2019-11-07 23:25:24 +01:00
\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 \\
$ ^ 1 A'' $ [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
$ ^ 1 B _ 1 ( n \rightarrow \pi ^ \star ) $ & 4.32 & 4.22 & 4.21 & 4.23 & 4.22& 4.23 & 4.23\\
$ ^ 1 A _ 2 ( n \rightarrow \pi ^ \star ) $ & 5.68 & 5.59 & 5.57 & 5.58 & 5.57& 5.58 & 5.58\\
$ ^ 1 B _ 2 ( n \rightarrow 3 s ) $ & 6.39 & 6.21 & 6.32 & 6.37 & 6.38& 6.36 & 6.38\\ %
$ ^ 1 B _ 2 ( \pi \rightarrow \pi ^ \star ) $ & 6.70 & 6.56 & 6.54 & 6.56 & 6.56& 6.56 & 6.56\\
$ ^ 1 B _ 2 ( n \rightarrow 3 p ) $ & 6.92 & 6.88 & 6.96 & 6.99 & 7.00& 6.96 & 6.99\\
$ ^ 1 A _ 1 ( n \rightarrow 3 p ) $ & 7.00 & 6.88 & 7.00 & 7.05 & 7.06& 7.03 & 7.06\\
$ ^ 1 A _ 1 ( \pi \rightarrow \pi ^ \star ) $ & 8.51 & 8.32 & 8.28 & 8.28 & 8.28& 8.22 & 8.26\\
$ ^ 3 B _ 1 ( n \rightarrow \pi ^ \star ) $ & 4.02 & 3.90 & 3.91 & 3.93 & 3.92& 3.93 & 3.94\\
$ ^ 3 B _ 2 ( \pi \rightarrow \pi ^ \star ) $ & 4.92 & 4.90 & 4.89 & 4.91 & 4.90& 4.91 & 4.92\\
$ ^ 3 A _ 2 ( n \rightarrow \pi ^ \star ) $ & 5.48 & 5.38 & 5.37 & 5.39 & 5.37& 5.39 & 5.39\\
$ ^ 3 A _ 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
$ ^ 1 A _ 2 ( n \rightarrow \pi ^ \star ) $ & 3.46 & 3.47 & 3.43 & 3.44 & 3.42& 3.44 & 3.43 \\
$ ^ 1 B _ 1 ( n \rightarrow \pi ^ \star ) $ & 3.45 & 3.42 & 3.43 & 3.45 & 3.43& 3.45 & 3.46\\
$ ^ 1 B _ 2 ( \pi \rightarrow \pi ^ \star ) $ & 4.67 & 4.66 & 4.64 & 4.66 & 4.64& 4.66 & 4.66 \\
$ ^ 1 B _ 2 ( n \rightarrow 3 s ) $ & 5.26 & 5.23 & 5.34 & 5.39 & 5.39& 5.38 & 5.40 \\
$ ^ 1 A _ 1 ( \pi \rightarrow \pi ^ \star ) $ & 5.53 & 5.52 & 5.49 & 5.49 & 5.48& 5.49 & 5.49\\
$ ^ 1 B _ 2 ( n \rightarrow 3 p ) $ & 5.83 & 5.86 & 5.93 & 5.95 & 5.95& 5.91 & 5.95 \\ %$^a$, mais les autres aussi !!
$ ^ 3 A _ 2 ( n \rightarrow \pi ^ \star ) $ & 3.33 & 3.34 & 3.31 & 3.31 & 3.29& 3.31 & 3.31 \\
$ ^ 3 B _ 1 ( n \rightarrow \pi ^ \star ) $ & 3.34 & 3.30 & 3.31 & 3.34 & 3.32& 3.34 & 3.35\\
$ ^ 3 B _ 2 ( \pi \rightarrow \pi ^ \star ) $ & 4.01 & 4.03 & 4.02 & 4.04 & 4.03& 4.04 & 4.05 \\
$ ^ 3 A _ 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
$ ^ 1 B _ 2 ( \pi \rightarrow \pi ^ \star ) $ & 4.38 & 4.32 & 4.31 & 4.31 & 4.31& 4.31& 4.32 \\ % 5Z: 4.32
$ ^ 1 B _ 1 ( \pi \rightarrow 3 s ) $ & 5.65 & 5.35 & 5.44 & 5.47 & 5.48& 5.46& 5.47\\ % 5Z: 5.47
$ ^ 1 A _ 2 ( \pi \rightarrow 3 p ) $ & 5.97 & 5.86 & 5.95 & 5.98 & 5.99& 5.96& \hl { xxx} \\ %N122
$ ^ 1 A _ 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 italus<75> dans la liste des TBE ?
$ ^ 3 B _ 2 ( \pi \rightarrow \pi ^ \star ) $ & 3.50 & 3.49 & 3.50 & 3.50 & 3.50& 3.50& \hl { xxx} \\ %N122
$ ^ 3 A _ 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
$ ^ 1 A'' ( n \rightarrow \pi ^ \star ) $ & 3.83 & 3.77 & 3.74 & 3.75 & 3.74\\
$ ^ 1 A' ( \pi \rightarrow \pi ^ \star ) $ & 6.83 & 6.67 & 6.65 & 6.65 & 6.65\\
$ ^ 1 A'' ( n \rightarrow \pi ^ \star ) $ & 6.94 & 6.75 & 6.75 & 6.77 & 6.76\\
$ ^ 1 A' ( n \rightarrow 3 s ) $ & 7.22 & 6.99 & 7.07 & 7.11 & 7.11\\
$ ^ 3 A'' ( n \rightarrow \pi ^ \star ) $ & 3.55 & 3.47 & 3.46 & 3.47 & 3.46\\
$ ^ 3 A' ( \pi \rightarrow \pi ^ \star ) $ & 3.94 & 3.95 & 3.94 & 3.95 & 3.94\\
$ ^ 3 A' ( \pi \rightarrow \pi ^ \star ) $ & 6.25 & 6.22 & 6.19 & 6.20 & 6.19\\
$ ^ 3 A'' ( n \rightarrow \pi ^ \star ) $ & 6.81 & 6.60 & 6.61 & 6.63 & 6.62\\
\hline
& \multicolumn { 6} { c} { Butadiene} \\
\hline
$ ^ 1 B _ u ( \pi \rightarrow \pi ^ \star ) $ & 6.41 & 6.25 & 6.22 & 6.21 & 6.22\\
$ ^ 1 B _ g ( \pi \rightarrow 3 s ) $ & 6.53 & 6.26 & 6.33 & 6.35 & 6.36\\
$ ^ 1 A _ g ( \pi \rightarrow \pi ^ \star ) $ & 6.73 & 6.68 & 6.67 & 6.67 & 6.67& 6.67\\
$ ^ 1 A _ u ( \pi \rightarrow 3 p ) $ & 6.87 & 6.57 & 6.64 & 6.66 & 6.67\\
$ ^ 1 A _ u ( \pi \rightarrow 3 p ) $ & 6.93 & 6.73 & 6.80 & 6.82 & 6.83\\
$ ^ 1 B _ u ( \pi \rightarrow 3 p ) $ & 7.98 & 7.86 & 7.68 & 7.54 & 7.55\\
$ ^ 3 B _ u ( \pi \rightarrow \pi ^ \star ) $ & 3.35 & 3.36 & 3.36 & 3.37 & 3.36\\
$ ^ 3 A _ g ( \pi \rightarrow \pi ^ \star ) $ & 5.22 & 5.21 & 5.20 & 5.21 & 5.20\\
$ ^ 3 B _ g ( \pi \rightarrow 3 s ) $ & 6.46 & 6.20 & 6.28 & 6.30 & 6.31\\
\hline
& \multicolumn { 6} { c} { Glyoxal} \\
\hline
$ ^ 1 A _ u ( n \rightarrow \pi ^ \star ) $ & 2.94 & 2.90 & 2.88 & 2.88 & 2.87& 2.88& 2.88\\
$ ^ 1 B _ g ( n \rightarrow \pi ^ \star ) $ & 4.34 & 4.30 & 4.27 & 4.27 & 4.27& 4.27& \\
$ ^ 1 A _ g ( n,n \rightarrow \pi ^ \star , \pi ^ \star ) $ & 6.74 & 6.70 & 6.76 & 6.76 & 6.74& 6.76& 6.75 \\
$ ^ 1 B _ g ( n \rightarrow \pi ^ \star ) $ & 6.81 & 6.59 & 6.58 & 6.59 & 6.58& 6.58& \\
$ ^ 1 B _ u ( n \rightarrow 3 p ) $ & 7.72 & 7.55 & 7.67 & 7.72 & 7.73& 7.72& 7.74\\
$ ^ 3 A _ u ( n \rightarrow \pi ^ \star ) $ & 2.55 & 2.49 & 2.49 & 2.49 & 2.49& 2.49& 2.50\\
$ ^ 3 B _ g ( n \rightarrow \pi ^ \star ) $ & 3.97 & 3.91 & 3.90 & 3.91 & 3.90& 3.91& \\
$ ^ 3 B _ u ( \pi \rightarrow \pi ^ \star ) $ & 5.22 & 5.20 & 5.17 & 5.18 & 5.17& 5.18& 5.19\\
$ ^ 3 A _ 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
$ ^ 1 A _ 2 ( n \rightarrow \pi ^ \star ) $ & 4.55 & 4.50 & 4.48 & 4.49 & 4.48\\
$ ^ 1 B _ 2 ( n \rightarrow 3 s ) $ & 6.65 & 6.31 & 6.43 & 6.48 & 6.49\\
$ ^ 1 A _ 2 ( n \rightarrow 3 p ) $ & 7.83 & 7.37 & 7.45 & 7.48 & 7.49\\
$ ^ 1 A _ 1 ( n \rightarrow 3 p ) $ & 7.81 & 7.39 & 7.48 & 7.52 & 7.53\\
$ ^ 1 B _ 2 ( n \rightarrow 3 p ) $ & 7.87 & 7.56 & 7.59 & 7.60 & 7.61\\
$ ^ 3 A _ 2 ( n \rightarrow \pi ^ \star ) $ & 4.21 & 4.16 & 4.15 & 4.17 & 4.16\\
$ ^ 3 A _ 1 ( \pi \rightarrow \pi ^ \star ) $ & 6.32 & 6.31 & 6.28 & 6.30 & 6.28\\
\hline
& \multicolumn { 6} { c} { Cyanoformaldehyde} \\
\hline
$ ^ 1 A'' ( n \rightarrow \pi ^ \star ) $ & 3.91 & 3.86 & 3.83 & 3.84 & 3.83 & 3.84\\
$ ^ 1 A'' ( \pi \rightarrow \pi ^ \star ) $ & 6.64 & 6.51 & 6.42 & 6.41 & 6.41 & 6.41\\
$ ^ 3 A'' ( n \rightarrow \pi ^ \star ) $ & 3.53 & 3.47 & 3.46 & 3.47 & 3.46 & 3.47\\
$ ^ 3 A' ( \pi \rightarrow \pi ^ \star ) $ & 5.07 & 5.03 & 5.01 & 5.02 & 5.01 & 5.02\\
\hline
& \multicolumn { 6} { c} { Isobutene} \\
\hline
$ ^ 1 B _ 1 ( \pi \rightarrow 3 s ) $ & 6.77 & 6.39 & 6.45 & 6.47 & 6.49\\
$ ^ 1 A _ 1 ( \pi \rightarrow 3 p ) $ & 7.16 & 7.00 & 7.00 & 6.99 & 7.00\\
$ ^ 3 A _ 1 ( \pi \rightarrow \pi ^ \star ) $ & 4.52 & 4.54 & 4.53 & 4.54 & 4.54\\
\hline
& \multicolumn { 6} { c} { Propynal} \\
\hline
$ ^ 1 A'' ( n \rightarrow \pi ^ \star ) $ & 3.90 & 3.85 & 3.82 & 3.83 & 3.82 & 3.83\\
$ ^ 1 A'' ( \pi \rightarrow \pi ^ \star ) $ & 5.69 & 5.59 & 5.51 & 5.50 & 5.50 & 5.50\\
$ ^ 3 A'' ( n \rightarrow \pi ^ \star ) $ & 3.56 & 3.50 & 3.49 & 3.50 & 3.49 & 3.50\\
$ ^ 3 A' ( \pi \rightarrow \pi ^ \star ) $ & 4.46 & 4.40 & 4.43 & 4.44 & 4.43 & 4.44\\
\hline
& \multicolumn { 6} { c} { Thioacetone} \\
\hline
$ ^ 1 A _ 2 ( n \rightarrow \pi ^ \star ) $ & 2.58 & 2.59 & 2.55 & 2.56 & \\
$ ^ 1 B _ 2 ( n \rightarrow 4 s ) $ & 5.65 & 5.44 & 5.55 & 5.60 & \\
$ ^ 1 A _ 1 ( \pi \rightarrow \pi ^ \star ) $ & 6.09 & 5.97 & 5.90 & 5.88 & \\
$ ^ 1 B _ 2 ( n \rightarrow 4 p ) $ & 6.59 & 6.45 & 6.51 & 6.52 & \\
$ ^ 1 A _ 1 ( n \rightarrow 4 p ) $ & 6.95 & 6.54 & 6.61 & 6.64 & 6.64\\
$ ^ 3 A _ 2 ( n \rightarrow \pi ^ \star ) $ & 2.36 & 2.36 & 2.34 & 2.35 & \\
$ ^ 3 A _ 1 ( \pi \rightarrow \pi ^ \star ) $ & 3.45 & 3.51 & 3.46 & 3.47 & \\
\hline
& \multicolumn { 5} { c} { Thiopropynal} \\
\hline
$ ^ 1 A'' ( n \rightarrow \pi ^ \star ) $ & 2.09 & 2.09 & 2.05 & 2.06 & 2.04\\
$ ^ 3 A'' ( 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
$ ^ 1 A _ 2 ( \pi \rightarrow 3 s ) $ & 6.26 & 6.00 & 6.08 & 6.10 & 6.12\\
$ ^ 1 B _ 2 ( \pi \rightarrow \pi ^ \star ) $ & 6.50 & 6.37 & 6.34 & 6.34 & 6.34\\
$ ^ 1 A _ 1 ( \pi \rightarrow \pi ^ \star ) $ & 6.71 & 6.62 & 6.58 & 6.58 & 6.58\\
$ ^ 1 B _ 1 ( \pi \rightarrow 3 p ) $ & 6.76 & 6.55 & 6.63 & 6.65 & 6.67\\
$ ^ 1 A _ 2 ( \pi \rightarrow 3 p ) $ & 6.97 & 6.73 & 6.80 & 6.82 & 6.83\\
$ ^ 1 B _ 2 ( \pi \rightarrow 3 p ) $ & 7.53 & 7.39 & 7.23 & 7.13 & 7.14\\
$ ^ 3 B _ 2 ( \pi \rightarrow \pi ^ \star ) $ & 4.28 & 4.25 & 4.22 & 4.22 & 4.22\\
$ ^ 3 A _ 1 ( \pi \rightarrow \pi ^ \star ) $ & 5.56 & 5.51 & 5.48 & 5.49 & 5.48\\
$ ^ 3 A _ 2 ( \pi \rightarrow 3 s ) $ & 6.18 & 5.94 & 6.02 & 6.05 & 6.07\\
$ ^ 3 B _ 1 ( \pi \rightarrow 3 p ) $ & 6.69 & 6.51 & 6.59 & 6.61 & 6.63\\
\hline
& \multicolumn { 5} { c} { Pyrrole} \\
\hline
$ ^ 1 A _ 2 ( \pi \rightarrow 3 s ) $ & 5.25 & 5.15 & 5.24 & 5.27 & \hl { XXX} \\
$ ^ 1 B _ 1 ( \pi \rightarrow 3 p ) $ & 5.99 & 5.89 & 5.98 & 6.01 & 6.02 \\
$ ^ 1 A _ 2 ( \pi \rightarrow 3 p ) $ & 6.27 & 5.94 & 6.01 & 6.03 & \hl { XXX} \\
$ ^ 1 B _ 2 ( \pi \rightarrow \pi ^ \star ) $ & 6.33 & 6.28 & 6.25 & 6.22 & 6.23 \\
$ ^ 1 A _ 1 ( \pi \rightarrow \pi ^ \star ) $ & 6.43 & 6.35 & 6.32 & 6.31 & 6.31 \\
$ ^ 1 B _ 2 ( \pi \rightarrow 3 p ) $ & 7.20 & 7.00 & 6.83 & 6.74 & 6.75 \\
$ ^ 3 B _ 2 ( \pi \rightarrow \pi ^ \star ) $ & 4.59 & 4.56 & 4.53 & 4.53 & 4.52 \\
$ ^ 3 A _ 2 ( \pi \rightarrow 3 s ) $ & 5.22 & 5.12 & 5.21 & 5.24 & \hl { XXX} \\
$ ^ 3 A _ 1 ( \pi \rightarrow \pi ^ \star ) $ & 5.54 & 5.49 & 5.46 & 5.47 & 5.46 \\
$ ^ 3 B _ 1 ( \pi \rightarrow 3 p ) $ & 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
$ ^ 1 B _ 2 ( \pi \rightarrow \pi ^ \star ) $ & 5.79 & 5.59 & 5.54 & 5.53 \\
$ ^ 1 A _ 2 ( \pi \rightarrow 3 s ) $ & 6.08 & 5.70 & 5.77 & 5.79 \\
$ ^ 1 B _ 1 ( \pi \rightarrow 3 p ) $ & 6.57 & 6.34 & 6.40 & 6.42 \\
$ ^ 1 A _ 2 ( \pi \rightarrow 3 p ) $ & 6.67 & 6.39 & 6.45 & 6.46 \\
$ ^ 1 B _ 2 ( \pi \rightarrow 3 p ) $ & 7.06 & 6.55 & 6.56 & 6.55 \\
$ ^ 1 A _ 1 ( \pi \rightarrow \pi ^ \star ) $ & 6.67 & 6.59 & 6.57 & 6.57 \\
$ ^ 3 B _ 2 ( \pi \rightarrow \pi ^ \star ) $ & 3.33 & 3.32 & 3.32 & 3.32 \\
$ ^ 3 A _ 1 ( \pi \rightarrow \pi ^ \star ) $ & 5.16 & 5.14 & 5.12 & 5.13 \\
$ ^ 3 A _ 2 ( \pi \rightarrow 3 s ) $ & 6.01 & 5.65 & 5.73 & 5.75 \\
$ ^ 3 B _ 1 ( \pi \rightarrow 3 p ) $ & 6.51 & 6.30 & 6.36 & 6.38 \\
\hline
& \multicolumn { 4} { c} { Imidazole} \\
\hline
$ ^ 1 A'' ( \pi \rightarrow 3 s ) $ & 5.77 & 5.60 & 5.71 & 5.73 \\
$ ^ 1 A' ( \pi \rightarrow \pi ^ \star ) $ & 6.51 & 6.43 & 6.41 & 6.41 \\
$ ^ 1 A'' ( n \rightarrow \pi ^ \star ) $ & 6.66 & 6.42 & 6.50 & 6.53 \\
$ ^ 1 A' ( \pi \rightarrow 3 p ) $ & 7.04 & 6.93 & 6.87 & 6.86 \\
$ ^ 3 A' ( \pi \rightarrow \pi ^ \star ) $ & 4.83 & 4.78 & 4.75 & 4.76 \\
$ ^ 3 A'' ( \pi \rightarrow 3 s ) $ & 5.72 & 5.57 & 5.67 & 5.70 \\
$ ^ 3 A' ( \pi \rightarrow \pi ^ \star ) $ & 5.88 & 5.78 & 5.74 & 5.75 \\
$ ^ 3 A'' ( n \rightarrow \pi ^ \star ) $ & 6.48 & 6.37 & 6.33 & 6.33 \\
\hline
& \multicolumn { 4} { c} { Thiophene} \\
\hline
$ ^ 1 A _ 1 ( \pi \rightarrow \pi ^ \star ) $ & 5.79 & 5.70 & 5.65 & 5.64\\
$ ^ 1 B _ 2 ( \pi \rightarrow \pi ^ \star ) $ & 6.23 & 6.05 & 5.96 & 5.94\\
$ ^ 1 A _ 2 ( \pi \rightarrow 3 s ) $ & 6.26 & 6.07 & 6.14 & 6.16\\
$ ^ 1 B _ 1 ( \pi \rightarrow 3 p ) $ & 6.18 & 6.19 & 6.14 & 6.11\\
$ ^ 1 A _ 2 ( \pi \rightarrow 3 p ) $ & 6.32 & 6.33 & 6.25 & 6.22\\
$ ^ 1 B _ 1 ( \pi \rightarrow 3 s ) $ & 6.62 & 6.42 & 6.50 & 6.53\\
$ ^ 1 B _ 2 ( \pi \rightarrow 3 p ) $ & 7.45 & 7.45 & 7.29 & 7.18\\
$ ^ 1 A _ 1 ( \pi \rightarrow \pi ^ \star ) $ & 7.50 & 7.41 & 7.35 & 7.33\\
$ ^ 3 B _ 2 ( \pi \rightarrow \pi ^ \star ) $ & 3.95 & 3.96 & 3.94 & 3.93\\
$ ^ 3 A _ 1 ( \pi \rightarrow \pi ^ \star ) $ & 4.90 & 4.82 & 4.77 & 4.77\\
$ ^ 3 B _ 1 ( \pi \rightarrow 3 p ) $ & 6.00 & 6.01 & 5.95 & 5.92\\
$ ^ 3 A _ 2 ( \pi \rightarrow 3 s ) $ & 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
$ ^ 1 B _ { 2 u } ( \pi \rightarrow \pi ^ \star ) $ & 5.13 & 5.11 & 5.09 & 5.09\\
$ ^ 1 B _ { 1 u } ( \pi \rightarrow \pi ^ \star ) $ & 6.68 & 6.50 & 6.44 & 6.43\\
$ ^ 1 E _ { 1 g } ( \pi \rightarrow 3 s ) $ & 6.75 & 6.46 & 6.52 & 6.54\\
$ ^ 1 A _ { 2 u } ( \pi \rightarrow 3 p ) $ & 7.24 & 7.02 & 7.08 & 7.10\\
$ ^ 1 E _ { 2 u } ( \pi \rightarrow 3 p ) $ & 7.34 & 7.09 & 7.15 & 7.16\\
$ ^ 3 B _ { 1 u } ( \pi \rightarrow \pi ^ \star ) $ & 4.18 & 4.19 & 4.18 & 4.19\\
$ ^ 3 E _ { 1 u } ( \pi \rightarrow \pi ^ \star ) $ & 4.95 & 4.89 & 4.86 & 4.87\\
$ ^ 3 B _ { 2 u } ( \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
$ ^ 1 B _ { 3 u } ( n \rightarrow \pi ^ \star ) $ & 4.28 & 4.19 & 4.14 & 4.14\\
$ ^ 1 A _ { u } ( n \rightarrow \pi ^ \star ) $ & 5.08 & 4.98 & 4.97 & 4.98\\
$ ^ 1 B _ { 2 u } ( \pi \rightarrow \pi ^ \star ) $ & 5.10 & 5.07 & 5.03 & 5.02\\
$ ^ 1 B _ { 2 g } ( n \rightarrow \pi ^ \star ) $ & 5.86 & 5.78 & 5.71 & 5.71\\
$ ^ 1 A _ { g } ( n \rightarrow 3 s ) $ & 6.74 & 6.54 & 6.66 & 6.70& 6.71\\
$ ^ 1 B _ { 1 g } ( n \rightarrow \pi ^ \star ) $ & 6.87 & 6.75 & 6.73 & 6.73\\
$ ^ 1 B _ { 1 u } ( \pi \rightarrow \pi ^ \star ) $ & 7.10 & 6.92 & 6.86 & 6.85& 6.85\\
$ ^ 1 B _ { 1 g } ( n \rightarrow 3 p ) $ & 7.36 & 7.13 & 7.20 & 7.23\\
$ ^ 1 B _ { 2 u } ( n \rightarrow 3 p ) $ & 7.39 & 7.14 & 7.25 & 7.29\\
$ ^ 1 B _ { 1 u } ( \pi \rightarrow 3 s ) $ & 7.56 & 7.38 & 7.45 & 7.48& 7.49\\
$ ^ 1 B _ { 1 u } ( \pi \rightarrow \pi ^ \star ) $ & 8.19 & 7.99 & 7.94 & 7.93& 7.93\\
$ ^ 3 B _ { 3 u } ( n \rightarrow \pi ^ \star ) $ & 3.68 & 3.60 & 3.59 & 3.59\\
$ ^ 3 B _ { 1 u } ( \pi \rightarrow \pi ^ \star ) $ & 4.39 & 4.40 & 4.39 & 4.40& 4.39\\
$ ^ 3 B _ { 2 u } ( \pi \rightarrow \pi ^ \star ) $ & 4.56 & 4.46 & 4.40 & 4.40\\
$ ^ 3 A _ { u } ( n \rightarrow \pi ^ \star ) $ & 5.05 & 4.93 & 4.93 & 4.94\\
$ ^ 3 B _ { 2 g } ( n \rightarrow \pi ^ \star ) $ & 5.18 & 5.11 & 5.08 & 5.09\\
$ ^ 3 B _ { 1 u } ( \pi \rightarrow \pi ^ \star ) $ & 5.38 & 5.32 & 5.29 & 5.29& 5.28\\
\hline
& \multicolumn { 5} { c} { Tetrazine} \\
\hline
$ ^ 1 B _ { 3 u } ( n \rightarrow \pi ^ \star ) $ & 2.53 & 2.49 & 2.46 & 2.45 & 2.45\\
$ ^ 1 A _ { u } ( n \rightarrow \pi ^ \star ) $ & 3.75 & 3.69 & 3.67 & 3.68 & 3.67\\
$ ^ 1 A _ { g } ( n,n \rightarrow \pi ^ \star , \pi ^ \star ) $ & 6.22 & 6.22 & 6.21 & 6.19 & 6.17\\
$ ^ 1 B _ { 1 g } ( n \rightarrow \pi ^ \star ) $ & 5.01 & 4.97 & 4.91 & 4.90 & 4.88\\
$ ^ 1 B _ { 2 u } ( \pi \rightarrow \pi ^ \star ) $ & 5.29 & 5.27 & 5.23 & 5.22 & 5.21\\
$ ^ 1 B _ { 2 g } ( n \rightarrow \pi ^ \star ) $ & 5.56 & 5.53 & 5.46 & 5.46 & 5.45\\
$ ^ 1 A _ { u } ( n \rightarrow \pi ^ \star ) $ & 5.61 & 5.59 & 5.52 & 5.52 & 5.50\\
$ ^ 1 B _ { 3 g } ( n,n \rightarrow \pi ^ \star , \pi ^ \star ) $ & 7.64 & 7.62 & 7.62 & 7.60 & 7.58\\
$ ^ 1 B _ { 2 g } ( n \rightarrow \pi ^ \star ) $ & 6.24 & 6.17 & 6.13 & 6.13 & 6.10\\
$ ^ 1 B _ { 1 g } ( n \rightarrow \pi ^ \star ) $ & 7.04 & 6.98 & 6.92 & 6.92 & 6.91\\
$ ^ 3 B _ { 3 u } ( n \rightarrow \pi ^ \star ) $ & 1.87 & 1.86 & 1.85 & 1.86 & 1.85\\
$ ^ 3 A _ { u } ( n \rightarrow \pi ^ \star ) $ & 3.48 & 3.43 & 3.44 & 3.45 & 3.43\\
$ ^ 3 B _ { 1 g } ( n \rightarrow \pi ^ \star ) $ & 4.25 & 4.23 & 4.20 & 4.21 & 4.18\\
$ ^ 3 B _ { 1 u } ( \pi \rightarrow \pi ^ \star ) $ & 4.54 & 4.54 & 4.54 & 4.54 & 4.53\\
$ ^ 3 B _ { 2 u } ( \pi \rightarrow \pi ^ \star ) $ & 4.65 & 4.58 & 4.52 & 4.52 & 4.51\\
$ ^ 3 B _ { 2 g } ( n \rightarrow \pi ^ \star ) $ & 5.11 & 5.09 & 5.05 & 5.05 & 5.04\\
$ ^ 3 A _ { u } ( n \rightarrow \pi ^ \star ) $ & 5.17 & 5.15 & 5.11 & 5.11 & 5.10\\
$ ^ 3 B _ { 3 g } ( n,n \rightarrow \pi ^ \star , \pi ^ \star ) $ & 7.35 & 7.33 & 7.35 & 7.34 & 7.32\\
$ ^ 3 B _ { 1 u } ( \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
$ ^ 1 B _ 1 ( n \rightarrow \pi ^ \star ) $ & 3.95 & 3.86 & 3.83 & \\
$ ^ 1 A _ 2 ( n \rightarrow \pi ^ \star ) $ & 4.49 & 4.39 & 4.37 & \\
$ ^ 1 A _ 1 ( \pi \rightarrow \pi ^ \star ) $ & 5.36 & 5.33 & 5.29 & 5.29\\
$ ^ 1 A _ 2 ( n \rightarrow \pi ^ \star ) $ & 5.88 & 5.80 & 5.74 & \\
$ ^ 1 B _ 2 ( n \rightarrow 3 s ) $ & 6.26 & 6.06 & 6.17 & \\
$ ^ 1 B _ 1 ( n \rightarrow \pi ^ \star ) $ & 6.51 & 6.41 & 6.37 & \\
$ ^ 1 B _ 2 ( \pi \rightarrow \pi ^ \star ) $ & 6.96 & 6.79 & 6.74 & \\
$ ^ 3 B _ 1 ( n \rightarrow \pi ^ \star ) $ & 3.27 & 3.20 & 3.19 & 3.20\\
$ ^ 3 A _ 2 ( n \rightarrow \pi ^ \star ) $ & 4.19 & 4.11 & 4.11 & \\
$ ^ 3 B _ 2 ( \pi \rightarrow \pi ^ \star ) $ & 4.39 & 4.39 & 4.38 & \\
$ ^ 3 A _ 1 ( \pi \rightarrow \pi ^ \star ) $ & 4.93 & 4.87 & 4.83 & 4.82\\
\hline
& \multicolumn { 4} { c} { Pyridine} \\
\hline
$ ^ 1 B _ 1 ( n \rightarrow \pi ^ \star ) $ & 5.12 & 5.01 & 4.96\\
$ ^ 1 B _ 2 ( \pi \rightarrow \pi ^ \star ) $ & 5.23 & 5.21 & 5.17\\
$ ^ 1 A _ 2 ( n \rightarrow \pi ^ \star ) $ & 5.55 & 5.41 & 5.40\\
$ ^ 1 A _ 1 ( \pi \rightarrow \pi ^ \star ) $ & 6.84 & 6.64 & 6.63\\
$ ^ 1 A _ 1 ( n \rightarrow 3 s ) $ & 6.92 & 6.71 & 6.76\\
$ ^ 1 A _ 2 ( \pi \rightarrow 3 s ) $ & 6.98 & 6.74 & 6.81\\
$ ^ 1 B _ 2 ( \pi \rightarrow \pi ^ \star ) $ & 7.50 & 7.40 & 7.35/7.38\\
$ ^ 1 B _ 1 ( \pi \rightarrow 3 p ) $ & 7.54 & 7.32 & 7.38\\
$ ^ 1 A _ 1 ( \pi \rightarrow \pi ^ \star ) $ & 7.56 & 7.34 & 7.39\\
$ ^ 3 A _ 1 ( \pi \rightarrow \pi ^ \star ) $ & 4.33 & 4.34 & 4.33\\
$ ^ 3 B _ 1 ( n \rightarrow \pi ^ \star ) $ & 4.57 & 4.47 & 4.46& 4.47\\
$ ^ 3 B _ 2 ( \pi \rightarrow \pi ^ \star ) $ & 4.92 & 4.83 & 4.79\\
$ ^ 3 A _ 1 ( \pi \rightarrow \pi ^ \star ) $ & 5.14 & 5.08 & 5.05\\
$ ^ 3 A _ 2 ( n \rightarrow \pi ^ \star ) $ & 5.51 & 5.37 & 5.35\\
$ ^ 3 B _ 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
$ ^ 1 B _ 1 ( n \rightarrow \pi ^ \star ) $ & 4.58 & 4.48 & 4.44 & \\
$ ^ 1 A _ 2 ( n \rightarrow \pi ^ \star ) $ & 4.99 & 4.89 & 4.86 & \\
$ ^ 1 B _ 2 ( \pi \rightarrow \pi ^ \star ) $ & 5.47 & 5.44 & 5.41 & \\
$ ^ 1 A _ 2 ( n \rightarrow \pi ^ \star ) $ & 6.07 & 5.98 & 5.93 & \\
$ ^ 1 B _ 1 ( n \rightarrow \pi ^ \star ) $ & 6.39 & 6.29 & 6.26 & \\
$ ^ 1 B _ 2 ( n \rightarrow 3 s ) $ & 6.81 & 6.61 & 6.72 & 6.76\\
$ ^ 1 A _ 1 ( \pi \rightarrow \pi ^ \star ) $ & 7.08 & 6.93 & 6.87 & 6.86\\
$ ^ 3 B _ 1 ( n \rightarrow \pi ^ \star ) $ & 4.20 & 4.12 & 4.10 & 4.11\\
$ ^ 3 A _ 1 ( \pi \rightarrow \pi ^ \star ) $ & 4.55 & 4.56 & 4.55 & 4.56\\
$ ^ 3 A _ 2 ( n \rightarrow \pi ^ \star ) $ & 4.77 & 4.67 & 4.66 & 4.67\\
$ ^ 3 B _ 2 ( \pi \rightarrow \pi ^ \star ) $ & 5.08 & 5.00 & 4.96 & 4.96\\
\hline
& \multicolumn { 4} { c} { Triazine} \\
\hline
$ ^ 1 A _ 1 '' ( n \rightarrow \pi ^ \star ) $ & 4.85 & 4.76 & 4.73 & 4.74\\
$ ^ 1 A _ 2 '' ( n \rightarrow \pi ^ \star ) $ & 4.84 & 4.78 & 4.74 & 4.74\\
$ ^ 1 E'' ( n \rightarrow \pi ^ \star ) $ & 4.89 & 4.82 & 4.78 & 4.79\\
$ ^ 1 A _ 2 ' ( \pi \rightarrow \pi ^ \star ) $ & 5.84 & 5.81 & 5.78 & 5.78\\
$ ^ 1 A _ 1 ' ( \pi \rightarrow \pi ^ \star ) $ & 7.45 & 7.31 & 7.24 & 7.23\\
$ ^ 1 E' ( n \rightarrow 3 s ) $ & 7.44 & 7.24 & 7.35 & 7.39\\
$ ^ 1 E'' ( n \rightarrow \pi ^ \star ) $ & 7.89 & 7.82 & 7.79 & 7.78\\
$ ^ 1 E' ( \pi \rightarrow \pi ^ \star ) $ & 8.12 & 7.97 & 7.92 & 7.92\\
$ ^ 3 A _ 2 '' ( n \rightarrow \pi ^ \star ) $ & 4.40 & 4.35 & 4.33 & 4.34\\
$ ^ 3 E'' ( n \rightarrow \pi ^ \star ) $ & 4.59 & 4.52 & 4.51 & 4.51\\
$ ^ 3 A _ 1 '' ( n \rightarrow \pi ^ \star ) $ & 4.87 & 4.78 & 4.75 & 4.76\\
$ ^ 3 A _ 1 ' ( \pi \rightarrow \pi ^ \star ) $ & 4.88 & 4.88 & 4.88 & 4.89\\
$ ^ 3 E' ( \pi \rightarrow \pi ^ \star ) $ & 5.70 & 5.64 & 5.61 & 5.61\\
$ ^ 3 A _ 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 & $ ^ 1 A _ 2 ( \Val ; n \ra \pis ) $ & $ 26 \, 526 \, 782 $ & $ 4 . 55 $ & $ 4 . 60 \pm 0 . 05 $ \\
% & $^1B_2 (\Ryd; n \ra 3s)$ & $25\,1675\,94$ & $6.91$ & $6.83\pm0.08$ \\ %TO BE CHECKED !!!!!
% & $^1A_2 (\Ryd; n \ra 3p)$ & $$ & $$ & $$ \\
% & $^1A_1 (\Ryd; n \ra 3p)$ & $$ & $$ & $$ \\
% & $^1B_2 (\Ryd; n \ra 3p)$ & $$ & $$ & $$ \\
& $ ^ 3 A _ 2 ( \Val ; n \ra \pis ) $ & $ 26 \, 553 \, 941 $ & $ 4 . 22 $ & $ 4 . 18 \pm 0 . 04 $ \\
% & $^3A_1 (\Val; \pi \ra \pis)$ & $$ & $$ & $$ \\
Acrolein & $ ^ 1 A'' ( \Val ; n \ra \pis ) $ & $ 23 \, 273 \, 572 $ & $ 3 . 84 $ & $ 3 . 85 \pm 0 . 01 $ \\
% & $^1A' (\Val; \pi \ra \pis)$ & $$ & $$ & $$ \\
% & $^1A'' (\Val; n \ra \pis)$ & $$ & $$ & $$ \\
% & $^1A' (\Ryd; n \ra 3s)$ & $$ & $$ & $$ \\
& $ ^ 3 A'' ( \Val ; n \ra \pis ) $ & $ 26 \, 531 \, 491 $ & $ 3 . 59 $ & $ 3 . 60 \pm 0 . 01 $
& $ 15 \, 827 \, 189 $ & $ 3 . 58 $ & $ 3 . 51 \pm 0 . 07 $ \\
& $ ^ 3 A' ( \Val ; \pi \ra \pis ) $ & $ 37 \, 480 \, 261 $ & $ 4 . 01 $ & $ 3 . 98 \pm 0 . 03 $
& $ 15 \, 827 \, 189 $ & $ 4 . 05 $ & $ 3 . 96 \pm 0 . 09 $ \\
% & $^3A' (\Val; \pi \ra \pis)$ & $$ & $$ & $$ \\
% & $^3A'' (\Ryd; \pi \ra 3s)$ & $$ & $$ & $$ \\
Butadiene & $ ^ 1 B _ u ( \Val ; \pi \ra \pis ) $ & $ 20 \, 552 \, 493 $ & $ 6 . 43 $ & $ 6 . 41 \pm 0 . 02 $ \\
% & $^1B_g (\Ryd; \pi \ra 3s)$ & $$ & $$ & $$ \\
% & $^1A_g (\Val; \pi \ra \pis)$ & $92\,506\,300$ & $6.59$ & $6.55\pm0.04$
% & $59\,594\,588$ & $6.58$ & $6.51\pm0.07$ \\
% & $^1A_u (\Ryd; \pi \ra 3p)$ & $$ & $$ & $$ \\
& $ ^ 1 A _ u ( \Ryd ; \pi \ra 3 p ) $ & $ 20 \, 552 \, 493 $ & $ 6 . 96 $ & $ 6 . 95 \pm 0 . 01 $
& $ 12 \, 521 \, 242 $ & $ 6 . 72 $ & $ 6 . 72 \pm 0 . 00 $ \\
% & $^1B_u (\Ryd; \pi \ra 3p)$ & $$ & $$ & $$ \\
& $ ^ 3 B _ u ( \Val ; \pi \ra \pis ) $ & $ 49 \, 847 \, 526 $ & $ 3 . 40 $ & $ 3 . 37 \pm 0 . 03 $ \\
& $ ^ 3 A _ g ( \Val ; \pi \ra \pis ) $ & & &
& $ 17 \, 235 \, 280 $ & $ 6 . 29 $ & $ 6 . 21 \pm 0 . 08 $ \\
& $ ^ 3 B _ g ( \Val ; \pi \ra 3 s ) $ & $ 49 \, 847 \, 526 $ & $ 6 . 43 $ & $ 6 . 40 \pm 0 . 03 $ \\
Cyanoacetylene & $ ^ 1 \Sigma ^ - ( \Val ; \pi \ra \pis ) $ & $ 21 \, 269 \, 249 $ & $ 6 . 01 $ & $ 6 . 02 \pm 0 . 01 $
& $ 11 \, 023 \, 351 $ & $ 5 . 93 $ & $ 5 . 84 \pm 0 . 09 $ \\
& $ ^ 1 \Delta ( \Val ; \pi \ra \pis ) $ & $ 21 \, 269 \, 249 $ & $ 6 . 29 $ & $ 6 . 28 \pm 0 . 01 $
& $ 11 \, 023 \, 351 $ & $ 6 . 19 $ & $ 6 . 14 \pm 0 . 05 $ \\
& $ ^ 3 \Sigma ^ + ( \Val ; \pi \ra \pis ) $ & $ 18 \, 198 \, 954 $ & $ 4 . 48 $ & $ 4 . 45 \pm 0 . 03 $
& $ 25 \, 646 \, 703 $ & $ 4 . 47 $ & $ 4 . 41 \pm 0 . 06 $ \\
& $ ^ 3 \Delta ( \Val ; \pi \ra \pis ) $ & $ 18 \, 198 \, 954 $ & $ 5 . 35 $ & $ 5 . 32 \pm 0 . 03 $
& $ 25 \, 646 \, 703 $ & $ 5 . 28 $ & $ 5 . 20 \pm 0 . 08 $ \\
& $ ^ 1 A'' [ \Fl ] ( \Val ; \pi \ra \pis ) $ & $ 104 \, 485 \, 975 $ & $ 3 . 70 $ & $ 3 . 67 \pm 0 . 03 $
& $ 62 \, 248 \, 690 $ & $ 3 . 61 $ & $ 3 . 50 \pm 0 . 02 $ \\
Cyanoformaldehyde & $ ^ 1 A'' ( \Val ; n \ra \pis ) $ & $ 17 \, 778 \, 047 $ & $ 3 . 94 $ & $ 3 . 92 \pm 0 . 02 $
& $ 19 \, 020 \, 785 $ & $ 3 . 93 $ & $ 3 . 98 \pm 0 . 05 $ \\
& $ ^ 1 A'' ( \Val ; \pi \ra \pis ) $ & $ 17 \, 778 \, 047 $ & $ 6 . 67 $ & $ 6 . 60 \pm 0 . 07 $
& $ 19 \, 020 \, 785 $ & $ 6 . 57 $ & $ 6 . 58 \pm 0 . 01 $ \\
& $ ^ 3 A'' ( \Val ; n \ra \pis ) $ & $ 21 \, 011 \, 221 $ & $ 3 . 54 $ & $ 3 . 48 \pm 0 . 06 $
& $ 48 \, 532 \, 729 $ & $ 3 . 51 $ & $ 3 . 52 \pm 0 . 01 $ \\
& $ ^ 3 A' ( \Val ; \pi \ra \pis ) $ & & &
& $ 48 \, 5327 \, 29 $ & $ 5 . 10 $ & $ 5 . 07 \pm 0 . 03 $ \\
Cyanogen & $ ^ 1 \Sigma _ u ^ - ( \Val ; \pi \ra \pis ) $ & $ 12 \, 1991 \, 55 $ & $ 6 . 61 $ & $ 6 . 58 \pm 0 . 03 $
& $ 20 \, 9495 \, 13 $ & $ 6 . 52 $ & $ 6 . 44 \pm 0 . 08 $ \\
& $ ^ 1 \Delta _ u ( \Val ; \pi \ra \pis ) $ & $ 12 \, 1991 \, 55 $ & $ 6 . 89 $ & $ 6 . 87 \pm 0 . 02 $
& $ 20 \, 9495 \, 13 $ & $ 6 . 78 $ & $ 6 . 74 \pm 0 . 04 $ \\
& $ ^ 3 \Sigma _ u ^ + ( \Val ; \pi \ra \pis ) $ & $ 34 \, 1277 \, 36 $ & $ 4 . 97 $ & $ 4 . 91 \pm 0 . 06 $
& $ 25 \, 7606 \, 68 $ & $ 4 . 94 $ & $ 4 . 87 \pm 0 . 07 $ \\
& $ ^ 1 \Sigma _ u ^ - [ \Fl ] ( \Val ; \pi \ra \pis ) $ & $ 21 \, 4163 \, 04 $ & $ 5 . 36 $ & $ 5 . 31 \pm 0 . 05 $
& $ 28 \, 8841 \, 38 $ & $ 5 . 17 $ & $ 5 . 26 \pm 0 . 09 $ \\
Cyclopropenone & $ ^ 1 B _ 1 ( \Val ; n \ra \pis ) $ & $ 48 \, 8976 \, 96 $ & $ 4 . 40 $ & $ 4 . 38 \pm 0 . 02 $ \\
& $ ^ 1 A _ 2 ( \Val ; n \ra \pis ) $ & $ 24 \, 5411 \, 16 $ & $ 5 . 70 $ & $ 5 . 64 \pm 0 . 06 $ \\
% & $^1B_2 (\Ryd; n \ra 3s)$ & $$ & $$ & $$ \\
% & $^1B_2 (\Val; \pi \ra \pis$) & $$ & $$ & $$ \\
% & $^1B_2 (\Ryd; n \ra 3p)$ & $$ & $$ & $$ \\
% & $^1A_1 (\Ryd; n \ra 3p)$ & $$ & $$ & $$ \\
% & $^1A_1 (\Val; \pi \ra \pis)$ & $$ & $$ & $$ \\
& $ ^ 3 B _ 1 ( \Val ; n \ra \pis ) $ & $ 24 \, 008 \, 328 $ & $ 4 . 07 $ & $ 4 . 00 \pm 0 . 07 $ \\
& $ ^ 3 B _ 2 ( \Val ; \pi \ra \pis ) $ & $ 48 \, 311 \, 362 $ & $ 4 . 95 $ & $ 4 . 95 \pm 0 . 00 $ \\
% & $^3A_2 (\Val; n \ra \pis)$ & $$ & $$ & $$ \\
% & $^3A_1 (\Val; \pi \ra \pis)$ & $$ & $$ & $$ \\
Cyclopropenethione & $ ^ 1 A _ 2 ( \Val ; n \ra \pis ) $ & $ 39 \, 385 \, 657 $ & $ 3 . 46 $ & $ 3 . 45 \pm 0 . 01 $ \\
& $ ^ 1 B _ 1 ( \Val ; n \ra \pis ) $ & $ 39 \, 385 \, 657 $ & $ 3 . 50 $ & $ 3 . 44 \pm 0 . 05 $ \\
& $ ^ 1 B _ 2 ( \Val ; \pi \ra \pis ) $ & $ 39 \, 385 \, 657 $ & $ 4 . 68 $ & $ 4 . 59 \pm 0 . 09 $ \\
% & $^1B_2 (\Ryd; n \ra 3s)$ & $$ & $$ & $$ \\
% & $^1A_1 (\Val; \pi \ra \pis)$ & $$ & $$ & $$ \\
% & $^1B_2 (\Ryd; n \ra 3p)$ & $$ & $$ & $$ \\
& $ ^ 3 A _ 2 ( \Val ; n \ra \pis ) $ & $ 23 \, 904 \, 962 $ & $ 3 . 32 $ & $ 3 . 29 \pm 0 . 03 $ \\
% & $^3B_1 (\Val; n \ra \pis)$ & $$ & $$ & $$ \\
& $ ^ 3 B _ 2 ( \Val ; \pi \ra \pis ) $ & $ 23 \, 904 \, 962 $ & $ 4 . 06 $ & $ 4 . 03 \pm 0 . 03 $ \\
% & $^3A_1 (\Val; \pi \ra \pis)$ & $$ & $$ & $$ \\
Diacetylene & $ ^ 1 \Sigma _ u ^ - ( \Val ; \pi \ra \pis ) $ & $ 18 \, 955 \, 451 $ & $ 5 . 58 $ & $ 5 . 52 \pm 0 . 06 $
& $ 19 \, 192 \, 556 $ & $ 5 . 45 $ & $ 5 . 47 \pm 0 . 02 $ \\
& $ ^ 1 \Delta _ u ( \Val ; \pi \ra \pis ) $ & $ 18 \, 955 \, 451 $ & $ 5 . 85 $ & $ 5 . 84 \pm 0 . 01 $
& $ 19 \, 192 \, 556 $ & $ 5 . 45 $ & $ 5 . 69 \pm 0 . 02 $ \\
& $ ^ 3 \Sigma _ u ^ + ( \Val ; \pi \ra \pis ) $ & $ 13 \, 777 \, 757 $ & $ 4 . 11 $ & $ 4 . 04 \pm 0 . 07 $
& $ 26 \, 668 \, 471 $ & $ 4 . 11 $ & $ 4 . 07 \pm 0 . 04 $ \\
& $ ^ 3 \Delta _ u ( \Val ; \pi \ra \pis ) $ & $ 13 \, 777 \, 757 $ & $ 4 . 93 $ & $ 4 . 94 \pm 0 . 01 $
& $ 26 \, 668 \, 471 $ & $ 4 . 87 $ & $ 4 . 85 \pm 0 . 02 $ \\
Glyoxal & $ ^ 1 A _ u ( \Val ; n \ra \pis ) $ & $ 51 \, 656 \, 090 $ & $ 2 . 96 $ & $ 2 . 93 \pm 0 . 03 $
& $ 34 \, 125 \, 394 $ & $ 2 . 94 $ & $ 2 . 93 \pm 0 . 01 $ \\
& $ ^ 1 B _ g ( \Val ; n \ra \pis ) $ & $ 24 \, 394 \, 242 $ & $ 4 . 34 $ & $ 4 . 28 \pm 0 . 06 $ \\
% & $^1A_g (\Val; n,n \ra \pis,\pis)$ & $118\,275\,835$ & $5.69$ & $5.60\pm0.09$ \\
% & $^1B_g (\Val; n \ra \pis)$ & $$ & $$ & $$ \\
% & $^1B_u (\Ryd; n \ra 3p)$ & $$ & $$ & $$ \\
& $ ^ 3 A _ u ( \Val ; n \ra \pis ) $ & $ 47 \, 693 \, 908 $ & $ 2 . 58 $ & $ 2 . 54 \pm 0 . 04 $ \\
% & $^3B_g (\Val; n \ra \pis)$ & $$ & $$ & $$ \\
% & $^3B_u (\Val; \pi \ra \pis)$ & $$ & $$ & $$ \\
% & $^3A_g (\Val; \pi \ra \pis)$ & $$ & $$ & $$ \\
Isobutene & $ ^ 1 B _ 1 ( \Ryd ; \pi \ra 3 s ) $ & $ 28 \, 095 \, 377 $ & $ 6 . 86 $ & $ 6 . 78 \pm 0 . 08 $ \\
& $ ^ 1 A _ 1 ( \Ryd ; \pi \ra 3 p ) $ & $ 59 \, 728 \, 169 $ & $ 7 . 22 $ & $ 7 . 16 \pm 0 . 02 $ \\
& $ ^ 3 A _ 1 \Val ; ( \pi \ra \pis ) $ & $ 32 \, 440 \, 621 $ & $ 4 . 54 $ & $ 4 . 56 \pm 0 . 02 $ \\
Methylenecyclopropene & $ ^ 1 B _ 2 ( \Val ; \pi \ra \pis ) $ & $ 51 \, 918 \, 524 $ & $ 4 . 35 $ & $ 4 . 32 \pm 0 . 03 $ \\
% & $^1B_1 (\Ryd; \pi \ra \sigma^\star)$ & $$ & $$ & $$ \\
& $ ^ 1 A _ 2 ( \Ryd ; \pi \ra 3 p ) $ & $ 25 \, 146 \, 911 $ & $ 6 . 02 $ & $ 5 . 92 \pm 0 . 10 $ \\
& $ ^ 1 A _ 1 ( \Val ; \pi \ra \pis ) $ & $ 31 \, 721 \, 213 $ & $ 6 . 21 $ & $ 6 . 20 \pm 0 . 01 $ \\
& $ ^ 3 B _ 2 ( \Val ; \pi \ra \pis ) $ & $ 24 \, 379 \, 551 $ & $ 3 . 50 $ & $ 3 . 44 \pm 0 . 06 $
& $ 43 \, 090 \, 114 $ & $ 3 . 49 $ & $ 3 . 45 \pm 0 . 04 $ \\
& $ ^ 3 A _ 1 ( \Val ; \pi \ra \pis ) $ & $ 24 \, 379 \, 551 $ & $ 4 . 77 $ & $ 4 . 67 \pm 0 . 10 $
& $ 43 \, 090 \, 114 $ & $ 4 . 77 $ & $ 4 . 79 \pm 0 . 02 $ \\
Propynal & $ ^ 1 A'' ( \Val ; n \ra \pis ) $ & $ 48 \, 945 \, 252 $ & $ 3 . 90 $ & $ 3 . 84 \pm 0 . 06 $
& $ 28 \, 249 \, 344 $ & $ 3 . 92 $ & $ 3 . 89 \pm 0 . 03 $ \\
& $ ^ 1 A'' ( \Val ; \pi \ra \pis ) $ & $ 26 \, 554 \, 616 $ & $ 5 . 72 $ & $ 5 . 64 \pm 0 . 08 $
& $ 28 \, 249 \, 344 $ & $ 5 . 72 $ & $ 5 . 63 \pm 0 . 09 $ \\
& $ ^ 3 A'' ( \Val ; n \ra \pis ) $ & $ 23 \, 182 \, 284 $ & $ 3 . 58 $ & $ 3 . 54 \pm 0 . 04 $ \\
& $ ^ 3 A' ( \Val ; \pi \ra \pis ) $ & $ 39 \, 375 \, 360 $ & $ 4 . 52 $ & $ 4 . 44 \pm 0 . 08 $ \\
Thioacetone & $ ^ 1 A _ 2 ( \Val ; n \ra \pis ) $ & $ 26 \, 515 \, 070 $ & $ 2 . 56 $ & $ 2 . 61 \pm 0 . 05 $ \\
% & $^1B_2 (\Ryd; n \ra 4s)$ & $??$ & $??$ & $5.60\pm0.04$ \\
% & $^1A_1 (\Val; \pi \ra \pis)$ & $$ & $$ & $$ \\
% & $^1A_1 (\Ryd; n \ra 4p)$ & $$ & $$ & $$ \\
% & $^1B_2 (\Ryd; n \ra 4p)$ & $$ & $$ & $$ \\
& $ ^ 3 A _ 2 ( \Val ; n \ra \pis ) $ & $ 63 \, 669 \, 401 $ & $ 2 . 36 $ & $ 2 . 36 \pm 0 . 00 $ \\
% & $^3A_1 (\Val; \pi \ra \pis)$ & $$ & $$ & $$ \\
Thiopropynal & $ ^ 1 A'' ( \Val ; n \ra \pis ) $ & $ 15 \, 782 \, 429 $ & $ 2 . 07 $ & $ 2 . 08 \pm 0 . 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}
