$0.01&3.77&3.74& 3.74&3.73&3.76 &3.63&3.83&3.71 \\ +$^1A' (\pi \rightarrow \pi^\star)$ &6.83&6.86& &6.59$\pm$0.05$^f$&6.67&6.70& 6.65&6.69&6.67 &6.10&6.92&6.41 \\ +$^1A'' (n \rightarrow \pi^\star)$ &6.94&6.89& & &6.75&6.72& 6.75& &7.16 &6.26&7.40& \\ +$^1A' (n \rightarrow 3s)$ &7.22&7.23& & &6.99&7.00& 7.07& &7.05 &6.97&7.19&7.08 \\ +$^3A'' (n \rightarrow \pi^\star)$ &3.55&3.53& &3.60$\pm$0.01&3.47&3.45& 3.46& &3.46 &3.39&3.61& \\ +$^3A' (\pi \rightarrow \pi^\star)$ &3.94&3.95& &3.98$\pm$0.03&3.95&3.95& 3.94& &3.95 &3.81&3.87& \\ +$^3A' (\pi \rightarrow \pi^\star)$ &6.25&6.23& & &6.22&6.21& 6.19& &6.23 & &6.21& \\ +$^3A'' (n \rightarrow \pi^\star)$ &6.81&6.74& & &6.60& & 6.61& &6.83 & &7.36& \\ +\hline + \multicolumn{12}{c}{Butadiene}\\ + & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{3}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV} & Th.$^b$ & Th.$^d$ & Exp$^e$ \\ +\hline +$^1B_u (\pi \rightarrow \pi^\star)$ &6.41&6.43&6.41&6.41$\pm$0.02 &6.25&6.27& 6.22&6.24 &6.68 &6.33&6.36&5.92\\ +$^1B_g (\pi \rightarrow 3s)$ &6.53&6.55&6.54& &6.26&6.27& 6.33&6.34 &6.44 &6.18&6.32&6.21\\ +$^1A_g (\pi \rightarrow \pi^\star)$ &6.73&6.63&6.56&6.55$\pm$0.04$^f$ &6.68&6.59& 6.67&6.60 &6.70 &6.56&6.60& \\ +$^1A_u (\pi \rightarrow 3p)$ &6.87&6.89&6.87& &6.57&6.59& 6.64&6.66 &6.84 &6.45&6.56&6.64\\ +$^1A_u (\pi \rightarrow 3p)$ &6.93&6.95&6.94&6.95$\pm$0.01 &6.73&6.74& 6.80&6.81 &7.01 &6.65&6.74&6.80\\ +$^1B_u (\pi \rightarrow 3p)$ &7.98&8.00&7.98& &7.86&7.87& 7.68& &7.45 &7.08&7.02&7.07\\ +$^3B_u (\pi \rightarrow \pi^\star)$ &3.35&3.36& &3.37$\pm$0.03 &3.36&3.36& 3.36& &3.40 &3.20& &3.22\\ +$^3A_g (\pi \rightarrow \pi^\star)$ &5.22&5.22& & &5.21&5.21& 5.20& &5.30 &5.08& &4.91\\ +$^3B_g (\pi \rightarrow 3s)$ &6.46&6.47& &6.40$\pm$0.03 &6.20&6.21& 6.28& &6.38 &6.14& &\\ +\hline + \multicolumn{12}{c}{Glyoxal}\\ + & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{3}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV} & Th.$^b$ & Th.$^g$ & Exp.$^h$\\ +\hline +$^1A_u (n \rightarrow \pi^\star)$ &2.94&2.94&2.94& 2.93$\pm$0.03 &2.90&2.90& 2.88&2.88 &2.90 &3.10&2.93 &2.8 \\ +$^1B_g (n \rightarrow \pi^\star)$ &4.34&4.32&4.31&4.28$\pm$0.06 &4.30&4.28& 4.27&4.25 &4.30 &4.68&4.39 &$\sim$4.4\\ +$^1A_g (n,n \rightarrow \pi^\star,\pi^\star)$&6.74&6.24&5.67&5.60$\pm$0.09$^f$ &6.70&6.22& 6.76&6.35 &5.52 &5.66& &\\ +$^1B_g (n \rightarrow \pi^\star)$ &6.81&6.83&6.79& &6.59&6.61& 6.58&6.61 &6.64 &7.54&6.63 &7.45\\ +$^1B_u (n \rightarrow 3p)$ &7.72&7.74&7.76& &7.55&7.56& 7.67&7.69 &7.84 &7.83&7.61 &$\sim$7.7\\ +$^3A_u (n \rightarrow \pi^\star)$ &2.55&2.55& &2.54$\pm$0.04 &2.49&2.49& 2.49&2.49 &2.49 &2.63& &2.5\\ +$^3B_g (n \rightarrow \pi^\star)$ &3.97&3.95& & &3.91&3.90& 3.90&3.89 &3.99 &4.12& &$\sim$3.8\\ +$^3B_u (\pi \rightarrow \pi^\star)$ &5.22&5.20& & &5.20&5.19& 5.17&5.15 &5.17 &5.35& &$\sim$5.2\\ +$^3A_g (\pi \rightarrow \pi^\star)$ &6.35&6.35& & &6.34&6.34& 6.30&6.30 &6.33 & & &\\ +\hline +\end{tabular} + \end{footnotesize} +\vspace{-0.5 cm} +\begin{flushleft} +\begin{footnotesize} +$^a${{\CASPT} of Ref. \citenum{Aqu03};} +$^b${SAC-CI of Ref. \citenum{Sah06};} +$^c${Vacuum UV spectra from Ref. \citenum{Wal45}; for the lowest state, the same 3.71 eV value is reported in Ref. \citenum{Bec70}.} +$^d${MR-AQCC of Ref. \citenum{Dal04}, theoretical best estimates listed for the lowest $B_u$ and $A_g$ states;} +$^e${Electron impact experiment from Refs. \citenum{Fli78} and \citenum{Doe81} for the singlet states and from Ref. \citenum{Mos73} for the two lowest triplet transitions; +note that for the lowest $B_u$ state, there is a vibrational structure with peaks at 5.76, 5.92, and 6.05 eV;} +$^f${From Ref. \citenum{Loo19c};} +$^g${{\CCT} of Ref. \citenum{Sch17};} +$^h${Electron impact experiment from Ref. \citenum{Ver80} but for the second $^1B_g$ ES for which the value is from another work; \cite{Rob85b} note that +for the lowest $^1B_g$ ($^1B_u$) ES, a range of 4.2--4.5 (7.4--7.9) eV is given Ref. \citenum{Ver80}. } +\end{footnotesize} +\end{flushleft} +\end{table} + + +Acrolein, due to its lower symmetry and high density of ES with mixed characters, is challenging for theory and {\CCSDTQ} calculations were technically impossible despite our efforts. For the lowest $n \rightarrow \pi^\star$ +transitions of both spin symmetries, the {\FCI} estimates come with a tiny error bar, and it is obvious that the CC estimates are slightly too low, especially with {\CCSDT}. Nevertheless, at the exception the second singlet +and triplet $A''$ ES, the {\CCT} and {\CCSDT} estimates are within $\pm$0.03 eV of each other. These $A''$ ES are also the only two transitions for which the discrepancies between {\CCT} and {\NEV} exceed 0.20 eV. This hints +at a good accuracy for all other transitions. This statement is supported by the fact that the current CC values are nearly systematically bracketed by previous {\CASPT} (lower bound)\cite{Aqu03} and SAC-CI (higher bound)\cite{Sah06} results, +consistently with the typical error signs of these two models. For the two lowest triplet states, the present {\CCT}/{\AVTZ} values are also within $\pm$0.05 eV of recent MR-CI estimates (3.50 and 3.89 eV). \cite{Mai14} As +can be seen in Table S3, {\AVTZ} allows being very close from basis set convergence, the largest variation when going to {\AVQZ} (+0.04 eV) is obtained for the second $^1A'$ ES of Rydberg nature. As the experimental data +are limited to measured UV spectra, \cite{Wal45,Bec70} one has therefore to be cautious in establishing TBE for acrolein (\emph{vide infra}). + +The nature and relative energies of the lowest bright $B_u$ and dark $A_g$ ES of butadiene have been puzzling theoretical chemists for many years. It is beyond our scope to provide an exhaustive +list of previous calculations and experimental estimates for these two hallmark ES, and we refer the readers to Refs. \citenum{Wat12} and \citenum{Shu17} for overviews and references. For the $B_u$ transition +the best previous TBE we are aware of is the 6.21 eV value obtained by Watson and Chan using a computational strategy similar to ours. \cite{Wat12} Our {\CCSDT}/{\AVTZ} value of 6.24 eV is obviously compatible +with this reference value, and our TBE value is actually 6.21 eV as well (\emph{vide infra}). For the $A_g$ state, we believe that our previous basis-corrected exCI estimate of 6.50 eV \cite{Loo19c} remains +the most accurate available to date. These two values are slightly smaller than the heath-bath CI data obtained by Chien \emph{et al.} with a double-$\zeta$ basis and a slightly different geometry: 6.45 and 6.58 eV for $B_u$ and $A_g$, +respectively. \cite{Chi18} One can of course find many other estimates, e.g., at the SAC-CI, \cite{Sah06} {\CCT}, \cite{Sil10c,Sch17} {\CASPT}, \cite{Sil10c} and {\NEV} levels, \cite{Sok17} for these two ES. +More globally, in butadiene, we find an excellent coherence between the {\CCT}, {\CCSDT}, and {\CCSDTQ} estimates, that all fall in a $\pm$0.02 eV window. Unsurprisingly, this does not apply for the +already mentioned $^1A_g$ ES that is 0.2 and 0.1 eV too high with the two former CC methods, consistent with the large electronic reorganization taking place in that state. For all the other butadiene ES listed in +Table \ref{Table-3}, both {\CCT} and {\CCSDT} can be trusted. We also note that the {\NEV} estimates are within 0.1--0.2 eV of the CC values, but for the lowest $B_u$ ES, which is very dependent on the selected +active space (see the SI). Finally, as can be seen in Table S3, {\AVTZ} is sufficient for most ES, but a significant basis set effect exists for the Rydberg $^1B_u (\pi \rightarrow 3p)$ ES with an energy decrease as large as -0.12 eV +when going from {\AVTZ} to {\AVQZ}. For the records, we note that the available electron impact data \cite{Mos73,Fli78,Doe81} provide the very same ES ordering value as our calculations. + +Globally, the conclusions obtained for acrolein and butadiene pertain for glyoxal, i.e., highly consistent CC estimates, reasonable agreement between {\NEV} and {\CCT} estimates, and limited basis set effects beyond {\AVTZ} +but for the considered Rydberg state (see Tables \ref{Table-3} and S3). This Rydberg $^1B_u (n \rightarrow 3p)$ state also hows a comparatively large deviation between {\CCT} and {\CCSDTQ}, that is 0.04 eV. More interestingly, +glyoxal presents a low-lying ``true'' double ES, $^1A_g (n,n \rightarrow \pi^\star,\pi^\star)$, a transition that is totally unseen by approaches that do not explicitly include double excitations during the calculation of transition energies, e.g., TD-DFT, {\CCSD}, +or {\AD}. Compared to the {\exCI} values, the {\CCT} and {\CCSDT} estimates for this transition are too large by ca. 1.0 and 0.5 eV, respectively, whereas both the {\CCSDTQ} and {\NEV} approaches are much closer to the spot, as already +mentioned in our previous work. \cite{Loo19c} For the other transitions, the present {\CCT} estimates are logically coherent with the values of Ref. \citenum{Sch17} obtained with the same approach on a different +geometry, and remain slightly lower than the SAC-CI estimates of Ref. \citenum{Sah06}. Once more, the experimental data \cite{Ver80,Rob85b} make an unhelpful guide in view of the targeted accuracy. + +\subsubsection{Acetone, cyanoformaldehyde, isobutene, propynal, thioacetone, and thiopropynal} + +Let us now turn towards six other four-atom compounds. There are several earlier estimates of vertical transition energies for both acetone \cite{Gwa95,Mer96b,Roo96,Wib98,Toz99b,Wib02,Sch08,Sil10c,Car10,Pas12,Ise12,Gua13,Sch17} +and isobutene. \cite{Wib02,Car10,Ise12} To the best of our knowledge, the previous computational efforts were mainly focussed on 0-0 energies of the lowest-lying states for the four other compounds. \cite{Koh03,Hat05c,Sen11b,Loo18b,Loo19a} +There are also a few experimental values available for all six derivatives. \cite{Bir73,Jud83,Bra74,Sta75,Joh79,Jud83,Jud84c,Rob85,Pal87,Kar91b,Xin93} Our main data are reported in Tables \ref{Table-4} +and S4. + +\begin{table}[htp] +\caption{\small Vertical transition energies determined in acetone, cyanonformaldehyde, isobutene, propynal, thioacetone, and thiopropynal. All values are in eV.} +\label{Table-4} + \begin{footnotesize} +\begin{tabular}{l|p{.5cm}p{.9cm}p{1.1cm}p{1.4cm}|p{.5cm}p{.9cm}|p{.5cm}p{.9cm}p{1.2cm}|p{.6cm}p{.6cm}p{.6cm}} +\hline + \multicolumn{12}{c}{Acetone}\\ + & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{3}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV} & Th.$^a$ & Th.$^b$ & Exp.$^c$ \\ +\hline +$^1A_2 (n \rightarrow \pi^\star)$ &4.55&4.52&4.53&4.60$\pm$0.05 &4.50&4.48& 4.48&4.46&4.48 &4.18&4.18&4.48\\ +$^1B_2 (n \rightarrow 3s)$ &6.65&6.64&6.68& &6.31&6.30& 6.43&6.42&6.81 &6.58&6.58&6.36\\ +$^1A_2 (n \rightarrow 3p)$ &7.83&7.83&7.87& &7.37&7.36& 7.45&7.43 &7.65 &7.34&7.34&7.36\\ +$^1A_1 (n \rightarrow 3p)$ &7.81&7.81&7.84& &7.39&7.38& 7.48&7.48&7.75 &7.26&7.26&7.41\\ +$^1B_2 (n \rightarrow 3p)$ &7.87&7.87&7.91& &7.56&7.55& 7.59&7.58 &7.91 &7.48&7.48&7.45\\ +$^3A_2 (n \rightarrow \pi^\star)$ &4.21&4.19& &4.18$\pm$0.04 &4.16&4.14& 4.15& &4.20 &3.90&3.90&4.15\\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &6.32&6.30& & &6.31&6.28& 6.28& &6.28 &5.98&5.98&\\ +\hline + \multicolumn{12}{c}{Cyanoformaldehyde}\\ + & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{1}{c}{Litt.}\\\ +State & {\CCT} & {\CCSDT} & & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV} & Exp$^d$ \\ +\hline +$^1A'' (n \rightarrow \pi^\star)$ &3.91&3.89& &3.92$\pm$0.02 &3.86&3.84&3.83 &3.81&3.98& 3.26\\ +$^1A'' (\pi \rightarrow \pi^\star)$ &6.64&6.67& &6.60$\pm$0.07 &6.51&6.54&6.42 &6.46&6.44& \\ +$^3A'' (n \rightarrow \pi^\star)$ &3.53&3.51& &3.48$\pm$0.06 &3.47&3.45&3.46 & &3.58& \\ +$^3A' (\pi \rightarrow \pi^\star)$ &5.07&5.07& & &5.03&5.03&5.01 & &5.35& \\ +\hline + \multicolumn{12}{c}{Isobutene}\\ + & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{3}{c}{Litt.}\\\ +State & {\CCT} & {\CCSDT} & & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV} & Th.$^e$ & Exp.$^f$ & Exp.$^g$ \\ +\hline +$^1B_1 (\pi \rightarrow 3s)$ &6.77&6.77& &6.78$\pm$0.08 &6.39&6.39& 6.45&6.46&6.63&6.40&6.15&6.17 \\ +$^1A_1 (\pi \rightarrow 3p)$ &7.16&7.17& &7.16$\pm$0.02 &7.00&7.00& 7.00&7.01&7.20&6.96& &6.71 \\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &4.52&4.53& &4.56$\pm$0.02 &4.54&4.54& 4.53& &4.61& &4.21 &4.3 \\ +\hline + \multicolumn{12}{c}{Propynal}\\ + & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{1}{c}{Litt.} \\ +State & {\CCT} & {\CCSDT} & & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV} & Exp$^h$ \\ +\hline +$^1A'' (n \rightarrow \pi^\star)$ &3.90&3.87& &3.84$\pm$0.06 &3.85&3.82&3.82 &3.80&3.95& 3.24\\ +$^1A'' (\pi \rightarrow \pi^\star)$ &5.69&5.73& &5.64$\pm$0.08 &5.59&5.62&5.51 &5.54&5.50& \\ +$^3A'' (n \rightarrow \pi^\star)$ &3.56&3.54& &3.54$\pm$0.04 &3.50&3.48&3.49 & &3.59& 2.99\\ +$^3A' (\pi \rightarrow \pi^\star)$ &4.46&4.47& &4.44$\pm$0.08 &4.40&4.44&4.43 & &4.63& \\ +\hline + \multicolumn{12}{c}{Thioacetone}\\ + & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{1}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV} & Exp$^i$ \\ +\hline +$^1A_2 (n \rightarrow \pi^\star)$ &2.58&2.56&2.56&2.61$\pm$0.05 &2.59&2.57&2.55 &2.53&2.55 &2.33\\ +$^1B_2 (n \rightarrow 4s)$ &5.65&5.64&5.66& &5.44&5.43&5.55 &5.54&5.72 &5.49\\ +$^1A_1 (\pi \rightarrow \pi^\star)$ &6.09&6.10&6.07& &5.97&5.98&5.90 &5.91&6.24 &5.64\\ +$^1B_2 (n \rightarrow 4p)$ &6.59&6.59&6.59& &6.45&6.44&6.51 & &6.62 &6.40\\ +$^1A_1 (n \rightarrow 4p)$ &6.95&6.95&6.96& &6.54&6.53&6.61 &6.60&6.52 &6.52\\ +$^3A_2 (n \rightarrow \pi^\star)$ &2.36&2.34& &2.36$\pm$0.00 &2.36&2.35&2.34 & &2.32 &2.14\\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &3.45&3.45& & &3.51&3.50&3.46 & &3.46 &\\ +\hline + \multicolumn{12}{c}{Thiopropynal}\\ + & \multicolumn{4}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{1}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & & {\FCI} & {\CCT} & {\CCSDT}& {\CCT} & {\CCSDT} & {\NEV} & Exp$^j$ \\ +\hline +$^1A'' (n \rightarrow \pi^\star)$ &2.09&2.06& &2.08$\pm$0.01 &2.09&2.06&2.05 &2.03&2.05 &1.82\\ +$^3A'' (n \rightarrow \pi^\star)$ &1.84&1.82& & &1.83&1.82&1.81 & &1.81 &1.64\\ +\hline +\end{tabular} + \end{footnotesize} +\vspace{-0.5 cm} +\begin{flushleft} +\begin{footnotesize} +$^a${{\CASPT} of Ref. \citenum{Mer96b};} +$^b${EOM-CCSD of Ref. \citenum{Gwa95};} +$^c${Two lowest singlet states: various experiments summarized in Ref. \citenum{Rob85}; three next singlet states: REMPI experiments from Ref. \citenum{Xin93}; lowest triplet: trapped electron measurements from Ref. \citenum{Sta75};} +$^d${0-0 energy reported in Ref. \citenum{Kar91b};} +$^e${EOM-CCSD from Ref. \citenum{Car10};} +$^f${Energy loss experiment from Ref. \citenum{Joh79};} +$^g${VUV experiment from Ref. \citenum{Pal87} (we report the lowest of the $\pi \rightarrow 3p$ state for the $^1A_1$ state)}; +$^h${0-0 energies of Refs. \citenum{Bra74} (singlet) and \citenum{Bir73} (triplet);} +$^i${0-0 energies from Ref. \citenum{Jud83};} +$^i${0-0 energies from Ref. \citenum{Jud84c}.} +\end{footnotesize} +\end{flushleft} +\end{table} + +For acetone, one should clearly distinguish the valence ES, for which both methodological and basis set effects are small, and the Rydberg transitions that, not only are very +sensitive to the basis set, but are upshifted by ca. 0.04 eV with {\CCSDTQ} as compared to {\CCT} and {\CCSDT}. For this compound, the 1996 {\CASPT} transition energies of Merch\'an and coworkers listed on the +r.h.s. of Table \ref{Table-4} are quite clearly too small, especially for the three valence ES. \cite{Mer96b} As expected, this error can be partially ascribed to the details of the calculations, as the Urban group obtained {\CASPT} +excitation energies of 4.40, 4.09 and 6.22 eV for the $^1A_2$, $^3A_2$, and $^3A_1$ ES, \cite{Pas12} in much better agreement with ours. Their estimates for the three $n \rightarrow 3p$ transitions of 7.52, 7.57, and 7.53 eV +for the $^1A_2$, $^1A_1$, and $^1B_2$ ES also systematically fall within 0.10 eV of our current CC values, whereas for these three ES, the current {\NEV} values are quite clearly too large. + +In contrast to acetone, both valence and Rydberg ES of thioacetone are rather insensitive to the CC expansion, as illustrated by the maximal discrepancies of $\pm$0.02 eV between the {\CCT} and {\CCSDTQ} results +with the {\Pop} basis set. While the lowest $n \rightarrow \pi^\star$ transition of both spin symmetries are rather insensitive to the selected basis set, all other states need quite large bases to be correctly described (Table S4). +As expected our theoretical vertical transition energies show the same ranking but are systematically larger than the available experimental 0-0 energies. + +For the isoleectronic isobutene, we considered two singlet Rydberg and one triplet valence ES. For all three cases, we note very nice agreement between {\CCT} and {\CCSDT} results for all considered basis sets, the +CC results being also within or very close to the {\FCI} estimates with Pople's basis set. The match with the {\CCSD} results of Caricato and coworkers, \cite{Car10} is also very satisfying. + +For the three remaining compounds, namely, cyanoformaldehyde, propynal, and thiopropynal, we report low-lying valence transitions all showing a largely dominant single excitation character. The basis set +effects are clearly under control (they are only significant for the second $^1A''$ ES of cyanoformaldehyde) and we could not detect any variation larger than 0.03 eV between the {\CCT} and {\CCSDT} values for +a given basis, hinting that the CC values should be close to the spot, as confirmed by the {\FCI} data. + +\subsubsection{Intermediate conclusions} +\label{sec-ic} + +As we have seen for the 15 four-atom molecules considered here, we found extremely consistent transition energies between the tested CC approaches and the {\FCI} estimates in the vast majority of cases, +Importantly, we confirm the previous conclusions obtained on smaller compounds:\cite{Loo18a} i) {\CCSDTQ} values systematically fall within, or are extremely close from, the {\FCI} error bar, +ii) both {\CCT} and {\CCSDT} are also highly trustable when the considered ES does not show a very strong double excitation character. Indeed, considering all the 54 ``single transitions'' +for which {\CCSDTQ} estimates could be obtained (only excluding the lowest $^1A_g$ ES of butadiene and glyoxal), we determined trifling mean signed errors (MSE of 0.00 eV), tiny +MAE (0.01 and 0.02 eV), and small maximal deviations (0.05 and 0.04 eV) for {\CCT} and {\CCSDT}, respectively. This clearly indicates that these two approaches provide chemically-accurate +estimates (errors $<$ 1 kcal.mol$^{-1}$ or 0.043 eV) for most electronic transitions. Interestingly, some of us have shown that {\CCT} also provides chemically-accurate 0-0 energies as compared +to experimental values for most valence transitions. \cite{Loo18b,Loo19a,Sue19} When comparing the {\NEV} and {\CCT} ({\CCSDT}) results obtained with {\AVTZ} for all transitions in four-atom molecules, +one obtains a mean signed deviation of +0.09 (+0.09) eV and a mean absolute deviation of 0.11 (0.12) eV, considering all 91 (65) ES for which comparisons are possible, again excluding only +the lowest $^1A_g$ states of butadiene and glyoxal. Although the error cannot be fully ascribed to the multi-reference method, that is additionally dependent of the selected active space, it seems to +indicate that {\NEV}, as applied here, has a slight tendency to overestimate the transition energies. This contrasts with the {\CASPT} approach that, from the comparisons discussed above, +generally undershoots the transition energies. + +\subsection{Five-atom molecules} + +Let us now turn towards five-member rings. We treat here five classical derivatives that have been considered in several previous theoretical studies (\emph{vide infra}): cyclopentadiene, furan, imidazole, pyrrole, and thiophene. As the most +advanced levels of theory used in the previous Section, namely {\CCSDTQ} and {\FCI}, become beyond reach for these compounds, one has to rely on the nature of the ES and the consistency between the results of +different approaches to deduce TBE. + +For furan, previous theoretical works have been performed with almost all possible wavefunction approaches, \cite{Ser93b,Nak96,Tro97b,Chr98b,Chr98c,Wan00,Gro03,Pas06b,Sch08,She09b,Li10c,Sau11,Sil10b,Sil10c,Hol15,Sch17} but the +present work is, to the best of our knowledge, the first to disclose {\CCSDT} values as well as {\CCT} energies obtained with a quadruple-$\zeta$ basis set. Our results for ten low-lying states are listed in Tables \ref{Table-5} and S5. +All computed singlet (triplet) transitions show $\%T_1$ in the 92--94 \%\ (97--99) \%\ range, and consistently the maximal discrepancies between the {\CCT} and {\CCSDT} transition energies are small (0.04 eV). In addition there is a +good consistency between the present data and both the {\NEV} results of Ref. \citenum{Pas06b} and the MR-CC values of Ref. \citenum{Li10c} for almost all transitions, but the $^1B_2 (\pi \rightarrow 3p)$ excitation that we predict to +be significantly higher than in most previous works, even after accounting for the quite large basis set effects (-0.10 eV between {\AVTZ} and {\AVQZ} estimates, see Table S5). We trust that our estimate is the most accurate to date for that ES. +Interestingly, the recent {\AT} values of Ref. \citenum{Hol15} are smaller by ca. -0.2 eV as compared to {\CCSDT} values for all transitions (see Table \ref{Table-6}), consistent with the error sign we found in smaller compounds with ADC(3). \cite{Loo18a} +Eventually, we note that the experimental data, \cite{Vee76b,Fli76,Rob85b} provide the same state ordering as our calculations. + +\begin{table}[htp] +\caption{\small Vertical transition energies determined in furan and pyrrole. All values are in eV.} +\label{Table-5} +\begin{footnotesize} +\begin{tabular}{l|p{.5cm}p{1.0cm}|p{.5cm}p{1.0cm}|p{.5cm}p{1.0cm}p{1.2cm}|p{.5cm}p{.5cm}p{.5cm}p{.5cm}p{.5cm}p{.6cm}p{.6cm}} +\hline + \multicolumn{15}{c}{Furan}\\ + & \multicolumn{2}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{7}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & {\CCT} & {\CCSDT} & {\CCT} & {\CCSDT} & {\NEV} &Th.$^a$ &Th.$^b$ &Th.$^c$ &Th.$^d$ &Th.$^e$ &Exp.$^f$&Exp.$^g$\\ +\hline +$^1A_2 (\pi \rightarrow 3s)$ &6.26&6.28 &6.00&6.00 &6.08&6.09& &5.92&6.13&5.94&5.91&6.10&5.91 & \\ +$^1B_2 (\pi \rightarrow \pi^\star)$ &6.50&6.52 &6.37&6.39 &6.34&6.37& &6.04&6.42&6.51&6.10&6.42&6.04 & 6.06\\ +$^1A_1 (\pi \rightarrow \pi^\star)$ &6.71&6.67 &6.62&6.58 &6.58&6.56& &6.16&6.71&6.89&6.44& & & 6.44 \\ +$^1B_1 (\pi \rightarrow 3p)$ &6.76&6.77 &6.55&6.56 &6.63&6.64& &6.46&6.68&6.46&6.45&6.66&6.47 & \\ +$^1A_2 (\pi \rightarrow 3p)$ &6.97&6.99 &6.73&6.74 &6.80&6.81& &6.59&6.79&6.61&6.60&6.83&6.61 & \\ +$^1B_2 (\pi \rightarrow 3p)$ &7.53&7.54 &7.39&7.40 &7.23& & &6.48&6.91&6.87&6.72&7.36&6.75 & \\ +$^3B_2 (\pi \rightarrow \pi^\star)$ &4.28&4.28 &4.25&4.23 &4.22& & &3.99& &4.26& & & &4.0\\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &5.56&5.54 &5.51&5.49 &5.48& & &5.15& &5.53& & & &5.2\\ +$^3A_2 (\pi \rightarrow 3s)$ &6.18&6.19 &5.94&5.94 &6.02& & &5.86& &5.89& & & &\\ +$^3B_1 (\pi \rightarrow 3p)$ &6.69&6.71 &6.51&6.51 &6.59& & &6.42& &6.41& & & &\\ +\hline + \multicolumn{15}{c}{Pyrrole}\\ + & \multicolumn{2}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{7}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & {\CCT} & {\CCSDT} & {\CCT} & {\CCSDT} & {\NEV} &Th.$^a$ &Th.$^h$ &Th.$^c$ &Th.$^i$ &Th.$^j$ &Exp.$^l$&Exp.$^l$\\ +\hline +$^1A_2 (\pi \rightarrow 3s)$ &5.25&5.25 &5.15&5.14 &5.24&5.24&& 5.08&5.45&5.10&5.20&5.27&5.22&\\ +$^1B_1 (\pi \rightarrow 3p)$ &5.99&5.98 &5.89&5.87 &5.98&6.00&& 5.85&6.21&5.79&5.95&6.00& &\\ +$^1A_2 (\pi \rightarrow 3p)$ &6.27&6.27 &5.94&5.93 &6.01& && 5.83&6.14&5.81&5.94&7.03& &5.87\\ +$^1B_2 (\pi \rightarrow \pi^\star)$ &6.33&6.33 &6.28&6.28 &6.25&6.26&& 5.92&6.95&5.96&6.04&6.08& &5.98\\ +$^1A_1 (\pi \rightarrow \pi^\star)$ &6.43&6.40 &6.35&6.32 &6.32&6.30&& 5.92&6.59&6.53&6.37&6.15& &\\ +$^1B_2 (\pi \rightarrow 3p)$ &7.20&7.20 &7.00&7.00 &6.83& && 5.78&6.26&6.61&6.57& &\\ +$^3B_2 (\pi \rightarrow \pi^\star)$ &4.59&4.58 &4.56&4.54 &4.53& && 4.27& &4.53& & &4.21\\ +$^3A_2 (\pi \rightarrow 3s)$ &5.22&5.22 &5.12&5.12 &5.21& && 5.04& &5.07& & &5.1\\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &5.54&5.54 &5.49&5.48 &5.46& && 5.16& &5.53& & &\\ +$^3B_1 (\pi \rightarrow 3p)$ &5.91&5.90 &5.82&5.81 &5.92& && 5.82& &5.74& & &\\ +\hline + \end{tabular} + \end{footnotesize} +\vspace{-0.5 cm} +\begin{flushleft} +\begin{footnotesize} +$^a${{\CASPT} from Ref. \citenum{Ser93b};} +$^b${{\NEV} from Ref. \citenum{Pas06b};} +$^c${MR-CC from Ref. \citenum{Li10c};} +$^d${{\AT} from Ref. \citenum{Hol15};} +$^e${{\CCT} from Ref. \citenum{Sch17};} +$^f${Various experiments summarized in Ref. \citenum{Wan00};} +$^g${Electron impact from Ref. \citenum{Vee76b}: for the $^1A_1$ state two values (6.44 and 6.61 eV) are reported, whereas for the two lowest triplet states, 3.99 eV and 5.22 eV values can be found in Ref. \citenum{Fli76};} +$^h${{\NEV} from Ref. \citenum{Pas06c};} +$^i${Best estimate from Ref. \citenum{Chr99}, based on CC calculations;} +$^j${XMS-{\CASPT} from Ref. \citenum{Hei19};} +$^k${Electron impact from Refs. \citenum{Vee76b} and \citenum{Fli76b};} +$^l${Vapour UV spectra from Refs. \citenum{Pal03b}, \citenum{Hor67}, and \citenum{Bav76}.} +\end{footnotesize} +\end{flushleft} +\end{table} + +Like furan, pyrrole has been extensively investigated previously using a large palette of approaches. \cite{Ser93b,Nak96,Tro97,Pal98,Chr99,Wan00,Roo02,Pal03b,Pas06c,Sch08,She09b,Li10c,Sau11,Sil10b,Sil10c,Nev14,Sch17,Hei19} +We report six low-lying singlet and four triplet ES in Tables \ref{Table-5} and S5. All considered transitions have very large $\%T_1$ but for the totally symmetric $\pi \rightarrow \pi^\star$ excitation ($\%T_1 = 86\%$). For all states, we found +highly consistent {\CCT} and {\CCSDT} results, often significantly larger than older multi-reference estimates, \cite{Ser93b,Roo02,Li10c} but in nice agreement with the very recent XMS-{\CASPT} results of the Gonzalez' +group, \cite{Hei19} at the exception of the $^1A_2 (\pi \rightarrow 3p)$ transition. The match obtained with the 20-years old extrapolated CC values of Christiansen and coworkers \cite{Chr99} is also remarkable but for the two +$B_2$ transitions that were reported as significantly mixed in that venerable work. For the lowest singlet ES, the {\FCI}/{\Pop} value is 5.24$\pm$0.02 eV confirming the performances of both {\CCT} and {\CCSDT} for that transition. +As can be seen in Table S5, {\AVTZ} yields basis-set converged transition energies, but, like in furan, for the Rydberg $^1B_2 (\pi \rightarrow 3p)$ transition that is significantly redshifted (-0.09 eV) when going to the +quadruple-$\zeta$ basis set. As mentioned in Thiel's work, \cite{Sch08} the experimental spectra of pyrrole are quite broad and the few available experiments \cite{Hor67,Bav76,Fli76b,Vee76b,Pal98,Pal03b} can only be used as general guidelines. + +\begin{table}[htp] +\caption{\small Vertical transition energies determined in cyclopentadiene, imidazole, and thiophene. All values are in eV.} +\label{Table-6} +\begin{footnotesize} +\begin{tabular}{l|p{.5cm}p{1.0cm}|p{.5cm}p{1.0cm}|p{.5cm}p{1.0cm}p{1.2cm}|p{.5cm}p{.5cm}p{.5cm}p{.5cm}p{.6cm}p{.6cm}p{.6cm}} +\hline + \multicolumn{15}{c}{Cyclopentadiene}\\ + & \multicolumn{2}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{7}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & {\CCT} & {\CCSDT} & {\CCT} & {\CCSDT} & {\NEV} &Th.$^a$ &Th.$^b$ &Th.$^c$ &Th.$^d$ &Exp.$^e$ &Exp.$^f$&Exp.$^g$\\ +\hline +$^1B_2 (\pi \rightarrow \pi^\star)$ &5.79&5.80 &5.59&5.60 &5.54&5.56&5.65 &5.27 &5.54&5.19 &5.58 &5.26 & &5.20\\ +$^1A_2 (\pi \rightarrow 3s)$ &6.08&6.08 &5.70&5.70 &5.77&5.78&5.92 &5.65 &5.58&5.62 &5.79 &5.68 &5.63 &\\ +$^1B_1 (\pi \rightarrow 3p)$ &6.57&6.58 &6.34&6.34 &6.40&6.41&6.42 &6.24 &6.17&6.24 &6.43 & &6.35 &\\ +$^1A_2 (\pi \rightarrow 3p)$ &6.67&6.67 &6.39&6.39 &6.45&6.46&6.59 &6.30 &6.21&6.25 &6.47 & & &6.26\\ +$^1B_2 (\pi \rightarrow 3p)$ &7.06&7.07 &6.55&6.55 &6.56&6.56&6.58 &6.25 &6.22&6.27 &6.58 & &6.31 &\\ +$^1A_1 (\pi \rightarrow \pi^\star)$ &6.67&6.60 &6.59&6.53 &6.57&\hl{XXX}&6.75 &6.31 &6.76&6.42 &6.65 & & &$\sim$6.2\\ +$^3B_2 (\pi \rightarrow \pi^\star)$ &3.33&3.33 &3.32&3.31 &3.32& &3.41 &3.15 &3.40& & &3.10 &\\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &5.16&5.15 &5.14&5.13 &5.12& &5.36 &4.90 &5.18& & &$>$4.7 & &\\ +$^3A_2 (\pi \rightarrow 3s)$ &6.01&6.02 &5.65&5.65 &5.73& &5.73 &5.63 &5.56& & &\\ +$^3B_1 (\pi \rightarrow 3p)$ &6.51&6.52 &6.30&6.30 &6.36& &6.40 &6.25 &6.19& & &\\ +\hline + \multicolumn{15}{c}{Imidazole}\\ + & \multicolumn{2}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{7}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & {\CCT} & {\CCSDT} & {\CCT} & & {\NEV} &Th.$^h$ &Th.$^i$ &&&Exp.$^j$\\ +\hline +$^1A'' (\pi \rightarrow 3s)$ &5.77&5.77 &5.60&5.60 &5.71&& &5.71& &&&$\sim$5.2\\ +$^1A' (\pi \rightarrow \pi^\star)$ &6.51&6.51 &6.43&6.43 &6.41&& &6.72&6.25&&&$\sim$6.4\\ +$^1A'' (n \rightarrow \pi^\star)$ &6.66&6.66 &6.42&6.42 &6.50&& &6.52&6.65&&& \\ +$^1A' (\pi \rightarrow 3p)$ &7.04&7.02 &6.93&6.89 &6.87&& &6.49& &&&\\ +$^3A' (\pi \rightarrow \pi^\star)$ &4.83&4.81 &4.78& &4.75&& &4.49&4.65&&&\\ +$^3A'' (\pi \rightarrow 3s)$ &5.72&5.72 &5.57&5.56 &5.67&& &5.68& &&&\\ +$^3A' (\pi \rightarrow \pi^\star)$ &5.88&5.88 &5.78& &5.74&& &5.47&5.64&&&\\ +$^3A'' (n \rightarrow \pi^\star)$ &6.48&6.46 &6.37&6.35 &6.33&& &6.07&6.25&&&\\ +\hline + \multicolumn{15}{c}{Thiophene}\\ + & \multicolumn{2}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{7}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & {\CCT} & {\CCSDT} & {\CCT} & {\CCSDT} & {\NEV} &Th.$^k$ &Th.$^l$ &Th.$^m$ &Th.$^n$ &Exp.$^o$ &Exp.$^p$&Exp.$^q$\\ +\hline +$^1A_1 (\pi \rightarrow \pi^\star)$ &5.79&5.77 &5.70&5.68 &5.65&5.64& &5.33&5.41&5.70&5.64&5.16&5.13&5.16\\ +$^1B_2 (\pi \rightarrow \pi^\star)$ &6.23&6.24 &6.05&6.06 &5.96&5.98& &5.72&5.72&6.10&5.97&5.99&5.83&\\ +$^1A_2 (\pi \rightarrow 3s)$ &6.26&6.26 &6.07&6.06 &6.14&6.14& &5.93&5.70&6.05&6.23& & &\\ +$^1B_1 (\pi \rightarrow 3p)$ &6.18&6.17 &6.19&6.17 &6.14&6.14& &6.30&5.87&6.30&6.17& & &6.71\\ +$^1A_2 (\pi \rightarrow 3p)$ &6.32& &6.33&6.31 &6.25&6.21& &6.35&6.03&6.28&6.33& &\\ +$^1B_1 (\pi \rightarrow 3s)$ &6.62&6.62 &6.42&6.41 &6.50&6.49& &6.23&6.12&6.36&6.68& & &6.47\\ +$^1B_2 (\pi \rightarrow 3p)$ &7.45&7.44 &7.45&7.44 &7.29&7.29& &6.56&6.41&6.81&6.97& & &6.60\\ +$^1A_1 (\pi \rightarrow \pi^\star)$ &7.50&7.46 &7.41& &7.35& & &6.69&7.32&7.71&7.74&6.61&\\ +$^3B_2 (\pi \rightarrow \pi^\star)$ &3.95&3.94 &3.96&3.94 &3.94& & &3.75&3.94& &3.96&&3.74&\\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &4.90&4.90 &4.82&4.81 &4.77& & &4.50&4.86& &4.87&&4.62&\\ +$^3B_1 (\pi \rightarrow 3p)$ &6.00&5.98 &6.01&5.99 &5.95& & &5.90&5.94& &6.01&\\ +$^3A_2 (\pi \rightarrow 3s)$ &6.20&6.20 &6.01&6.00 &6.09& & &5.88&5.75& &5.83&\\ +\hline + \end{tabular} + \end{footnotesize} +\vspace{-0.5 cm} +\begin{flushleft} +\begin{footnotesize} +$^a${{\CASPT} from Ref. \citenum{Ser93b};} +$^b${SAC-CI from Ref. \citenum{Wan00b};} +$^c${MR-MP from Ref. \citenum{Nak96};} +$^d${{\CCT} from Ref. \citenum{Sch17};} +$^e${Electron impact from Ref. \citenum{Fru79};} +$^f${Gas phase absorption from Ref. \citenum{McD91b};} +$^g${Energy loss from Ref. \citenum{McD85} for the two valence state; two-photon resonant experiment from Ref. \citenum{Sab92} for the $^1A_2$ Rydberg ES;} +$^h${{\CASPT} from Ref. \citenum{Ser96b};} +$^i${{\CCT} from Ref. \citenum{Sil10c};} +$^j${Gas-phase experimental estimates from Ref. \citenum{Dev06};} +$^k${{\CASPT} from Ref. \citenum{Ser93c};} +$^l${SAC-CI from Ref. \citenum{Wan01};} +$^m${CCSDR(3) from Ref. \citenum{Pas07};}%, this work also contains {\NEV} estimates;} +$^n${TBE from Ref. \citenum{Hol14}, based on EOM-CCSD for singlet and ADC(2) for triplets;} +$^o${0-0 energies from Ref. \citenum{Dil72};} +$^p${0-0 energies from Ref. \citenum{Var82} for the singlets and energy loss experiment from Ref. \citenum{Hab03} for the triplet ES;} +$^q${0-0 energies from Ref. \citenum{Hol14}.} +\end{footnotesize} +\end{flushleft} +\end{table} + +Although a quite significant array of previous wavefunction studies has been performed for cyclopentadiene not only at the {\CASPT}, \cite{Ser93b,Sch08,Sil10c} and CC \cite{Sch08,Sil10b,Sch17} levels but also with +SAC-CI \cite{Wan00b} and various multi-reference approaches, \cite{Nak96,She09b} this compound has been less intensively studied than furan and pyrrole (\emph{vide infra}), probably due to the presence of the +methylene group that renders the computations significantly more expensive. All transitions listed in Tables \ref{Table-6} and S6 are characterized by $\%T_1$ exceeding 93\%\ but for the $^1A_1 (\pi \rightarrow \pi^\star)$ +excitation that has a nature similar to the lowest $A_g$ state of butadiene ($\%T_1 = 79\%$). Consistently, the {\CCT} and {\CCSDT} results are nearly identical for all ES but for that transition. By comparing the results +obtained for this $A_1 (\pi \rightarrow \pi^\star)$ transition to its butadiene counterpart, one can infer that the {\CCSDT} estimate is probably too large by ca. 0.04--0.08 eV, and that the {\NEV} value is likely not more accurate +than the {\CCSDT} one. This statement is also in line with the results of Ref. \citenum{Loo19c}. For the two $B_2 (\pi \rightarrow \pi^\star)$ transitions, we could obtain a {\FCI}/{\Pop} estimates of 5.78$\pm$0.02 eV and +(singlet) 3.33$\pm$0.05 eV (triplet); the {\CCT} and {\CCSDT} transition energies falling inside these energetic windows in both cases. As can be seen in Tables \ref{Table-6} and S6, the basis set effects are rather moderate +for all transitions, with no variations larger than 0.10 eV (0.02 eV) between {\AVDZ} and {\AVTZ} ({\AVTZ} and {\AVQZ}). When comparing to literature data, our values are unsurprisingly consistent with the {\CCT} values of +Schwabe and Goerigk, \cite{Sch17} and tend to be significantly larger than earlier {\CASPT} \cite{Ser93b,Sil10c} and MR-MP \cite{Nak96} estimates. As expected, a few gas-phase experiments are available as well for this +derivative, \cite{Fru79,McD85,McD91b,Sab92} but hardly allow to make the final call. + + +Due to its lower symmetry, imidazole has been less investigated, the most advanced studies available probably remaining the 1996 {\CASPT} work of Serrano-Andres \emph{et al}, \cite{Ser96b} and the +basis-set extrapolated {\CCT} investigation of Silva-Junior \emph{et al} for the valence transitions. \cite{Sil10c} The experimental data in gas-phase are also limited.\cite{Dev06} +Our results are displayed in Tables \ref{Table-6} and S6. The {\CCT} and {\CCSDT} values are quite consistent despite the fact that the $\%T_1$ of the two singlet $A'$ states +are slightly smaller 90\%. For all eight considered transitions, the basis set effects are moderate and {\AVTZ} yield results within 0.03 eV of {\AVQZ} (Table S6 in the SI). \hl{NEV ?} + +Finally, the ES thiophene, which is one of the most important building block in organic electronic devices, were the subject of a few previous theoretical investigations, \cite{Ser93c,Pal99,Wan01,Kle02,Pas07,Hol14} that unveiled a series of +transitions that were not yet characterized in the available measurements. \cite{Dil72,Fli76,Fli76b,Var82,Hab03,Pal99,Hol14} To our knowledge, the present work is the first to report CC calculations obtained with (iterative) +triples and therefore constitutes the most accurate estimates to date. Indeed, all the transitions listed in Tables \ref{Table-6} and S6 are characterized by a largely dominant single excitation character, with $\%T_1$ above +90\%\ but for the two $^1A_1$ transitions that show $\%T_1$ of 88\%\ and 87\%. The agreement between {\CCT} and {\CCSDT} remains nevertheless excellent for the lowest totally symmetric transition. Thiophene is +also a typical compound in which unambiguous characterization of the nature of the ES is difficult, with e.g., a strong mixing between the second and third singlet $B_2$ ES rendering the assignment of the valence +($\pi \rightarrow \pi^\star$) or Rydberg ($\pi \rightarrow 3p$) character of that transittion uneasy at the {\CCT} level. We note that contradictory assignments can be found in the literature. \cite{Ser93c,Wan01,Pas07} As for the +previously discussed isostructural systems, the only ES that undergoes significant basis set effects beyond {\AVTZ} is the Rydberg $^1B_2 (\pi \rightarrow 3p)$ (-0.09 eV when upgrading to {\AVQZ}, see Table S6). +The data of Table \ref{Table-6} are globally in good agreement with the previously reported values with discrepancies that are however significant for the three highest-lying singlet states. + +\subsection{Six-atom molecules} + +Let us now turn towards six-member cycles playing a key role in chemistry: benzene, pyrazine, pyridazine, pyridine, pyrimidine, tetrazine, and triazine. To the best of our knowledge, the present work +is the first to propose {\CCSDT} reference energies as well as {\CCT} values obtained with a {\AVQZ} for all these compounds. Of course, these systems have been investigated before, and beyond Thiel's +benchmarks, \cite{Sch08,Sil10b,Sil10c} it is worth to point out the investigations of Del Bene and coworkers, \cite{Del97b} performed with a CC approach including perturbative corrections for the triples, and of Nooijen, \cite{Noo99} +who used {\STEOM}, to study the ES of all these derivatives with a theoretically consistent protocol. However, these two works considered the singlet ES only. + +\subsubsection{Benzene, pyrazine, and tetrazine} + + \hl{Martial: please do check Rydberg assignments throughout} + +These three highly-symmetric systems allow to directly perform {\CCSDT}/{\AVTZ} calculations for singlet states without the need for basis set extrapolation. Benzene was studied many times +before, \cite{Sob93,Lor95b,Chr96c,Pac96,Del97b,Noo99,Hal02,Li07b,Sch08,Dev08,Sil10b,Sil10c,Li11,Lea12,Kan14,Sch17,Dut18,Sha19,Loo19c} and we report in Tables \ref{Table-7} and S7 estimates obtained for +five singlet and three triplet ES, all characterized by $\%T_1$ exceeding 90\%\ but the lowest singlet (86\%). As can be seen, the two CC approaches are again yielding very consistent transitions energies +and {\AVTZ} is essentially providing basis set converged transition energies. The present estimates are also very consistent with early {\CCT}\cite{Chr96c} and very recent RASPT2 values. \cite{Sha19} +For both the singlet and triplet transitions, our values are slightly larger than available electron impact/multi-photon measurements. \cite{Doe69,Nak80,Joh76,Joh83,Hir91} + +\begin{table}[htp] +\caption{\small Vertical transition energies determined in benzene All values are in eV.} +\label{Table-7} +\begin{footnotesize} +\begin{tabular}{l|p{.5cm}p{1.0cm}|p{.5cm}p{1.0cm}|p{.5cm}p{1.0cm}p{1.2cm}|p{.5cm}p{.5cm}p{.5cm}p{.5cm}p{.6cm}p{.6cm}} +\hline + & \multicolumn{2}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{6}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & {\CCT} & {\CCSDT} & {\CCT} & {\CCSDT} & {\NEV} &Th.$^a$ &Th.$^b$ &Th.$^c$ &Th.$^d$ &Exp.$^e$ &Exp.$^f$\\ +\hline +$^1B_{2u} (\pi \rightarrow \pi^\star)$ &5.13&5.10 &5.11&5.08 &5.09&5.06& &4.84&5.08&5.06&5.03& &4.90\\ +$^1B_{1u} (\pi \rightarrow \pi^\star)$ &6.68&6.69 &6.50&6.50 &6.44&6.45& &6.30&6.54&6.22&6.23& &6.20\\ +$^1E_{1g} (\pi \rightarrow 3s)$ &6.75&6.76 &6.46&6.46 &6.52&6.52& &6.38&6.51&6.42& & &6.33\\ +$^1A_{2u} (\pi \rightarrow 3p)$ &7.24&7.25 &7.02&7.02 &7.08&7.08& &6.86&6.97&7.06& & &6.93\\ +$^1E_{2u} (\pi \rightarrow 3p)$ &7.34&7.35 &7.09&7.09 &7.15&7.15& &6.91&7.03&7.12& & &6.95\\ +$^3B_{1u} (\pi \rightarrow \pi^\star)$ &4.18&4.16 &4.19&4.17 &4.18& & &3.89&4.15&3.88&4.11&3.95&\\ +$^3E_{1u}(\pi \rightarrow \pi^\star)$ &4.95&4.94 &4.89&4.88 &4.86& & &4.49&4.86&4.72&4.75&4.75&\\ +$^3B_{2u} (\pi \rightarrow \pi^\star)$ &6.06&6.06 &5.86&5.86 &5.81& & &5.49&5.88&5.54&5.67&5.60&\\ +\hline + \end{tabular} + \end{footnotesize} +\vspace{-0.5 cm} +\begin{flushleft} +\begin{footnotesize} +$^a${{\CASPT} from Ref. \citenum{Lor95b};} +$^b${{\CCT} from Ref. \citenum{Chr96c};} +$^c${SAC-CI from Ref. \citenum{Li07b};} +$^d${RASPT2(18,18) from Ref. \citenum{Sha19};} +$^e${Electron impact from Ref. \citenum{Doe69};} +$^f${Jet-cooled experiment from Ref. \citenum{Hir91} for the two lowest states, multi-photon experiments from Refs. \citenum{Joh76} and \citenum{Joh83} for the Rydberg states.} +\end{footnotesize} +\end{flushleft} +\end{table} + +\begin{table}[htp] +\caption{\small Vertical transition energies determined in pyrazine and tetrazine. All values are in eV.} +\label{Table-8} +\begin{footnotesize} +\vspace{-0.3 cm} +\begin{tabular}{p{2.18cm}|p{.5cm}p{1.cm}|p{.5cm}p{.9cm}|p{.5cm}p{1.0cm}p{1.2cm}|p{.5cm}p{.5cm}p{.5cm}p{.5cm}p{.5cm}p{.6cm}} +\hline + \multicolumn{14}{c}{Pyrazine}\\ + & \multicolumn{2}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{6}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & {\CCT} & {\CCSDT} & {\CCT} & {\CCSDT} & {\NEV} &Th.$^a$ &Th.$^b$ &Th.$^c$&Th.$^d$ &Exp.$^e$ &Exp.$^f$\\ +\hline +$^1B_{3u} (n \rightarrow \pi^\star)$ &4.28&4.28 &4.19&4.19 &4.14&4.15& &3.83&4.12&4.25&4.19&3.93\\ +$^1A_{u} (n \rightarrow \pi^\star)$ &5.08&5.08 &4.98&4.98 &4.97&4.98& &4.36&4.93&5.24&4.93&\\ +$^1B_{2u} (\pi \rightarrow \pi^\star)$ &5.10&5.08 &5.07&5.05 &5.03&5.02& &4.79&4.75&4.84&5.19&4.8&4.81\\ +$^1B_{2g} (n \rightarrow \pi^\star)$ &5.86&5.85 &5.78&5.77 &5.71&5.71& &5.50&5.85&6.04&5.81&5.19\\ +$^1A_{g} (n \rightarrow 3s)$ &6.74&6.73 &6.54&6.53 &6.66&6.65& & &6.83&7.07&6.46&\\ +$^1B_{1g} (n \rightarrow \pi^\star)$ &6.87&6.87 &6.75&6.75 &6.73&6.74& &6.26&6.73& &6.73&&6.10\\ +$^1B_{1u} (\pi \rightarrow \pi^\star)$ &7.10&7.11 &6.92&6.93 &6.86&6.88& &6.60&6.89&6.68&6.99&6.5&6.51\\ +$^1B_{1g} (n \rightarrow 3p)$ &7.36&7.37 &7.13&7.14 &7.20&7.21& & &7.31&7.08& &\\ +$^1B_{2u} (n \rightarrow 3p)$ &7.39&7.39 &7.14&7.13 &7.25& & & &7.45&7.67&7.06&\\ +$^1B_{1u} (\pi \rightarrow 3s)$ &7.56&7.55 &7.38&7.37 &7.45& & &7.28&7.50&7.73&7.31&&7.67\\ +$^1B_{1u} (\pi \rightarrow \pi^\star)$ &8.19&8.23 &7.99&8.03 &7.94& & &7.43&7.96&8.24&8.08&\\ +$^3B_{3u} (n \rightarrow \pi^\star)$ &3.68&3.68 &3.60&3.60 &3.59& & &3.16& & & &3.33\\ +$^3B_{1u} (\pi \rightarrow \pi^\star)$ &4.39&4.36 &4.40&4.36 &4.39& & &4.15& & & &4.04\\ +$^3B_{2u} (\pi \rightarrow \pi^\star)$ &4.56&4.55 &4.46&4.45 &4.40& & &4.28& & & &$\sim$4.4\\ +$^3A_{u} (n \rightarrow \pi^\star)$ &5.05&5.05 &4.93&4.93 &4.93& & &4.19& & & &4.2\\ +$^3B_{2g} (n \rightarrow \pi^\star)$ &5.18&5.17 &5.11&5.11 &5.08& & &4.81& & & &4.49\\ +$^3B_{1u} (\pi \rightarrow \pi^\star)$ &5.38&5.37 &5.32&5.31 &5.29& & &4.98& & & &\\ +\hline + \multicolumn{14}{c}{Tetrazine}\\ + & \multicolumn{2}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{6}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & {\CCT} & {\CCSDT} & {\CCT} & {\CCSDT} & {\NEV} &Th.$^g$ &Th.$^h$ &Th.$^i$&Th.$^j$ &Th.$^k$ &Exp.$^l$\\ +\hline +$^1B_{3u} (n \rightarrow \pi^\star)$ &2.53&2.54 &2.49&2.50 &2.46&2.47& &1.96&2.22&2.01&2.29&2.46&2.35\\ +$^1A_{u} (n \rightarrow \pi^\star)$ &3.75&3.75 &3.69&3.70 &3.67&3.69& &3.06&3.62&3.09&3.41&3.78&3.6\\ +$^1A_{g} (\mathrm{double})$$^m$ &6.22&5.86 &6.22&5.86 &6.21&5.96&4.61 &4.37&5.06&4.34&4.66& &\\ +$^1B_{1g} (n \rightarrow \pi^\star)$ &5.01&5.02 &4.97&4.98 &4.91&4.93& &4.51&4.73&4.47&4.53&4.87&\\ +$^1B_{2u} (\pi \rightarrow \pi^\star)$ &5.29&5.26 &5.27&5.25 &5.23&5.21& &4.89&4.90& &5.59&5.08&4.97\\ +$^1B_{2g} (n \rightarrow \pi^\star)$ &5.56&5.52 &5.53&5.50 &5.46&5.45& &5.05&5.09&4.92&5.59&5.28&\\ +$^1A_{u} (n \rightarrow \pi^\star)$ &5.61&5.61 &5.59&5.59 &5.52&5.53& &5.28&5.23&5.32&5.95&5.39&5.5\\ +$^1B_{3g} (\mathrm{double})$$^m$ &7.64& &7.62& &7.62& &6.15 &5.16&6.30&5.26&6.01& &5.92\\ +$^1B_{2g} (n \rightarrow \pi^\star)$ &6.24&6.22 &6.17&6.16 &6.13& & &5.48&6.16&5.78&6.05&6.16&\\ +$^1B_{1g} (n \rightarrow \pi^\star)$ &7.04&7.04 &6.98&6.98 &6.92& & &5.99&6.73&6.20&6.92&6.80&\\ +$^3B_{3u} (n \rightarrow \pi^\star)$ &1.87&1.88 &1.86&1.86 &1.85& & &1.45&1.71& & &1.87&1.7\\ +$^3A_{u} (n \rightarrow \pi^\star)$ &3.48&3.49 &3.43&3.44 &3.44& & &2.81&3.47& & &3.49&2.90\\ +$^3B_{1g} (n \rightarrow \pi^\star)$ &4.25&4.25 &4.23&4.23 &4.20& & &3.76&3.97& & &4.18&\\ +$^3B_{1u} (\pi \rightarrow \pi^\star)$ &4.54&4.49 &4.54&4.49 &4.54& & &4.25&3.67& & &4.36&\\ +$^3B_{2u} (\pi \rightarrow \pi^\star)$ &4.65&4.64 &4.58&4.58 &4.52& & &4.29&4.35& & &4.39&\\ +$^3B_{2g} (n \rightarrow \pi^\star)$ &5.11&5.11 &5.09&5.08 &5.05& & &4.67&4.78& & &4.89&\\ +$^3A_{u} (n \rightarrow \pi^\star)$ &5.17&5.17 &5.15&5.15 &5.11& & &4.85&4.89& & &4.96&\\ +$^3B_{3g} (\mathrm{double})$$^m$ &7.35& &7.33& &7.35& &5.51 &5.08& & & & &\\ +$^3B_{1u} (\pi \rightarrow \pi^\star)$ &5.51&5.50 &5.46&5.46 &5.42& & &5.09&5.31& & &5.32&\\ + +\hline + \end{tabular} + \end{footnotesize} +\vspace{-0.5 cm} +\begin{flushleft} +\begin{footnotesize} +$^a${{\CASPT} from Ref. \citenum{Web99};} +$^b${{\STEOM} from Ref. \citenum{Noo99};} +$^c${SAC-CI from Ref. \citenum{Li07b};} +$^d${{\CCT} from Ref. \citenum{Sch17};} +$^e${Dip spectroscopy from Ref. \citenum{Oku90} ($B_{3u}$ and $B_{2g}$ states) and EEL from Ref. \citenum{Wal91} (other states);} +$^f${UV max from Ref. \citenum{Bol84};} +$^g${{\CASPT} from Ref. \citenum{Rub99};} +$^h${Ext-{\STEOM} from Ref. \citenum{Noo00};} +$^i${GVVPT2 from Ref. \citenum{Dev08};} +$^j${{\NEV} from Ref. \citenum{Ang09};} +$^k${{\CCT} from Ref. \citenum{Sil10c};} +$^l${From Ref. \citenum{Pal97}, the singlets are from EEL, but for the 4.97 and 5.92 eV values that are from VUV; the triplets are from EEL, and other triplet peaks are mentioned at 4.21, 4.6, and 5.2 eV but not identified;} +$^m${all these doubly ES have a $(n,n \rightarrow \pi^\star, \pi^\star)$ character.} +\end{footnotesize} +\end{flushleft} +\end{table} + + +Numerous previous theoretical estimates are available for both pyrazine, \cite{Ful92,Del97b,Web99,Noo99,Li07b,Sch08,Sau09,Sil10c,Woy10,Car10,Lea12,Kan14,Sch17,Dut18} and tetrazine, \cite{Sta96,Del97b,Rub99,Noo99,Ada00,Noo00,Ang09,Sch08,Sau09,Sil10b,Sil10c,Car10,Lea12,Kan14,Sch17,Dut18,Pas18b} +for which the $D_{2h}$ symmetry helps distinguishing the different ES. Our results are collected in Tables \ref{Table-8} and S8. In pyrazine, all transitions are characterized by $\%T_1 > 85\%$, but for $^1B_{1g} (n \rightarrow \pi^\star)$, and the +changes in going from {\CCT} to {\CCSDT} are always trifling but for the highest-lying singlet state considered here. When going from triple-$\zeta$ to quadruple-$\zeta$, the variations do not exceed 0.04 eV, even for the four considered Rydberg +ES. This indicates that one can probably be highly confident in the present estimates. Again, the previous {\CASPT} estimates, \cite{Ful92,Web99,Sch08} appear to be globally too low, whereas the unconventional CASPT3 results that are +available, \cite{Woy10} are too large. The same holds for the SAC-CI results. \cite{Li07b} In fact we obtain globally our best match with the {\STEOM} values of Nooijen (but for the highest ES), \cite{Noo99} and recent {\CCT} estimates. +\cite{Sch17}. The experimental data we are aware of, \cite{Bol84,Oku90,Wal91,Ste11c} do not report all transitions, but provide globally a similar ranking for the triplet transitions. + + +For tetrazine, we consider valence ES only, but three transitions present a true double excitation nature ($\%T_1 < 10\%$), for which {\CCT} nor {\CCSDT} can not be viewed as reliable, and the best approach is likely {\NEV}. \cite{Loo19c} +For all other transitions, the $\%T_1$ are in the 80-90\%\ range for singlets and larger than 95\%\ for triplets, and the results of the two CC approaches are very consistent, but for the lowest $^3B_{1u} (\pi \rightarrow \pi^\star)$ excitation. +In all other cases, there is a good consistency between the values we obtained with the two CC models, and the basis set effects are very small beyond {\AVTZ} with maximal variations of 0.02 eV only (Table S8). The present values are +almost systematically larger than previous {\CASPT},\cite{Rub99} {\STEOM}, \cite{Noo00} and GVVPT2 \cite{Dev08} estimates, and are globally in agreement with Thiel's {\CCT}/{\AVTZ} values, \cite{Sil10c} although we note variations +of ca. 0.20 eV for some specific transitions like the $B_{2g}$ transitions, likely due to the use of different geometries in that work. The experimental EEL values from Palmer's work, \cite{Pal97} show a reasonable agreement with our estimates. + + +\subsubsection{Pyridazine, pyridine, pyrimidine, and triazine} + +Those four azabenzenes, of $C_{2v}$ and $D_{3h}$ symmetry, are also popular molecules for ES calculations. \cite{Pal91,Ful92,Wal92,Lor95,Del97b,Noo97,Noo99,Fis00,Cai00b,Wan01b,Sch08,Sil10b,Sil10c,Car10,Lea12,Kan14,Sch17,Dut18} +Our results for pyridazine and pyridine are collected in Tables \ref{Table-9} and S9. For the former compounds, the available wavefunction results \cite{Pal91,Ful92,Del97b,Noo99,Fis00,Sch08,Sil10b,Sil10c,Kan14,Sch17,Dut18} +have all considered the singlet transitions only, at the exception of rather old MRCI, \cite{Pal91} and {\CASPT} investigations. \cite{Fis00} The $\%T_1$ are larger than 85\%\ (95\%) for the singlet (triplet) transitions, +and the only state for which there is a variation larger than 0.03 eV between the {\AVDZ} {\CCT} and {\CCSDT} energies, but for the $^3B_2 (\pi \rightarrow \pi^\star)$ transition. \hl{BASIS SETS} For the valence singlet +ES, we find again a quite good agreement with previous {\STEOM} \cite{Noo99} and CC \cite{Del97b,Sil10c} estimates, but are again significantly higher than {\CASPT} estimates. \cite{Ful92,Sil10c} For the triplets, the +present data represents the best published to date. Interestingly, beyond the usually cited experiments, \cite{Inn88,Pal91} there is a very recent experimental EEL analysis for pyridazine, \cite{Lin19} that localized +almost all ES. The transition energies reported in this very recent effort are systematically smaller than our CC estimates, by ca. -0.20 eV, but remarkably show exactly the exact same ranking. + + For pyridine, that has been more thoroughly investigated with wavefunction approaches, \cite{Ful92,Lor95,Del97b,Noo97,Noo99,Cai00b,Wan01b,Sch08,Sil10b,Sil10c,Car10,Kan14,Sch17,Dut18} and for which we could found two + detailed EEL experiments, \cite{Wal90,Lin16} the general trends described for pyridazine pertain: i) large $\%T_1$ and good CC consistency for all transitions listed in Table \ref{Table-9}; ii) \hl{basis}; iii) good agreement with previous +CC estimates; and iv) same ranking of the ES as in the most recent measurements. \cite{Lin16} Beyond those aspects, it is worth to underline that the second $^1B_2 (\pi \rightarrow \pi^\star)$ ES is strongly mixed with a nearby +Rydberg transition that is separated by only 0.03 eV at the {\CCT}/{AVTZ} level, making the analysis particularly challenging for that specific transition. \hl{Keep or not A1 transitiion} + +\begin{table}[htp] +\caption{\small Vertical transition energies determined in pyridazine and pyridine. All values are in eV.} +\label{Table-9} +\begin{footnotesize} +\begin{tabular}{l|p{.5cm}p{1.0cm}|p{.5cm}p{1.0cm}|p{.5cm}p{1.2cm}|p{.5cm}p{.5cm}p{.5cm}p{.5cm}p{.6cm}p{.6cm}} +\hline + \multicolumn{13}{c}{Pyridazine}\\ + & \multicolumn{2}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{2}{c}{\AVTZ} & \multicolumn{6}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & {\CCT} & {\CCSDT} & {\CCT} & {\NEV} &Th.$^a$ &Th.$^b$ &Th.$^c$&Th.$^d$ &Exp.$^e$ &Exp.$^f$\\ +\hline +$^1B_1 (n \rightarrow \pi^\star)$ &3.95&3.95 &3.86&3.86 &3.83& &3.48&3.76&3.65&3.85&&3.36\\ +$^1A_2 (n \rightarrow \pi^\star)$ &4.49&4.48 &4.39&4.39 &4.37& &3.66&4.46&4.28&4.44&&4.02\\ +$^1A_1 (\pi \rightarrow \pi^\star)$ &5.36&5.32 &5.33&5.30 &5.29& &4.86&4.92&4.86&5.20&5.0&5.01\\ +$^1A_2 (n \rightarrow \pi^\star)$ &5.88&5.86 &5.80&5.78 &5.74& &5.09&5.66&5.52&5.66&&5.61\\ +$^1B_2 (n \rightarrow 3s)$ &6.26&6.27 &6.06&6.06 &6.17& & &6.45& & && \\ +$^1B_1 (n \rightarrow \pi^\star)$ &6.51&6.51 &6.41&6.41 &6.37& &5.80&6.41&6.20&6.33&&6.00\\ +$^1B_2 (\pi \rightarrow \pi^\star)$ &6.96&6.97 &6.79&6.80 &6.74& &6.61&6.77&6.44&6.68&&6.50\\ +$^3B_1 (n \rightarrow \pi^\star)$ &3.27&3.26 &3.20&3.20 &3.19& & & & & &&3.06\\ +$^3A_2 (n \rightarrow \pi^\star)$ &4.19&4.19 &4.11&4.11 &4.11& & & & & &&3.55\\ +$^3B_2 (\pi \rightarrow \pi^\star)$ &4.39&4.36 &4.39&4.35 &4.38& & & & & &4.0&4.33\\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &4.93&4.94 &4.87&4.86 &4.83& & & & & &4.4&4.68\\ +\hline + \multicolumn{13}{c}{Pyridine}\\ + & \multicolumn{2}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{2}{c}{\AVTZ} & \multicolumn{6}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & {\CCT} & {\CCSDT} & {\CCT} & {\NEV} &Th.$^g$ &Th.$^b$ &Th.$^c$&Th.$^d$ &Exp.$^h$ &Exp.$^i$ \\ +\hline +$^1B_1 (n \rightarrow \pi^\star)$ &5.12&5.10 &5.01&5.00 &4.96& &4.91&4.90&4.80&4.95&5.24&4.78\\ +$^1B_2 (\pi \rightarrow \pi^\star)$ &5.23&5.20 &5.21&5.18 &5.17& &4.84&4.82&4.81&5.12&4.99&4.99\\ +$^1A_2 (n \rightarrow \pi^\star)$ &5.55&5.54 &5.41&5.41 &5.40& &5.17&5.31&5.24&5.41&5.43&5.40\\ +$^1A_1 (\pi \rightarrow \pi^\star)$ &6.84&6.84 &6.64&6.63 &6.63& &6.42&6.62&6.36&6.60&6.38& \\ +$^1A_1 (n \rightarrow 3s)$ &6.92&6.92 &6.71&6.71 &6.76& &6.70&6.96&6.64& &6.28&6.25\\ +$^1A_2 (\pi \rightarrow 3s)$ &6.98&6.99 &6.74&6.75 &6.81& &6.75&6.90&6.53& & & \\ +$^1B_2 (\pi \rightarrow \pi^\star)$$^j$ &7.50&7.52 &7.40&\hl{xxx} &\hl{xxx} & &7.48&7.29&7.14&7.33&7.22&7.20\\ +$^1B_1 (\pi \rightarrow 3p)$ &7.54&7.55 &7.32& \hl{xxx} &7.38& &7.25&7.42&7.10& & & \\ +$^1A_1 (\pi \rightarrow \pi^\star)$ &7.56& &7.34&\hl{xxx} &7.39& &7.23&7.37&7.26&7.39&7.22&6.39\\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &4.33&4.31 &4.34&4.31 &4.33& &4.05& & &4.28& &3.86\\ +$^3B_1 (n \rightarrow \pi^\star)$ &4.57&4.56 &4.47&4.47 &4.46& &4.41& & &4.42& &4.12\\ +$^3B_2 (\pi \rightarrow \pi^\star)$ &4.92&4.91 &4.83&4.83 &4.79& &4.56& & &4.72& &4.47\\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &5.14&5.13 &5.08&\hl{xxx} &5.05& &4.73& & &4.96& & \\ +$^3A_2 (n \rightarrow \pi^\star)$ &5.51&5.49 &5.37&5.36 &5.35& &5.10& & &5.53& &5.40\\ +$^3B_2 (\pi \rightarrow \pi^\star)$ &6.46&6.45 &6.30&6.29 &6.25& &6.02& & &6.22& &6.09\\ +\hline + \end{tabular} + \end{footnotesize} +\vspace{-0.4 cm} +\begin{flushleft} +\begin{footnotesize} +$^a${{\CASPT} from Ref. \citenum{Ful92};} +$^b${{\STEOM} from Ref. \citenum{Noo99};} +$^c${EOM-CCSD({$\tilde{{T}}$}) from Ref. \citenum{Del97b};} +$^d${CC3-ext. from Ref. \citenum{Sil10c};} +$^e${EEL from Ref. \citenum{Pal91};} +$^f${EEL from Ref. \citenum{Lin19};} +$^g${{\CASPT} from Ref. \citenum{Lor95};} +$^h${EEL from Ref. \citenum{Wal90};} +$^i${EEL from Ref. \citenum{Lin16};} +$^j${Significant state mixing with a close-lying Rydberg transition, rendering unambiguous attribution difficult.} +\end{footnotesize} +\end{flushleft} +\end{table} + + The results obtained for both pyrimidine and triazine are listed in Tables \ref{Table-10} and S10. For the former derivative previous theoretical \cite{Ful92,Del97b,Ser97b,Noo99,Ohr01,Fis03b,Li07b,Sch08,Sil10b,Sil10c,Car10,Kan14,Sch17,Dut18} + and experimental \cite{Bol84,Pal90,Lin15} studies are rather extensive, as it can be viewed as the smallest model of DNA bases. For triazine, which does not have an abelian point group, one finds less theoretical studies, + \cite{Ful92,Wal92,Pal95,Del97b,Noo99,Oli05,Sch08,Sil10b,Sil10c,Kan14,Sch17,Dut18}, especially for the triplet transitions. \cite{Wal92,Pal95,Oli05} The experimental data are also less numerous. \cite{Bol84,Wal92} + As in pyridazine and pyridine, all the ES listed in Table \ref{Table-10} show $\%T_1$ larger than 85\%\ for singlet and 95\%\ for triplet, so that {\CCT} and {\CCSDT} are highly coherent, but possibly in one case, the + $^3A_1 (\pi \rightarrow \pi^\star)$ transitions in pyrimidine. The basis set effects are also small, with no variations larger than 0.10 (0.03) eV between double-$\zeta$ and triple-$\zeta$ (triple-$\zeta$ and quadruple-$\zeta$) and only + slightly larger variations for the two Rydberg transitions. For both compounds, the current values are almost systematically larger than most previously published data. For the triplets of triazine, the three lowest ES estimated + by {\CASPT} previously are too low by ca. -0.5 eV. + +s + \begin{table}[htp] +\caption{\small Vertical transition energies determined in pyrimidine and triazine. All values are in eV.} +\label{Table-10} +\begin{footnotesize} +\begin{tabular}{l|p{.5cm}p{1.0cm}|p{.5cm}p{1.0cm}|p{.5cm}p{1.0cm}p{1.2cm}|p{.5cm}p{.5cm}p{.5cm}p{.5cm}p{.6cm}p{.6cm}} +\hline + \multicolumn{14}{c}{Pyrimidine}\\ + & \multicolumn{2}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{6}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & {\CCT} & {\CCSDT} & {\CCT} & & {\NEV} &Th.$^a$ &Th.$^b$ &Th.$^c$&Th.$^d$ &Exp.$^e$ &Exp.$^f$\\ +\hline +$^1B_1 (n \rightarrow \pi^\star)$ &4.58&4.57 &4.48&4.48 &4.44&& &4.26&4.40&4.32&4.24& 4.2 &4.18 \\ +$^1A_2 (n \rightarrow \pi^\star)$ &4.99&4.99 &4.89&4.88 &4.86&& &4.49&4.72&4.74&4.74& &4.69 \\ +$^1B_2 (\pi \rightarrow \pi^\star)$ &5.47&5.44 &5.44&5.41 &5.41&& &5.47&5.04&5.29&5.01& 5.12 &5.18 \\ +$^1A_2 (n \rightarrow \pi^\star)$ &6.07&6.06 &5.98&5.97 &5.93&& & &5.94&5.98&5.84& 6.05 &5.67 \\ +$^1B_1 (n \rightarrow \pi^\star)$ &6.39& &6.29&6.29 &6.26&& &6.03&6.18&6.35&6.11& &6.02 \\ +$^1B_2 (n \rightarrow 3s)$ &6.81&6.80 &6.61&6.59 &6.72&& & &6.85&6.84&6.57& & \\ +$^1A_1 (\pi \rightarrow \pi^\star)$ &7.08&7.09 &6.93&6.94 &6.87&& &7.10&6.87&6.86&6.57& 6.7 &6.69 \\ +$^3B_1 (n \rightarrow \pi^\star)$ &4.20&4.20 &4.12&4.11 &4.10&& &3.81& &4.11& & &3.85 \\ +$^3A_1 (\pi \rightarrow \pi^\star)$ &4.55&4.52 &4.56&4.52 &4.55&& &4.35& &4.39& & &4.42 \\ +$^3A_2 (n \rightarrow \pi^\star)$ &4.77&4.76 &4.67&4.67 &4.66&& &4.24& &4.71& & &4.18 \\ +$^3B_2 (\pi \rightarrow \pi^\star)$ &5.08&5.08 &5.00&5.00 &4.96&& &4.83& &4.81& & &4.93 \\ +\hline + \multicolumn{14}{c}{Triazine}\\ + & \multicolumn{2}{c}{\Pop} & \multicolumn{2}{c}{\AVDZ}& \multicolumn{3}{c}{\AVTZ} & \multicolumn{6}{c}{Litt.}\\ +State & {\CCT} & {\CCSDT} & {\CCT} & {\CCSDT} & {\CCT} & {\CCSDT} & {\NEV} &Th.$^g$ &Th.$^b$ &Th.$^d$&Th.$^h$ &Exp.$^h$ \\ +\hline +$^1A_1'' (n \rightarrow \pi^\star)$ &4.85&4.84 &4.76&4.74 &4.73&4.72& &4.11&4.58&4.49&4.70 &\\ +$^1A_2'' (n \rightarrow \pi^\star)$ &4.84&4.84 &4.78&4.78 &4.74&4.75& &4.30&4.74&4.54&4.71 &4.59\\ +$^1E'' (n \rightarrow \pi^\star)$ &4.89&4.89 &4.82&4.81 &4.78&4.78& &4.32&4.69&4.56&4.75 &3.97\\ +$^1A_2' (\pi \rightarrow \pi^\star)$ &5.84&5.80 &5.81&5.78 &5.78&5.75& &5.59&5.35&5.36&5.71 &5.70\\ +$^1A_1' (\pi \rightarrow \pi^\star)$ &7.45&7.45 &7.31&7.31 &7.24&7.24& & &7.21&6.90&7.18 &6.86\\ +$^1E' (n \rightarrow 3s)$ &7.44&7.41 &7.24&7.21 &7.35&7.32& & &7.38&7.16& & \\ +$^1E'' (n \rightarrow \pi^\star)$ &7.89&7.86 &7.82&7.80 &7.79&7.78& & & &7.78&7.78 &\\ +$^1E' (\pi \rightarrow \pi^\star)$ &8.12&8.13 &7.97& &7.92&7.94& & &7.82&7.72&7.84 &7.76\\ +$^3A_2'' (n \rightarrow \pi^\star)$ &4.40&4.40 &4.35&4.35 &4.33& & &3.87&\\ +$^3E'' (n \rightarrow \pi^\star)$ &4.59&4.59 &4.52&4.52 &4.51& & &4.04&\\ +$^3A_1'' (n \rightarrow \pi^\star)$ &4.87& &4.78&4.76 &4.75& & &4.15&\\ +$^3A_1' (\pi \rightarrow \pi^\star)$ &4.88&4.85 &4.88&4.85 &4.88& & & &\\ +$^3E' (\pi \rightarrow \pi^\star)$ &5.70&5.68 &5.64& &5.61& & & &\\ +$^3A_2' (\pi \rightarrow \pi^\star)$ &6.85&6.84 &6.69&6.68 &6.63& & &4.76&\\ +\hline + \end{tabular} + \end{footnotesize} +\vspace{-0.4 cm} +\begin{flushleft} +\begin{footnotesize} +$^a${{\CASPT} from Ref. \citenum{Fis03b};} +$^b${{\STEOM} from Ref. \citenum{Noo99};} +$^c${SAC-CI from Ref. \citenum{Li07b};} +$^d${EOM-CCSD({$\tilde{{T}}$}) from Ref. \citenum{Del97b};} +$^e${UV max from Ref. \citenum{Bol84};} +$^f${EEL from Ref. \citenum{Lin15};} +$^g${{\CASPT} from Ref. \citenum{Oli05};} +$^h${CC3-ext. from Ref. \citenum{Sil10c}.} +\end{footnotesize} +\end{flushleft} +\end{table} + +\clearpage + + +\section{Theoretical Best Estimates} + +In Table \ref{Table-tbe}, we present our theoretical best estimates as obtained with the {\AVTZ} basis set or further corrected for basis set effects. The details of the approach used to get all the TBE are given as well. +For all states with a dominant single-excitation character, that is when $\%T_1 > 80$\%, we rely on CC results, using the incremental strategy to determine the TBE. For ES with $\%T_1$ between 70\%\ and 80\%, +our previous works indicated that {\CCSDT} tends to overshoot the transition energies by ca. 0.05--0.10 eV, but that the {\NEV} error tends to be slightly larger (on average). \cite{Loo19c} Therefore, if {\CCSDTQ} or {\FCI} +results are unavailable, it is hard to make the final call. For the other transitions, we relied either on the current or previous FCI or the {\NEV} values as reference. We indicate some transition energies +in italics in Table \ref{Table-tbe} to underline that they are (relatively) less accurate. This is the case when: i) {\NEV} results have to be selected; ii) the affordable CC calculations yield quite large changes from one expansion order to another +despite large $\%T_1$; and iii) there is a very large ES mixing making hard to follow a specific transition from one method (or one basis) to another. To determine the basis set corrections beyond augmented triple-$\zeta$, +we use the {\CCT}/{\AVQZ} or {\CCT}/{\AVFZ} results. For several compounds, we also provide in the SI, {\CCT}/{\DAVQZ} transition energies. However, we are not using these values as reference. This is because, +the addition of a second set of diffuse orbitals tends to modify the computed transition energies significantly only when it induces a more complex state mixing. We also stick to the +frozen-core approximation for two reasons: i) the corrections brought by ``full-correlation'' are generally trifling (typically $\pm$ 0.02 eV) for the compounds under study (see the SI for many examples); and ii) it would be, +in principle, necessary to add core polarization functions in such ``full'' calculations. + +Table \ref{Table-tbe} encompasses 238 ES, all at least obtained at the {\CCSDT} level. This set that can be decomposed as follows: 144 singlet and 94 triplet transitions, or 174 valence (99 $\pi \rightarrow \pi^\star$, 71 +$n \rightarrow \pi^\star$ and 4 double excitation) and 64 Rydberg transitions. Amongst the reported transition energies, fifteen can be considered as ``unsafe''. This is a significant extension of all previously +proposed ES datasets (see Introduction). The Table also reports 90 oscillator strengths, $f$ which is, to our knowledge, the largest set of {\CCT}/{\AVTZ} $f$ reported to date, the previous effort being mostly performed +at the {\CCT}/TZVP level for Thiel's set. \cite{Kan14} It should also be recalled that all these data are obtained on {\CCT}/{\AVTZ} geometries, consistently with our previous works. \cite{Loo18a,Loo19c} Taken +together they offer a consistent ensemble of transition energies of ca. 350 electronic transitions of various natures in small and medium-sized organic compounds. + +\renewcommand*{\arraystretch}{.55} +\LTcapwidth=\textwidth + +\begin{footnotesize} +\begin{longtable}{p{3.3cm}lcccccc} +\caption{\small TBE values determined for all considered states. For each state, we provide the oscillator strength and percentage of single excitations obtained at the \CCT/{\AVTZ} level, +as well TBE obtained with the same basis set together with the method used to obtain that TBE. In the right-most columns, we list the values obtained by including further basis set corrections, +that have always been obtained at the {\CCT} level. Values displayed in italics are likelt relatively less accurate. All values are in the FC approximation.} \label{Table-tbe}\\ +\hline + & & & & \multicolumn{2}{l}{TBE/{\AVTZ}} & \multicolumn{2}{l}{TBE/CBS} \\ + & State & $f$ & $\%T_1$ & Value & Method$^a$ & Value & Corr. \\ +\hline +\endfirsthead +\hline + & & & & \multicolumn{2}{l}{TBE/{\AVTZ}} & \multicolumn{2}{l}{TBE/CBS} \\ + & State & $f$ & $\%T_1$ & Value & Method $^a$ & Value & Corr. \\ +\hline +\endhead +\hline \multicolumn{7}{r}{{Continued on next page}} \\ +\endfoot +\hline +\endlastfoot +Acetone &$^1A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 91.1 & 4.47 & B & 4.48 & AVQZ \\ + &$^1B_2 (\mathrm{R}; n \rightarrow 3s)$ &0.000 & 90.5 & 6.46 & B & 6.51 & AVQZ \\ + &$^1A_2 (\mathrm{R}; n \rightarrow 3p)$ & & 90.9 & 7.47 & B & 7.44 & AVQZ \\ + &$^1A_1 (\mathrm{R}; n \rightarrow 3p)$ &0.004 & 90.6 & 7.51 & B & 7.55 & AVQZ \\ + &$^1B_2 (\mathrm{R}; n \rightarrow 3p)$ &0.029 & 91.2 & 7.62 & B & 7.63 & AVQZ \\ + &$^3A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.8 & 4.13 & D & 4.15 & AVQZ \\ + &$^3A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.7 & 6.25 & D & 6.27 & AVQZ \\ +Acrolein &$^1A'' (\mathrm{V}; n \rightarrow \pi^\star)$ &0.000 & 87.6 & 3.73 & {\CCSDT}/AVTZ & 3.74 & AVQZ \\ + &$^1A' (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.344 & 91.2 & 6.69 & {\CCSDT}/AVTZ & 6.69 & AVQZ \\ + &$^1A'' (\mathrm{V}; n \rightarrow \pi^\star)$ &0.000 & 79.4 & \emph{6.72} & D &\emph{6.74} & AVQZ \\ + &$^1A' (\mathrm{R}; n \rightarrow 3s)$ &0.109 & 89.4 & 7.08 & D & 7.12 & AVQZ \\ + &$^3A'' (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.0 & 3.44 & D & 3.43 & AVQZ \\ + &$^3A' (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.6 & 3.94 & D & 3.95 & AVQZ \\ + &$^3A' (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.4 & 6.18 & D & 6.19 & AVQZ \\ + &$^3A'' (\mathrm{V}; n \rightarrow \pi^\star)$ & & 92.7 & \emph{6.54} & E & \emph{6.55}& AVQZ \\%remove +Benzene &$^1B_{2u} (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 86.3 & 5.06 & {\CCSDT}/AVTZ & 5.06 &AVQZ \\ + &$^1B_{1u} (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 92.9 & 6.45 & {\CCSDT}/AVTZ &6.44 &AVQZ \\ + &$^1E_{1g} (\mathrm{R}; \pi \rightarrow 3s)$ & & 92.8 & 6.52 & {\CCSDT}/AVTZ &6.54 &AVQZ \\ + &$^1A_{2u} (\mathrm{R}; \pi \rightarrow 3p)$ &0.066 & 93.4 & 7.08 & {\CCSDT}/AVTZ &7.10 &AVQZ \\ + &$^1E_{2u} (\mathrm{R}; \pi \rightarrow 3p)$ & & 92.8 & 7.15 & {\CCSDT}/AVTZ &7.16 &AVQZ \\ + &$^3B_{1u} (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.6 & 4.16 & D &4.17 &AVQZ \\ + &$^3E_{1u}(\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 97.1 & 4.85 & D &4.86 &AVQZ \\ + &$^3B_{2u} (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.1 & 5.81 & D & 5.81 &AVQZ \\ +Butadiene &$^1B_u (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.664 & 93.3 & 6.22 & B & 6.21 & AVQZ \\ + &$^1B_g (\mathrm{R}; \pi \rightarrow 3s)$ & & 94.1 & 6.33 & B & 6.35 & AVQZ \\ + &$^1A_g (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 75.1 & 6.50 & F & 6.50 & AVQZ \\ + &$^1A_u (\mathrm{R}; \pi \rightarrow 3p)$ &0.001 & 94.1 & 6.64 & B & 6.66 & AVQZ \\ + &$^1A_u (\mathrm{R}; \pi \rightarrow 3p)$ &0.049 & 94.1 & 6.80 & B & 6.82 & AVQZ \\ + &$^1B_u (\mathrm{R}; \pi \rightarrow 3p)$ &0.055 & 93.8 & 7.68 & C & 7.54 & AVQZ \\ + &$^3B_u (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.4 & 3.36 & D & 3.37 & AVQZ \\ + &$^3A_g (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.7 & 5.20 & D & 5.21 & AVQZ \\ + &$^3B_g (\mathrm{R}; \pi \rightarrow 3s)$ & & 97.9 & 6.29 & D & 6.31 & AVQZ \\ +Cyanoacetylene &$^1\Sigma^- (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 94.3 & 5.80 & A & 5.79 & AV5Z\\ + &$^1\Delta (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 94.0 & 6.07 & A & 6.05 &AV5Z\\ + &$^3\Sigma^+ (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.5 & 4.44 & {\CCSDT}/AVTZ & 4.46 &AV5Z \\ + &$^3\Delta (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.2 & 5.21 & {\CCSDT}/AVTZ & 5.21 & AV5Z\\ + &$^1A'' [\mathrm{F}] (\mathrm{V}; \pi \rightarrow \pi^\star)$ & 0.004 & 93.6 & 3.54 & A & 3.54 & AVQZ \\ +Cyanoformaldehyde &$^1A'' (\mathrm{V}; n \rightarrow \pi^\star)$ & 0.001 & 89.8 & 3.81 & {\CCSDT}/AVTZ & 3.82 & AVQZ \\ + &$^1A'' (\mathrm{V}; \pi \rightarrow \pi^\star)$ & 0.000 & 91.9 & 6.46 & {\CCSDT}/AVTZ & 6.45 & AVQZ \\ + &$^3A'' (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.6 & 3.44 & D & 3.45 & AVQZ \\ + &$^3A' (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.4 & 5.01 & D & 5.02 & AVQZ \\ +Cyanogen & $^1\Sigma_u^- (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 94.1 & 6.39 & A & 6.38 & AV5Z\\ + & $^1\Delta_u (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 93.4 & 6.66 & A & 6.64 & AV5Z\\ + & $^3\Sigma_u^+ (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.5 & 4.91 & B & 4.93 & AV5Z \\ + & $^1\Sigma_u^- [\mathrm{F}] (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 93.4 & 5.05 & A & 5.03 & AV5Z \\ +Cyclopentadiene &$^1B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.084 & 93.8 & 5.56 & {\CCSDT}/AVTZ & 5.55 & AVQZ \\ + &$^1A_2 (\mathrm{R}; \pi \rightarrow 3s)$ & & 94.0 & 5.78 & {\CCSDT}/AVTZ & 5.80 & AVQZ \\ + &$^1B_1 (\mathrm{R}; \pi \rightarrow 3p)$ &0.037 & 94.2 & 6.41 & {\CCSDT}/AVTZ & 6.42 & AVQZ \\ + &$^1A_2 (\mathrm{R}; \pi \rightarrow 3p)$ & & 93.8 & 6.46 & {\CCSDT}/AVTZ & 6.47 & AVQZ \\ + &$^1B_2 (\mathrm{R}; \pi \rightarrow 3p)$ &0.046 & 94.2 & 6.56 &{\CCSDT}/AVTZ & 6.55 & AVQZ\\ + &$^1A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.001 & 78.9 & \emph{6.51} & D & \emph{6.51} & AVQZ \\ + &$^3B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.4 & 3.31 & D & 3.31 & AVQZ \\ + &$^3A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.6 & 5.11 & D & 5.12 & AVQZ \\ + &$^3A_2 (\mathrm{R}; \pi \rightarrow 3s)$ & & 97.9 & 5.73 & D & 5.75 & AVQZ \\ + &$^3B_1 (\mathrm{R}; \pi \rightarrow 3p)$ & & 97.9 & 6.36 & D & 6.38 & AVQZ \\ +Cyclopropenone &$^1B_1 (\mathrm{V}; n \rightarrow \pi^\star)$ &0.000 & 87.7 & 4.26 & B & 4.28 & AV5Z \\ + &$^1A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 91.0 & 5.55 & B & 5.56 &AV5Z \\ + &$^1B_2 (\mathrm{R}; n \rightarrow 3s)$ &0.003 & 90.8 & 6.34 & B & 6.40 & AV5Z \\ + &$^1B_2 (\mathrm{V}; \pi \rightarrow \pi^\star$) &0.047 & 86.5 & 6.54 & B & 6.56 & AV5Z\\ + &$^1B_2 (\mathrm{R}; n \rightarrow 3p)$ &0.018 & 91.1 & 6.98 & B & 7.01 & AV5Z \\ + &$^1A_1 (\mathrm{R}; n \rightarrow 3p)$ &0.003 & 91.2 & 7.02 & B & 7.08 &AV5Z \\ + &$^1A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.320 & 90.8 & 8.28 & B & 8.26 &AV5Z \\ + &$^3B_1 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 96.0 & 3.93 & {\CCSDT}/AVTZ & 3.96 & AV5Z \\ + &$^3B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 97.9 & 4.88 & {\CCSDT}/AVTZ & 4.91 & AV5Z \\ + &$^3A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.5 & 5.35 & {\CCSDT}/AVTZ & 5.37 & AV5Z \\ + &$^3A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.1 & 6.79 & {\CCSDT}/AVTZ & 6.81 & AV5Z\\ +Cyclopropenethione &$^1A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 89.6 & 3.41 & B & 3.41 & AV5Z \\ + &$^1B_1 (\mathrm{V}; n \rightarrow \pi^\star)$ &0.000 & 84.8 & 3.45 & B & 3.48 & AV5Z \\ + &$^1B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.007 & 83.0 & 4.60 & B & 4.62 & AV5Z \\ + &$^1B_2 (\mathrm{R}; n \rightarrow 3s)$ &0.048 & 91.8 & 5.34 & B & 5.40 & AV5Z \\ + &$^1A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.228 & 89.0 & 5.46 & B & 5.46 & AV5Z \\ + &$^1B_2 (\mathrm{R}; n \rightarrow 3p)$ &0.084 & 91.3 & 5.92 & B & 5.94 & AV5Z \\ + &$^3A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.2 & 3.28 & D & 3.28 & AV5Z \\ + &$^3B_1 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 94.5 & 3.32 & {\CCSDT}/AVTZ & 3.36 & AV5Z \\ + &$^3B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 96.5 & 4.01 & D & 4.04 & AV5Z \\ + &$^3A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.2 & 4.01 & D & 4.01 & AV5Z \\ +Diacetylene &$^1\Sigma_u^- (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 94.4 & 5.33 & A & 5.32 & AV5Z \\ + &$^1\Delta_u (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 94.1 & 5.61 & A & 5.60 & AV5Z \\ + &$^3\Sigma_u^+ (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.5 & 4.10 & C & 4.13 & AV5Z \\ + &$^3\Delta_u (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.2 & 4.78 & B & 4.78 &AV5Z \\ +Furan &$^1A_2 (\mathrm{R}; \pi \rightarrow 3s)$ & & 93.8 & 6.09 &{\CCSDT}/AVTZ & 6.11 &AVQZ \\ + &$^1B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.163 & 93.0 & 6.37 &{\CCSDT}/AVTZ & 6.37 &AVQZ \\ + &$^1A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.000 & 92.4 & 6.56 &{\CCSDT}/AVTZ & 6.56 &AVQZ \\ + &$^1B_1 (\mathrm{R}; \pi \rightarrow 3p)$ &0.038 & 93.9 & 6.64 &{\CCSDT}/AVTZ & 6.66 &AVQZ \\ + &$^1A_2 (\mathrm{R}; \pi \rightarrow 3p)$ & & 93.6 & 6.81 &{\CCSDT}/AVTZ & 6.83 &AVQZ \\ + &$^1B_2 (\mathrm{R}; \pi \rightarrow 3p)$ &0.008 & 93.5 & 7.24 & D & 7.14 &AVQZ \\ + &$^3B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.4 & 4.20 & D & 4.20 &AVQZ \\ + &$^3A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.1 & 5.46 & D & 5.47 &AVQZ \\ + &$^3A_2 (\mathrm{R}; \pi \rightarrow 3s)$ & & 97.9 & 6.02 & D & 6.05 &AVQZ \\ + &$^3B_1 (\mathrm{R}; \pi \rightarrow 3p)$ & & 97.9 & 6.59 & D & 6.61 &AVQZ \\ +Glyoxal &$^1A_u (\mathrm{V}; n \rightarrow \pi^\star)$ & 0.000 & 91.0 & 2.88 & B & 2.88 & AV5Z \\ + &$^1B_g (\mathrm{V}; n \rightarrow \pi^\star)$ & & 88.3 & 4.24 & B & 4.24 & AVQZ \\ + &$^1A_g (\mathrm{V}; n,n \rightarrow \pi^\star,\pi^\star)$ & & 0.5 & 5.61 & F & 5.60 & AV5Z \\%to be remade with CCSDT correction ?? + &$^1B_g (\mathrm{V}; n \rightarrow \pi^\star)$ & & 83.9 & 6.57 & B & 6.58 & AVQZ \\ + &$^1B_u (\mathrm{R}; n \rightarrow 3p)$ & 0.095 & 91.7 & 7.71 & B & 7.78 & AV5Z \\ + &$^3A_u (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.6 & 2.49 & {\CCSDT}/AVTZ & 2.50 & AV5Z \\ + &$^3B_g (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.4 & 3.89 & {\CCSDT}/AVTZ & 3.90 & AVQZ \\ + &$^3B_u (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.5 & 5.15 & {\CCSDT}/AVTZ & 5.17 & AV5Z \\ + &$^3A_g (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.8 & 6.30 & {\CCSDT}/AVTZ & 6.31 & AV5Z \\ +Imidazole &$^1A'' (\mathrm{R}; \pi \rightarrow 3s)$ & 0.001 & 93.0 & 5.71 & D & 5.73 & AVQZ \\ + &$^1A' (\mathrm{V}; \pi \rightarrow \pi^\star)$ & 0.124 & 89.6 & 6.41 & D & 6.41s & AVQZ \\ + &$^1A'' (\mathrm{V}; n \rightarrow \pi^\star)$ & 0.028 & 93.6 & 6.50 & D & 6.53 & AVQZ \\ + &$^1A' (\mathrm{R};\pi \rightarrow 3p)$ & 0.035 & 88.9 & \emph{6.83} & D &\emph{6.82} & AVQZ \\ + &$^3A' (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.3 & 4.73 & E & 4.74 & AVQZ \\ + &$^3A'' (\mathrm{R};(\pi \rightarrow 3s)$ & & 97.6 & 5.66 & D & 5.69 & AVQZ \\ + &$^3A' (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 97.9 & 5.74 & E & 5.75 & AVQZ \\ + &$^3A'' (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.3 & 6.31 & D & 6.31 & AVQZ \\ +Isobutene &$^1B_1 (\mathrm{R}; \pi \rightarrow 3s)$ & 0.006 & 94.1 & 6.46 & {\CCSDT}/AVTZ & 6.48 & AVQZ \\ + &$^1A_1 (\mathrm{R}; \pi \rightarrow 3p)$ & 0.228 & 94.2 & 7.01 & {\CCSDT}/AVTZ & 7.00 & AVQZ \\ + &$^3A_1 (\mathrm{V}; (\pi \rightarrow \pi^\star)$ & & 98.9 & 4.53 & D & 4.54 & AVQZ \\ +Methylenecyclopropene& $^1B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & 0.011 & 85.4 & 4.28 & B & 4.29 & AV5Z \\ + &$^1B_1 (\mathrm{R}; \pi \rightarrow 3s)$ & 0.005 & 93.6 & 5.44 & B & 5.47 & AV5Z \\ + &$^1A_2 (\mathrm{R}; \pi \rightarrow 3p)$ & & 93.3 & 5.96 & B & 5.99 & AVQZ \\ + &$^1A_1(\mathrm{V}; \pi \rightarrow \pi^\star)$ & 0.224 & 92.8 & \emph{6.12} & B & \emph{6.03} & AV5Z \\ + &$^3B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 97.2 & 3.49 & {\CCSDT}/AVTZ & 3.49 & AVQZ \\ + &$^3A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.6 & 4.74 & D & 4.75 & AV5Z \\ +Propynal & $^1A'' (\mathrm{V}; n \rightarrow \pi^\star)$ & 0.000 & 89.0 & 3.80 & {\CCSDT}/AVTZ & 3.81 & AVQZ \\ + &$^1A'' (\mathrm{V}; \pi \rightarrow \pi^\star)$ & 0.000 & 92.9 & 5.54 & {\CCSDT}/AVTZ & 5.53 & AVQZ \\ + &$^3A'' (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.4 & 3.47 & D & 3.48 & AVQZ \\ + &$^3A' (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.3 & 4.47 & D & 4.48 & AVQZ \\ +Pyrazine &$^1B_{3u} (\mathrm{V}; n \rightarrow \pi^\star)$ &0.006 & 90.1 & 4.15 & {\CCSDT}/AVTZ & 4.15 & AVQZ \\ + &$^1A_{u} (\mathrm{V}; n \rightarrow \pi^\star)$ & & 88.6 & 4.98 & {\CCSDT}/AVTZ & 4.99 & AVQZ \\ + &$^1B_{2u} (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.078 & 86.9 & 5.02 & {\CCSDT}/AVTZ & 5.01 & AVQZ \\ + &$^1B_{2g} (\mathrm{V}; n \rightarrow \pi^\star)$ & & 85.6 & 5.71 & {\CCSDT}/AVTZ & 5.71 & AVQZ \\ + &$^1A_{g} (\mathrm{R};n \rightarrow 3s)$ & & 91.1 & 6.65 & {\CCSDT}/AVTZ & 6.69 & AVQZ \\ + &$^1B_{1g} (\mathrm{V}; n \rightarrow \pi^\star)$ & & 84.2 & 6.74 & {\CCSDT}/AVTZ & 6.74 & AVQZ \\ + &$^1B_{1u} (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.063 & 92.8 & 6.88 & {\CCSDT}/AVTZ & 6.87 & AVQZ \\ + &$^1B_{1g} (\mathrm{R};n \rightarrow 3p)$ & & 93.8 & 7.21 & {\CCSDT}/AVTZ & 7.24 & AVQZ \\ + &$^1B_{2u} (\mathrm{R};n \rightarrow 3p)$ &0.037 & 90.8 & 7.24 & D & 7.28 &AVQZ \\ + &$^1B_{1u} (\mathrm{R};\pi \rightarrow 3s)$ &0.128 & 91.4 & 7.44 & D & 7.47 &AVQZ \\ + &$^1B_{1u} (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.285 & 90.5 & \emph{7.98}& D & \emph{7.97} &AVQZ \\ + &$^3B_{3u} (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.3 & 3.59 & D & 3.59 & AVQZ \\ + &$^3B_{1u} (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.5 & 4.35 & D & 4.36 & AVQZ \\ + &$^3B_{2u} (\mathrm{V}; (\pi \rightarrow \pi^\star)$ & & 97.6 & 4.39 & D & 4.39 & AVQZ \\ + &$^3A_{u} (\mathrm{V}; n \rightarrow \pi^\star)$ & & 96.1 & 4.93 & D & 4.94 & AVQZ \\ + &$^3B_{2g} (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.0 & 5.08 & D & 5.09 & AVQZ \\ + &$^3B_{1u} (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 97.0 & 5.28 & D & 5.28 & AVQZ \\ +Pyridazine &$^1B_1 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 89.0 & 3.83 & D &\hl{XXXX} & \hl{XXXXX} \\ + &$^1A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 86.9 & 4.37 & D &\hl{XXXX} & \hl{XXXXX} \\ + &$^1A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 85.8 & 5.26 & D & 5.26 & AVQZ \\ + &$^1A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 86.2 & 5.72 & D &\hl{XXXX} & \hl{XXXXX} \\ + &$^1B_2 (\mathrm{R}; n \rightarrow 3s)$ & & 88.5 & 6.17 & D &\hl{XXXX} & \hl{XXXXX} \\ + &$^1B_1 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 87.0 & 6.37 & D &\hl{XXXX} & \hl{XXXXX} \\ + &$^1B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 90.6 & 6.75 & D &\hl{XXXX} & \hl{XXXXX} \\ + &$^3B_1 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.1 & 3.19 & D &3.20 & AVQZ \\ + &$^3A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 96.2 & 4.11 & D &\hl{XXXX} & \hl{XXXXX} \\ + &$^3B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.5 & \emph{4.34} & D &\hl{XXXX} & \hl{XXXXX} \\ + &$^3A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 97.3 & 4.82 & D & 4.81 & AVQZ \\ +Pyridine &$^1B_1 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 88.4 & 4.95 & D &\hl{XXXX} & \hl{XXXXX} \\ + &$^1B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 86.5 & 5.14 & D &\hl{XXXX} & \hl{XXXXX} \\ + &$^1A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 87.9 & 5.40 & D &\hl{XXXX} & \hl{XXXXX} \\ + &$^1A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 92.1 & 6.62 & D &\hl{XXXX} & \hl{XXXXX} \\ + &$^1A_1 (\mathrm{R}; n \rightarrow 3s)$ & & 89.7 & 6.76 & D &\hl{XXXX} & \hl{XXXXX} \\ + &$^1A_2 (\mathrm{R}; \pi \rightarrow 3s)$ & & 93.2 & 6.82 & D &\hl{XXXX} & \hl{XXXXX} \\ + &$^1B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & \hl{xxx} & \emph{xxx} & &\emph{XXXX} & \hl{XXXXX} \\ + &$^1B_1 (\mathrm{R}; \pi \rightarrow 3p)$ & & 93.6 & 7.39 & E &\hl{XXXX} & \hl{XXXXX} \\ + &$^1A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 90.5 & \hl{xxx} & &\hl{XXXX} & \hl{XXXXX} \\ + &$^3A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.5 & 4.30 & D &\hl{XXXX} & \hl{XXXXX} \\ + &$^3B_1 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.0 & 4.46 & D &\hl{XXXX} & \hl{XXXXX} \\ + &$^3B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 97.3 & 4.79 & D &\hl{XXXX} & \hl{XXXXX} \\ + &$^3A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 97.1 & 5.04 & E &\hl{XXXX} & \hl{XXXXX} \\ + &$^3A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 95.8 & 5.36 & D &\hl{XXXX} & \hl{XXXXX} \\ + &$^3B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 97.7 & 6.24 & D &\hl{XXXX} & \hl{XXXXX} \\ +Pyrimidine &$^1B_1 (\mathrm{V}; n \rightarrow \pi^\star)$ & 0.005 & 88.6 & 4.44 & D &\hl{XXXX} & \hl{XXXXX} \\ + &$^1A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 88.5 & 4.85 & D &\hl{XXXX} & \hl{XXXXX} \\ + &$^1B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.028 & 86.3 & 5.38 & D &\hl{XXXX} & \hl{XXXXX} \\ + &$^1A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 86.7 & 5.92 & D &\hl{XXXX} & \hl{XXXXX} \\ + &$^1B_1 (\mathrm{V}; n \rightarrow \pi^\star)$ &0.005 & 86.7 & 6.26 & D &\hl{XXXX} & \hl{XXXXX} \\ + &$^1B_2 (\mathrm{R} ;n \rightarrow 3s)$ &0.005 & 90.3 & 6.70 & D &6.74 & AVQZ \\ + &$^1A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.036 & 91.5 & 6.88 & D &6.87 & AVQZ \\ + &$^3B_1 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 96.8 & 4.09 & D &4.10 & AVQZ \\ + &$^3A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.3 & \emph{4.51} & D &\emph{4.52} & AVQZ \\ + &$^3A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 96.5 & 4.66 & D &4.67 & AVQZ \\ + &$^3B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 97.4 & 4.96 & D &4.96 & AVQZ \\ + Pyrrole &$^1A_2 (\mathrm{R}; \pi \rightarrow 3s)$ & & 92.9 & 5.24 & {\CCSDT}/AVTZ & 5.27 & AVQZ \\ + &$^1B_1 (\mathrm{R};\pi \rightarrow 3p)$ &0.015 & 92.4 & 6.00 & {\CCSDT}/AVTZ & 6.03 & AVQZ \\ + &$^1A_2 (\mathrm{R};\pi \rightarrow 3p)$ & & 93.0 & 6.00 & D & 6.02 & AVQZ \\ + &$^1B_2 (\mathrm{V}; (\pi \rightarrow \pi^\star)$ &0.164 & 92.5 & 6.26 & {\CCSDT}/AVTZ & 6.23 & AVQZ \\ + &$^1A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.001 & 86.3 & 6.30 & {\CCSDT}/AVTZ & 6.29 & AVQZ \\ + &$^1B_2 (\mathrm{R};\pi \rightarrow 3p)$ &0.003 & 92.6 & 6.83 & D & 6.74 & AVQZ \\ + &$^3B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.3 & 4.51 & D & 4.51 & AVQZ \\ + &$^3A_2 (\mathrm{R};\pi \rightarrow 3s)$ & & 97.6 & 5.21 & D & 5.24 & AVQZ \\ + &$^3A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 97.8 & 5.45 & D & 5.46 & AVQZ \\ + &$^3B_1 (\mathrm{R};\pi \rightarrow 3p)$ & & 97.4 & 5.91 & D & 5.94 & AVQZ \\ +Tetrazine &$^1B_{3u} (\mathrm{V}; n \rightarrow \pi^\star)$ & 0.006 & 89.8 & 2.47 & {\CCSDT}/AVTZ & 2.46 & AVQZ \\ + &$^1A_{u} (\mathrm{V}; n \rightarrow \pi^\star)$ & & 87.9 & 3.69 & {\CCSDT}/AVTZ & 3.70 & AVQZ \\ + &$^1A_{g} (\mathrm{V}; n,n \rightarrow \pi^\star, \pi^\star)$ & & 0.7 & \emph{4.61} & {\NEV}/AVTZ & \emph{4.59} & AVQZ\\%to be remade with CCSDT correction ??? + &$^1B_{1g} (\mathrm{V}; n \rightarrow \pi^\star)$ & & 83.1 & 4.93 & {\CCSDT}/AVTZ & 4.92 & AVQZ \\ + &$^1B_{2u} (\mathrm{V}; \pi \rightarrow \pi^\star)$ & 0.055 & 85.4 & 5.21 & {\CCSDT}/AVTZ & 5.20 & AVQZ \\ + &$^1B_{2g} (\mathrm{V}; n \rightarrow \pi^\star)$ & & 81.7 & 5.45 & {\CCSDT}/AVTZ & 5.45 & AVQZ \\ + &$^1A_{u} (\mathrm{V}; n \rightarrow \pi^\star)$ & & 87.7 & 5.53 & {\CCSDT}/AVTZ & 5.53 & AVQZ \\ + &$^1B_{3g} (\mathrm{V}; n,n \rightarrow \pi^\star, \pi^\star)$ & & 0.7 & \emph{6.15} & {\NEV}/AVTZ & \emph{6.13} & AVQZ\\ + &$^1B_{2g} (\mathrm{V}; n \rightarrow \pi^\star)$ & & 80.2 & 6.12 & D & 6.12 & AVQZ \\ + &$^1B_{1g} (\mathrm{V}; n \rightarrow \pi^\star)$ & & 85.1 & 6.91 & D & 6.91 & AVQZ \\ + &$^3B_{3u} (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.1 & 1.85 & D & 1.86 & AVQZ \\ + &$^3A_{u} (\mathrm{V}; n \rightarrow \pi^\star)$ & & 96.3 & 3.45 & D & 3.46 & AVQZ \\ + &$^3B_{1g} (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.0 & 4.20 & D & 4.21 & AVQZ \\ + &$^3B_{1u} (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.5 & \emph{4.49} & D & \emph{4.49} & AVQZ \\ + &$^3B_{2u} (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 97.5 & 4.52 & D & 4.52 & AVQZ \\ + &$^3B_{2g} (\mathrm{V}; n \rightarrow \pi^\star)$ & & 96.4 & 5.04 & D & 5.04 & AVQZ \\ + &$^3A_{u} (\mathrm{V}; n \rightarrow \pi^\star)$ & & 96.6 & 5.11 & D & 5.11 & AVQZ \\ + &$^3B_{3g} (\mathrm{V}; n,n \rightarrow \pi^\star, \pi^\star)$ & & 5.7 & \emph{5.51} &{\NEV}/AVTZ & \emph{5.50} & AVQZ\\ + &$^3B_{1u} (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 96.6 & 5.42 & D & 5.43 & AVQZ \\ +Thioacetone &$^1A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 88.9 & 2.53 & B & 2.54 & AVQZ \\ + &$^1B_2 (\mathrm{R}; n \rightarrow 4s)$ & 0.052 & 91.3 & 5.56 & B & 5.61 & AVQZ \\ + &$^1A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & 0.242 & 90.6 & 5.88 & B & 5.86 & AVQZ \\ + &$^1B_2 (\mathrm{R}; n \rightarrow 4p)$ & 0.028 & 92.4 & 6.51 & C & 6.52 & AVQZ \\ + &$^1A_1 (\mathrm{R}; n \rightarrow 4p)$ & 0.023 & 91.6 & 6.61 &B & 6.64 & AVQZ \\ + &$^3A_2 (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.4 & 2.33 & D & 2.34 & AVQZ \\ + &$^3A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.7 & 3.45 & D & 3.46 & AVQZ \\ +Thiophene &$^1A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.070 & 87.6 & 5.64 & {\CCSDT}/AVTZ & 5.63 & AVQZ \\ + &$^1B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.079 & 91.5 & 5.98 & {\CCSDT}/AVTZ & 5.96 & AVQZ \\ + &$^1A_2 (\mathrm{R}; \pi \rightarrow 3s)$ & & 92.6 & 6.14 & {\CCSDT}/AVTZ & 6.16 & AVQZ \\ + &$^1B_1 (\mathrm{R}; \pi \rightarrow 3p)$ &0.010 & 90.1 & 6.14 & {\CCSDT}/AVTZ & 6.11 & AVQZ \\ + &$^1A_2 (\mathrm{R}; \pi \rightarrow 3p)$ & & 91.8 & 6.21 & {\CCSDT}/AVTZ & 6.18 & AVQZ \\ + &$^1B_1 (\mathrm{R}; \pi \rightarrow 3s)$ &0.000 & 92.8 & 6.49 & {\CCSDT}/AVTZ & 6.52 & AVQZ \\ + &$^1B_2 (\mathrm{R}; \pi \rightarrow 3p)$ &0.082 & 92.4 & 7.29 & {\CCSDT}/AVTZ & 7.18 & AVQZ \\ + &$^1A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.314 & 86.5 & \emph{7.31}& E & \emph{7.29} & AVQZ \\ + &$^3B_2 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.2 & 3.92 & D & 3.91 & AVQZ \\ + &$^3A_1 (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 97.7 & 4.76 & D & 4.76 & AVQZ \\ + &$^3B_1 (\mathrm{R}; \pi \rightarrow 3p)$ & & 96.6 & 5.93 & D & 5.90 & AVQZ \\ + &$^3A_2 (\mathrm{R}; \pi \rightarrow 3s)$ & & 97.5 & 6.08 & D & 5.98 & AVQZ \\ +Thiopropynal &$^1A'' (\mathrm{V}; n \rightarrow \pi^\star)$ & 0.000 & 87.5 & 2.03 & {\CCSDT}/AVTZ & 2.04 & AVQZ \\ + &$^3A'' (\mathrm{V}; n \rightarrow \pi^\star)$ & & 97.2 & 1.80 & D & 1.81 & AVQZ \\ +Triazine &$^1A_1'' (\mathrm{V}; n \rightarrow \pi^\star)$ & & 88.3 & 4.72 & {\CCSDT}/AVTZ & 4.72 & AVQZ \\ + &$^1A_2'' (\mathrm{V}; n \rightarrow \pi^\star)$ &0.014 & 88.3 & 4.75 & {\CCSDT}/AVTZ & 4.74 & AVQZ \\ + &$^1E'' (\mathrm{V}; n \rightarrow \pi^\star)$ & & 88.3 & 4.78 & {\CCSDT}/AVTZ & 4.78 & AVQZ \\ + &$^1A_2' (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 85.7 & 5.75 & {\CCSDT}/AVTZ &5.75 &AVQZ\\ + &$^1A_1' (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 90.4 & 7.24 & {\CCSDT}/AVTZ & 7.23 & AVQZ \\ + &$^1E' (\mathrm{R}; n \rightarrow 3s)$ &0.016 & 90.9 & 7.32 & {\CCSDT}/AVTZ & 7.36 & AVQZ \\ + &$^1E'' (\mathrm{V}; n \rightarrow \pi^\star)$ & & 82.6 & 7.78 & {\CCSDT}/AVTZ & 7.76 & AVQZ \\ + &$^1E' (\mathrm{V}; \pi \rightarrow \pi^\star)$ &0.451 & 90.0 & 7.94 & {\CCSDT}/AVTZ & 7.93 & AVQZ \\ + &$^3A_2'' (\mathrm{V}; n \rightarrow \pi^\star)$ & & 96.7 & 4.33 & D & 4.34 & AVQZ \\ + &$^3E'' (\mathrm{V}; n \rightarrow \pi^\star)$ & & 96.6 & 4.51 & D & 4.51 & AVQZ \\ + &$^3A_1'' (\mathrm{V}; n \rightarrow \pi^\star)$ & & 96.2 & 4.73 & D & 4.74 & AVQZ \\ + &$^3A_1' (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 98.2 & 4.85 & D & 4.86 & AVQZ \\ + &$^3E' (\mathrm{V}; \pi \rightarrow \pi^\star)$ & & 96.9 & 5.59 & E & 5.59 & AVQZ \\ + &$^3A_2' (\mathrm{V}; (\pi \rightarrow \pi^\star)$ & & 97.6 & 6.62 & D & 6.61 & AVQZ \\ + \end{longtable} + \end{footnotesize} +\begin{flushleft}\begin{footnotesize}\begin{singlespace} + \vspace{-0.6 cm} +$^a${ +Method A: {\CCSDT}/{\AVTZ} value corrected by the difference between {\CCSDTQ}/{\AVDZ} and {\CCSDT}/{\AVDZ} results; +Method B: {\CCSDT}/{\AVTZ} value corrected by the difference between {\CCSDTQ}/{\Pop} and {\CCSDT}/{\Pop} results; +Method C: {\CCT}/{\AVTZ} value corrected by the difference between {\CCSDTQ}/{\Pop} and {\CCT}/{\Pop} results; +Method D: {\CCT}/{\AVTZ} value corrected by the difference between {\CCSDT}/{\AVDZ} and {\CCT}/{\AVDZ} results; +Method E: {\CCT}/{\AVTZ} value corrected by the difference between {\CCSDT}/{\Pop} and {\CCT}/{\Pop} results; +Method F: {exCI}/{\AVDZ} value (from Ref. \citenum{Loo19c}) corrected by the difference between {\CCSDT}/{\AVTZ} and {\CCSDT}/{\AVDZ} results. +} +\end{singlespace}\end{footnotesize}\end{flushleft} + +\clearpage + +\section{Benchmarks} + +Having at hand such a large set of accurate transition energies, it seems natural to pursue previous benchmarking efforts. More specifically, we assess here the performances of eight popular wavefunction approaches, namely, CIS(D), {\AD}, +{\CCD}, {\STEOM}, {\CCSD}, CCSDR(3), CCSDT-3 and {\CCT}. The complete list of results can be found in Table \hl{SXXX} in the SI. As all these approaches are single-reference methods, we have removed from the +benchmark not only the unsafe transition energies (in italics in Table \ref{Table-tbe}), but also the four transitions with a dominant double excitation character ($\%T_1 < 50\%$ listed in Table \ref{Table-tbe}). +Our global results are collected in Table \ref{Table-bench} that presents the MSE, MAE, root mean square deviation (RMS), standard deviation (SD), as well as the positive [\MaxP] and negative [\MaxN] maximum deviations. +Figure \ref{Fig-1} shows histograms of the error distributions for all eight methods. Before discussing the obtained results, let us underline two obvious bias of this benchmark: i) it encompasses only conjugated organic molecules +containing 4 to 6 non-hydrogen atoms; and ii) we mainly used {\CCSDTQ} (4 atoms) or {\CCSDT} (5--6 atoms) reference values. As discussed in Section \ref{sec-ic} and in our previous work, \cite{Loo18a} the MAE obtained +with these two methods are of the order of 0.01 and 0.03 eV, respectively. This means that any deviation (or difference of deviations) smaller than ca. 0.02--0.03 eV is likely irrelevant. + +\renewcommand*{\arraystretch}{1.0} +\begin{table}[htp] +\caption{Mean signed error (MSE), mean absolute error (MAE), root-mean square deviation (RMS), standard deviation (SD), positive [\MaxP] and negative [\MaxN] maximal deviations with respect to the TBE. +All values are in eV and have been obtained with the {\AVTZ} basis set.} +\label{Table-bench} +\begin{tabular}{lccccccc} +\hline +Method & Nb. States & MSE &MAE &RMS &SD &\MaxP &\MaxN \\ +\hline +CIS(D) &220 &0.16 &0.23 &0.29 &0.24 &0.96 &-0.69\\ +{\AD} &217 &0.01 &0.14 &0.20 &0.19 &0.64 &-0.73\\ +{\CCD} &222 &0.02 &0.15 &0.21 &0.20 &0.59 &-0.68\\ +{\STEOM} &190 &0.00 &0.12 &0.15 &0.14 &0.59 &-0.42\\ + {\CCSD} &222 &0.11 &0.13 &0.16 &0.12 &0.62 &-0.16\\ +CCSDR(3) &133 &0.05 &0.05 &0.07 &0.05 &0.36 &-0.03\\ +CCSDT-3 &126 &0.05 &0.05 &0.07 &0.04 &0.26 &0.00\\ +{\CCT} &222 &0.00 &0.01 &0.02 &0.02 &0.17 &-0.05\\ +\hline + \end{tabular} + \end{table} + +\begin{figure}[htp] + \includegraphics[scale=0.98,viewport=2cm 14.5cm 19cm 27.5cm,clip]{Figure-1.pdf} + \caption{Histograms of the error patterns obtained with various leveles of theory, taking the TBE/{\AVTZ} of Table \ref{Table-bench} as references. Note the different $Y$ scales.} + \label{Fig-1} +\end{figure} + +Let us analyse the global performances of all methods, starting with the most refined models. The relative accuracies of {\CCT} and {\CCSDT}-3 as compared to {\CCSDT} remains an open question in the literature. \cite{Wat13,Dem13} +Indeed, to our knowledge, the only two previous reports discussing this specific aspect are limited to tiny compounds. \cite{Kan17,Loo18a} According to the results of Table \ref{Table-bench}, it appears that {\CCT} has the edge, although +{\CCSDT}-3 is closer to {\CCSDT} in formal terms. Indeed, {\CCSDT}-3 seems to provide slightly too large transition energies (MSE of +0.05 eV). These conclusions are qualitatively consistent with the analyses performed for smaller derivatives, +\cite{Kan17,Loo18a} but the amplitude of {\CCSDT}-3's errors are larger with the present set. Although the performances of {\CCT} might be unduly inflated by the use of {\CCSDT} and {\CCSDTQ} reference values, it is also clear that this +method very rarely fails (Figure \ref{Fig-1}). Consequently, {\CCT} transition energies can be viewed as very solid references for all transitions with a dominant single-excitation character. This conclusion is again consistent with previous +analyses performed for smaller compounds, \cite{Kan17,Loo18a} as well as with recent comparisons between theoretical and experimental 0-0 energies that have been performed by some of us on medium-sized molecules.\cite{Loo18b,Loo19a,Sue19} +To state it more bluntly: it appears likely that {\CCT} is even more accurate than previously thought. In addition, from all the comparisons made in this work, one can conclude that {\CCT} regularly outperforms {\CASPT} and {\NEV}, even when +these methods are combined with active space chosen by specialists, a statement that seems true as long as the considered ES does not show a strong multiple excitation character, that is, when $\%T_1 < 70\%$. The perturbative +inclusion of triples as made in CCSDR(3) offers a very small MAE (0.05 eV) for a much reduced computational cost as compared to {\CCSDT}. Nevertheless, as with {\CCSDT}-3, the CCSDR(3) transition energies have a clear tendency +of being too large, an error sign likely inherited from the parent {\CCSD} model. This 0.05 eV MAE for CCSDR(3) is rather similar to the one obtained for small compounds when comparing to {\FCI} (0.04 eV), \cite{Loo18a} and is also inline with the +2009 benchmark of Sauer et al. \cite{Sau09} {\CCSD} provides an interesting case. The calculated MSE (+0.11 eV), indicating an overestimation of the transition energies, fits well many previous reports, +\cite{Sch08,Car10,Wat13,Kan14,Jac17b,Kan17,Dut18,Jac18a,Loo18a} but is larger than the one determined for smaller molecules (+0.05 eV), \cite{Loo18a} hinting that the performances of {\CCSD} deteriorates when larger compounds +are considered. The {\CCSD} MAE (0.13 eV) is much smaller than the one reported by Thiel in its original work (0.49 eV) \cite{Sch08} but of the same order of magnitude as in the more recent study of Kannar and Szalay performed +on Thiel's set (0.18 eV for transitions with $\%T_1 > 90\%$ ). \cite{Kan14} In retrospect, the much larger value obtained by Thiel is likely related to the use of {\CASPT} reference values in the 2008 work. Indeed, as we have shown +in many of the proposed examples, {\CASPT} transitions energies tend to be significantly too low, therefore exacerbating {\CCSD}'s overestimation. The {\STEOM} approach, which received relatively less attention to date -- we are +aware of one detailed benchmark \cite{Dut18} only -- provides a smaller MSE than {\CCSD} and comparable MAE and RMS. The spread of the error is however slightly larger as can be seen in Figure \ref{Fig-1} and from the SD values +in Table \ref{Table-bench}. These trends are the same as for smaller compounds. \cite{Loo18a} For Thiel's set using {\CCT}/TZVP results as references, Dutta and coworkers also reported a rather good performance +of {\STEOM}, though in that case a slightly negative MSE is obtained, \cite{Dut18} which could possibly be due to the different basis sets used. It should be nevertheless stressed that we consider here only ``clean'' {\STEOM} results +(see Computational details), therefore removing several difficult cases that are included in the {\CCSD} statistics, e.g., the $A_g$ excitation in butadiene, which can slightly bias the relative accuracies when comparing the two models. Finally, for the three +second-order methods, namely CIS(D), {\AD}, and {\CCD}, that are often used as reference to benchmark TD-DFT for ``real-life'' applications, we obtain clearly worse performances for the former approach than for the two latter, that show very +similar statistical behaviors. These trends were also reported in several previous works. \cite{Hat05c,Jac18a,Sch08,Sil10c,Win13,Har14,Jac15b,Kan17,Loo18a} Interestingly, the {\CCD} MAE obtained here, 0.15 eV, is significantly +smaller than the one we found for the smaller compounds (0.22 eV): \cite{Loo18a} in contrast to {\CCSD}, {\CCD} seems to improve with molecular size. As above, Thiel's original MAE for {\CCD} (0.29 eV) was likely too large due +to the selection of {\CASPT} reference values. \cite{Sch08} As already noticed by Szalay's group, \cite{Kan14,Kan17} although the MSE of {\CCD} is smaller than the one of {\CCSD}, the standard deviation is significantly larger +with the former model, i.e., {\CCD} is less consistent in terms of trends than {\CCSD}. + +In Table \ref{Table-bench2}, we report a decomposition of the MAE for different subsets of ES. Only singlet ES could be determined with both CCSDR(3) and CCSDT-3, which is why no value appears in the triplet +column for these two methods. A few interesting conclusions emerge from the displayed data. First, the errors for the singlet and triplet transitions are rather similar with all models, but with {\CCSD} that +is significantly more effective for the triplets. Dutta and coworkers obtained the same conclusions for Thiel's set with MAE of 0.20 eV and 0.11 eV for the singlet and triplet ES, respectively. \cite{Dut18} +When turning to the comparison between valence and Rydberg states, it is found that {\CCD} actually performs more effectively for the former, whereas {\CCSD} (and higher order methods) yields the opposite trend. +In fact {\CCD} has a tendency to overestimate the energies of the valence ES (MSE of +0.10 eV), but to underestimate their Rydberg counterparts (MSE of -0.17 eV), whereas {\CCSD} is much more consistent +with MSE of 0.12 and 0.09 eV, respectively (see the SI). This relatively poorer performance of {\CCD} as compared to {\CCSD} for Rydberg ES is again consistent with other benchmarks, \cite{Kan17,Dut18} although the MAE +for {\CCD} (0.18 eV) reported in Table \ref{Table-bench2} remains relatively small as compared to the one given in Ref. \citenum{Kan17}. This is likely a side effect of the consideration of (relatively) low-lying +Rydberg transitions in medium-sized molecules in the present work, whereas Kannar and Szalay (mostly) investigated higher-lying Rydberg in smaller compounds. Eventually, CIS(D), {\AD}, {\CCD}, and {\STEOM} +better describe $n\rightarrow\pi^\star$ transitions, whereas {\CCSD} seems more suited for $\pi\rightarrow\pi^\star$ transitions; the variations between the two subsets being probably not very significant for the +higher-order approaches. The former finding agrees with the results obtained for smaller compounds, \cite{Loo18a} as well for Thiel's set, \cite{Sch08,Kan14} whereas the latter, less expected conclusions, seems to be significantly +dependent on the selected subset of ES. \cite{Sch08,Kan17} + +\renewcommand*{\arraystretch}{1.0} +\begin{table}[htp] +\caption{MAE (in eV) obtained with different methods for various classes of excited states.} +\label{Table-bench2} +\begin{tabular}{lcccccc} +\hline +Method & Singlet & Triplet & Valence & Rydberg & $n \ra \pis$ & $\pi \ra \pis$ \\ +\hline +CIS(D) &0.21 &0.25 &0.26 &0.15 &0.22 &0.28\\ +{\AD} &0.15 &0.13 &0.13 &0.17 &0.08 &0.17\\ +{\CCD} &0.16 &0.15 &0.15 &0.18 &0.08 &0.20\\%moins grosse diffˇrence entre V et Ry que dans Kan17 +{\STEOM} &0.11 &0.13 &0.12 &0.12 &0.08 &0.15\\ + {\CCSD} &0.16 &0.09 &0.15 &0.09 &0.20 &0.11\\%CCSD error smaller for pi-pi* than n-pi* different from Kan14 +CCSDR(3) &0.05 & &0.07 &0.02 &0.08 &0.06\\ +CCSDT-3 &0.05 & &0.06 &0.03 &0.08 &0.04\\ +{\CCT} &0.01 &0.01 &0.01 &0.01 &0.01 &0.02\\ +\hline + \end{tabular} + \end{table} + +\section{Conclusions and outlook} + +We have determined highly-accurate vertical transition energies for a set of 27 medium-sized organic molecules containing from 4 to 6 (non-hydrogen) atoms. To this end, we used several theoretical levels +and basis sets, but our theoretical best estimates are mainly based on {\CCSDTQ} (4 atoms) or {\CCSDT} (5 and 6 atoms) values determined with diffuse containing basis sets. For the vast majority of the +listed excited-states, this contribution is the first to disclose (sometimes basis-set extrapolated) {\CCSDT}/{\AVTZ} and (true) {\CCT}/{\AVQZ} transition energies as well as {\CCT}/{\AVTZ} oscillator strengths +for all dipole-allowed transitions. The set contains a total of 238 transition energies and 90 oscillator strengths, including a reasonably good balance between singlet and triplet transition energies and valence +and Rydberg states. Amongst these 238 transitions, we consider that 224 are ``safe'' TBE, that is, that they are chemically accurate (mean error below $0.043$ eV or $1$ kcal.mol$^{-1}$ for the considered geometry), +allowing to establish a reasonable error bar for lower-cost ES models daily used by computational chemists. In this framework, we benchmarked eight popular methods, CIS(D), {\AD}, {\CCD}, {\STEOM}, {\CCSD}, +CCSDR(3), CCSDT-3, and {\CCT}. It turned out that the latter approach is extremely accurate, and, very likely should be more trusted than {\CASPT} or {\NEV} but for ES dominated by a double +excitation character. Other methods including corrections for the triples yield a mean absolute deviation of ca. 0.05 eV, whereas none of the second-order approach is chemically accurate, with MAE +in the 0.12--0.23 eV range. + +Paraphrasing Thiel and coworkers, \cite{Sch08} we hope that this new set of vertical transition energies, combined or not with the ones described in our previous works, \cite{Loo18a,Loo19c} will be useful for the community, +will stimulate further developments and analyses in the field, and will provide new grounds for appraising the \emph{pros} and \emph{cons} of ES approaches already available or under development. We can +crystal-ball that the emergence of new {\sCI} algorithms optimized for modern computer architectures will likely lead to the revision of some the present TBE, further allowing to climb one step on the accuracy +ladder. + +\begin{suppinfo} +Geometries. +Basis set and frozen core effects. +Definition of the active spaces for the multi-reference calculations. +Additional details about the {\sCI} calculations and their extrapolation. +Benchmark data and further statistical analysis. +\end{suppinfo} + +\begin{acknowledgement} +P.F.L.~would like to thank \textit{Centre National de la Recherche Scientifique} for funding. +D.J.~acknowledges the \emph{R\'egion des Pays de la Loire} for financial support. This research used resources of i) the GENCI-TGCC (Grant No.~2018-A0040801738); ii) CCIPL (\emph{Centre de Calcul Intensif des Pays de Loire}); +iii) the Troy cluster installed in Nantes; and iv) CALMIP under allocations 2019-18005 (Toulouse). +This work has been supported through the EUR grant NanoX ANR-17-EURE-0009 in the framework of the \textit{``Programme des Investissements d'Avenir''}. +\end{acknowledgement} + +\bibliography{biblio-new} +\clearpage + +\begin{tocentry} +\begin{center} +%\includegraphics[scale=.17]{TOC.png} +\end{center} +\end{tocentry} + + +\end{document} diff --git a/Manuscript/Figure-1.pdf b/Manuscript/Figure-1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..64ba5abf486f06a74bc60800bc10ad0f7c84d80c GIT binary patch literal 1636925 zcmeFZWn5Kjw>~UvkPcA<$)%KlfRuE1cOwXhlyo;3Al)Uc)S@LtQkQ}>(v3(-ch~=3 zEVual&UyBE&inN}UqmN+&w0=L9^)F*4%RLc1F+VW=syq zeTc2GB_=;Vghk%e#>~ka!U-;^LRcg%o;sO2fS*r|oJ_?{O>7^VLIedd9i1FZjjS=< 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Mol. Struct. (THEOCHEM)}} +@article{Ang02, + Author = {Angeli, Celestino and Cimiraglia, Renzo and Malrieu, Jean-Paul}, + Date-Added = {2019-11-07 23:20:49 +0100}, + Date-Modified = {2019-11-07 23:20:53 +0100}, + Doi = {10.1063/1.1515317}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = nov, + Number = {20}, + Pages = {9138-9153}, + Shorttitle = {{\emph{N}} -Electron Valence State Perturbation Theory}, + Title = {{\emph{N}} -Electron Valence State Perturbation Theory: {{A}} Spinless Formulation and an Efficient Implementation of the Strongly Contracted and of the Partially Contracted Variants}, + Volume = {117}, + Year = {2002}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.1515317}} + +@article{Ang01b, + Author = {Angeli, Celestino and Cimiraglia, Renzo and Malrieu, Jean-Paul}, + Date-Added = {2019-11-07 23:20:00 +0100}, + Date-Modified = {2019-11-07 23:20:20 +0100}, + Doi = {10.1016/S0009-2614(01)01303-3}, + Issn = {00092614}, + Journal = {Chem. Phys. Lett.}, + Language = {en}, + Month = dec, + Number = {3-4}, + Pages = {297-305}, + Shorttitle = {N-Electron Valence State Perturbation Theory}, + Title = {N-Electron Valence State Perturbation Theory: A Fast Implementation of the Strongly Contracted Variant}, + Volume = {350}, + Year = {2001}, + Bdsk-Url-1 = {https://doi.org/10.1016/S0009-2614(01)01303-3}} + +@article{molpro, + Abstract = {Abstract Molpro (available at http://www.molpro.net) is a general-purpose quantum chemical program. The original focus was on high-accuracy wave function calculations for small molecules, but using local approximations combined with explicit correlation treatments, highly accurate coupled-cluster calculations are now possible for molecules with up to approximately 100 atoms. Recently, multireference correlation treatments were also made applicable to larger molecules. Furthermore, an efficient implementation of density functional theory is available. {\copyright} 2011 John Wiley \& Sons, Ltd. This article is categorized under: Software > Quantum Chemistry}, + Author = {Werner, Hans-Joachim and Knowles, Peter J. and Knizia, Gerald and Manby, Frederick R. and Sch{\"u}tz, Martin}, + Date-Added = {2019-11-07 23:18:29 +0100}, + Date-Modified = {2019-11-07 23:18:29 +0100}, + Doi = {10.1002/wcms.82}, + Eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/wcms.82}, + Journal = {Wiley Interdisciplinary Reviews: Computational Molecular Science}, + Number = {2}, + Pages = {242-253}, + Title = {Molpro: a general-purpose quantum chemistry program package}, + Url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/wcms.82}, + Volume = {2}, + Year = {2011}, + Bdsk-Url-1 = {https://onlinelibrary.wiley.com/doi/abs/10.1002/wcms.82}, + Bdsk-Url-2 = {https://doi.org/10.1002/wcms.82}} + +@article{Pal95, + Abstract = {Ultraviolet photoelectron (UPS), ultraviolet (UV) and vacuum ultraviolet (VUV) absorption and electron energy loss (EEL) spectra are presented for 1,2,4-triazine in the gas phase and interpreted using the results of ab initio multi-reference configuration interaction calculations. The lowest optical band (1nĻ€ā—, Emaxā‰3.1 eV) is highly structured. The corresponding triplet state is detected in EEL at 2.7 eV. Other valence states of type nĻ€ā— are assigned to EEL bands at 3.6 eV (1,3n Ļ€ā—) and ā‰6.0 eV(1nĻ€ā—). The 1Ļ€Ļ€ā— states are positioned about 5.0, 6.7, 7.8 and 7.9 eV, the last two relating to the benzene 1E1u state. Electron energy loss processes observed around 4.1 and 4.9 eV are attributed to excitation of 3Ļ€Ļ€ā— states. Low-lying Rydberg states of type 1n3s and 1n3p have been assigned, but Rydberg series are not strong in the experimental spectra. The UPS has been interpreted by means of non-diagonal Green's function and Tamm-Dancoff calculations.}, + Author = {Michael H. Palmer and Isobel C. Walker and Martyn F. Guest and Michele R.F. Siggel}, + Date-Added = {2019-11-07 20:49:49 +0100}, + Date-Modified = {2019-11-07 20:50:31 +0100}, + Doi = {https://doi.org/10.1016/0301-0104(95)00308-8}, + Issn = {0301-0104}, + Journal = {Chem. Phys.}, + Number = {2}, + Pages = {381--391}, + Title = {The Electronic States of the Azines. VII. 1,2,4-Triazine, Studied by Photon Absorption, Near-Threshold Electron Energy Loss Spectroscopy and ab initio Multi-Reference Configuration Interaction Calculations}, + Url = {http://www.sciencedirect.com/science/article/pii/0301010495003088}, + Volume = {201}, + Year = {1995}, + Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/0301010495003088}, + Bdsk-Url-2 = {https://doi.org/10.1016/0301-0104(95)00308-8}} + +@article{Ser97b, + Author = {Serrano-Andr{\'e}s, Luis and F{\"u}lscher, Markus P. and Karlstr{\"o}m, Gunnar}, + Date-Added = {2019-11-07 20:39:45 +0100}, + Date-Modified = {2019-11-07 20:39:45 +0100}, + Doi = {10.1002/(SICI)1097-461X(1997)65:2<167::AID-QUA8>3.0.CO;2-U}, + Journal = {Int. J. Quantum Chem.}, + Keywords = {Solvent model, self-consistent reaction field, CASSCF, CASPT2, spectroscopy}, + Number = {2}, + Pages = {167--181}, + Title = {Solvent Effects on Electronic Spectra Studied by Multiconfigurational Perturbation Theory}, + Volume = {65}, + Year = {1997}, + Bdsk-Url-1 = {https://doi.org/10.1002/(SICI)1097-461X(1997)65:2%3C167::AID-QUA8%3E3.0.CO;2-U}} + +@inbook{:bs, + Date-Added = {2019-11-07 20:38:28 +0100}, + Date-Modified = {2019-11-07 20:38:28 +0100}, + Bdsk-File-1 = {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}} + +@article{Chr08, + Author = {Christensen, Ronald L. and Galinato, Mary Grace I. and Chu, Emily F. and Howard, Jason N. and Broene, Richard D. and Frank, Harry A.}, + Date-Added = {2019-11-02 14:53:42 +0100}, + Date-Modified = {2019-11-02 14:53:56 +0100}, + Doi = {10.1021/jp8060202}, + Eprint = {https://doi.org/10.1021/jp8060202}, + Journal = {J. Phys. Chem. A}, + Note = {PMID: 19007144}, + Number = {49}, + Pages = {12629--12636}, + Title = {Energies of Low-Lying Excited States of Linear Polyenes}, + Url = {https://doi.org/10.1021/jp8060202}, + Volume = {112}, + Year = {2008}, + Bdsk-Url-1 = {https://doi.org/10.1021/jp8060202}} + +@article{Edw71, + Abstract = {Vapor absorption in the range 800-200 mĪ¼ are given for porphin, free-base tetraphenylporphin (H2TPP), and the Mg, Cr(III), Mn(III), Fe(III), Co, Ni, Cu, Zn, Cd, Sn(IV), and PbTPP complexes. Electronic bands Q, B, and M characteristic of the ring are found in the regions 540 mĪ¼ (18 500 cmā’1), 405 mĪ¼ (24 700 cmā’1), and 205 mĪ¼ (48 800 cmā’1). The region between the B and the M shows rather unstructured absorption, an order of magnitude less intense than the B region. Based on spectroscopic measurements, the Ī”H of vaporization and absolute vapor pressures are calculated. The pressures average to ā¼0.05 Torr at 390$\,^{\circ}$C. Vacuum uv spectra of H2TPP, NiTPP, CuTPP, and ZnTPP down to 145 mĪ¼ are presented which show absorption across the entire range with more intense bands at 185 mĪ¼ (54 000 cmā’1), 164 mĪ¼ (61 000 cmā’1), and 150 mĪ¼ (67 000 cmā’1), and no evidence of Rydberg structure. The vapors of Cr, Mn, Fe, and Sn complexes show unusually different spectra from their solutions. Spectral changes on electrolytic reduction establish that in the Mn, Fe, and Sn cases the vapors are those of the divalent metal. Solution spectra of H2TPP, CuTPP, and FeClTPP were studied up to 300$\,^{\circ}$C. Broadening comparable to the vapor spectra is observed. Also the visible bands shift to the red while the Soret band shows no change.}, + Author = {L. Edwards and D.H. Dolphin and M. Gouterman and A.D. Adler}, + Date-Added = {2019-11-02 13:49:21 +0100}, + Date-Modified = {2019-11-02 13:49:46 +0100}, + Doi = {https://doi.org/10.1016/0022-2852(71)90090-7}, + Issn = {0022-2852}, + Journal = {J. Mol. Spectrosc.}, + Number = {1}, + Pages = {16--32}, + Title = {Porphyrins XVII. Vapor Absorption Spectra and Redox Reactions: Tetraphenylporphins and Porphin}, + Url = {http://www.sciencedirect.com/science/article/pii/0022285271900907}, + Volume = {38}, + Year = {1971}, + Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/0022285271900907}, + Bdsk-Url-2 = {https://doi.org/10.1016/0022-2852(71)90090-7}} + +@article{Avi19, + Abstract = {Abstract We face the challenging description of the excited states responsible for one photon (OPA) and two photon (TPA) absorption in squaraine dyes, adopting both time-dependent density functional theory and a large variety of post Hartree Fock methods, including coupled cluster and adiabatic diagrammatic construction methods (ADC, to the second and third order), symmetry adapted cluster configuration interaction (CI), CASSCF including second-order perturbative corrections (PT2) with standard CASPT2 recipe and according to n-electron valence PT2 (NEVPT2) approach, and an additional multireference CI with PT2 corrections (CI-MRPT2). We selected a small prototypical symmetric squaraine dye for which these accurate computations are feasible and experimental data are available. We show that while all methods reasonably reproduce the OPA spectrum, an acceptable description and assignment of the states responsible for TPA is only possible through ADC(3) and multireference calculations, due to the strong involvement of double-excitations. The nature of ground state and OPA and TPA states is investigated with a rigorous reading of the CASSCF wavefunctions in terms of localized molecular orbitals on the donor and acceptor fragments, showing that these states arise from a balance of many different contributions including biradical configurations, local excitations and charge-transfer states where both side aromatic rings and the carbonyls of the squarylium moiety act as donors.}, + Author = {Avilaā€…Ferrer, Francisco J. and Angeli, Celestino and Cerezo, Javier and Coriani, Sonia and Ferretti, Alessandro and Santoro, Fabrizio}, + Date-Added = {2019-11-01 17:31:50 +0100}, + Date-Modified = {2019-11-01 17:31:59 +0100}, + Doi = {10.1002/cptc.201900121}, + Eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/cptc.201900121}, + Journal = {ChemPhotoChem}, + Keywords = {biradicaloid character, charge transfer, computational photochemistry, density functional calculations, vibronic spectra}, + Number = {9}, + Pages = {778--793}, + Title = {The Intriguing Case of the One-Photon and Two-Photon Absorption of a Prototypical Symmetric Squaraine: Comparison of TDDFT and Wave-Function Methods}, + Url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/cptc.201900121}, + Volume = {3}, + Year = {2019}, + Bdsk-Url-1 = {https://onlinelibrary.wiley.com/doi/abs/10.1002/cptc.201900121}, + Bdsk-Url-2 = {https://doi.org/10.1002/cptc.201900121}} + +@article{Tik19, + Abstract = {The electronic structure and optical properties of the isomeric difluoroboron Ī²-diketonates, 2,2-difluoro-4-methylnaphtho-[2,1-e]-1,3,2-dioxaborin (I) and 2,2-difluoro-4-methylnaphtho-[1,2-e]-1,3,2-dioxaborin (II), were studied by means of X-ray photoelectron, absorption and luminescence spectroscopies. The experimental results were interpreted using high-level ab initio quantum chemical computations, including the algebraic-diagrammatic construction method for the polarization propagator of the second and third orders (ADC(2) and ADC(3)), the outer-valence Green's function (OVGF) method, and the time-dependent density functional (TDDFT) approach. The X-ray photoelectron measurements were assigned in the entire energy range using the results of the Kohn-Sham orbital calculations which employed the B3LYP functional. Pronounced hypsochromic shift of crystal-state fluorescence was observed in I upon the lowering of temperature, which can be explained by the deterioration of the conditions for excimers formation. According to our results, remarkable feature of II, absent in I, is its phosphorescence at room temperature. Basing on our calculations, a decay mechanism for the S1 state was proposed, explaining the observed differences in the phosphorescence of I and II.}, + Author = {Sergey A. Tikhonov and Elena V. Fedorenko and Anatolii G. Mirochnik and Ivan S. Osmushko and Anna D. Skitnevskaya and Alexander B. Trofimov and Vitaliy I. Vovna}, + Date-Added = {2019-11-01 17:30:10 +0100}, + Date-Modified = {2019-11-01 17:30:45 +0100}, + Doi = {https://doi.org/10.1016/j.saa.2019.02.002}, + Issn = {1386-1425}, + Journal = {SpectroChim. Acta A}, + Keywords = {Luminophores, Boron difluoride Ī²-diketonates, Electronic structure, Photoelectron spectroscopy, Luminescence, Phosphorescence, Intersystem crossing, Density functional theory, Polarization propagator, Algebraic-diagrammatic construction (ADC) method, Outer-valence Green's function (OVGF) method, Isomerism}, + Pages = {67--78}, + Title = {Spectroscopic and Quantum Chemical Study of Difluoroboron $\beta$-Diketonate Luminophores: Isomeric Acetylnaphtholate Chelates}, + Url = {http://www.sciencedirect.com/science/article/pii/S1386142519301118}, + Volume = {214}, + Year = {2019}, + Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S1386142519301118}, + Bdsk-Url-2 = {https://doi.org/10.1016/j.saa.2019.02.002}} + +@article{Srs18, + Abstract = {Criegee intermediates (CIs) are increasingly recognized as important intermediates in atmospheric and combustion chemistry. Modelling in these fields requires reliable characterization of the CI{'}s UV absorption cross sections. Different experimental approaches provided seemingly contradictory results both for the simplest CI as well as for higher analogues. To resolve these discrepancies{,} we model simultaneously the positions{,} widths{,} shapes and absolute intensities of the first absorption bands of CIs using the semiclassical reflection principle approach based on the path integral molecular dynamics. The UV spectra were efficiently processed via the kernel density estimation method. We show that the multireference character complicates the description of the system and the appropriate treatment of the electron correlation is vital. Multi-reference methods with dynamical correlation are problematic due to high sensitivity of the results with respect to the active space. Single-reference based methods become reliable once the triple excitations components are included. Interestingly{,} the very similar CC2 and ADC(2) methods provide highly conflicting results which are{,} however{,} reconciled at the CC3 and ADC(3) levels. To calculate the spectra of higher CIs{,} we introduce composite EOM-CCSD/T and CC2/3 methods providing excellent absorption cross sections at an acceptable computational cost. We provide the first absolute intensities for individual conformers of the CH3CHOO molecule.}, + Author = {Sr{\v s}e{\v n}, {\v S}. and Hollas, D. and Slav{\'\i}{\v c}ek, P.}, + Date-Added = {2019-11-01 17:26:23 +0100}, + Date-Modified = {2019-11-01 17:26:46 +0100}, + Doi = {10.1039/C8CP00199E}, + Issue = {9}, + Journal = {Phys. Chem. Chem. Phys.}, + Pages = {6421--6430}, + Publisher = {The Royal Society of Chemistry}, + Title = {UV Absorption of Criegee Intermediates: Quantitative Cross Sections from High-level ab initio Theory}, + Url = {http://dx.doi.org/10.1039/C8CP00199E}, + Volume = {20}, + Year = {2018}, + Bdsk-Url-1 = {http://dx.doi.org/10.1039/C8CP00199E}} + +@article{Hol17b, + Author = {Holland,D. M. P. and Powis,I. and Trofimov,A. B. and Menzies,R. C. and Potts,A. W. and Karlsson,L. and Badsyuk,I. L. and Moskovskaya,T. E. and Gromov,E. V. and Schirmer,J.}, + Date-Added = {2019-11-01 17:23:29 +0100}, + Date-Modified = {2019-11-01 17:24:04 +0100}, + Doi = {10.1063/1.4999433}, + Eprint = {https://doi.org/10.1063/1.4999433}, + Journal = {J. Chem. Phys.}, + Number = {16}, + Pages = {164307}, + Title = {An Experimental and Theoretical Study of the Valence Shell Photoelectron Spectra of 2-Chloropyridine and 3-Chloropyridine}, + Url = {https://doi.org/10.1063/1.4999433}, + Volume = {147}, + Year = {2017}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.4999433}} + +@article{Kni16, + Author = {Knippenberg, Stefan and Gieseking, Rebecca L. and Rehn, Dirk R. and Mukhopadhyay, Sukrit and Dreuw, Andreas and Br{\'e}das, Jean-Luc}, + Date-Added = {2019-11-01 17:21:20 +0100}, + Date-Modified = {2019-11-01 17:21:35 +0100}, + Doi = {10.1021/acs.jctc.6b00615}, + Eprint = {https://doi.org/10.1021/acs.jctc.6b00615}, + Journal = {J. Chem. Theory Comput.}, + Number = {11}, + Pages = {5465--5476}, + Title = {Benchmarking Post-Hartree--Fock Methods To Describe the Nonlinear Optical Properties of Polymethines: An Investigation of the Accuracy of Algebraic Diagrammatic Construction (ADC) Approaches}, + Url = {https://doi.org/10.1021/acs.jctc.6b00615}, + Volume = {12}, + Year = {2016}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.6b00615}} + +@article{Mew16, + Abstract = {Excitonic effects play a fundamental role in the photophysics of organic semiconductors such as poly(para phenylene vinylene) (PPV). The emergence of these effects is examined for PPV oligomers based on high level ab initio excited-state calculations. The computed many-body wavefunctions are subjected to our recently developed exciton analysis protocols to provide a qualitative and quantitative characterization of excitonic effects. The discussion is started by providing high-level benchmark calculations using the algebraic-diagrammatic construction for the polarization propagator in third order of perturbation theory (ADC(3)). These calculations support the general adequacy of the computationally more efficient ADC(2) method in the case of singly excited states but also reveal the existence of low-energy doubly excited states. In a next step{,} a series of oligomers with chains of two to eight phenyl rings is studied at the ADC(2) level showing that the confinement effects are dominant for small oligomers{,} while delocalized exciton bands emerge for larger systems. In the case of the largest oligomer{,} the first twenty singlet and triplet excited states are computed and a detailed analysis in terms of the Wannier and Frenkel models is presented. The presence of different Wannier bands becomes apparent{,} showing a general trend that exciton sizes are lowered with increasing quasi-momentum within the bands.}, + Author = {Mewes, Stefanie A. and Mewes, Jan-Michael and Dreuw, Andreas and Plasser, Felix}, + Date-Added = {2019-11-01 17:16:49 +0100}, + Date-Modified = {2019-11-01 17:17:10 +0100}, + Doi = {10.1039/C5CP07077E}, + Issue = {4}, + Journal = {Phys. Chem. Chem. Phys.}, + Pages = {2548--2563}, + Publisher = {The Royal Society of Chemistry}, + Title = {Excitons in Poly(para phenylene vinylene): a Quantum-Chemical Perspective Based on High-Level ab initio Calculations}, + Url = {http://dx.doi.org/10.1039/C5CP07077E}, + Volume = {18}, + Year = {2016}, + Bdsk-Url-1 = {http://dx.doi.org/10.1039/C5CP07077E}} + +@article{Boh16, + Author = {Bohnwagner, Mercedes V. and Burghardt, Irene and Dreuw, Andreas}, + Date-Added = {2019-11-01 17:15:31 +0100}, + Date-Modified = {2019-11-01 17:15:46 +0100}, + Doi = {10.1021/acs.jpca.5b09115}, + Eprint = {https://doi.org/10.1021/acs.jpca.5b09115}, + Journal = {J. Phys. Chem. A}, + Number = {1}, + Pages = {14--27}, + Title = {Solvent Polarity Tunes the Barrier Height for Twisted Intramolecular Charge Transfer in N-Pyrrolobenzonitrile (PBN)}, + Url = {https://doi.org/10.1021/acs.jpca.5b09115}, + Volume = {120}, + Year = {2016}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpca.5b09115}} + +@article{Prl16b, + Author = {Prlj, Antonio and Sandoval-Salinas, Mar{\'\i}a Eugenia and Casanova, David and Jacquemin, Denis and Corminboeuf, Cl{\'e}mence}, + Date-Added = {2019-11-01 17:09:09 +0100}, + Date-Modified = {2019-11-01 17:09:30 +0100}, + Doi = {10.1021/acs.jctc.6b00245}, + Eprint = {https://doi.org/10.1021/acs.jctc.6b00245}, + Journal = {J. Chem. Theory Comput.}, + Note = {PMID: 27144975}, + Number = {6}, + Pages = {2652--2660}, + Title = {Low-Lying $\pi\pi^*$ States of Heteroaromatic Molecules: A Challenge for Excited State Methods}, + Url = {https://doi.org/10.1021/acs.jctc.6b00245}, + Volume = {12}, + Year = {2016}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.6b00245}} + +@article{Ste11c, + Abstract = {The valence shell electronic states of pyrimidine and pyrazine have been studied experimentally and theoretically. The absolute photoabsorption cross sections have been measured between 4 and 40 eV, using synchrotron radiation, and are dominated by prominent bands associated with intravalence transitions. In contrast, the structure due to Rydberg excitations is weak, but series have been observed converging onto the or limits in pyrimidine and the or limits in pyrazine. A comparison between the photoabsorption spectrum of pyrazine-h4 and that for pyrazine-d4, together with calculated transition energies, has helped clarify the assignments of the 6agā†’npb1u and npb2u Rydberg series. The vibrational progressions associated with these states have been assigned through analogy with those in the corresponding photoelectron band. The time-dependent version of density functional theory has been used to calculate oscillator strengths and excitation energies for the optically allowed singlet--singlet valence transitions, and also to obtain the excitation energies for electric-dipole-forbidden and/or spin-forbidden transitions. These theoretical results have allowed many of the experimentally observed bands to be assigned and provide a generally satisfactory description of the valence shell photoabsorption spectrum. Several of the prominent bands appearing above the ionization threshold can be correlated with predicted intense intravalence transitions.}, + Author = {M Stener and P Decleva and D M P Holland and D A Shaw}, + Date-Added = {2019-10-14 16:38:26 +0200}, + Date-Modified = {2019-10-14 16:39:17 +0200}, + Doi = {10.1088/0953-4075/44/7/075203}, + Journal = {J. Phys. B}, + Month = {mar}, + Number = {7}, + Pages = {075203}, + Publisher = {{IOP} Publishing}, + Title = {A Study of the Valence Shell Electronic States of Pyrimidine and Pyrazine by Photoabsorption Spectroscopy and Time-Dependent Density Functional Theory Calculations}, + Url = {https://doi.org/10.1088%2F0953-4075%2F44%2F7%2F075203}, + Volume = {44}, + Year = 2011, + Bdsk-Url-1 = {https://doi.org/10.1088%2F0953-4075%2F44%2F7%2F075203}, + Bdsk-Url-2 = {https://doi.org/10.1088/0953-4075/44/7/075203}} + +@article{Oku90, + Abstract = {UV---IR fluorescence and phosphorescence dip spectroscopy have been applied for the observation of the second excited 1,3(n,Ļ€*) states pyrazine in the vapor. The observed state energies agree very well with those of the ab initio calculation with DZCI.}, + Author = {Yasuo Okuzawa and Masaaki Fujii and Mitsuo Ito}, + Date-Added = {2019-10-14 16:28:43 +0200}, + Date-Modified = {2019-10-14 16:40:44 +0200}, + Doi = {https://doi.org/10.1016/0009-2614(90)85374-L}, + Issn = {0009-2614}, + Journal = {Chem. Phys. Lett.}, + Number = {4}, + Pages = {341--346}, + Title = {Direct Observation of Second Excited $^{1,3} (n,\pi^\star)$ States of Pyrazine by UV-IR Double Resonance dip Spectroscopy}, + Url = {http://www.sciencedirect.com/science/article/pii/000926149085374L}, + Volume = {171}, + Year = {1990}, + Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/000926149085374L}, + Bdsk-Url-2 = {https://doi.org/10.1016/0009-2614(90)85374-L}} + +@article{Fis00, + Abstract = {The first singlet--singlet and singlet--triplet band systems of the absorption spectrum of pyridazine vapour are analysed using ab initio and vibronic coupling calculations. The lowest singlet--triplet absorption involves a comparatively unperturbed (Ļ€ā—,n)3B1 state, and contrasts with the highly perturbed singlet--singlet spectrum. The major source of vibronic perturbation in the singlet--singlet absorption is attributed to coupling between near-resonant (Ļ€ā—,n)1A2 and (Ļ€ā—,n)1B1 states, with the former being slightly lower in energy. Many features of this complex and unusual spectrum, and its associated single vibronic level fluorescence spectrum, can be explained using a simple vibronic model. This provides experimental support for recent relaxed CASPT2 and EOM-CCSD calculations, but contrasts with earlier assignments of the spectrum. Theory and experiment suggest that the spacing between the lowest A2 and B1 states is larger in the triplet manifold, leading to a simpler spectrum.}, + Author = {Gad Fischer and Paul Wormell}, + Date-Added = {2019-10-08 09:37:52 +0200}, + Date-Modified = {2019-10-08 09:38:28 +0200}, + Doi = {https://doi.org/10.1016/S0301-0104(00)00137-3}, + Issn = {0301-0104}, + Journal = {Chem. Phys.}, + Number = {1}, + Pages = {1--20}, + Title = {Vibronic Analyses of the Lowest Singlet--Singlet and Singlet--Triplet Band Systems of Pyridazine}, + Url = {http://www.sciencedirect.com/science/article/pii/S0301010400001373}, + Volume = {257}, + Year = {2000}, + Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0301010400001373}, + Bdsk-Url-2 = {https://doi.org/10.1016/S0301-0104(00)00137-3}} + +@article{Lin16, + Abstract = {Electron energy-loss spectra of the pyridine, C5H5N, molecules in the gas phase have been measured toinvestigate electronic excitation in the energy range 3.5--10 eV. The applied wide range ofresidual electron energy and the scattering angle range from 10{\textdegree} to 180{\textdegree} enabled to differentiate betweenoptically-allowed and -forbidden transitions. These measurements have allowed verticalexcitation energies of the triplet excited states of pyridine to be determined andtentative assignments of these states to be proposed. Some of these states have not beenidentified in the previous works.}, + Author = {Linert, Ireneusz and Zubek, Mariusz}, + Date-Added = {2019-10-07 16:30:30 +0200}, + Date-Modified = {2019-10-07 16:30:52 +0200}, + Day = {05}, + Doi = {10.1140/epjd/e2016-60715-7}, + Issn = {1434-6079}, + Journal = {Eur. J. Phys. D}, + Month = {Apr}, + Number = {4}, + Pages = {74}, + Title = {Electron Energy-Loss Spectroscopy of Excited States of the Pyridine Molecules}, + Url = {https://doi.org/10.1140/epjd/e2016-60715-7}, + Volume = {70}, + Year = {2016}, + Bdsk-Url-1 = {https://doi.org/10.1140/epjd/e2016-60715-7}} + +@article{Lin19, + Abstract = {Excitation of the valence electronic states of the pyridazine molecules in the gas phase have been studied using the technique of electron energy-loss spectroscopy. Varying the electron scattering conditions, the residual electron energy and scattering angle, enabled the optically-allowed and -forbidden excitations to be differentiated. The measured energy-loss spectra enabled the vertical excitation energies of the observed states to be determined and tentative assignments for them to be obtained. Comparison of the available vertical excitation energies of the correlating triplet and singlet states of the diazine molecules, pyridazine, pyrimidine and pyrazine, allowed systematic trends in the energy shifts to be determined.}, + Author = {Ireneusz Linert and Mariusz Zubek}, + Date-Added = {2019-10-07 15:54:20 +0200}, + Date-Modified = {2019-10-07 16:27:06 +0200}, + Doi = {https://doi.org/10.1016/j.elspec.2019.04.003}, + Issn = {0368-2048}, + Journal = {J. Elec. Spect. Rel. Phen.}, + Keywords = {Electronic states, Pyridazine, Energy-loss, Excitation energy, Triplet states}, + Pages = {69--76}, + Title = {Electron Energy-loss Spectroscopy of Excited States of the Diazine Molecules: Pyridazine}, + Url = {http://www.sciencedirect.com/science/article/pii/S0368204819300337}, + Volume = {233}, + Year = {2019}, + Bdsk-File-1 = {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}, + Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0368204819300337}, + Bdsk-Url-2 = {https://doi.org/10.1016/j.elspec.2019.04.003}} + +@article{Ful92, + Author = {Fulscher, Markus P. and Andersson, Kerstin and Roos, Bjoern O.}, + Date-Added = {2019-10-07 15:30:34 +0200}, + Date-Modified = {2019-10-07 15:31:09 +0200}, + Doi = {10.1021/j100202a026}, + Eprint = {https://doi.org/10.1021/j100202a026}, + Journal = {J. Phys. Chem.}, + Number = {23}, + Pages = {9204--9212}, + Title = {Toward an Accurate Molecular Orbital Theory for Excited States: the Azabenzenes}, + Url = {https://doi.org/10.1021/j100202a026}, + Volume = {96}, + Year = {1992}, + Bdsk-Url-1 = {https://doi.org/10.1021/j100202a026}} + @article{Hod19, Abstract = {Abstract Optical absorption and emission properties as well as fluorescence quenching via introduction of an additional unsaturated five-membered ring in some azaacenes are investigated computationally. It is shown that non-radiative decay via conical intersections or intersystem crossing is rather unlikely. Instead, the additional double bond alters the electronic structure of the first excited singlet state, turning it into a dark state with long lifetime and hence low fluorescence rate, that cannot be seen anymore with the naked eye.}, Author = {Hodecker, Manuel and Ganschow, Michael and Abu-Odeh, Mahmud and Bunz, Uwe H. F. and Dreuw, Andreas}, - Date-Added = {2019-08-20 21:09:44 +0200}, - Date-Modified = {2019-08-20 21:18:22 +0200}, + Date-Added = {2019-10-07 13:54:04 +0200}, + Date-Modified = {2019-10-07 13:54:08 +0200}, Doi = {10.1002/cptc.201900135}, Eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/cptc.201900135}, Journal = {ChemPhotoChem}, Keywords = {computational photochemistry, conical intersections, fluorescence quenching, optical spectra, vibronic spectra}, - Pages = {000-000}, + Number = {9}, + Pages = {755-762}, Title = {Optical Spectra and Fluorescence Quenching in Azaacenes Bearing Five-Membered Rings}, Url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/cptc.201900135}, - Volume = {0}, + Volume = {3}, Year = {2019}, Bdsk-Url-1 = {https://onlinelibrary.wiley.com/doi/abs/10.1002/cptc.201900135}, Bdsk-Url-2 = {https://doi.org/10.1002/cptc.201900135}} +@article{Jon17, + Author = {Jones,D. B. and Lim{\~a}o-Vieira,P. and Mendes,M. and Jones,N. C. and Hoffmann,S. V. and da Costa,R. F. and Varella,M. T. do N. and Bettega,M. H. F. and Blanco,F. and Garc{\'\i}a,G. and Ing{\'o}lfsson,O. and Lima,M. A. P. and Brunger,M. J.}, + Date-Added = {2019-10-05 16:48:22 +0200}, + Date-Modified = {2019-10-05 16:48:51 +0200}, + Doi = {10.1063/1.4982940}, + Eprint = {https://doi.org/10.1063/1.4982940}, + Journal = {J. Chem. Phys.}, + Number = {18}, + Pages = {184303}, + Title = {An Experimental and Theoretical Investigation into the Electronically Excited States of \emph{para}-Benzoquinone}, + Url = {https://doi.org/10.1063/1.4982940}, + Volume = {146}, + Year = {2017}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.4982940}} + +@article{Cos18, + Author = {da Costa,R. F. and Ruivo,J. C. and Kossoski,F. and Varella,M. T. do N. and Bettega,M. H. F. and Jones,D. B. and Brunger,M. J. and Lima,M. A. P.}, + Date-Added = {2019-10-05 16:38:09 +0200}, + Date-Modified = {2019-10-05 16:38:39 +0200}, + Doi = {10.1063/1.5050622}, + Eprint = {https://doi.org/10.1063/1.5050622}, + Journal = {J. Chem. Phys.}, + Number = {17}, + Pages = {174308}, + Title = {An ab initio Investigation for Elastic and Electronically Inelastic Electron Scattering from \emph{para}-Nenzoquinone}, + Url = {https://doi.org/10.1063/1.5050622}, + Volume = {149}, + Year = {2018}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.5050622}} + +@article{Pou99, + Author = {Pou-Am{\'e}rigo,Rosendo and Merch{\'a}n,Manuela and OrtıĢ,Enrique}, + Date-Added = {2019-10-05 16:21:01 +0200}, + Date-Modified = {2019-10-05 16:21:23 +0200}, + Doi = {10.1063/1.478918}, + Eprint = {https://doi.org/10.1063/1.478918}, + Journal = {J. Chem. Phys.}, + Number = {19}, + Pages = {9536--9546}, + Title = {Theoretical Study of the Electronic Spectrum of p-Benzoquinone}, + Url = {https://doi.org/10.1063/1.478918}, + Volume = {110}, + Year = {1999}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.478918}} + +@article{Hon02, + Author = {Honda, Yasushi and Hada, Masahiko and Ehara, Masahiro and Nakatsuji, Hiroshi}, + Date-Added = {2019-10-05 16:16:30 +0200}, + Date-Modified = {2019-10-05 16:16:43 +0200}, + Doi = {10.1021/jp013166a}, + Eprint = {https://doi.org/10.1021/jp013166a}, + Journal = {J. Phys. Chem. A}, + Number = {15}, + Pages = {3838--3849}, + Title = {Excited and Ionized States of p-Benzoquinone and Its Anion Radical:ā€‰ SACā’CI Theoretical Study}, + Url = {https://doi.org/10.1021/jp013166a}, + Volume = {106}, + Year = {2002}, + Bdsk-Url-1 = {https://doi.org/10.1021/jp013166a}} + +@article{Dev08, + Author = {Devarajan, Ajitha and Gaenko, Alexander V. and Khait, Yuri G. and Hoffmann, Mark R.}, + Date-Added = {2019-10-03 15:23:17 +0200}, + Date-Modified = {2019-10-03 15:23:30 +0200}, + Doi = {10.1021/jp077702w}, + Eprint = {https://doi.org/10.1021/jp077702w}, + Journal = {J. Phys. Chem. A}, + Note = {PMID: 18271567}, + Number = {12}, + Pages = {2677--2682}, + Title = {Generalized van Vleck Perturbation Theory (GVVPT2) Study of the Excited States of Benzene and the Azabenzenes}, + Url = {https://doi.org/10.1021/jp077702w}, + Volume = {112}, + Year = {2008}, + Bdsk-Url-1 = {https://doi.org/10.1021/jp077702w}} + +@article{Noo00, + Author = {Nooijen, Marcel}, + Date-Added = {2019-10-03 14:44:51 +0200}, + Date-Modified = {2019-10-03 14:45:02 +0200}, + Doi = {10.1021/jp993983z}, + Eprint = {https://doi.org/10.1021/jp993983z}, + Journal = {J. Phys. Chem. A}, + Number = {19}, + Pages = {4553--4561}, + Title = {Electronic Excitation Spectrum of s-Tetrazine: An Extended-STEOM-CCSD Study}, + Url = {https://doi.org/10.1021/jp993983z}, + Volume = {104}, + Year = {2000}, + Bdsk-Url-1 = {https://doi.org/10.1021/jp993983z}} + +@article{Pas18b, + Author = {Pastorczak, Ewa and Pernal, Katarzyna}, + Date-Added = {2019-10-03 14:43:20 +0200}, + Date-Modified = {2019-10-03 16:50:54 +0200}, + Doi = {10.1021/acs.jpclett.8b02391}, + Eprint = {https://doi.org/10.1021/acs.jpclett.8b02391}, + Journal = {J. Phys. Chem. Lett.}, + Number = {18}, + Pages = {5534--5538}, + Title = {Electronic Excited States from the Adiabatic-Connection Formalism with Complete Active Space Wave Functions}, + Url = {https://doi.org/10.1021/acs.jpclett.8b02391}, + Volume = {9}, + Year = {2018}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpclett.8b02391}} + +@article{Hel19, + Author = {Helmich-Paris, Benjamin}, + Date-Added = {2019-10-03 14:41:29 +0200}, + Date-Modified = {2019-11-07 11:28:42 +0100}, + Doi = {10.1021/acs.jctc.9b00325}, + Eprint = {https://doi.org/10.1021/acs.jctc.9b00325}, + Journal = {J. Chem. Theory Comput.}, + Number = {7}, + Pages = {4170--4179}, + Title = {Benchmarks for Electronically Excited States with CASSCF Methods}, + Url = {https://doi.org/10.1021/acs.jctc.9b00325}, + Volume = {15}, + Year = {2019}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.9b00325}} + +@article{Joh76, + Author = {Johnson,Philip M.}, + Date-Added = {2019-10-03 13:39:59 +0200}, + Date-Modified = {2019-11-07 11:33:05 +0100}, + Doi = {10.1063/1.431983}, + Eprint = {https://doi.org/10.1063/1.431983}, + Journal = {J. Chem. Phys.}, + Number = {10}, + Pages = {4143--4148}, + Title = {The Multiphoton Ionization Spectrum of Benzene}, + Url = {https://doi.org/10.1063/1.431983}, + Volume = {64}, + Year = {1976}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.431983}} + +@article{Fin00, + Author = {Finley,James P. and Witek,Henryk A.}, + Date-Added = {2019-10-03 13:38:42 +0200}, + Date-Modified = {2019-10-03 13:39:16 +0200}, + Doi = {10.1063/1.480947}, + Eprint = {https://doi.org/10.1063/1.480947}, + Journal = {J. Chem. Phys.}, + Number = {9}, + Pages = {3958--3963}, + Title = {Diagrammatic Complete Active Space Perturbation Theory: Calculations on Benzene, N$_2$, and LiF}, + Url = {https://doi.org/10.1063/1.480947}, + Volume = {112}, + Year = {2000}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.480947}} + +@article{Joh83, + Abstract = {A new 1E2u 3px,y Rydberg state is found in the three-photon spectrum of benzene at 56080 cmā’1 near the previously known 1A2u state. The vibronic structure of these states is found to be intertwined and in e2g, vibration previously assigned to the 1A2u state is suggested to belong to 1E2u. This vibration is of such a frequency in both states as to indicate a considerable amount of valence character due to mixing with the nearby 1E1u valence state.}, + Author = {P.M. Johnson and G.M. Korenowski}, + Date-Added = {2019-10-03 13:35:48 +0200}, + Date-Modified = {2019-10-03 13:36:27 +0200}, + Doi = {https://doi.org/10.1016/0009-2614(83)87182-6}, + Issn = {0009-2614}, + Journal = {Chem. Phys. Lett.}, + Number = {1}, + Pages = {53--56}, + Title = {The Discovery of a $3p$ Rydberg State in Benzene by Three-Photon Resonant Multiphoton Ionization Spectroscopy}, + Url = {http://www.sciencedirect.com/science/article/pii/0009261483871826}, + Volume = {97}, + Year = {1983}, + Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/0009261483871826}, + Bdsk-Url-2 = {https://doi.org/10.1016/0009-2614(83)87182-6}} + +@article{Lor95b, + Abstract = {The valence excited states and the 3s, 3p, and 3d (united atom) Rydberg states of benzene and phenol have been obtained by the CASPT2 method, which computes a second-order perturbation correction to complete active space self-consistent field (CASSCF) energies. All non-zero dipole oscillator strengths are also computed, at the CASSCF level. For benzene, 16 singlet and 16 triplet states with excitation energies up to ca. 7.86 eV (63 400 cm--1) are obtained. Of these, 12 singlet and three triplet energies are experimentally known well enough to allow meaningful comparison. The average error is around 0.1 eV. The highest of these singlet states (21 E2g) is the highest valence $\pi$$\pi$* state predicted by elementary $\pi$-electron theory. Its energy is then considerably lower than has been suggested from laser flash experiments, but in perfect agreement with a reinterpretation of that experiment. For phenol, 27 singlet states are obtained, in the range 4.53--7.84 eV (63 300 cmā’1). Only the lowest has a well-known experimental energy, which agrees with the computed result within 0.03 eV. The ionization energy is in error by 0.05 eV.}, + Author = {Lorentzon, Johan and Malmqvist, Per-{\AA}ke and F{\"u}lscher, Markus and Roos, Bj{\"o}rn O.}, + Date-Added = {2019-10-03 13:25:10 +0200}, + Date-Modified = {2019-10-03 13:25:39 +0200}, + Day = {01}, + Doi = {10.1007/BF01113865}, + Issn = {1432-2234}, + Journal = {Theor. Chim. Acta}, + Month = {Apr}, + Number = {1}, + Pages = {91--108}, + Title = {A CASPT2 Study of the Valence and Lowest Rydberg Electronic States of Benzene and Phenol}, + Url = {https://doi.org/10.1007/BF01113865}, + Volume = {91}, + Year = {1995}, + Bdsk-Url-1 = {https://doi.org/10.1007/BF01113865}} + +@article{Kle02, + Abstract = {Abstract During the past decade the one-center mean-field approximation has proven to be a very appropriate framework for the accurate description of spin-orbit effects at the correlated all-electron level. Here, a new efficient code, SPOCK, is introduced that calculates spin-orbit matrix elements in the one-center mean-field approximation for multireference CI wave functions. For the first time, the computation of spin-dependent interactions within a Kohn-Sham orbital based CI (DFT/MRCI) scheme1 is made possible. The latter approach is suitable for large scale systems with up to 100--200 valence electrons. Test calculations are performed on well-known diatomic molecules and the thiocarbonyl pyranthione. Spin-orbit matrix elements show good agreement with their Hartree-Fock orbital based counterparts but are obtained at considerably lower expense, thus demonstrating the power of the method. As an application singlet-triplet couplings in thiophene are investigated that are important for the photophysics and photochemistry. Spin-orbit matrix elements between all Ļ€ ā†’ Ļ€* excited states are found to be small. Considerably larger spin-orbit matrix elements are observed only for cases in which Ļ€ ā†’ Ļ* excited configurations are involved. {\copyright} 2002 Wiley Periodicals, Inc. J Comput Chem 23: 824--833, 2002}, + Author = {Kleinschmidt, Martin and Tatchen, J{\"o}rg and Marian, Christel M.}, + Date-Added = {2019-10-03 11:24:07 +0200}, + Date-Modified = {2019-10-03 11:24:37 +0200}, + Doi = {10.1002/jcc.10064}, + Eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/jcc.10064}, + Journal = {J. Comput. Chem.}, + Keywords = {spin-orbit coupling, multireference configuration interaction, Kohn-Sham orbitals, program development, thiophene}, + Number = {8}, + Pages = {824--833}, + Title = {Spin-Orbit Coupling of DFT/MRCI Wavefunctions: Method, Test Calculations, and Application to Thiophene}, + Url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/jcc.10064}, + Volume = {23}, + Year = {2002}, + Bdsk-Url-1 = {https://onlinelibrary.wiley.com/doi/abs/10.1002/jcc.10064}, + Bdsk-Url-2 = {https://doi.org/10.1002/jcc.10064}} + +@article{Chr98c, + Author = {Christiansen, Ove and J{\o}rgensen, Poul}, + Date-Added = {2019-10-03 08:48:23 +0200}, + Date-Modified = {2019-10-03 08:48:33 +0200}, + Doi = {10.1021/ja973437o}, + Eprint = {https://doi.org/10.1021/ja973437o}, + Journal = {J. Am. Chem. Soc.}, + Number = {14}, + Pages = {3423--3430}, + Title = {The Electronic Spectrum of Furan}, + Url = {https://doi.org/10.1021/ja973437o}, + Volume = {120}, + Year = {1998}, + Bdsk-Url-1 = {https://doi.org/10.1021/ja973437o}} + +@article{Pal03b, + Author = {Michael H. Palmer and Philip J. Wilson}, + Date-Added = {2019-10-02 21:57:32 +0200}, + Date-Modified = {2019-10-02 22:51:54 +0200}, + Doi = {10.1080/0026897031000108050}, + Eprint = {https://doi.org/10.1080/0026897031000108050}, + Journal = {Mol. Phys.}, + Number = {15}, + Pages = {2391--2408}, + Publisher = {Taylor & Francis}, + Title = {The Singlet Electronic States of Pyrrole: a Theoretical Study by Both ab initio Multi-Reference Configuration Interaction Methods and Time-Dependent Density Functional Theory and a Reconsideration of the Experimental VUV Spectral Data}, + Url = {https://doi.org/10.1080/0026897031000108050}, + Volume = {101}, + Year = {2003}, + Bdsk-Url-1 = {https://doi.org/10.1080/0026897031000108050}} + +@article{Pal98, + Abstract = {A reinvestigation and extension of the observed VUV and EEL spectrum of pyrrole has been carried out, and the spectra assigned by means of high level multi-reference multi-root CI studies. A similar reasssessment of the UV-photoelectron spectrum leads to the conclusion that our previous assignment of IP3 to ionisation of the inner Ļ€-level (1b1) is correct and that most other assignments to ionisation of a Ļ-electron are incorrect. This is supported by the calculation of a wide range of Rydberg states derived from the five least bound orbitals, in the IP order: 1a2ā’1 < 2b1ā’1 < 1b1ā’1 < 9a1ā’1 < 6b2ā’1 < 5b2ā’1 < 8a1ā’1 < 7a1ā’1 < 4b2ā’1. It is concluded that each of the two strong absorption bands centred around 6 and 7.5 eV respectively owe their intensity to excitation of two 1Ļ€Ļ€ā— states of symmetry 1A1 and 1B2. The range of calculated valence states of Ļ€Ļ€ā—-type has been extended to include those from 1b1.}, + Author = {Michael H. Palmer and Isobel C. Walker and Martyn F. Guest}, + Date-Added = {2019-10-02 21:46:40 +0200}, + Date-Modified = {2019-10-02 22:49:38 +0200}, + Doi = {https://doi.org/10.1016/S0301-0104(98)00285-7}, + Issn = {0301-0104}, + Journal = {Chem. Phys.}, + Number = {2}, + Pages = {179--199}, + Title = {The Electronic States of Pyrrole Studied by Optical (VUV) Absorption, Near-Threshold Electron Energy-Loss (EEL) Spectroscopy and ab initio Multi-Reference Configuration Interaction Calculations}, + Url = {http://www.sciencedirect.com/science/article/pii/S0301010498002857}, + Volume = {238}, + Year = {1998}, + Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0301010498002857}, + Bdsk-Url-2 = {https://doi.org/10.1016/S0301-0104(98)00285-7}} + +@article{Nev14, + Author = {Neville,S. P. and Worth,G. A.}, + Date-Added = {2019-10-02 21:40:39 +0200}, + Date-Modified = {2019-10-02 22:52:25 +0200}, + Doi = {10.1063/1.4861223}, + Eprint = {https://doi.org/10.1063/1.4861223}, + Journal = {J. Chem. Phys.}, + Number = {3}, + Pages = {034317}, + Title = {A Reinterpretation of the Electronic Spectrum of Pyrrole: A Quantum Dynamics Study}, + Url = {https://doi.org/10.1063/1.4861223}, + Volume = {140}, + Year = {2014}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.4861223}} + +@article{Hei19, + Abstract = {The photoinduced dynamics of pyrrole is revisited employing the independent trajectory surface hopping methodology based on extended multi-state second order perturbation theory (XMS-CASPT2). Excitation at 200ā€Ænm into a high density of states region gives rise to ultrafast deactivation via internal conversion. The primary dissociation channel was found to be NH hydrogen abstraction, resulting in pyrrolyl radical formation. The associated time constant for hydrogen dissociation was determined to be 64ā€Æ$\pm$ā€Æ13ā€Æfs, in good agreement with the experimental value of 52ā€Æ$\pm$ā€Æ12ā€Æfs (Roberts et al., 2013). A total kinetic energy spectrum was also computed, that is in qualitative agreement with experiment. Radiationless decay via the ring-puckering crossing seam was identified as a minor deactivation channel.}, + Author = {Moritz Heindl and Leticia Gonz{\'a}lez}, + Date-Added = {2019-10-02 21:33:08 +0200}, + Date-Modified = {2019-10-02 22:52:45 +0200}, + Doi = {https://doi.org/10.1016/j.comptc.2019.03.012}, + Issn = {2210-271X}, + Journal = {Comput. Theor. Chem.}, + Keywords = {Pyrrole, Non-adiabatic dynamics, SHARC, CASPT2}, + Pages = {38--46}, + Title = {A XMS-CASPT2 non-Adiabatic Dynamics Study on Pyrrole}, + Url = {http://www.sciencedirect.com/science/article/pii/S2210271X19300738}, + Volume = {1155}, + Year = {2019}, + Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S2210271X19300738}, + Bdsk-Url-2 = {https://doi.org/10.1016/j.comptc.2019.03.012}} + +@article{Dev06, + Author = {Devine,Adam L. and Cronin,Br{\'\i}d and Nix,Michael G. D. and Ashfold,Michael N. R.}, + Date-Added = {2019-10-02 20:41:52 +0200}, + Date-Modified = {2019-10-02 22:48:35 +0200}, + Doi = {10.1063/1.2364504}, + Eprint = {https://doi.org/10.1063/1.2364504}, + Journal = {J. Chem. Phys.}, + Number = {18}, + Pages = {184302}, + Title = {High Resolution Photofragment Translational Spectroscopy Studies of the near Ultraviolet Photolysis of Imidazole}, + Url = {https://doi.org/10.1063/1.2364504}, + Volume = {125}, + Year = {2006}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.2364504}} + +@article{Tro97b, + Abstract = {The electronic spectrum of furan is investigated theoretically beyond the previous vertical-electronic description. A polarization propagator method referred to as second-order algebraic-diagrammatic construction (ADC(2)) has been used in the electronic structure calculations. The vibrational excitation accompanying the electronic transitions is described with the aid of a linear electron-vibrational coupling model. The spectral information thereby obtained permits extensive comparison with experiment. The average accuracy of the present method, estimated by comparing adiabatic transition energies, is better than 0.4 eV. Only for the lowest Ļ€-Ļ€ā— valance transition, Vā€²(1A1) and Vā€²(1B2), and for the Rydberg excitations agree The results for the other Ļ€-Ļ€ā— valence transitions, V(1B2), and for the Rydberg excitations agree well with findings of previous experimental and theoretical work. A (multistate) vibronic coupling effect involving the Vā€²(1A1) and V(1B2) valence transitions and the 3s(1A2 Rydberg excitation is suggested as the reason for the highly diffuse character of the 5.7--6.7 eV photoabsorption band.}, + Author = {A.B. Trofimov and J. Schirmer}, + Date-Added = {2019-10-02 17:51:29 +0200}, + Date-Modified = {2019-10-02 22:45:10 +0200}, + Doi = {https://doi.org/10.1016/S0301-0104(97)00256-5}, + Issn = {0301-0104}, + Journal = {Chem. Phys.}, + Number = {2}, + Pages = {175--190}, + Title = {Polarization Propagator Study of Electronic Excitation in key Heterocyclic Molecules II. Furan}, + Url = {http://www.sciencedirect.com/science/article/pii/S0301010497002565}, + Volume = {224}, + Year = {1997}, + Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0301010497002565}, + Bdsk-Url-2 = {https://doi.org/10.1016/S0301-0104(97)00256-5}} + +@article{Tro97, + Abstract = {The electronic excitation spectrum of pyrrole is studied using a polarization propagator method referred to as the second-order algebraic-diagrammatic construction (ADC(2)), along with a simple model for vibrational excitation accounting for all totally symmetric modes. The method describes the optical absorption profile of pyrrole with an expected accuracy of 0.2 -- 0.4 eV for the vertical excitation energies. The vibrational analysis provides for detailed additional spectroscopic information. In the singlet spectrum, besides the ns, np and nd (n = 3,4) Rydberg excitations, three Ļ€-Ļ€ā— valence transitions, Vā€²(1A1), V(1B2) and V(1A1) can clearly be distinguished. No evidence is found for Rydberg-valence interaction near the equilibrium geometry. Substantial vibrational widths and distinct vibrational excitation patterns are predicted for the Rydberg series converging to the first and second ionization thresholds. Some new assignments of major spectral features are proposed. The long-wave absorption maximum in the 5.6 -- 6.6. eV region is explained exclusively by the presence of Rydberg transitions, while the most intense absorption in the short-wave band system (7.0 -- 8.3 ev) predominantly originates from the V(1B2) and V(1A1) valence transitions.}, + Author = {A.B. Trofimov and J. Schirmer}, + Date-Added = {2019-10-02 17:50:55 +0200}, + Date-Modified = {2019-10-02 22:45:04 +0200}, + Doi = {https://doi.org/10.1016/S0301-0104(96)00303-5}, + Issn = {0301-0104}, + Journal = {Chem. Phys.}, + Number = {2}, + Pages = {153--170}, + Title = {Polarization Propagator Study of Electronic Excitation in key Heterocyclic Molecules I. Pyrrole}, + Url = {http://www.sciencedirect.com/science/article/pii/S0301010496003035}, + Volume = {214}, + Year = {1997}, + Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0301010496003035}, + Bdsk-Url-2 = {https://doi.org/10.1016/S0301-0104(96)00303-5}} + +@article{Wan00b, + Author = {Wan,Jian and Ehara,Masahiro and Hada,Masahiko and Nakatsuji,Hiroshi}, + Date-Added = {2019-10-02 17:45:18 +0200}, + Date-Modified = {2019-10-02 22:41:21 +0200}, + Doi = {10.1063/1.1290004}, + Eprint = {https://aip.scitation.org/doi/pdf/10.1063/1.1290004}, + Journal = {J. Chem. Phys.}, + Number = {13}, + Pages = {5245--5252}, + Title = {Electronic Excitation and Ionization Spectra of Cyclopentadiene: Revisit by the Symmetry-Adapted Cluster--Configuration Interaction Method}, + Url = {https://aip.scitation.org/doi/abs/10.1063/1.1290004}, + Volume = {113}, + Year = {2000}, + Bdsk-Url-1 = {https://aip.scitation.org/doi/abs/10.1063/1.1290004}, + Bdsk-Url-2 = {https://doi.org/10.1063/1.1290004}} + +@article{Nak96, + Author = {Nakano,Haruyuki and Tsuneda,Takao and Hashimoto,Tomohiro and Hirao,Kimihiko}, + Date-Added = {2019-10-02 17:41:31 +0200}, + Date-Modified = {2019-10-02 22:42:46 +0200}, + Doi = {10.1063/1.470926}, + Eprint = {https://doi.org/10.1063/1.470926}, + Journal = {J. Chem. Phys.}, + Number = {6}, + Pages = {2312--2320}, + Title = {Theoretical Study of the Excitation Spectra of Fiveā€Membered Ring Compounds: Cyclopentadiene, Furan, and Pyrrole}, + Url = {https://doi.org/10.1063/1.470926}, + Volume = {104}, + Year = {1996}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.470926}} + +@article{Gro03, + Author = {Gromov,E. V. and Trofimov,A. B. and Vitkovskaya,N. M. and Schirmer,J. and K{\"o}ppel,H.}, + Date-Added = {2019-10-02 17:15:38 +0200}, + Date-Modified = {2019-10-02 22:46:31 +0200}, + Doi = {10.1063/1.1578051}, + Eprint = {https://doi.org/10.1063/1.1578051}, + Journal = {J. Chem. Phys.}, + Number = {2}, + Pages = {737--753}, + Title = {Theoretical Study of the Low-Lying Excited Singlet States of Furan}, + Url = {https://doi.org/10.1063/1.1578051}, + Volume = {119}, + Year = {2003}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.1578051}} + +@article{Lor95, + Abstract = {The electronic excitation spectra of pyridine and phosphabenzene have been studied using theoretical methods. The electronic states are described by wave functions derived from second-order perturbation theory based on multiconfigurational reference functions. The study includes singlet and triplet valences excited states as well as a number of Rydberg states. For both molecules the transition energies to the two lowest $\pi$ {\textrightarrow} $\pi$* excited singlet states are known from experiment and reproduced with an accuracy of 0.15 eV or better, while then {\textrightarrow} $\pi$* transition energies are predicted with a somewhat uncertain error of about 0.2 eV. The calculations suggest the lowestn {\textrightarrow} $\pi$* transition detected experimentally in pyridine corresponds to an adiabatic transition. 43 electronic states have been determined in each of the molecules.}, + Author = {Lorentzon, J. and F{\"u}lscher, M. P. and Roos, B. O.}, + Date-Added = {2019-09-28 07:49:08 +0200}, + Date-Modified = {2019-09-28 07:49:32 +0200}, + Day = {01}, + Doi = {10.1007/BF01134214}, + Issn = {1432-2234}, + Journal = {Theor. Chim. Acta}, + Month = {Aug}, + Number = {2}, + Pages = {67--81}, + Title = {A Theoretical Study of the Electronic Spectra of Pyridine and Phosphabenzene}, + Url = {https://doi.org/10.1007/BF01134214}, + Volume = {92}, + Year = {1995}, + Bdsk-Url-1 = {https://doi.org/10.1007/BF01134214}} + +@article{Wan01b, + Author = {Wan,Jian and Hada,Masahiko and Ehara,Masahiro and Nakatsuji,Hiroshi}, + Date-Added = {2019-09-28 07:37:33 +0200}, + Date-Modified = {2019-09-28 07:38:04 +0200}, + Doi = {10.1063/1.1351880}, + Eprint = {https://doi.org/10.1063/1.1351880}, + Journal = {J. Chem. Phys.}, + Number = {12}, + Pages = {5117--5123}, + Title = {Electronic Excitation and Ionization Spectra of Azabenzenes: Pyridine Revisited by the Symmetry-Adapted Cluster Configuration Interaction Method}, + Url = {https://doi.org/10.1063/1.1351880}, + Volume = {114}, + Year = {2001}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.1351880}} + +@article{Lin15, + Abstract = {The electron energy loss spectra were measured in pyrimidine at the constant electron residual energy varied from 15meV to 10eV and in the scattering angle range 0--180$\,^{\circ}$. The spectra were analysed applying an iteration fitting procedure to resolve the energy loss bands corresponding to excitation of the electronic states of pyrimidine. The vertical excitation energies of the singlet states of pyrimidine and of a number of the triplet states were determined. The presently observed triplet states were tentatively assigned.}, + Author = {Ireneusz Linert and Mariusz Zubek}, + Date-Added = {2019-09-23 16:23:44 +0200}, + Date-Modified = {2019-11-07 11:35:09 +0100}, + Doi = {https://doi.org/10.1016/j.cplett.2015.02.005}, + Issn = {0009-2614}, + Journal = {Chem. Phys. Lett.}, + Pages = {1--5}, + Title = {A Study of the Electronic States of Pyrimidine by Electron Energy Loss Spectroscopy}, + Url = {http://www.sciencedirect.com/science/article/pii/S0009261415000858}, + Volume = {624}, + Year = {2015}, + Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0009261415000858}, + Bdsk-Url-2 = {https://doi.org/10.1016/j.cplett.2015.02.005}} + +@article{Mal92, + Abstract = {Ab initio calculations of a number of singlet electronic states of pyrimidine are presented. In addition to the ground 1A1 state, ten valence excited states were studied: three 1A1 and three 1B2 states, which are Ļ€Ļ€* excited states, and two 1B1 and two 1A2 states, which are nĻ€* excited. Rydberg states were encountered, but since these were irrelevant to the present study, the basis set employed was not designed to describe these states well, and their energy relative to the valence states will be incorrect. Such spurious states may perturb the valence states by accidental near-degeneracy, and care was taken to effectively remove them to prevent such perturbation. The calculation were performed by the CASSCF and MRCI methods, using a modest basis set (C, N: 3s3p1d; H: 2s; 116 basis functions) of ANO type. Energies, dipole and quadrupole moments, transition moments, and oscillator strengths are reported. All calculations were made using the experimental equilibrium geometry, and all excitation data are therefore vertical. The MRCI excitation energies, corrected for unlinked clusters, give results in good agreement with known experimental data. The error in the computed excitation energy is in no case larger than 0.4 eV. In some cases, alternative assignments of experimental energies are indicated.}, + Author = {Per-{\AA}ke Malmqvist and Bj{\"o}rn O. Roos and Markus P. F{\"u}lscher and Alistair P. Rendell}, + Date-Added = {2019-09-23 16:20:30 +0200}, + Date-Modified = {2019-09-23 16:20:43 +0200}, + Doi = {https://doi.org/10.1016/0301-0104(92)85012-J}, + Issn = {0301-0104}, + Journal = {Chem. Phys.}, + Number = {2}, + Pages = {359--367}, + Title = {An ab initio quantum chemical study of vertically excited singlet states of pyrimidine}, + Url = {http://www.sciencedirect.com/science/article/pii/030101049285012J}, + Volume = {162}, + Year = {1992}, + Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/030101049285012J}, + Bdsk-Url-2 = {https://doi.org/10.1016/0301-0104(92)85012-J}} + +@article{Pal90, + Abstract = {The electronic states of pyrimidine have been investigated by VUV absorption and near-threshold electron energy-loss spectroscopy, together with ab initio multi-reference configuration interaction calculations. This approach has allowed the experimental assignment of all the low-lying valence-excited nĻ€* and Ļ€Ļ€* singlet states. In contrast to Ļ€Ļ€* excitations, some of which are difficult to compute within 0.5 eV, the nĻ€* states are more accurately calculated, as are the lowest Rydberg excited states. The experimental identification of many low-lying Rydberg states is not yet possible. The UV-photoelectron spectral assignments by large-scale CI are similar to earlier Green's function results, except for the inner Ļ€ level (1b1) ionisation; many shake-up states are computed below 17 eV and it is clear that the TDA method, with the same basis set, leads to a much later onset.}, + Author = {Michael H. Palmer and Isobel C. Walker and Martyn F. Guest and Andrew Hopkirk}, + Date-Added = {2019-09-23 13:15:33 +0200}, + Date-Modified = {2019-11-07 11:34:46 +0100}, + Doi = {https://doi.org/10.1016/0301-0104(90)85017-Q}, + Issn = {0301-0104}, + Journal = {Chem. Phys.}, + Number = {1}, + Pages = {19--33}, + Title = {The Electronic States of the Azines. iii. Pyrimidine, Studied by VUV Absorption, Near-Threshold Electron Energy-Loss Spectroscopy and ab initio Multi-Reference Configuration Calculations}, + Url = {http://www.sciencedirect.com/science/article/pii/030101049085017Q}, + Volume = {147}, + Year = {1990}, + Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/030101049085017Q}, + Bdsk-Url-2 = {https://doi.org/10.1016/0301-0104(90)85017-Q}} + +@article{Ohr01, + Abstract = {Coupled cluster (CC) response theory is used to study the excited singlet states of pyrimidine. Both valence excitations (Ļ€ ā†’ Ļ€* and Ļ€ ā†’ Ļ€*) and excitations to the lowest = 3{,} 4 Rydberg states are calculated. The dependency of vertical excitation energies on several factors are investigated{,} such as (i) the effect of different molecular geometries on the vertical excitation energies; (ii) the dependency of the predictions on various features of the basis set (diffuseness{,} cardinal number in the correlation consistent series{,} inclusion of molecule centered functions and the position of such); and (iii) the level of electron correlation model (studied by a hierarchy of CC methods: CCS{,} CC2{,} CCSD and triple corrected CCSD by means of CCSDR(3)). Geometrical relaxation and zero-point vibrational motion in the excited states are accounted for by explicit calculations for the valence states and indirectly through studying ionized states for the Rydberg states. Best estimates of vertical and 0-0 transition energies are given and compared to previous calculations and experiments. Excellent agreement with available experimental 0-0 energies is obtained. For the lowest excited state we question a structure recently derived from experimental data{,} and argue that reasonable agreement with experiment is obtained with our structure.}, + Author = {{\"O}hrn, Anders and Christiansen, Ove}, + Date-Added = {2019-09-23 13:03:47 +0200}, + Date-Modified = {2019-11-07 11:33:58 +0100}, + Doi = {10.1039/B007949I}, + Issue = {5}, + Journal = {Phys. Chem. Chem. Phys.}, + Pages = {730--740}, + Publisher = {The Royal Society of Chemistry}, + Title = {Electronic Excitation Energies of Pyrimidine Studied using Coupled Cluster Response Theory}, + Url = {http://dx.doi.org/10.1039/B007949I}, + Volume = {3}, + Year = {2001}, + Bdsk-Url-1 = {http://dx.doi.org/10.1039/B007949I}} + +@article{Sce19, + Abstract = {Due to their diverse nature, the faithful description of excited states within electronic structure theory methods remains one of the grand challenges of modern theoretical chemistry. Quantum Monte Carlo (QMC) methods have been applied very successfully to ground state properties but still remain generally less effective than other non-stochastic methods for electronically excited states. Nonetheless, we have recently reported accurate excitation energies for small organic molecules at the fixed-node diffusion Monte Carlo (FN-DMC) within a Jastrow-free QMC protocol relying on a deterministic and systematic construction of nodal surfaces using the selected configuration interaction (sCI) algorithm known as CIPSI (Configuration Interaction using a Perturbative Selection made Iteratively). Albeit highly accurate, these all-electron calculations are computationally expensive due to the presence of core electrons. One very popular approach to remove these chemically-inert electrons from the QMC simulation is to introduce pseudopotentials (also known as effective core potentials). Taking the water molecule as an example, we investigate the influence of Burkatzki-Filippi-Dolg (BFD) pseudopotentials and their associated basis sets on vertical excitation energies obtained with sCI and FN-DMC methods. Although these pseudopotentials are known to be relatively safe for ground state properties, we evidence that special care may be required if one strives for highly accurate vertical transition energies. Indeed, comparing all-electron and valence-only calculations, we show that using pseudopotentials with the associated basis sets can induce differences of the order of 0.05ā€ÆeV on the excitation energies. Fortunately, a reasonable estimate of this shift can be estimated at the sCI level.}, + Author = {Anthony Scemama and Michel Caffarel and Anouar Benali and Denis Jacquemin and Pierre-Fran{\c c}ois Loos}, + Date-Added = {2019-09-07 12:10:14 +0200}, + Date-Modified = {2019-09-07 12:10:35 +0200}, + Doi = {https://doi.org/10.1016/j.rechem.2019.100002}, + Issn = {2211-7156}, + Journal = {Res. Chem.}, + Keywords = {Quantum Monte Carlo, Fixed-node error, Excited states, Pseudopotential, Effective core potential}, + Pages = {100002}, + Title = {Influence of Pseudopotentials on Excitation Energies from Selected Configuration Interaction and Diffusion Monte Carlo}, + Url = {http://www.sciencedirect.com/science/article/pii/S2211715619300025}, + Volume = {1}, + Year = {2019}, + Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S2211715619300025}, + Bdsk-Url-2 = {https://doi.org/10.1016/j.rechem.2019.100002}} + +@article{Gar19, + Annote = {doi: 10.1021/acs.jctc.9b00176}, + Author = {Garniron, Yann and Applencourt, Thomas and Gasperich, Kevin and Benali, Anouar and Fert{\'e}, Anthony and Paquier, Julien and Pradines, Barth{\'e}l{\'e}my and Assaraf, Roland and Reinhardt, Peter and Toulouse, Julien and Barbaresco, Pierrette and Renon, Nicolas and David, Gr{\'e}goire and Malrieu, Jean-Paul and V{\'e}ril, Micka{\"e}l and Caffarel, Michel and Loos, Pierre-Fran{\c c}ois and Giner, Emmanuel and Scemama, Anthony}, + Booktitle = {Journal of Chemical Theory and Computation}, + Da = {2019/06/11}, + Date = {2019/06/11}, + Date-Added = {2019-09-07 12:08:27 +0200}, + Date-Modified = {2019-09-07 12:08:38 +0200}, + Doi = {10.1021/acs.jctc.9b00176}, + Isbn = {1549-9618}, + Journal = {J. Chem. Theory Comput.}, + Journal1 = {J. Chem. Theory Comput.}, + M3 = {doi: 10.1021/acs.jctc.9b00176}, + Month = {06}, + Number = {6}, + Pages = {3591--3609}, + Publisher = {American Chemical Society}, + Title = {Quantum Package 2.0: An Open-Source Determinant-Driven Suite of Programs}, + Ty = {JOUR}, + Url = {https://doi.org/10.1021/acs.jctc.9b00176}, + Volume = {15}, + Year = {2019}, + Year1 = {2019}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.9b00176}} + +@article{Con13b, + Abstract = {Benzo- and azino-fused bis(1,2,3-dithiazoles) were investigated computationally using density functional theory (DFT) in an attempt to relate structure to ground state multiplicity preference. Structural changes on the central arene by substitution with electron donating (EDG) and electron withdrawing groups (EWG) or replacement of the central arene by pyridino or pyrazino rings, were studied by optimizing the structures as singlet and triplet ground states. The aromaticity of each ring was probed using nucleus independent chemical shift (NICS) calculations. Molecular orbital analysis identified the substituent effects on the energy of the frontier orbitals. Calculations show that the ground state multiplicity can be effectively controlled with strategic substitutions. EWG directly attached on the negative cyanine of the central arene stabilize zwitterionic singlet states whereas EDG attached at the same position favor a triplet ground state. NICS calculations indicate that the central arenes sacrifice their aromaticity and become non-aromatic for molecules with zwitterionic ground states as an effective way to avoid their overall 4n Ļ€ antiaromaticity.}, + Author = {Christos P. Constantinides and Theodosia A. Ioannou and Panayiotis A. Koutentis}, + Date-Added = {2019-08-26 15:04:09 +0200}, + Date-Modified = {2019-08-26 15:05:51 +0200}, + Doi = {https://doi.org/10.1016/j.poly.2013.03.054}, + Issn = {0277-5387}, + Journal = {Polyhedron}, + Pages = {172--180}, + Title = {Manipulating the singlet--triplet energy gaps of arene-fused bis(1,2,3-dithiazoles): A computational study}, + Url = {http://www.sciencedirect.com/science/article/pii/S0277538713002647}, + Volume = {64}, + Year = {2013}, + Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0277538713002647}, + Bdsk-Url-2 = {https://doi.org/10.1016/j.poly.2013.03.054}} + +@inbook{Con04, + Author = {Constantinides, Christos P. and Koutentis, Panayiotis A.}, + Date-Added = {2019-08-26 14:53:11 +0200}, + Date-Modified = {2019-08-26 14:55:14 +0200}, + Publisher = {University of Wollongong}, + Series = {Proceedings of the International Conference on the Science and Technology of Synthetic Metals (ICSM 2004)}, + Title = {Effects of substitution on the ground-state multiplicities of zwitterionic polyazaacenes: A DFT study combined with broken symmetry approach}, + Year = {2004}} + +@article{Wan04c, + Author = {Wanko,M. and Garavelli,M. and Bernardi,F. and Niehaus,T. A. and Frauenheim,T. and Elstner,M.}, + Date-Added = {2019-08-23 09:39:15 +0200}, + Date-Modified = {2019-08-23 18:11:56 +0200}, + Doi = {10.1063/1.1635798}, + Eprint = {https://doi.org/10.1063/1.1635798}, + Journal = {J. Chem. Phys.}, + Number = {4}, + Pages = {1674--1692}, + Title = {A Global Investigation of Excited State Surfaces Within Time-Dependent Density-Functional Response Theory}, + Url = {https://doi.org/10.1063/1.1635798}, + Volume = {120}, + Year = {2004}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.1635798}} + @article{Bun13, Abstract = {Abstract Azaacenes have been known for a very long time, either as N,Nā€²-dihydro compounds or in their oxidized form as 4ā€‰n+2Ļ€ systems, but only recently have processable and charcterizable derivatives been sought. In the last three years synthetic routes to large N-heteroacenes have been developed. In particular, the Pd-catalyzed coupling of aromatic diamines with activated aromatic dihalogenides has enabled simple access to numerous new azaacenes. Since 2010, azapentacene and stabile oligoazahexacene have been synthesized, as well as a symmetrical tetraazapentacene, which acts as an excellent electron-transport material for thin-film transistors.}, Author = {Bunz, Uwe H. F. and Engelhart, Jens U. and Lindner, Benjamin D. and Schaffroth, Manuel}, @@ -458,8 +1369,8 @@ @unpublished{zzz-p1, Date-Added = {2019-07-23 10:11:17 +0200}, - Date-Modified = {2019-07-23 10:12:43 +0200}, - Note = {For \textbf{2}, the computed $\lambda_{\mathrm{max}}$ are 671 and 642 nm with and without the phenyl rings (experimental value: 683 nm). For \textbf{23}, the computed $\lambda_{\mathrm{max}}$ are 761 and 805 nm with and without the phenyl rings (experimental value: 775 nm).}} + Date-Modified = {2019-08-29 14:31:33 +0200}, + Note = {For \textbf{2}, the computed $\lambda_{\mathrm{max}}$ are 671 and 642 nm with and without the phenyl rings (experimental value: 683 nm). For \textbf{3}, the computed $\lambda_{\mathrm{max}}$ are 805 and 761 nm with and without the phenyl rings (experimental value: 775 nm).}} @article{Zis18b, Author = {Zissimou, Georgia A and Kourtellaris, Andreas and Koutentis, Panayiotis A}, @@ -582,15 +1493,15 @@ Bdsk-Url-1 = {https://doi.org/10.1021/acs.joc.8b00554}} @article{Chr98b, - Author = {Christiansen,Ove and Halkier,Asger and Koch,Henrik and Jo/rgensen,Poul and Helgaker,Trygve}, + Author = {Christiansen,Ove and Halkier,Asger and Koch,Henrik and Jorgensen,Poul and Helgaker,Trygve}, Date-Added = {2019-07-17 16:40:29 +0200}, - Date-Modified = {2019-07-17 16:40:44 +0200}, + Date-Modified = {2019-10-02 22:45:50 +0200}, Doi = {10.1063/1.475671}, Eprint = {https://doi.org/10.1063/1.475671}, Journal = {J. Chem. Phys.}, Number = {7}, Pages = {2801--2816}, - Title = {Integral-direct coupled cluster calculations of frequency-dependent polarizabilities, transition probabilities and excited-state properties}, + Title = {Integral-Direct Coupled Cluster Calculations of Frequency-Dependent Polarizabilities, Transition Probabilities and Excited-State Properties}, Url = {https://doi.org/10.1063/1.475671}, Volume = {108}, Year = {1998}, @@ -774,13 +1685,13 @@ @article{Pat06, Author = {Paterson,Martin J. and Christiansen,Ove and Paw{\l}owski,Filip and J{\o}rgensen,Poul and H{\"a}ttig,Christof and Helgaker,Trygve and Sa{\l}ek,Pawe{\l}}, Date-Added = {2019-07-15 09:54:29 +0200}, - Date-Modified = {2019-07-15 09:54:55 +0200}, + Date-Modified = {2019-11-07 11:29:13 +0100}, Doi = {10.1063/1.2163874}, Eprint = {https://doi.org/10.1063/1.2163874}, Journal = {J. Chem. Phys.}, Number = {5}, Pages = {054322}, - Title = {Benchmarking Two-Photon Absorption with Cc3 Quadratic Response Theory, and Comparison with Density-Functional Response Theory}, + Title = {Benchmarking Two-Photon Absorption with CC3 Quadratic Response Theory, and Comparison with Density-Functional Response Theory}, Url = {https://doi.org/10.1063/1.2163874}, Volume = {124}, Year = {2006}, @@ -834,14 +1745,14 @@ @article{Rub99, Author = {Mercedes Rubio and Bjorn O. Roos}, Date-Added = {2019-07-14 11:57:32 +0200}, - Date-Modified = {2019-07-14 11:57:45 +0200}, + Date-Modified = {2019-11-07 11:33:38 +0100}, Doi = {10.1080/00268979909482997}, Eprint = {https://doi.org/10.1080/00268979909482997}, Journal = {Mol. Phys.}, Number = {4}, Pages = {603--615}, Publisher = {Taylor & Francis}, - Title = {A theoretical study of the electronic spectrum of s-tetrazine}, + Title = {A Theoretical Study of the Electronic Spectrum of $s$-Tetrazine}, Url = {https://doi.org/10.1080/00268979909482997}, Volume = {96}, Year = {1999}, @@ -904,13 +1815,14 @@ @article{Sue19, Author = {Suellen, Cinthia and Garcia Freitas, Renato and Loos, Pierre-Francois and Jacquemin, Denis}, Date-Added = {2019-07-10 07:39:16 +0200}, - Date-Modified = {2019-07-10 07:39:40 +0200}, + Date-Modified = {2019-10-02 22:40:45 +0200}, Doi = {10.1021/acs.jctc.9b00446}, Eprint = {https://doi.org/10.1021/acs.jctc.9b00446}, Journal = {J. Chem. Theory Comput.}, - Note = {doi: 10.1021/acs.jctc.9b00446}, + Pages = {4581--4590}, Title = {Cross Comparisons Between Experiment, TD-DFT, CC, and ADC for Transition Energies}, Url = {https://doi.org/10.1021/acs.jctc.9b00446}, + Volume = {15}, Year = {2019}, Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.9b00446}} @@ -1383,13 +2295,13 @@ @article{Sha19, Author = {Sharma, Prachi and Bernales, Varinia and Truhlar, Donald G. and Gagliardi, Laura}, Date-Added = {2019-06-14 15:27:22 +0200}, - Date-Modified = {2019-06-14 15:27:33 +0200}, + Date-Modified = {2019-11-07 11:31:26 +0100}, Doi = {10.1021/acs.jpclett.8b03277}, Eprint = {https://doi.org/10.1021/acs.jpclett.8b03277}, Journal = {J. Phys. Chem. Lett.}, Number = {1}, Pages = {75--81}, - Title = {Valence Ļ€Ļ€* Excitations in Benzene Studied by Multiconfiguration Pair-Density Functional Theory}, + Title = {Valence $\pi\pi^\star$ Excitations in Benzene Studied by Multiconfiguration Pair-Density Functional Theory}, Url = {https://doi.org/10.1021/acs.jpclett.8b03277}, Volume = {10}, Year = {2019}, @@ -1414,7 +2326,7 @@ Abstract = {The description of Rydberg states by the complete active space self-consistent field (CASSCF) electronic structure method is known to be a difficult topic. In particular, two problems are frequently encountered: (a) the simultaneous presence of valence and Rydberg excited states in the same energy region can potentially lead to artificial valence--Rydberg mixing in the electronic wave functions. (b) Rydberg states have a tendency to be difficult to converge. We have implemented an approach for the consistent description of both valence and Rydberg excited states within the CASSCF electronic structure model. By employing the multiconfigurational second- and third-order perturbation theory (CASPT2/3) methods based on CASSCF reference wave functions, the procedure is verified by comparison with spectroscopic results for the example molecule pyrazine. Vertical excitation energies and other properties have been calculated for various electronic states. Basis sets and active spaces were selected to provide accurate results. Two combinations of aug-cc-pVTZ level basis sets complemented by Rydberg functions have been employed to calculate estimates for the properties of 19 singlet excited states of pyrazine. While many of the assignments made in previous studies could be confirmed, there are also several new aspects emerging from the present investigation.}, Author = {Woywod, Clemens and Papp, Attila and Hal{\'a}sz, G{\'a}bor J. and Vib{\'o}k, {\'A}gnes}, Date-Added = {2019-06-14 14:38:04 +0200}, - Date-Modified = {2019-06-14 14:38:11 +0200}, + Date-Modified = {2019-11-07 11:31:51 +0100}, Day = {01}, Doi = {10.1007/s00214-009-0678-x}, Issn = {1432-2234}, @@ -1422,7 +2334,7 @@ Month = {Mar}, Number = {3}, Pages = {521--533}, - Title = {Theoretical investigation of the electronic spectrum of pyrazine}, + Title = {Theoretical Investigation of the Electronic Spectrum of Pyrazine}, Url = {https://doi.org/10.1007/s00214-009-0678-x}, Volume = {125}, Year = {2010}, @@ -1447,13 +2359,13 @@ @article{Nak80, Author = {Nakashima,Nobuaki and Inoue,Haruo and Sumitani,Minoru and Yoshihara,Keitaro}, Date-Added = {2019-06-14 11:25:50 +0200}, - Date-Modified = {2019-06-14 11:26:01 +0200}, + Date-Modified = {2019-11-07 19:47:08 +0100}, Doi = {10.1063/1.440131}, Eprint = {https://doi.org/10.1063/1.440131}, Journal = {J. Chem. Phys.}, Number = {12}, Pages = {5976--5980}, - Title = {Laser flash photolysis of benzene. III. Snā†S1 absorption of gaseous benzene}, + Title = {Laser Flash Photolysis of Benzene. iii. $S_n \leftarrow S_1$ Absorption of Gaseous Benzene}, Url = {https://doi.org/10.1063/1.440131}, Volume = {73}, Year = {1980}, @@ -1477,28 +2389,28 @@ @article{Hal02, Author = {Hald,Kasper and J{\o}rgensen,Poul and Christiansen,Ove and Koch,Henrik}, Date-Added = {2019-06-14 11:11:24 +0200}, - Date-Modified = {2019-06-14 11:11:42 +0200}, + Date-Modified = {2019-10-03 13:43:04 +0200}, Doi = {10.1063/1.1457431}, Eprint = {https://doi.org/10.1063/1.1457431}, Journal = {J. Chem. Phys.}, Number = {14}, Pages = {5963--5970}, - Title = {Implementation of electronic ground states and singlet and triplet excitation energies in coupled cluster theory with approximate triples corrections}, + Title = {Implementation of Electronic Ground States and Singlet and Triplet Excitation Energies in Coupled Cluster Theory with Approximate Triples Corrections}, Url = {https://doi.org/10.1063/1.1457431}, Volume = {116}, Year = {2002}, Bdsk-Url-1 = {https://doi.org/10.1063/1.1457431}} @article{Chr96c, - Author = {Christiansen,Ove and Koch,Henrik and Halkier,Asger and Jo/rgensen,Poul and Helgaker,Trygve and S{\'a}nchez de Mer{\'a}s,Alfredo}, + Author = {Christiansen,Ove and Koch,Henrik and Halkier,Asger and Jorgensen,Poul and Helgaker,Trygve and S{\'a}nchez de Mer{\'a}s,Alfredo}, Date-Added = {2019-06-14 11:10:25 +0200}, - Date-Modified = {2019-06-14 11:10:41 +0200}, + Date-Modified = {2019-10-14 14:59:24 +0200}, Doi = {10.1063/1.471985}, Eprint = {https://doi.org/10.1063/1.471985}, Journal = {J. Chem. Phys.}, Number = {16}, Pages = {6921--6939}, - Title = {Largeā€scale calculations of excitation energies in coupled cluster theory: The singlet excited states of benzene}, + Title = {LargeSscale Calculations of Excitation Energies in Coupled Cluster Theory: The Singlet Excited States of Benzene}, Url = {https://doi.org/10.1063/1.471985}, Volume = {105}, Year = {1996}, @@ -1523,13 +2435,13 @@ Abstract = {The results of large-scale ab initio CI calculations on the electronic states of 1,3,5-triazine, using a multi-reference multi-root CI (MRD-CI) method are related to new VUV absorption and low-energy electron energy-loss (EEL) measurements, leading to detailed spectral assignments. Vertical transition energies are computed to within 0.6 eV for all and 0.3 eV for most of the low-lying electronic states. The computations are extended to cationic states and to the evaluation of ground state molecular electronic properties of the molecule.}, Author = {Isobel C. Walker and Michael H. Palmer and Charles C. Ballard}, Date-Added = {2019-06-14 10:42:01 +0200}, - Date-Modified = {2019-06-14 10:42:12 +0200}, + Date-Modified = {2019-11-07 11:35:52 +0100}, Doi = {https://doi.org/10.1016/0301-0104(92)80023-O}, Issn = {0301-0104}, Journal = {Chem. Phys.}, Number = {1}, Pages = {61--75}, - Title = {The electronic states of the azines. VI. 1,3,5-triazine, studied by VUV absorption, near-threshold electron energy-loss spectroscopy and ab initio multi-reference configuration interaction calculations}, + Title = {The Electronic States of the Azines. VI. 1,3,5-Triazine, Studied by VUV Absorption, Near-Threshold Electron Energy-Loss Spectroscopy and ab initio Multi-Reference Configuration Interaction Calculations}, Url = {http://www.sciencedirect.com/science/article/pii/030101049280023O}, Volume = {167}, Year = {1992}, @@ -1540,14 +2452,14 @@ Abstract = {The recently developed similarity transformed equation-of-motion coupled-cluster method (STEOM-CC) is applied to calculate the vertical excitation spectra and various 0-0 transitions of selected azabenzenes. The primary purpose of these studies is to gain further experience with the STEOM-CCSD approach, and to gauge its accuracy. It is shown that the accuracy of the method exceeds the accuracy of EOM-CCSD, and that results for valence excited states are often close to EOM-CCSD(TĢ). A number of low lying 0-0 transitions are determined in pyridine and the diazines. The geometries and vibrational frequencies of excited states are determined at the CI singles level, while final electronic energies are calculated through single point STEOM-CCSD. The manifold of excited states, ionized and electron attached states are analyzed as the geometries are distorted from the ground state equilibrium structures.}, Author = {Marcel Nooijen}, Date-Added = {2019-06-14 10:32:07 +0200}, - Date-Modified = {2019-06-14 10:32:28 +0200}, + Date-Modified = {2019-11-07 11:31:05 +0100}, Doi = {https://doi.org/10.1016/S1386-1425(98)00261-3}, Issn = {1386-1425}, Journal = {SpectroChim. Acta A}, Keywords = {Equation of motion, Coupled-cluster, Azabenzenes}, Number = {3}, Pages = {539--559}, - Title = {Similarity transformed equation of motion coupled-cluster study of excited states of selected azabenzenes}, + Title = {Similarity Transformed Equation of Motion Coupled-Cluster Study of Excited States of Selected Azabenzenes}, Url = {http://www.sciencedirect.com/science/article/pii/S1386142598002613}, Volume = {55}, Year = {1999}, @@ -1558,13 +2470,13 @@ Abstract = {Absolute extinction coefficient and oscillator strength of pyridine, pyrimidine, pyrazine, and s-triazine were recorded with moderate resolution in the region of 3.5--9.5 eV. Analogous to 1A1g ā†’ 1B2u, 1B1u, 1E1u Ļ€ ā†’ Ļ€ā— transitions of benzene, several n ā†’ Ļ€ā— and Rydberg transitions are presented and discussed.}, Author = {A. Bolovinos and P. Tsekeris and J. Philis and E. Pantos and G. Andritsopoulos}, Date-Added = {2019-06-14 10:28:21 +0200}, - Date-Modified = {2019-06-14 10:28:41 +0200}, + Date-Modified = {2019-11-07 11:32:07 +0100}, Doi = {https://doi.org/10.1016/0022-2852(84)90051-1}, Issn = {0022-2852}, Journal = {J. Mol. Spectrosc.}, Number = {2}, Pages = {240--256}, - Title = {Absolute vacuum ultraviolet absorption spectra of some gaseous azabenzenes}, + Title = {Absolute Vacuum Ultraviolet Absorption Spectra of Some Gaseous Azabenzenes}, Url = {http://www.sciencedirect.com/science/article/pii/0022285284900511}, Volume = {103}, Year = {1984}, @@ -1656,10 +2568,11 @@ @article{Loo19b, Author = {Loos, Pierre-Francois and Jacquemin, Denis}, Date-Added = {2019-04-02 10:03:00 +0200}, - Date-Modified = {2019-05-08 07:21:59 +0200}, + Date-Modified = {2019-11-07 11:28:26 +0100}, Journal = {ChemPhotoChem}, - Note = {doi: 10.1002/cptc.201700090}, + Pages = {684--696}, Title = {Evaluating 0-0 Energies with Theoretical Tools: a Short Review}, + Volume = {3}, Year = {2019}} @article{Lou18, @@ -1787,13 +2700,13 @@ @article{Ser02, Author = {Serrano-Andr{\'e}s,Luis and Pou-Am{\'e}rigo,Rosendo and F{\"u}lscher,Markus P. and Borin,Antonio Carlos}, Date-Added = {2019-03-14 14:01:45 +0100}, - Date-Modified = {2019-03-14 14:01:56 +0100}, + Date-Modified = {2019-11-07 11:29:50 +0100}, Doi = {10.1063/1.1482706}, Eprint = {https://doi.org/10.1063/1.1482706}, Journal = {J. Chem. Phys.}, Number = {4}, Pages = {1649--1659}, - Title = {Electronic excited states of conjugated cyclic ketones and thioketones: A theoretical study}, + Title = {Electronic Excited States of Conjugated Cyclic Ketones and Thioketones: A Theoretical Study}, Url = {https://doi.org/10.1063/1.1482706}, Volume = {117}, Year = {2002}, @@ -2013,14 +2926,13 @@ Abstract = {The photoabsorption spectra of C4H4O and C4D4O have been measured between ā¼5.5 and 17.7eV using a synchrotron radiation-based Fourier transform spectrometer. In addition to several broad bands due to transitions into valence states, the spectra exhibit numerous sharp bands associated with Rydberg states belonging to series converging onto the XĢ2A2 or the {\~A}2B1 state limits. Vertical excitation energies and oscillator strengths have been computed using the second- and third-order algebraic-diagrammic construction polarisation propagator methods (ADC(2) and ADC(3)), and the equation-of-motion coupled-cluster method at the level of singles and doubles model (EOM-CCSD). Adiabatic excitation energies have been estimated using previously computed corrections. The theoretical predictions have allowed assignments to be proposed for the Rydberg series observed in the present single-photon absorption spectra and for some additional series, mainly of A2 symmetry, reported in previous multiphoton excitation studies. The assignments of some of the Rydberg series converging onto the {\~A}2B1 state limit have been revised and, guided by our calculations, the principal series is ascribed to the 2b1ā†’nda2 1B2 and 2b1ā†’ndb1 1A1 transitions. f-type Rydberg series, previously observed only in the multiphoton absorption spectrum of furan, have been observed and assigned. Such f-type series, converging onto either the XĢ2A2 or the {\~A}2B1 state thresholds, contribute significantly to the single-photon absorption spectrum. Many of the absorption bands associated with Rydberg states display vibrational progressions which resemble those in the corresponding photoelectron band. It appears that some of the structure associated with the 1a2ā†’3pb2 1B1 and 1a2ā†’3pb1 1B2 transitions involves excitation of non-totally symmetric vibrational modes.}, Author = {D.M.P. Holland and E.A. Seddon and A.B. Trofimov and E.V. Gromov and M. Wormit and A. Dreuw and T. Korona and N. de Oliveira and L.E. Archer and D. Joyeux}, Date-Added = {2019-02-19 21:41:26 +0100}, - Date-Modified = {2019-02-19 21:41:39 +0100}, + Date-Modified = {2019-10-02 22:48:02 +0200}, Doi = {https://doi.org/10.1016/j.jms.2015.03.002}, Issn = {0022-2852}, Journal = {J. Mol. Spectrosc.}, Keywords = {Photoabsorption, Synchrotron radiation, Rydberg states, Ab initio excitation energies, Vibrational progressions}, - Note = {Spectroscopy with Synchrotron Radiation}, Pages = {184--195}, - Title = {A study of the excited electronic states of normal and fully deuterated furan by photoabsorption spectroscopy and high-level ab initio calculations}, + Title = {A Study of the Excited Electronic States of Normal and Fully Deuterated Furan by Photoabsorption Spectroscopy and High-Level ab initio Calculations}, Url = {http://www.sciencedirect.com/science/article/pii/S0022285215000533}, Volume = {315}, Year = {2015}, @@ -2197,10 +3109,10 @@ Year = {1988}, Bdsk-Url-1 = {https://doi.org/10.1021/j100316a019}} -@article{Mcd91b, +@article{McD91b, Author = {McDiarmid, Ruth and Sabljic, A.}, Date-Added = {2019-01-05 12:45:46 +0100}, - Date-Modified = {2019-08-02 15:57:15 +0200}, + Date-Modified = {2019-10-02 18:07:03 +0200}, Doi = {10.1021/j100170a014}, Eprint = {https://doi.org/10.1021/j100170a014}, Journal = {J. Phys. Chem.}, @@ -2230,13 +3142,13 @@ @article{McD85, Author = {McDiarmid,R. and Sablji{\'c},A. and Doering,J. P.}, Date-Added = {2019-01-05 12:19:07 +0100}, - Date-Modified = {2019-01-05 12:19:32 +0100}, + Date-Modified = {2019-10-02 22:44:36 +0200}, Doi = {10.1063/1.449304}, Eprint = {https://doi.org/10.1063/1.449304}, Journal = {J. Chem. Phys.}, Number = {5}, Pages = {2147--2152}, - Title = {Valence Transitions in 1,3ā€Cyclopentadiene, 1,3ā€Cyclohexadiene, and 1,3ā€Cycloheptadiene}, + Title = {Valence Transitions in 1,3-Cyclopentadiene, 1,3-Cyclohexadiene, and 1,3-Cycloheptadiene}, Url = {https://doi.org/10.1063/1.449304}, Volume = {83}, Year = {1985}, @@ -2245,13 +3157,13 @@ @article{Fru79, Author = {Frueholz,Robert P. and Flicker,Wayne M. and Mosher,Oren A. and Kuppermann,Aron}, Date-Added = {2019-01-05 12:07:09 +0100}, - Date-Modified = {2019-01-05 12:07:39 +0100}, + Date-Modified = {2019-10-02 22:44:17 +0200}, Doi = {10.1063/1.437626}, Eprint = {https://doi.org/10.1063/1.437626}, Journal = {J. Chem. Phys.}, Number = {4}, Pages = {2003--2013}, - Title = {Electronic Spectroscopy of 1,3ā€Cyclopentadiene, 1,3ā€Cyclohexadiene and 1,3ā€Cycloheptadiene by Electron Impact}, + Title = {Electronic Spectroscopy of 1,3-Cyclopentadiene, 1,3-Cyclohexadiene and 1,3-Cycloheptadiene by Electron Impact}, Url = {https://doi.org/10.1063/1.437626}, Volume = {70}, Year = {1979}, @@ -2454,13 +3366,13 @@ Abstract = {The ultraviolet absorption spectra of furan, thiophene and pyrrole were investigated in order to clarify the origin of the long wavelength absorptions. In all three cases it could be shown that they are brought about by impurities. The remaining very low intensity long wavelength shoulder should be ascribed to singlet-triplet transitions. An interpretation of the electronic spectra of the five-membered heterocyclic compounds is given. These compounds may be divided into two groups having cyclopentadiene or furan like spectra respectively, according to the position of the Ļ€ ā†’ Ļ€* transitions depending on the electron affinities of the hetero atoms.}, Author = {G. Horv{\`a}th and {\'A}.I. Kiss}, Date-Added = {2018-11-26 15:52:15 +0100}, - Date-Modified = {2019-07-15 14:11:13 +0200}, + Date-Modified = {2019-10-02 22:53:11 +0200}, Doi = {https://doi.org/10.1016/0584-8539(67)80018-7}, Issn = {0584-8539}, Journal = {Spectrochim. Acta A}, Number = {4}, Pages = {921--924}, - Title = {The electronic spectra of five-membered heterocyclic compounds}, + Title = {The Electronic Spectra of Five-membered Heterocyclic Compounds}, Url = {http://www.sciencedirect.com/science/article/pii/0584853967800187}, Volume = {23}, Year = {1967}, @@ -2470,14 +3382,14 @@ @article{Bav76, Author = {Mario Bavia and Franco Bertinelli and Carlo Taliani and Carlo Zauli}, Date-Added = {2018-11-26 15:47:14 +0100}, - Date-Modified = {2018-11-26 15:47:25 +0100}, + Date-Modified = {2019-10-02 22:53:39 +0200}, Doi = {10.1080/00268977600100361}, Eprint = {https://doi.org/10.1080/00268977600100361}, Journal = {Mol. Phys.}, Number = {2}, Pages = {479--489}, Publisher = {Taylor & Francis}, - Title = {The electronic spectrum of pyrrole in the vapour and crystal}, + Title = {The Electronic Spectrum of Pyrrole in the Vapour and Crystal}, Url = {https://doi.org/10.1080/00268977600100361}, Volume = {31}, Year = {1976}, @@ -2487,13 +3399,13 @@ Abstract = {Low-lying triplet electronic states have been detected in furan, thiophene, and pyrrole by the method of variable-angle, electron-impact spectroscopy. Singlet ā†’ triplet transitions occur with maximum intensity at 3.99 eV and 5.22 eV in furan, 3.75 eV and 4.62 eV in thiophene, and 4.21 eV in pyrrole. A weak transition at 5.22 eV in pyrrole is assigned as the lowest observed singlet ā†’ singlet excitation in that molecule.}, Author = {Wayne M. Flicker and Oren A. Mosher and Aron Kuppermann}, Date-Added = {2018-11-26 15:45:23 +0100}, - Date-Modified = {2018-11-26 15:45:40 +0100}, + Date-Modified = {2019-10-02 22:35:07 +0200}, Doi = {https://doi.org/10.1016/0009-2614(76)80023-1}, Issn = {0009-2614}, Journal = {Chem. Phys. Lett.}, Number = {3}, Pages = {489--492}, - Title = {Triplet states of furan, thiophene, and pyrrole}, + Title = {Triplet States of Furan, Thiophene, and Pyrrole}, Url = {http://www.sciencedirect.com/science/article/pii/0009261476800231}, Volume = {38}, Year = {1976}, @@ -3064,9 +3976,9 @@ @article{Bol75, Abstract = {The A2Ī£+ -X2II1(a) absorption system of the NCO free radical has been re-investigated with higher resolving power than in the earlier work of Dixon (i960). Particular emphasis has been directed to the rotational analyses of bands involving the three vibronic levels, Ī¼2Ī£(+), 2Ī”i-(a) and k2Ī£(-), associated with the first level of the bending vibration in the ground state. A misassignment in the earlier work has been corrected and a new value for the Renner parameter determined, namely Īµ = -0.144 {\textpm} 0.001. This revised value removes the discrepancy noted in the earlier electron resonance results.}, - Author = {and and and and}, + Author = {Bolman, P. S. H. and Brown, J. M. and Carrington, A. and Kopp, I. and Ramsay, D. A.}, Date-Added = {2018-10-09 13:59:36 +0200}, - Date-Modified = {2018-10-09 14:00:15 +0200}, + Date-Modified = {2019-10-25 10:06:14 +0200}, Doi = {10.1098/rspa.1975.0050}, Eprint = {http://rspa.royalsocietypublishing.org/content/343/1632/17.full.pdf}, Issn = {0080-4630}, @@ -4188,13 +5100,14 @@ Abstract = {A series of N-substituted diamino-benzoquinone diimines featuring tunable aryl electron-withdrawing functions were synthesized. For the first time{,} the subtle variation of electronic richness allows controlling the canonical vs. zwitterionic equilibrium through the tuning of an intramolecular proton transfer. The establishment of a ground-state zwitterionic electronic structure{,} in lieu of the canonical one{,} within a monocyclic architecture is evidenced by the X-ray structure of one compound (4) and the telltale absorption spectra of the whole series that display an unexpected signature at low energy (ca. 700 nm). The evolution of this peculiar band is concomitant with the electron-withdrawing strength of the aryl substituents and theoretical calculations highlight that this band can be attributed to a charge transfer transition from the anionic cyanine towards the cationic cyanine. Finally{,} such a color change is advantageously used for the rapid and naked-eye detection of N{,}N-dimethylformamide using 3a as a vapochromic material. This latter experiment shows the first case of intramolecular solid-state proton transfer occurring in a polar environment.}, Author = {Pascal, Simon and Lavaud, Lucien and Azarias, Cloe and Canard, Gabriel and Giorgi, Michel and Jacquemin, Denis and Siri, Olivier}, Date-Added = {2018-06-13 12:29:01 +0000}, - Date-Modified = {2018-06-13 12:29:15 +0000}, + Date-Modified = {2019-08-31 16:00:46 +0200}, Doi = {10.1039/C8QM00171E}, Journal = {Mater. Chem. Front.}, - Pages = {in press, 10.1039/C8QM00171E}, + Pages = {1618--1625}, Publisher = {The Royal Society of Chemistry}, Title = {Controlling the canonical/zwitterionic balance through intramolecular proton transfer: a strategy for vapochromism}, Url = {http://dx.doi.org/10.1039/C8QM00171E}, + Volume = {2}, Year = {2018}, Bdsk-Url-1 = {http://dx.doi.org/10.1039/C8QM00171E}} @@ -4958,13 +5871,13 @@ @article{Pal97, Author = {Michael H. Palmer and Hamish McNab and David Reed and Anne Pollacchi and Isobel C. Walker and Martyn F. Guest and Michele R.F. Siggel}, Date-Added = {2018-04-25 08:09:28 +0000}, - Date-Modified = {2018-04-25 08:09:41 +0000}, + Date-Modified = {2019-10-03 16:52:24 +0200}, Doi = {https://doi.org/10.1016/S0301-0104(96)00330-8}, Issn = {0301-0104}, Journal = {Chem. Phys.}, Number = {2}, Pages = {191--211}, - Title = {The molecular and electronic states of 1,2,4,5-tetrazine studied by VUV absorption, near-threshold electron energy-loss spectroscopy and ab initio multi-reference configuration interaction studies}, + Title = {The Molecular and Electronic States of 1,2,4,5-tetrazine Studied by VUV absorption, Near-Threshold Electron Energy-Loss Spectroscopy and ab initio Multi-Reference Configuration Interaction Studies}, Url = {http://www.sciencedirect.com/science/article/pii/S0301010496003308}, Volume = {214}, Year = {1997}, @@ -4974,13 +5887,13 @@ @article{Wan00, Author = {Jian Wan and Jaroslaw Meller and Masahiko Hada and Masahiro Ehara and Hiroshi Nakatsuji}, Date-Added = {2018-04-24 12:58:00 +0000}, - Date-Modified = {2018-04-24 12:58:12 +0000}, + Date-Modified = {2019-10-02 22:41:47 +0200}, Doi = {10.1063/1.1316034}, Eprint = {https://doi.org/10.1063/1.1316034}, - Journal = {J. chem. Phys.}, + Journal = {J. Chem. Phys.}, Number = {18}, Pages = {7853--7866}, - Title = {Electronic excitation spectra of furan and pyrrole: Revisited by the symmetry adapted cluster--configuration interaction method}, + Title = {Electronic Excitation Spectra of Furan and Pyrrole: Revisited by the Symmetry Adapted Cluster--Configuration Interaction Method}, Url = {https://doi.org/10.1063/1.1316034}, Volume = {113}, Year = {2000}, @@ -5005,11 +5918,10 @@ @article{Li10c, Author = {Li, Xiangzhu and Paldus, Josef}, Date-Added = {2018-04-24 12:27:09 +0000}, - Date-Modified = {2018-04-24 12:27:24 +0000}, + Date-Modified = {2019-10-02 22:46:47 +0200}, Doi = {10.1021/jp911602k}, Eprint = {https://doi.org/10.1021/jp911602k}, Journal = {J. Phys. Chem. A}, - Note = {PMID: 20155956}, Number = {33}, Pages = {8591--8600}, Title = {A Multireference Coupled-Cluster Study of Electronic Excitations in Furan and Pyrrole}, @@ -5521,13 +6433,13 @@ @article{All84, Author = {Michael Allan}, Date-Added = {2018-03-23 13:35:12 +0000}, - Date-Modified = {2019-08-19 13:49:28 +0200}, + Date-Modified = {2019-11-07 11:29:00 +0100}, Doi = {10.1063/1.446683}, Eprint = {https://doi.org/10.1063/1.446683}, Journal = {J. Chem. Phys.}, Number = {12}, Pages = {6020--6024}, - Title = {The Excited States of 1,3ā€Butadiyne Determined by Electron Energy Loss Spectroscopy}, + Title = {The Excited States of 1,3-Butadiyne Determined by Electron Energy Loss Spectroscopy}, Url = {https://doi.org/10.1063/1.446683}, Volume = {80}, Year = {1984}, @@ -7042,7 +7954,7 @@ @article{Boo09, Author = {Booth, George H. and Thom, Alex J. W. and Alavi, Ali}, Date-Added = {2018-02-28 19:56:23 +0000}, - Date-Modified = {2018-02-28 19:56:23 +0000}, + Date-Modified = {2019-10-02 22:37:52 +0200}, Doi = {10.1063/1.3193710}, File = {Full Text PDF:/home/scemama/Dropbox/Zotero/storage/2MNQC3DS/Booth et al. - 2009 - Fermion Monte Carlo without fixed nodes A game of.pdf:application/pdf;JChemPhys_131_054106.pdf:/home/scemama/Dropbox/Zotero/storage/AYB9I4U9/JChemPhys_131_054106.pdf:application/pdf;Snapshot:/home/scemama/Dropbox/Zotero/storage/U56UGSZM/Booth et al. - 2009 - Fermion Monte Carlo without fixed nodes A game of.html:text/html}, Issn = {0021-9606}, @@ -7051,7 +7963,7 @@ Number = {5}, Pages = {054106}, Shorttitle = {Fermion {Monte} {Carlo} without fixed nodes}, - Title = {Fermion {Monte} {Carlo} without fixed nodes: {A} game of life, death, and annihilation in {Slater} determinant space}, + Title = {Fermion {Monte} {Carlo} Without Fixed Nodes: {A} Game of Life, Death, and Annihilation in {Slater} Determinant Space}, Url = {http://aip.scitation.org/doi/full/10.1063/1.3193710}, Urldate = {2017-11-13}, Volume = {131}, @@ -8406,15 +9318,15 @@ Year = {2008}} @article{Chr99, - Author = {Ove Christiansen and J{\"u}rgen Gauss and John F. Stanton and Poul Jo/rgensen}, + Author = {Ove Christiansen and Jurgen Gauss and John F. Stanton and Poul Jorgensen}, Date-Added = {2017-11-16 08:24:07 +0000}, - Date-Modified = {2017-11-16 08:24:20 +0000}, + Date-Modified = {2019-10-02 22:49:58 +0200}, Doi = {10.1063/1.479332}, Eprint = {https://doi.org/10.1063/1.479332}, Journal = {J. Chem. Phys.}, Number = {2}, Pages = {525--537}, - Title = {The electronic spectrum of pyrrole}, + Title = {The Electronic Spectrum of Pyrrole}, Url = {https://doi.org/10.1063/1.479332}, Volume = {111}, Year = {1999}, @@ -8424,13 +9336,13 @@ @article{Roo02, Author = {Bj{\"o}rn O. Roos and Per-{\AA}ke Malmqvist and Vincent Molina and Luis Serrano-Andr{\'e}s and Manuela Merch{\'a}n}, Date-Added = {2017-11-16 08:21:48 +0000}, - Date-Modified = {2017-11-16 08:22:00 +0000}, + Date-Modified = {2019-10-03 09:36:18 +0200}, Doi = {10.1063/1.1465406}, Eprint = {https://doi.org/10.1063/1.1465406}, Journal = {J. Chem. Phys.}, Number = {17}, Pages = {7526--7536}, - Title = {Theoretical characterization of the lowest-energy absorption band of pyrrole}, + Title = {Theoretical Characterization of the Lowest-Energy Absorption Band of Pyrrole}, Url = {https://doi.org/10.1063/1.1465406}, Volume = {116}, Year = {2002}, @@ -8779,10 +9691,10 @@ @article{Luo08, Author = {Luo, C. and Du, W. N. and Duan, X. M. and Li, Z. S.}, Date-Added = {2017-08-23 09:34:59 +0000}, - Date-Modified = {2017-08-23 09:36:07 +0000}, + Date-Modified = {2019-10-02 22:38:32 +0200}, Journal = {Astrophys. J.}, Pages = {726--730}, - Title = {A theoretical Study of the Photodissociation Mechanism of Cyanoacetylene in its Lowest Singlet and Triplet Excited States}, + Title = {A Theoretical Study of the Photodissociation Mechanism of Cyanoacetylene in its Lowest Singlet and Triplet Excited States}, Volume = {687}, Year = {2008}} @@ -8857,7 +9769,7 @@ Journal = {J. Mol. Spectrosc.}, Number = {1}, Pages = {20--32}, - Title = {Rotational Structure in the $^1\Sigma_u^ā’ \leftarrow ^1\Sigma_g^+$ Transition of Cyanogen at 2200 \AA}, + Title = {Rotational Structure in the $^1\Sigma_u^- \leftarrow ^1\Sigma_g^+$ Transition of Cyanogen at 2200 \AA}, Url = {http://www.sciencedirect.com/science/article/pii/0022285272901191}, Volume = {41}, Year = {1972}, @@ -9079,13 +9991,13 @@ @article{Sob93, Author = {A. L. Sobolewski and C. Woywod and W. Domcke}, Date-Added = {2017-07-02 09:46:03 +0000}, - Date-Modified = {2019-08-02 15:57:00 +0200}, + Date-Modified = {2019-10-14 14:59:35 +0200}, Doi = {10.1063/1.464907}, Eprint = {http://dx.doi.org/10.1063/1.464907}, Journal = {J. Chem. Phys.}, Number = {7}, Pages = {5627--5641}, - Title = {Ab Initio Investigation of Potentialā€Energy Surfaces Involved in the Photophysics of Benzene and Pyrazine}, + Title = {Ab Initio Investigation of Potential-Energy Surfaces Involved in the Photophysics of Benzene and Pyrazine}, Url = {http://dx.doi.org/10.1063/1.464907}, Volume = {98}, Year = {1993}, @@ -12787,13 +13699,13 @@ Abstract = {The recently introduced synchrotron radiation-based Fourier transform spectroscopy has been employed to study the excited electronic states of thiophene. A highly resolved photoabsorption spectrum has been measured between [similar]5 and 12.5 eV{,} providing a wealth of new data. High-level ab initio computations have been performed using the second-order algebraic-diagrammatic construction (ADC(2)) polarization propagator approach{,} and the equation-of-motion coupled-cluster (EOM-CC) method at the CCSD and CC3 levels{,} to guide the assignment of the spectrum. The adiabatic energy corrections have been evaluated{,} thereby extending the theoretical study beyond the vertical excitation picture and leading to a significantly improved understanding of the spectrum. The low-lying [small pi] [rightward arrow] [small pi]* and [small pi] [rightward arrow] [sigma]* transitions result in prominent broad absorption bands. Two strong Rydberg series converging onto the [X with combining tilde] 2A2 state limit have been assigned to the 1a2 [rightward arrow] npb11B2 and the 1a2 [rightward arrow] nda21A1 transitions. A second{,} and much weaker{,} d-type series has been assigned to the 1a2 [rightward arrow] ndb11B2 transitions. Excitation into some of the Rydberg states belonging to the two strong series gives rise to vibrational structure{,} most of which has been interpreted in terms of excitations of the totally symmetric [small nu]4 and [small nu]8 modes. One Rydberg series{,} assigned to the 3b1 [rightward arrow] nsa11B1 transitions{,} has been identified converging onto the A 2B1 state limit{,} and at higher energies Rydberg states converging onto the [B with combining tilde] 2A1 state limit could be identified. The present spectra reveal highly irregular vibrational structure in certain low energy absorption bands{,} and thus provide a new source of information for the rapidly developing studies of excited state non-adiabatic dynamics and photochemistry.}, Author = {Holland, D. M. P. and Trofimov, A. B. and Seddon, E. A. and Gromov, E. V. and Korona, T. and de Oliveira, N. and Archer, L. E. and Joyeux, D. and Nahon, L.}, Date-Added = {2016-09-01 01:57:12 +0000}, - Date-Modified = {2016-09-01 01:57:15 +0000}, + Date-Modified = {2019-10-02 22:47:30 +0200}, Doi = {10.1039/C4CP02420F}, Issue = {39}, Journal = {Phys. Chem. Chem. Phys.}, Pages = {21629-21644}, Publisher = {The Royal Society of Chemistry}, - Title = {Excited electronic states of thiophene: high resolution photoabsorption Fourier transform spectroscopy and ab initio calculations}, + Title = {Excited Electronic States of Thiophene: High Resolution Photoabsorption Fourier Transform Spectroscopy and \emph{ab initio} Calculations}, Url = {http://dx.doi.org/10.1039/C4CP02420F}, Volume = {16}, Year = {2014}, @@ -37211,9 +38123,10 @@ The intention of the present work is to give an insight into both the vibrationa @article{Ada00, Author = {Adamo, C. and Barone, V.}, + Date-Modified = {2019-10-03 16:51:31 +0200}, Journal = CPL, Pages = {152--160}, - Title = {A TDDFT study of the electronic spectrum of s-tetrazine in the gas-phase and in aqueous solution}, + Title = {A TDDFT Study of the Electronic Spectrum of s-Tetrazine in the Gas-Phase and in Aqueous Solution}, Volume = 330, Year = 2000} @@ -40687,9 +41600,10 @@ The intention of the present work is to give an insight into both the vibrationa @article{Del97b, Author = {Del Bene, J. E. and Watts, J. D. and Bartlett, R. J.}, + Date-Modified = {2019-11-07 11:30:45 +0100}, Journal = JCP, Pages = {6051--6060}, - Title = {Coupled-cluster calculations of the excitation energies of benzene and the azabenzenes}, + Title = {Coupled-Cluster Calculations of the Excitation Energies of Benzene and the Azabenzenes}, Volume = 106, Year = 1997} @@ -41258,14 +42172,6 @@ The intention of the present work is to give an insight into both the vibrationa Volume = {34}, Year = 1961} -@article{Edw71, - Author = {Edwards, L. and Dolphin, D. H. and Gouterman, M. and Adler, A. D.}, - Date-Modified = {2016-08-28 20:26:48 +0000}, - Journal = {J. Mol. Spectrosc.}, - Pages = {16--32}, - Volume = {38}, - Year = 1971} - @book{Edw96, Address = {Englewood cliffs, New Jersey}, Author = {Edwards, C. H. and Penney, D. E.}, @@ -46529,13 +47435,6 @@ The intention of the present work is to give an insight into both the vibrationa Volume = {4}, Year = {2008}} -@article{Lor95, - Author = {Lorentzon, J. and Malmqvist, P. A. and F\"{u}lscher, M. and Roos, B. O.}, - Journal = {Theor. Chim. Acta}, - Pages = {91--108}, - Volume = 91, - Year = 1995} - @article{Low50, Author = {L\"{o}wdin, P. O.}, Journal = JCP, @@ -48168,9 +49067,10 @@ The intention of the present work is to give an insight into both the vibrationa @article{Pac96, Author = {Packer, M. K. and Dalskov, E. K. and Enevoldsen, T. and Jensen, H. J. and Oddershede, J.}, + Date-Modified = {2019-10-03 13:31:06 +0200}, Journal = JCP, Pages = {5886--5900}, - Title = {A new implementation of the second-order polarization propagator approximation (SOPPA): The excitation spectra of benzene and naphthalene}, + Title = {A New Implementation of the Second-Order Polarization Propagator Approximation (SOPPA): The Excitation Spectra of Benzene and Naphthalene}, Volume = 105, Year = 1996} diff --git a/Mountain2.nb b/Mountain2.nb index 19239fe..e1cc5e4 100644 --- a/Mountain2.nb +++ b/Mountain2.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 18464521, 401272] -NotebookOptionsPosition[ 18261209, 398438] -NotebookOutlinePosition[ 18261617, 398456] -CellTagsIndexPosition[ 18261574, 398453] +NotebookDataLength[ 21754965, 479912] +NotebookOptionsPosition[ 21436306, 475497] +NotebookOutlinePosition[ 21436716, 475515] +CellTagsIndexPosition[ 21436673, 475512] 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