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Pierre-Francois Loos 2019-11-07 23:25:24 +01:00
parent 2f48c80a2b
commit 34954a094a
8 changed files with 152264 additions and 71323 deletions
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98
Data/cyclopropenone_13_PopleDZ_2.dat
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@ -1,46 +1,54 @@
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Data/thioacetone_1_PopleDZ.dat
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Data/thiopropynal_13_PopleDZ.dat
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Manuscript/FCI2-SI.tex
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@ -25,6 +25,11 @@
\newcommand{\CASSCF}{CASSCF} \newcommand{\CASSCF}{CASSCF}
\newcommand{\CASPT}{CASPT2} \newcommand{\CASPT}{CASPT2}
\newcommand{\ADC}[1]{ADC(#1)} \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{\CC}[1]{CC#1}
\newcommand{\CCSD}{CCSD} \newcommand{\CCSD}{CCSD}
\newcommand{\EOMCCSD}{EOM-CCSD} \newcommand{\EOMCCSD}{EOM-CCSD}
@ -49,6 +54,10 @@
% units % units
\newcommand{\IneV}[1]{#1 eV} \newcommand{\IneV}[1]{#1 eV}
\newcommand{\InAU}[1]{#1 a.u.} \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} \newcommand{\SI}{Supporting Information}
@ -94,9 +103,7 @@
\section{Basis set and frozen-core effects} \section{Basis set and frozen-core effects}
\subsection{CC3} \subsection{Cyanoacetylene, cyanogen, and diacetylene}
\subsubsection{Cyanoacetylene, cyanogen, and diacetylene}
\begin{table}[htp] \begin{table}[htp]
\caption{\small CC3 vertical transition energies of cyanoacetylene, cyanogen, and diacetylene using various atomic basis sets. \caption{\small CC3 vertical transition energies of cyanoacetylene, cyanogen, and diacetylene using various atomic basis sets.
@ -114,6 +121,7 @@ $^1\Sigma^-$ &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 \\ $^1\Delta$ &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 \\ $^3\Sigma^+$ &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 \\ $^3\Delta$ &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 \hline
& \multicolumn{8}{c}{Cyanogen} \\ & \multicolumn{8}{c}{Cyanogen} \\
\hline \hline
@ -134,7 +142,7 @@ $^3\Delta_u$ &4.93 &4.86 &4.80 &4.80 &4.80 &4.80 &4.80 &4.80 \\
\end{table} \end{table}
\clearpage \clearpage
\subsubsection{Cyclopropenone, cyclopropenethione, and methylenecyclopropene} \subsection{Cyclopropenone, cyclopropenethione, and methylenecyclopropene}
\begin{table}[htp] \begin{table}[htp]
\caption{\small CC3 vertical transition energies of cyclopropenone, cyclopropenethione, and methylenecyclopropene using various atomic basis sets. \caption{\small CC3 vertical transition energies of cyclopropenone, cyclopropenethione, and methylenecyclopropene using various atomic basis sets.
@ -143,44 +151,44 @@ FC stands for frozen core. All values are in eV.}
\begin{small} \begin{small}
\begin{tabular}{l|ccccccc} \begin{tabular}{l|ccccccc}
\hline \hline
& {\Pop} & {\AVDZ} & {\AVTZ} & \multicolumn{2}{c}{\AVQZ} &{\DAVQZ} & {\AVFZ} \ \\ & {\Pop} & {\AVDZ} & {\AVTZ} & \multicolumn{2}{c}{\AVQZ} &{\DAVQZ} & {\AVFZ} \ \\
& FC & FC &FC & FC & Full & FC & FC \\ & FC & FC &FC & FC & Full & FC & FC \\
\hline \hline
& \multicolumn{7}{c}{Cyclopropenone} \\ & \multicolumn{7}{c}{Cyclopropenone} \\
\hline \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 $^1B_1 (n \rightarrow \pi^\star)$ &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\\% 5.58 en 5Z $^1A_2 (n \rightarrow \pi^\star)$ &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 & \hl{xxx}\\% $^1B_2 (n \rightarrow 3s)$ &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 & \hl{xxx}\\% $^1B_2 (\pi \rightarrow \pi^\star)$ &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 & \hl{xxx}\\% $^1B_2 (n \rightarrow 3p)$ &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\\%To be looked at 7.06 en 5Z $^1A_1 (n \rightarrow 3p)$ &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\\%To be looked at 8.26 en 5Z $^1A_1 (\pi \rightarrow \pi^\star)$ &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 & \hl{xxx}\\% N043, ~3.94, proche $^3B_1 (n \rightarrow \pi^\star)$ &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 & \hl{xxx} \\% $^3B_2 (\pi \rightarrow \pi^\star)$ &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 & \hl{xxx}\\% $^3A_2 (n \rightarrow \pi^\star)$ &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\\% 6.85 en 57 $^3A_1 (\pi \rightarrow \pi^\star)$ &6.89 &6.79 &6.83 &6.84 &6.83& 6.84 & 6.85\\
\hline \hline
& \multicolumn{7}{c}{Cyclopropenethione} \\ & \multicolumn{7}{c}{Cyclopropenethione} \\
\hline \hline
$^1A_2 (n \rightarrow \pi^\star)$ &3.46 &3.47 &3.43 &3.44 &3.42& 3.44 \\ $^1A_2 (n \rightarrow \pi^\star)$ &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 \\ $^1B_1 (n \rightarrow \pi^\star)$ &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 \\ $^1B_2 (\pi \rightarrow \pi^\star)$ &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 \\ $^1B_2 (n \rightarrow 3s)$ &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 \\ $^1A_1 (\pi \rightarrow \pi^\star)$ &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 \\%$^a$, mais les autres aussi !! $^1B_2 (n \rightarrow 3p)$ &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 \\ $^3A_2 (n \rightarrow \pi^\star)$ &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 \\ $^3B_1 (n \rightarrow \pi^\star)$ &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 \\ $^3B_2 (\pi \rightarrow \pi^\star)$ &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 \\ $^3A_1 (\pi \rightarrow \pi^\star)$ &4.06 &4.09 &4.03 &4.04 &4.02& 4.04& 4.03 \\
\hline \hline
& \multicolumn{7}{c}{Methylenecyclopropene} \\ & \multicolumn{7}{c}{Methylenecyclopropene} \\
\hline \hline
$^1B_2 (\pi \rightarrow \pi^\star)$ &4.38 &4.32 &4.31 &4.31 &4.31& 4.31 \\ $^1B_2 (\pi \rightarrow \pi^\star)$ &4.38 &4.32 &4.31 &4.31 &4.31& 4.31& 4.32 \\% 5Z: 4.32
$^1B_1 (\pi \rightarrow \sigma^\star)$ &5.65 &5.35 &5.44 &5.47 &5.48& 5.46\\ $^1B_1 (\pi \rightarrow 3s)$ &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\\ $^1A_2 (\pi \rightarrow 3p)$ &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\\%<= Stong mixing $^1A_1 (\pi \rightarrow \pi^\star)$ &6.17 &6.15 &6.13 &6.09 &6.10& 5.98& 6.04\\%<= Stong mixing 5Z: 6.04 <= A italusŽ dans la liste des TBE ?
$^3B_2 (\pi \rightarrow \pi^\star)$ &3.50 &3.49 &3.50 &3.50 &3.50& 3.50\\ $^3B_2 (\pi \rightarrow \pi^\star)$ &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\\ $^3A_1 (\pi \rightarrow \pi^\star)$ &4.74 &4.74 &4.74 &4.75 &4.74& 4.74& 4.75\\% 5Z: 4.75
\hline \hline
\end{tabular} \end{tabular}
\begin{flushleft} \begin{flushleft}
@ -193,17 +201,17 @@ $^3A_1 (\pi \rightarrow \pi^\star)$ &4.74 &4.74 &4.74 &4.75 &4.74& 4.74\\
\clearpage \clearpage
\subsubsection{Acrolein, butadiene, and glyoxal} \subsection{Acrolein, butadiene, and glyoxal}
\begin{table}[htp] \begin{sidewaystable}[htp]
\caption{\small CC3 vertical transition energies of acrolein, butadiene, and glyoxal using various atomic basis sets. \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.} FC stands for frozen core. All values are in eV.}
\label{Table-S3} \label{Table-S3}
\begin{small} \begin{small}
\begin{tabular}{l|cccccc} \begin{tabular}{l|ccccccc}
\hline \hline
& {\Pop} & {\AVDZ} & {\AVTZ} & \multicolumn{2}{c}{\AVQZ} &{\DAVQZ} \\ & {\Pop} & {\AVDZ} & {\AVTZ} & \multicolumn{2}{c}{\AVQZ} &{\DAVQZ} &{\AVFZ}\\
& FC & FC &FC & FC & Full & FC \\ & FC & FC &FC & FC & Full & FC & FC \\
\hline \hline
& \multicolumn{6}{c}{Acrolein} \\ & \multicolumn{6}{c}{Acrolein} \\
\hline \hline
@ -214,7 +222,7 @@ $^1A' (n \rightarrow 3s)$ &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\\ $^3A'' (n \rightarrow \pi^\star)$ &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\\ $^3A' (\pi \rightarrow \pi^\star)$ &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\\ $^3A' (\pi \rightarrow \pi^\star)$ &6.25 &6.22 &6.19 &6.20 &6.19\\
$^3A'' (\pi \rightarrow 3s)$ &6.81 &6.60 &6.61 &6.63 &6.62\\ $^3A'' (n \rightarrow \pi^\star)$ &6.81 &6.60 &6.61 &6.63 &6.62\\
\hline \hline
& \multicolumn{6}{c}{Butadiene} \\ & \multicolumn{6}{c}{Butadiene} \\
\hline \hline
@ -230,24 +238,24 @@ $^3B_g (\pi \rightarrow 3s)$ &6.46 &6.20 &6.28 &6.30 &6.31\\
\hline \hline
& \multicolumn{6}{c}{Glyoxal} \\ & \multicolumn{6}{c}{Glyoxal} \\
\hline \hline
$^1A_u (n \rightarrow \pi^\star)$ &2.94 &2.90 &2.88 &2.88 &2.87& 2.88\\ $^1A_u (n \rightarrow \pi^\star)$ &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\\ $^1B_g (n \rightarrow \pi^\star)$ &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\\ $^1A_g (n,n \rightarrow \pi^\star,\pi^\star)$&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\\ $^1B_g (n \rightarrow \pi^\star)$ &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\\ $^1B_u (n \rightarrow3p)$ &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\\ $^3A_u (n \rightarrow \pi^\star)$ &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\\ $^3B_g (n \rightarrow \pi^\star)$ &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\\ $^3B_u (\pi \rightarrow \pi^\star)$ &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\\ $^3A_g (\pi \rightarrow \pi^\star)$ &6.35 &6.34 &6.30 &6.31 &6.30& 6.31& 6.31\\
\hline \hline
\end{tabular} \end{tabular}
\end{small} \end{small}
\end{table} \end{sidewaystable}
\clearpage \clearpage
\subsubsection{Acetone, cyanoformaldehyde, isobutene, propynal, thioacetone, and thiopropynal} \subsection{Acetone, cyanoformaldehyde, isobutene, propynal, thioacetone, and thiopropynal}
\begin{table}[htp] \begin{table}[htp]
\caption{\small CC3 vertical transition energies of acetone, cyanoformaldehyde, isobutene, propynal, thioacetone, and thiopropynal using various atomic basis sets. \caption{\small CC3 vertical transition energies of acetone, cyanoformaldehyde, isobutene, propynal, thioacetone, and thiopropynal using various atomic basis sets.
@ -259,7 +267,7 @@ FC stands for frozen core. All values are in eV.}
& {\Pop} & {\AVDZ} & {\AVTZ} & \multicolumn{2}{c}{\AVQZ} &{\DAVQZ} \\ & {\Pop} & {\AVDZ} & {\AVTZ} & \multicolumn{2}{c}{\AVQZ} &{\DAVQZ} \\
& FC & FC &FC & FC & Full & FC\\ & FC & FC &FC & FC & Full & FC\\
\hline \hline
& \multicolumn{5}{c}{Acetone} \\ & \multicolumn{6}{c}{Acetone} \\
\hline \hline
$^1A_2 (n \rightarrow \pi^\star)$ &4.55 &4.50 &4.48 &4.49 &4.48\\ $^1A_2 (n \rightarrow \pi^\star)$ &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\\ $^1B_2 (n \rightarrow 3s)$ &6.65 &6.31 &6.43 &6.48 &6.49\\
@ -269,40 +277,141 @@ $^1B_2 (n \rightarrow 3p)$ &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\\ $^3A_2 (n \rightarrow \pi^\star)$ &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\\ $^3A_1 (\pi \rightarrow \pi^\star)$ &6.32 &6.31 &6.28 &6.30 &6.28\\
\hline \hline
& \multicolumn{5}{c}{Cyanoformaldehyde} \\ & \multicolumn{6}{c}{Cyanoformaldehyde} \\
\hline \hline
$^1A'' (n \rightarrow \pi^\star)$ &3.91 &3.86 &3.83 &3.84 &3.83 &3.84\\ $^1A'' (n \rightarrow \pi^\star)$ &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\\ $^1A'' (\pi \rightarrow \pi^\star)$ &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\\ $^3A'' (n \rightarrow \pi^\star)$ &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\\ $^3A' (\pi \rightarrow \pi^\star)$ &5.07 &5.03 &5.01 &5.02 &5.01 &5.02\\
\hline \hline
& \multicolumn{5}{c}{Isobutene} \\ & \multicolumn{6}{c}{Isobutene} \\
\hline \hline
$^1B_1 (\pi \rightarrow 3s)$ &6.77 &6.39 &6.45 &6.47 &\\ $^1B_1 (\pi \rightarrow 3s)$ &6.77 &6.39 &6.45 &6.47 &6.49\\
$^1A_1 (\pi \rightarrow 3p)$ &7.16 &7.00 &7.00 &6.99 &\\ $^1A_1 (\pi \rightarrow 3p)$ &7.16 &7.00 &7.00 &6.99 &7.00\\
$^3A_1 (\pi \rightarrow \pi^\star)$ &4.52 &4.54 &4.53 &4.54 &\\ $^3A_1 (\pi \rightarrow \pi^\star)$ &4.52 &4.54 &4.53 &4.54 &4.54\\
\hline \hline
& \multicolumn{5}{c}{Propynal} \\ & \multicolumn{6}{c}{Propynal} \\
\hline \hline
$^1A'' (n \rightarrow \pi^\star)$ &3.90 &3.85 &3.82 &3.83 &3.82 &3.83\\ $^1A'' (n \rightarrow \pi^\star)$ &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\\ $^1A'' (\pi \rightarrow \pi^\star)$ &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}\\ $^3A'' (n \rightarrow \pi^\star)$ &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\\ $^3A' (\pi \rightarrow \pi^\star)$ &4.46 &4.40 &4.43 &4.44 &4.43 &4.44\\
\hline \hline
& \multicolumn{5}{c}{Thioacetone} \\ & \multicolumn{6}{c}{Thioacetone} \\
\hline \hline
$^1A_2 (n \rightarrow \pi^\star)$ &2.58 &2.59 &2.55 &2.56 &\\ $^1A_2 (n \rightarrow \pi^\star)$ &2.58 &2.59 &2.55 &2.56 &\\
$^1B_2 (n \rightarrow 4s)$ &5.65 &5.44 &5.55 &5.60 &\\ $^1B_2 (n \rightarrow 4s)$ &5.65 &5.44 &5.55 &5.60 &\\
$^1A_1 (\pi \rightarrow \pi^\star)$ &6.09 &5.97 &5.90 &5.88 &\\ $^1A_1 (\pi \rightarrow \pi^\star)$ &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 &\\ $^1B_2 (n \rightarrow 4p)$ &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 &\\ $^3A_2 (n \rightarrow \pi^\star)$ &2.36 &2.36 &2.34 &2.35 &\\
$^3A_1 (\pi \rightarrow \pi^\star)$ s&3.45 &3.51 &3.46 &3.47 &\\ $^3A_1 (\pi \rightarrow \pi^\star)$ &3.45 &3.51 &3.46 &3.47 &\\
\hline \hline
& \multicolumn{5}{c}{Thiopropynal} \\ & \multicolumn{5}{c}{Thiopropynal} \\
\hline \hline
$^1A'' (n \rightarrow \pi^\star)$ &2.09 &2.09 &2.05 &2.06 &2.04\\ $^1A'' (n \rightarrow \pi^\star)$ &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}\\ $^3A'' (n \rightarrow \pi^\star)$ &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 \hline
\end{tabular} \end{tabular}
\end{small} \end{small}
@ -311,9 +420,198 @@ $^3A'' (n \rightarrow \pi^\star)$ &1.84 &1.83 &1.81 &1.82 &\hl{xxx}\\
\clearpage \clearpage
\subsection{Multi-reference results} \subsection{Benzene, pyrazine, and tetrazine}
\subsubsection{Cyanoacetylene, cyanogen, and diacetylene} \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] \begin{table}[htp]
\caption{\small Vertical transition energies of cyanoacetylene, cyanogen, and diacetylene using various atomic basis sets and \caption{\small Vertical transition energies of cyanoacetylene, cyanogen, and diacetylene using various atomic basis sets and
@ -351,6 +649,194 @@ $^3\Delta_u$ & & 4.89 & 4.81 & & & 4.86 & 4.78 & & & 4.90 & 4.82 & \\
\end{tabular} \end{tabular}
\end{footnotesize} \end{footnotesize}
\end{table} \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 \clearpage
@ -392,6 +878,26 @@ H 3.60951559 -2.33000749 0.00000000
\end{verbatim} \end{verbatim}
\end{singlespace} \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} \subsection{Butadiene}
@ -422,6 +928,19 @@ H 0.00000000 0.00000000 -5.59619886
\end{verbatim} \end{verbatim}
\end{singlespace} \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} \subsection{Cyanoformaldehyde}
\begin{singlespace} \begin{singlespace}
@ -454,10 +973,12 @@ C 0.00000000 0.00000000 1.22784115
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
N 0.00000000 0.00000000 -3.56462559 N 0.00000000 0.00000000 -3.56462559
\end{verbatim} \end{verbatim}
\end{singlespace} \end{singlespace}
\clearpage
\subsection{Cyclopentadiene} \subsection{Cyclopentadiene}
\begin{singlespace} \begin{singlespace}
@ -502,6 +1023,8 @@ H 0.00000000 -2.97773331 -3.95114059
\end{verbatim} \end{verbatim}
\end{singlespace} \end{singlespace}
\clearpage
\subsection{Diacetylene} \subsection{Diacetylene}
\begin{singlespace} \begin{singlespace}
@ -545,6 +1068,9 @@ H -0.96135276 -2.81883243 0.00000000
\end{verbatim} \end{verbatim}
\end{singlespace} \end{singlespace}
\clearpage
\subsection{Imidazole} \subsection{Imidazole}
\begin{singlespace} \begin{singlespace}
@ -611,6 +1137,74 @@ H 0.64026209 0.00000000 5.48853193
\end{verbatim} \end{verbatim}
\end{singlespace} \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} \subsection{Pyrrole}
@ -629,6 +1223,21 @@ H 0.00000000 -2.56726559 -3.47837232
\end{verbatim} \end{verbatim}
\end{singlespace} \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} \subsection{Thioacetone}
@ -677,6 +1286,22 @@ H -5.97712967 0.00000000 2.33206931
\end{singlespace} \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 \clearpage

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