From 431f8c92b575f6094b0561c2746310d00c71f546 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Mon, 30 Nov 2020 10:41:01 +0100 Subject: [PATCH] arXiv --- arXiv/AScemama.jpg | Bin 0 -> 647666 bytes arXiv/DJacquemin.jpg | Bin 0 -> 255385 bytes arXiv/FLipparini.png | Bin 0 -> 213542 bytes arXiv/MBoggioPasqua.jpg | Bin 0 -> 1786554 bytes arXiv/MCaffarel.jpeg | Bin 0 -> 140604 bytes arXiv/MVeril.jpg | Bin 0 -> 948914 bytes arXiv/PFLoos.png | Bin 0 -> 1141815 bytes arXiv/QUEST_WIREs.tex | 1407 +++++++++++++++++++++++++ arXiv/TOC.png | Bin 0 -> 2068111 bytes arXiv/fig1.pdf | Bin 0 -> 35598 bytes arXiv/fig2.pdf | Bin 0 -> 5422 bytes arXiv/fig3.pdf | Bin 0 -> 135869 bytes arXiv/fig4.pdf | Bin 0 -> 56351 bytes arXiv/fig5.pdf | Bin 0 -> 131987 bytes arXiv/vancouver-authoryear.bst | 1812 ++++++++++++++++++++++++++++++++ arXiv/wiley-article.cls | 670 ++++++++++++ 16 files changed, 3889 insertions(+) create mode 100644 arXiv/AScemama.jpg create mode 100644 arXiv/DJacquemin.jpg create mode 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z+uzeS;#=R~k6HU1DBWcT->Nx()Ua2Cb;?TGvK*w`wCt6r@-DsA@vSUsq@RSHxb41lw1lW( z_Z@dH6p^9K{}@eEv-PPRJM>eCSM|`=U6&_!i?%4M zV5p-j&mi$~uW@0jxX_IIF{%$#R&8`oH)*4O^|54dIDzm_9in@pjDL@dr~g10)!sDZ zvkE>{IKS194@Bql41K#&zLqslAb6`%?j$k=xp}}59#ZK^z%&f*nQPHuj(R>!T>WfA zKF6@1Wyt3n_>99JJb~D!5IOAWLf>jNuJAKyqSiCxm958S&YZ3%2$ computed transition energies are considered. $M$ is chosen such that $P(\mathcal{G})>0.8$ and such that the error bar is minimal. +If all the values of $P(\mathcal{G})$ are below $0.8$, $M$ is chosen such that $P(\mathcal{G})$ is maximal. +A Python code associated with this procedure is provided in the {\SupInf}. + +The singlet and triplet FCI/6-31+G(d) excitation energies and their corresponding error bars estimated with the method presented above based on Gaussian random variables are reported in Table \ref{tab:cycles}. +For the sake of comparison, we also report the CC3 and CCSDT vertical energies from Ref.~\cite{Loos_2020b} computed in the same basis. We note that there is for the vast majority of considered +states a very good agreement between the CC3 and CCSDT values, indicating that the CC values can be trusted. +The estimated values of the excitation energies obtained via a three-point linear extrapolation considering the three largest CIPSI wave functions are also gathered in Table \ref{tab:cycles}. +In this case, the error bar is estimated via the extrapolation distance, \ie, the difference in excitation energies obtained with the three-point linear extrapolation and the largest CIPSI wave function. +This strategy has been considered in some of our previous works \cite{Loos_2020b,Loos_2020c,Loos_2020e}. +The deviation from the CCSDT excitation energies for the same set of excitations are depicted in Fig.~\ref{fig:errors}, where the red dots correspond to the excitation energies and error bars estimated via the present method, and the blue dots correspond to the excitation energies obtained via a three-point linear fit and error bars estimated via the extrapolation distance. +These results contain a good balance between well-behaved and ill-behaved cases. +For example, cyclopentadiene and furan correspond to well-behaved scenarios where the two flavors of extrapolations yield nearly identical estimates and the error bars associated with these two methods nicely overlap. +In these cases, one can observe that our method based on Gaussian random variables provides almost systematically smaller error bars. +Even in less idealistic situations (like in imidazole, pyrrole, and thiophene), the results are very satisfactory and stable. +The six-membered rings represent much more challenging cases for SCI methods, and even for these systems the newly-developed method provides realistic error bars, and allows to easily detect problematic events (like pyridine for instance). +The present scheme has also been tested on smaller systems when one can tightly converge the CIPSI calculations. +In such cases, the agreement is nearly perfect in every scenario that we have encountered. +A selection of these results can be found in the {\SupInf}. + +%%% TABLE I %%% +\begin{table} +\centering +\caption{Singlet and triplet excitation energies (in eV) obtained at the CC3, CCSDT, and CIPSI levels of theory with the 6-31+G(d) basis set for various five- and six-membered rings.} +\label{tab:cycles} +\begin{threeparttable} +\begin{tabular}{lccccc} +\headrow +\thead{Molecule} & \thead{Transition} & \thead{CC3} & \thead{CCSDT} & \thead{CIPSI (Gaussian)$^a$} & \thead{CIPSI (3-point)$^b$}\\ + \mc{6}{c}{Five-membered rings} \\ +Cyclopentadiene & $^1 B_2 (\pi \ra \pis)$ & 5.79 & 5.80 & 5.80(2) & 5.79(2) \\ + & $^3 B_2 (\pi \ra \pis)$ & 3.33 & 3.33 & 3.32(4) & 3.29(7) \\ +Furan & $^1A_2(\pi \ra 3s)$ & 6.26 & 6.28 & 6.31(5) & 6.37(1) \\ + & $^3B_2(\pi \ra \pis)$ & 4.28 & 4.28 & 4.26(4) & 4.22(7) \\ +Imidazole & $^1A''(\pi \ra 3s)$ & 5.77 & 5.77 & 5.78(5) & 5.96(14) \\ + & $^3A'(\pi \ra \pis)$ & 4.83 & 4.81 & 4.82(7) & 4.65(22) \\ +Pyrrole & $^1A_2(\pi \ra 3s)$ & 5.25 & 5.25 & 5.23(7) & 5.31(1) \\ + & $^3B_2(\pi \ra \pis)$ & 4.59 & 4.58 & 4.54(7) & 4.37(23) \\ +Thiophene & $^1A_1(\pi \ra \pis)$ & 5.79 & 5.77 & 5.75(8) & 5.73(9) \\ + & $^3B_2(\pi \ra \pis)$ & 3.95 & 3.94 & 3.98(1) & 3.99(2) \\ + \mc{6}{c}{Six-membered rings} \\ +Benzene & $^1B_{2u}(\pi \ra \pis)$ & 5.13 & 5.10 & 5.06(9) & 5.21(7) \\ + & $^3B_{1u}(\pi \ra \pis)$ & 4.18 & 4.16 & 4.28(6) & 4.17(7) \\ +Cyclopentadienone & $^1A_2(n \ra \pis)$ & 3.03 & 3.03 & 3.08(2) & 3.13(3) \\ + & $^3B_2(\pi \ra \pis)$ & 2.30 & 2.32 & 2.37(5) & 2.10(25) \\ +Pyrazine & $^1B_{3u}(n \ra \pis)$ & 4.28 & 4.28 & 4.26(9) & 4.10(25) \\ + & $^3B_{3u}(n \ra \pis)$ & 3.68 & 3.68 & 3.70(3) & 3.70(1) \\ +Tetrazine & $^1B_{3u}(n \ra \pis)$ & 2.53 & 2.54 & 2.56(5) & 5.07(16) \\ + & $^3B_{3u}(n \ra \pis)$ & 1.87 & 1.88 & 1.91(3) & 4.04(49) \\ +Pyridazine & $^1B_1(n \ra \pis)$ & 3.95 & 3.95 & 3.97(10)& 3.60(43) \\ + & $^3B_1(n \ra \pis)$ & 3.27 & 3.26 & 3.27(15)& 3.46(14) \\ +Pyridine & $^1B_1(n \ra \pis)$ & 5.12 & 5.10 & 5.15(12)& 4.90(24) \\ + & $^3A_1(\pi \ra \pis)$ & 4.33 & 4.31 & 4.42(85)& 3.68(105) \\ +Pyrimidine & $^1B_1(n \ra \pis)$ & 4.58 & 4.57 & 4.64(11)& 2.54(5) \\ + & $^3B_1(n \ra \pis)$ & 4.20 & 4.20 & 4.55(37)& 2.18(27) \\ +Triazine & $^1A_1''(n \ra \pis)$ & 4.85 & 4.84 & 4.77(13)& 5.12(51) \\ + & $^3A_2''(n \ra \pis)$ & 4.40 & 4.40 & 4.45(39)& 4.73(6) \\ +%\hiderowcolors +\hline % Please only put a hline at the end of the table +\end{tabular} +\begin{tablenotes} +\item $^a$ Excitation energies and error bars estimated via the novel statistical method based on Gaussian random variables (see Sec.~\ref{sec:error}). +The error bars reported in parenthesis correspond to one standard deviation. +\item $^b$ Excitation energies obtained via a three-point linear fit using the three largest CIPSI variational wave functions, and error bars estimated via the extrapolation distance, \ie, the difference in excitation energies obtained with the three-point linear extrapolation and the largest CIPSI wave function. +\end{tablenotes} +\end{threeparttable} +\end{table} + +%%% FIGURE 3 %%% +\begin{figure} + \centering + \includegraphics[width=\linewidth]{fig3} + \caption{Deviation from the CCSDT excitation energies for the lowest singlet and triplet excitation energies (in eV) of five- and six-membered rings obtained at the CIPSI/6-31+G(d) level of theory. Red dots: excitation energies and error bars estimated via the present method (see Sec.~\ref{sec:error}). Blue dots: excitation energies obtained via a three-point linear fit using the three largest CIPSI wave functions, and error bars estimated via the extrapolation distance, \ie, the difference in excitation energies obtained with the three-point linear extrapolation and the largest CIPSI wave function.} + \label{fig:errors} +\end{figure} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{The QUEST database} +\label{sec:QUEST} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%======================= +\subsection{Overview} +%======================= +The QUEST database gathers more than 500 highly-accurate excitation energies of various natures (valence, Rydberg, $n \ra \pis$, $\pi \ra \pis$, singlet, doublet, triplet, and double excitations) for molecules ranging +from diatomics to molecules as large as naphthalene (see Fig.~\ref{fig:molecules}). This set is also chemically diverse, with organic and inorganic systems, open- and closed-shell compounds, acyclic and cyclic systems, +pure hydrocarbons and various heteroatomic structures, etc. Each of the five subsets making up the QUEST dataset is detailed below. Throughout the present review, we report several statistical indicators: the mean signed +error (MSE), mean absolute error (MAE), root-mean square error (RMSE), and standard deviation of the errors (SDE), as well as the maximum positive [Max(+)] and maximum negative [Max($-$)] errors. + +%%% FIGURE 4 %%% +\begin{figure} + \centering + \includegraphics[width=\linewidth]{fig4} + \caption{Molecules from each of the five subsets making up the present QUEST dataset of highly-accurate vertical excitation energies: + QUEST\#1 (red), QUEST\#2 (magenta and/or underlined), QUEST\#3 (black), QUEST\#4 (green), and QUEST\#5 (blue).} + \label{fig:molecules} +\end{figure} + +%======================= +\subsection{QUEST\#1} +%======================= +The QUEST\#1 benchmark set \cite{Loos_2018a} consists of 110 vertical excitation energies (as well as oscillator strengths) from 18 molecules with sizes ranging from one to three non-hydrogen atoms +(water, hydrogen sulfide, ammonia, hydrogen chloride, dinitrogen, carbon monoxide, acetylene, ethylene, formaldehyde, methanimine, thioformaldehyde, acetaldehyde, cyclopropene, diazomethane, +formamide, ketene, nitrosomethane, and the smallest streptocyanine). For this set, we provided two sets of TBEs: i) one obtained within the frozen-core approximation and the aug-cc-pVTZ basis set, and ii) +another one including further corrections for basis set incompleteness and ``all electron'' effects. For the former set, we systematically employed FCI/aug-cc-pVTZ values to define our TBEs, except for a few cases. +For the latter set, both the ``all electron'' correlation and the basis set corrections were systematically obtained at the CC3 level of theory and with the d-aug-cc-pV5Z basis for the nine smallest molecules, and +slightly more compact basis sets for the larger compounds. Our TBE/aug-cc-pVTZ reference excitation energies were employed to benchmark a series of popular excited-state wave function methods partially +or fully accounting for double and triple excitations, namely CIS(D), CC2, CCSD, STEOM-CCSD, CCSDR(3), CCSDT-3, CC3, ADC(2), and ADC(3). Our main conclusions were that i) ADC(2) and CC2 show +strong similarities in terms of accuracy, ii) STEOM-CCSD is, on average, as accurate as CCSD, the latter overestimating transition energies, iii) CC3 is extremely accurate (with a mean absolute error of only +$\sim 0.03$ eV) and that although slightly less accurate than CC3, CCSDT-3 could be used as a reliable reference for benchmark studies, and iv) ADC(3) was found to be significantly less accurate than CC3 +by overcorrecting ADC(2) excitation energies. + +%======================= +\subsection{QUEST\#2} +%======================= +The QUEST\#2 benchmark set \cite{Loos_2019} reports reference energies for double excitations. This set gathers 20 vertical transitions from 14 small- and medium-sized molecules (acrolein, benzene, beryllium atom, +butadiene, carbon dimer and trimer, ethylene, formaldehyde, glyoxal, hexatriene, nitrosomethane, nitroxyl, pyrazine, and tetrazine). The TBEs of the QUEST\#2 set are obtained with SCI and/or multiconfigurational +[CASSCF, CASPT2, (X)MS-CASPT2, and NEVPT2] calculations depending on the size of the molecules and the level of theory that we could afford. An important addition to this second study was also the inclusion of +various flavors of multiconfigurational methods (CASSCF, CASPT2, and NEVPT2) in addition to high-order CC methods including, at least, perturbative triples (CC3, CCSDT, CCSDTQ, etc). +Our results demonstrated that the error of CC methods is intimately linked to the amount of double-excitation character in the vertical transition. For ``pure'' double excitations (i.e., for transitions which do not mix with +single excitations), the error in CC3 and CCSDT can easily reach $1$ and $0.5$ eV, respectively, while it goes down to a few tenths of an eV for more common transitions involving a significant amount of single excitations +(such as the well-known $A_g$ transition in butadiene or the $E_{2g}$ excitation in benzene). The quality of the excitation energies obtained with CASPT2 and NEVPT2 was harder to predict as the overall accuracy of +these methods is highly dependent on both the system and the selected active space. Nevertheless, these two methods were found to be more accurate for transitions with a very small percentage of single excitations +(error usually below $0.1$ eV) than for excitations dominated by single excitations where the error is closer to $0.1$--$0.2$ eV. + +%======================= +\subsection{QUEST\#3} +%======================= +The QUEST\#3 benchmark set \cite{Loos_2020b} is, by far, our largest set, and consists of highly accurate vertical transition energies and oscillator strengths obtained for 27 molecules encompassing 4, 5, and +6 non-hydrogen atoms (acetone, acrolein, benzene, butadiene, cyanoacetylene, cyanoformaldehyde, cyanogen, cyclopentadiene, cyclopropenone, cyclopropenethione, diacetylene, furan, glyoxal, imidazole, isobutene, +methylenecyclopropene, propynal, pyrazine, pyridazine, pyridine, pyrimidine, pyrrole, tetrazine, thioacetone, thiophene, thiopropynal, and triazine) for a total of 238 vertical transition energies and 90 oscillator strengths +with a reasonably good balance between singlet, triplet, valence, and Rydberg excited states. For these 238 transitions, we have estimated that 224 are chemically accurate for the aug-cc-pVTZ basis and for the +considered geometry. To define the TBEs of the QUEST\#3 set, we employed CC methods up to the highest technically possible order (CC3, CCSDT, and CCSDTQ), and, when affordable SCI calculations with very +large reference spaces (up to hundred million determinants in certain cases), as well as one of the most reliable multiconfigurational methods, NEVPT2, for double excitations. Most of our TBEs are based on CCSDTQ +(4 non-hydrogen atoms) or CCSDT (5 and 6 non-hydrogen atoms) excitation energies. For all the transitions of the QUEST\#3 set, we reported at least CCSDT/aug-cc-pVTZ (sometimes with basis set extrapolation) +and CC3/aug-cc-pVQZ transition energies as well as CC3/aug-cc-pVTZ oscillator strengths for each dipole-allowed transition. Pursuing our previous benchmarking efforts, we confirmed that CC3 almost systematically +delivers transition energies in agreement with higher-level theoretical models ($\pm0.04$ eV) except for transitions presenting a dominant double-excitation character where multiconfigurational methods like NEVPT2 have +logically the edge. This settles down, at least for now, the debate by demonstrating the superiority of CC3 (in terms of accuracy) compared to methods like CCSDT-3 or ADC(3). For the latter model, this was further +demonstrated in a recent study by two of the present authors \cite{Loos_2020d}. + +%======================= +\subsection{QUEST\#4} +%======================= +The QUEST\#4 benchmark set \cite{Loos_2020c} consists of two subsets of excitations and oscillator strengths. An ``exotic'' subset of 30 excited states for closed-shell molecules containing F, Cl, P, and Si atoms +(carbonyl fluoride, \ce{CCl2}, \ce{CClF}, \ce{CF2}, difluorodiazirine, formyl fluoride, \ce{HCCl}, \ce{HCF}, \ce{HCP}, \ce{HPO}, \ce{HPS}, \ce{HSiF}, \ce{SiCl2}, and silylidene) and a ``radical'' subset of 51 doublet-doublet +transitions in 24 small radicals (allyl, \ce{BeF}, \ce{BeH}, \ce{BH2}, \ce{CH}, \ce{CH3}, \ce{CN}, \ce{CNO}, \ce{CON}, \ce{CO+}, \ce{F2BO}, \ce{F2BS}, \ce{H2BO}, \ce{HCO}, \ce{HOC}, \ce{H2PO}, \ce{H2PS}, \ce{NCO}, +\ce{NH2}, nitromethyl, \ce{NO}, \ce{OH}, \ce{PH2}, and vinyl) characterized by open-shell electronic configurations and an unpaired electron. This represents a total of 81 high-quality TBEs, the vast majority being obtained +at the FCI level with at least the aug-cc-pVTZ basis set. We additionnaly performed high-order CC calculations to ascertain these estimates. For the exotic set, these TBEs have been used to assess the performances of +15 ``lower-order'' wave function approaches, including several CC and ADC variants. Consistent with our previous works, we found that CC3 is very accurate, whereas the trends for the other methods are similar to that +obtained on more standard CNOSH organic compounds. In contrast, for the radical set, even the refined ROCC3 method yields a comparatively large MAE of $0.05$ eV. Likewise, the excitation energies obtained with CCSD +are much less satisfying for open-shell derivatives (MAE of $0.20$ eV with UCCSD and $0.15$ eV with ROCCSD) than for closed-shell systems of similar size (MAE of $0.07$ eV). + +%======================= +\subsection{QUEST\#5} +%======================= + +The QUEST\#5 subset is composed of additional accurate excitation energies that we have produced for the present article. This new set gathers 13 new systems composed by small molecules as well as larger molecules +(see blue molecules in Fig.~\ref{fig:molecules}): aza-naphthalene, benzoquinone, cyclopentadienone, cyclopentadienethione, diazirine, hexatriene, maleimide, naphthalene, nitroxyl, octatetraene, streptocyanine-C3, streptocyanine-C5, +and thioacrolein. For these new transitions, we report again quality vertical transition energies, the vast majority being of CCSDT quality, and we consider that, out of these 80 new transitions, 55 of them can be labeled +as ``safe'', \ie, considered as chemically accurate or within 0.05 eV of the FCI limit for the given geometry and basis set. We refer the interested reader to the {\SupInf} for a detailed discussion of each molecule for which comparisons +are made with literature data. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Theoretical best estimates} +\label{sec:TBE} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +We discuss in this section the generation of the TBEs obtained with the aug-cc-pVTZ basis. +For the closed-shell compounds, the exhaustive list of TBEs can be found in Table \ref{tab:TBE} alongside various specifications: the molecule's name, the excitation, its nature (valence, Rydberg, or charge transfer), its oscillator strength (when symmetry- and spin-allowed), +and its percentage of single excitations $\%T_1$ (computed at the LR-CC3 level). All these quantities are computed with the same aug-cc-pVTZ basis. +Importantly, we also report the composite approach considered to compute the TBEs (see column ``Method''). +Following an ONIOM-like strategy \cite{Svensson_1996a,Svensson_1996b}, the TBEs are computed as ``A/SB + [B/TB - B/SB]'', where A/SB is the excitation energy computed with a method A in a smaller basis (SB), and B/SB and B/TB are excitation energies computed with a method B in the small basis and target basis TB, respectively. +Table \ref{tab:rad} reports the TBEs for the open-shell molecules belonging to the QUEST\#4 subset. + +Talking about numbers, the QUEST database is composed of 551 excitation energies, including 302 singlet, 197 triplet, 51 doublet, 412 valence, and 176 Rydberg excited states. +Amongst the valence transitions in closed-shell compounds, 135 transitions correspond to $n \ra \pis$ excitations, 200 to $\pi \ra \pis$ excitations, and 23 are doubly-excited states. In terms of molecular sizes, 146 excitations are obtained +in molecules having in-between 1 and 3 non-hydrogen atoms, 97 excitations from 4 non-hydrogen atom compounds, 177 from molecules composed by 5 and 6 non-hydrogen atoms, and, finally, 68 excitations are obtained from systems with 7 to 10 non-hydrogen atoms. +In addition, QUEST is composed by 24 open-shell molecules with a single unpaired electron. +Amongst these excited states, 485 of them are considered as ``safe'', \ie, chemically-accurate for the considered basis set and geometry. +Besides this energetic criterion, we consider as ``safe'' transitions that are either: i) computed with FCI or CCSDTQ, or ii) in which the difference between CC3 and CCSDT excitation energies is small (\ie, around $0.03$--$0.04$ eV) with a large $\%T_1$ value. + +\begin{ThreePartTable} +\scriptsize +\centering +\begin{longtable}{clccccclc} +\caption{Theoretical best estimates TBEs (in eV), oscillator strengths $f$, percentage of single excitations $\%T_1$ involved in the transition (computed at the CC3 level) for the full set of closed-shell compounds of the QUEST database. +``Method'' provides the protocol employed to compute the TBEs. +The nature of the excitation is also provided: V, R, and CT stands for valence, Rydberg, and charge transfer, respectively. +[F] indicates a fluorescence transition, \ie, a vertical transition energy computed from an excited-state geometry. +AVXZ stands for aug-cc-pVXZ. +\label{tab:TBE}} +\\ +\hline +\# &\thead{Molecule} & \thead{Excitation} & \thead{Nature} & \thead{$\%T_1$} & \thead{f} & \thead{TBE} & \thead{Method} & \thead{Safe?}\\ +\hline +\endfirsthead +\multicolumn{9}{c}{\tablename\ \thetable\ -- \textit{Continued from previous page}} \\ +\hline +\thead{\#} &\thead{Molecule} & \thead{Excitation} & \thead{Nature} & \thead{$\%T_1$} & \thead{f} & \thead{TBE} & \thead{Method} & \thead{Safe?}\\ +\hline +\endhead +\hline \multicolumn{9}{r}{\textit{Continued on next page}} \\ +\endfoot +\hline +\endlastfoot +1 & Acetaldehyde & $^1A'' (n \ra \pi^*)$ & V & 91 & 0.000 & 4.31 & FCI/AVTZ & Y \\ +2 & & $^3A'' (n \ra \pi^*)$ & V & 97 & & 3.97 & FCI/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +3 & Acetone & $^1A_2 (n \ra \pi^*)$ & V & 91 & & 4.47 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +4 & & $^1B_2 (n \ra 3s)$ & R & 90 & 0.000 & 6.46 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +5 & & $^1A_2 (n \ra 3p)$ & R & 90 & & 7.47 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +6 & & $^1A_1 (n \ra 3p)$ & R & 90 & 0.004 & 7.51 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +7 & & $^1B_2 (n \ra 3p)$ & R & 91 & 0.029 & 7.62 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +8 & & $^3A_2 (n \ra \pi^*)$ & V & 97 & & 4.13 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +9 & & $^3A_1 (\pi \ra \pi^*)$ & V & 98 & & 6.25 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +10 & Acetylene & $^1\Sigma_u^- (\pi \ra \pi^*)$ & V & 96 & & 7.10 & FCI/AVTZ & Y \\ +11 & & $^1\Delta_u (\pi \ra \pi^*)$ & V & 93 & & 7.44 & FCI/AVTZ & Y \\ +12 & & $^3\Sigma_u^+ (\pi \ra \pi^*)$ & V & 99 & & 5.53 & FCI/AVTZ & Y \\ +13 & & $^3\Delta_u (\pi \ra \pi^*)$ & V & 99 & & 6.40 & FCI/AVTZ & Y \\ +14 & & $^3\Sigma_u^- (\pi \ra \pi^*)$ & V & 98 & & 7.08 & FCI/AVTZ & Y \\ +15 & & $^1A_u [F] (\pi \ra \pi^*)$ & V & 95 & & 3.64 & FCI/AVTZ & Y \\ +16 & & $^1A_2 [F] (\pi \ra \pi^*)$ & V & 95 & & 3.85 & FCI/AVTZ & Y \\ +17 & Acrolein & $^1A'' (n \ra \pi^*)$ & V & 87 & 0.000 & 3.78 & FCI/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +18 & & $^1A' (\pi \ra \pi^*)$ & V & 91 & 0.344 & 6.69 & CCSDT/AVTZ & Y \\ +19 & & $^1A'' (n \ra \pi^*)$ & V & 79 & 0.000 & 6.72 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & N \\ +20 & & $^1A' (n \ra 3s)$ & R & 89 & 0.109 & 7.08 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +21 & & $^1A' (\text{double})$ & V & 75 & (\text{n.d.}) & 7.87 & FCI/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +22 & & $^3A'' (n \ra \pi^*)$ & V & 97 & & 3.51 & FCI/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +23 & & $^3A' (\pi \ra \pi^*)$ & V & 98 & & 3.94 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +24 & & $^3A' (\pi \ra \pi^*)$ & V & 98 & & 6.18 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +25 & & $^3A'' (n \ra \pi^*)$ & V & 92 & & 6.54 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & N \\ +26 & Ammonia & $^1A_2 (n \ra 3s)$ & R & 93 & 0.086 & 6.59 & FCI/AVTZ & Y \\ +27 & & $^1E (n \ra 3p)$ & R & 93 & 0.006 & 8.16 & FCI/AVTZ & Y \\ +28 & & $^1A_1 (n \ra 3p)$ & R & 94 & 0.003 & 9.33 & FCI/AVTZ & Y \\ +29 & & $^1A_2 (n \ra 3s)$ & R & 93 & 0.008 & 9.96 & FCI/AVTZ & Y \\ +30 & & $^3A_2 (n \ra 3s)$ & R & 98 & & 6.31 & FCI/AVTZ & Y \\ +31 & Aza-naphthalene & $^1B_{3g} (n \ra \pi^*)$ & V & 88 & & 3.14 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +32 & & $^1B_{2u} (\pi \ra \pi^*)$ & V & 86 & 0.190 & 4.28 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +33 & & $^1B_{1u} (n \ra \pi^*)$ & V & 88 & (\text{n.d.}) & 4.34 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +34 & & $^1B_{2g} (n \ra \pi^*)$ & V & 87 & & 4.55 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +35 & & $^1B_{2g} (n \ra \pi^*)$ & V & 84 & & 4.89 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +36 & & $^1B_{1u} (n \ra \pi^*)$ & V & 82 & (\text{n.d.}) & 5.24 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & N \\ +37 & & $^1A_u (n \ra \pi^*)$ & V & 83 & & 5.34 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +38 & & $^1B_{3u} (\pi \ra \pi^*)$ & V & 88 & 0.028 & 5.68 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & N \\ +39 & & $^1A_g (\pi \ra \pi^*)$ & V & 85 & & 5.80 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +40 & & $^1A_u (n \ra \pi^*)$ & V & 84 & & 5.92 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +41 & & $^1A_g (n \ra 3s)$ & R & 90 & & 6.50 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +42 & & $^3B_{3g} (n \ra \pi^*)$ & V & 96 & & 2.82 & CC3/AVTZ & N \\ +43 & & $^3B_{2u} (\pi \ra \pi^*)$ & V & 97 & & 3.67 & CC3/AVTZ & N \\ +44 & & $^3B_{3u} (\pi \ra \pi^*)$ & V & 97 & & 3.75 & CC3/AVTZ & N \\ +45 & & $^3B_{1u} (n \ra \pi^*)$ & V & 97 & & 3.77 & CC3/AVTZ & N \\ +46 & & $^3B_{2g} (n \ra \pi^*)$ & V & 96 & & 4.34 & CC3/AVTZ & N \\ +47 & & $^3B_{2g} (n \ra \pi^*)$ & V & 95 & & 4.61 & CC3/AVTZ & N \\ +48 & & $^3B_{3u} (\pi \ra \pi^*)$ & V & 96 & & 4.75 & CC3/AVTZ & N \\ +49 & & $^3A_u (n \ra \pi^*)$ & V & 96 & & 4.87 & CC3/AVTZ & N \\ +50 & Beryllium & $^1D (\text{double})$ & R & 32 & & 7.15 & FCI/AVTZ & Y \\ +51 & Benzene & $^1B_{2u} (\pi \ra \pi^*)$ & V & 86 & & 5.06 & CCSDT/AVTZ & Y \\ +52 & & $^1B_{1u} (\pi \ra \pi^*)$ & V & 92 & & 6.45 & CCSDT/AVTZ & Y \\ +53 & & $^1E_{1g} (\pi \ra 3s)$ & R & 92 & & 6.52 & CCSDT/AVTZ & Y \\ +54 & & $^1A_{2u} (\pi \ra 3p)$ & R & 93 & 0.066 & 7.08 & CCSDT/AVTZ & Y \\ +55 & & $^1E_{2u} (\pi \ra 3p)$ & R & 92 & & 7.15 & CCSDT/AVTZ & Y \\ +56 & & $^1E_{2g} (\pi \ra \pi^*)$ & V & 73 & & 8.28 & FCI/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +57 & & $^1A_{1g} (\text{double})$ & V & n.d. & & 10.55 & XMS-CASPT2/AVTZ & N \\ +58 & & $^3B_{1u} (\pi \ra \pi^*)$ & V & 98 & & 4.16 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +59 & & $^3E_{1u} (\pi \ra \pi^*)$ & V & 97 & & 4.85 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +60 & & $^3B_{2u} (\pi \ra \pi^*)$ & V & 98 & & 5.81 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +61 & Benzoquinone & $^1B_{1g} (n \ra \pi^*)$ & V & 85 & & 2.82 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +62 & & $^1A_u (n \ra \pi^*)$ & V & 84 & & 2.96 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +63 & & $^1A_g (\text{double})$ & V & 0 & & 4.57 & NEVPT2/AVTZ & N \\ +64 & & $^1B_{3g} (\pi \ra \pi^*)$ & V & 88 & & 4.58 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & N \\ +65 & & $^1B_{1u} (\pi \ra \pi^*)$ & V & 88 & 0.471 & 5.62 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & N \\ +66 & & $^1B_{3u} (n \ra \pi^*)$ & V & 79 & 0.001 & 5.79 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & N \\ +67 & & $^1B_{2g} (n \ra \pi^*)$ & V & 76 & & 5.95 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +68 & & $^1A_u (n \ra \pi^*)$ & V & 74 & & 6.35 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & N \\ +69 & & $^1B_{1g} (n \ra \pi^*)$ & V & 83 & & 6.38 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & N \\ +70 & & $^1B_{2g} (n \ra \pi^*)$ & V & 86 & & 7.22 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +71 & & $^3B_{1g} (n \ra \pi^*)$ & V & 96 & & 2.58 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +72 & & $^3A_u (n \ra \pi^*)$ & V & 95 & & 2.72 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +73 & & $^3B_{1u} (\pi \ra \pi^*)$ & V & 97 & & 3.12 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +74 & & $^3B_{3g} (\pi \ra \pi^*)$ & V & 97 & & 3.46 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +75 & Butadiene & $^1B_u (\pi \ra \pi^*)$ & V & 93 & 0.664 & 6.22 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +76 & & $^1B_g (\pi \ra 3s)$ & R & 94 & & 6.33 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +77 & & $^1A_g (\pi \ra \pi^*)$ & V & 75 & & 6.50 & FCI/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +78 & & $^1A_u (\pi \ra 3p)$ & R & 94 & 0.001 & 6.64 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +79 & & $^1A_u (\pi \ra 3p)$ & R & 94 & 0.049 & 6.80 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +80 & & $^1B_u (\pi \ra 3p)$ & R & 93 & 0.055 & 7.68 & CCSDTQ/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +81 & & $^3B_u (\pi \ra \pi^*)$ & V & 98 & & 3.36 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +82 & & $^3A_g (\pi \ra \pi^*)$ & V & 98 & & 5.20 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +83 & & $^3B_g (\pi \ra 3s)$ & R & 97 & & 6.29 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +84 & Carbon Dimer & $^1\Delta_g (\text{double})$ & R & 0 & & 2.09 & FCI/AVTZ & Y \\ +85 & & $^1\Sigma^+_g (\text{double})$ & R & 0 & & 2.42 & FCI/AVTZ & Y \\ +86 & Carbon monoxide & $^1\Pi (n \ra \pi^*)$ & V & 93 & 0.168 & 8.49 & FCI/AVTZ & Y \\ +87 & & $^1\Sigma^- (\pi \ra \pi^*)$ & V & 93 & & 9.92 & FCI/AVTZ & Y \\ +88 & & $^1\Delta (\pi \ra \pi^*)$ & V & 91 & & 10.06 & FCI/AVTZ & Y \\ +89 & & $^1\Sigma^+ (\text{n.d.})$ & R & 91 & 0.003 & 10.95 & FCI/AVTZ & Y \\ +90 & & $^1\Sigma^+ (\text{n.d.})$ & R & 92 & 0.200 & 11.52 & FCI/AVTZ & Y \\ +91 & & $^1\Pi (\text{n.d.})$ & R & 92 & 0.106 & 11.72 & FCI/AVTZ & Y \\ +92 & & $^3\Pi (n \ra \pi^*)$ & V & 98 & & 6.28 & FCI/AVTZ & Y \\ +93 & & $^3\Sigma^+ (\pi \ra \pi^*)$ & V & 98 & & 8.45 & FCI/AVTZ & Y \\ +94 & & $^3\Delta (\pi \ra \pi^*)$ & V & 98 & & 9.27 & FCI/AVTZ & Y \\ +95 & & $^3\Sigma^- (\pi \ra \pi^*)$ & V & 97 & & 9.80 & FCI/AVTZ & Y \\ +96 & & $^3\Sigma^+ (\text{n.d.})$ & R & 98 & & 10.47 & FCI/AVTZ & Y \\ +97 & Carbon Dimer & $^1\Delta_g (\text{double})$ & R & 1 & & 5.22 & FCI/AVTZ & Y \\ +98 & & $^1\Sigma^+_g (\text{double})$ & R & 1 & & 5.91 & FCI/AVTZ & Y \\ +99 & Carbonylfluoride & $^1A_2 (n \ra \pi^*)$ & V & 91 & & 7.31 & FCI/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +100 & & $^3A_2 (n \ra \pi^*)$ & V & 97 & & 7.06 & FCI/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +101 & CCl2 & $^1B_1 (\sigma \ra \pi^*)$ & V & 93 & 0.002 & 2.59 & FCI/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +102 & & $^1A_2 (\text{n.d.})$ & V & 88 & & 4.40 & FCI/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +103 & & $^3B_1 (\sigma \ra \pi^*)$ & V & 98 & & 1.22 & FCI/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +104 & & $^3A_2 (\text{n.d.})$ & V & 96 & & 4.31 & FCI/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +105 & CClF & $^1A" (\sigma \ra \pi^*)$ & V & 93 & 0.007 & 3.57 & FCI/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +106 & CF2 & $^1B_1 (\sigma \ra \pi^*)$ & V & 94 & 0.034 & 5.09 & FCI/AVTZ & Y \\ +107 & & $^3B_1 (\sigma \ra \pi^*)$ & V & 99 & & 2.77 & FCI/AVTZ & Y \\ +108 & Cyanoacetylene & $^1\Sigma^- (\pi \ra \pi^*)$ & V & 94 & & 5.80 & CCSDTQ/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +109 & & $^1\Delta (\pi \ra \pi^*)$ & V & 94 & & 6.07 & CCSDTQ/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +110 & & $^3\Sigma^+ (\pi \ra \pi^*)$ & V & 98 & & 4.44 & CCSDT/AVTZ & Y \\ +111 & & $^3\Delta (\pi \ra \pi^*)$ & V & 98 & & 5.21 & CCSDT/AVTZ & Y \\ +112 & & $^1A'' [F] (\pi \ra \pi^*)$ & V & 93 & 0.004 & 3.54 & CCSDTQ/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +113 & Cyanoformaldehyde & $^1A'' (n \ra \pi^*)$ & V & 89 & 0.001 & 3.81 & CCSDT/AVTZ & Y \\ +114 & & $^1A'' (\pi \ra \pi^*)$ & V & 91 & 0.000 & 6.46 & CCSDT/AVTZ & Y \\ +115 & & $^3A'' (n \ra \pi^*)$ & V & 97 & & 3.44 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +116 & & $^3A' (\pi \ra \pi^*)$ & V & 98 & & 5.01 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +117 & Cyanogen & $ ^1\Sigma_u^- (\pi \ra \pi^*)$ & V & 94 & & 6.39 & CCSDTQ/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +118 & & $ ^1\Delta_u (\pi \ra \pi^*)$ & V & 93 & & 6.66 & CCSDTQ/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +119 & & $ ^3\Sigma_u^+ (\pi \ra \pi^*)$ & V & 98 & & 4.91 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +120 & & $ ^1\Sigma_u^- [F] (\pi \ra \pi^*)$ & V & 93 & & 5.05 & CCSDTQ/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +121 & Cyclopentadiene & $^1B_2 (\pi \ra \pi^*)$ & V & 93 & 0.084 & 5.54 & FCI/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +122 & & $^1A_2 (\pi \ra 3s)$ & R & 94 & & 5.78 & CCSDT/AVTZ & Y \\ +123 & & $^1B_1 (\pi \ra 3p)$ & R & 94 & 0.037 & 6.41 & CCSDT/AVTZ & Y \\ +124 & & $^1A_2 (\pi \ra 3p)$ & R & 93 & & 6.46 & CCSDT/AVTZ & Y \\ +125 & & $^1B_2 (\pi \ra 3p)$ & R & 94 & 0.046 & 6.56 & CCSDT/AVTZ & Y \\ +126 & & $^1A_1 (\pi \ra \pi^*)$ & V & 78 & 0.010 & 6.52 & CCSDT/AVTZ & N \\ +127 & & $^3B_2 (\pi \ra \pi^*)$ & V & 98 & & 3.31 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +128 & & $^3A_1 (\pi \ra \pi^*)$ & V & 98 & & 5.11 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +129 & & $^3A_2 (\pi \ra 3s)$ & R & 97 & & 5.73 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +130 & & $^3B_1 (\pi \ra 3p)$ & R & 97 & & 6.36 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +131 & Cyclopentadienone & $^1A_2 (n \ra \pi^*)$ & V & 88 & & 2.94 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +132 & & $^1B_2 (\pi \ra \pi^*)$ & V & 91 & 0.004 & 3.58 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +133 & & $^1B_1 (\text{double})$ & V & 3 & 0.000 & 5.02 & NEVPT2/AVTZ & N \\ +134 & & $^1A_1 (\text{double})$ & V & 49 & 0.131 & 6.00 & NEVPT2/AVTZ & N \\ +135 & & $^1A_1 (\pi \ra \pi^*)$ & V & 73 & 0.090 & 6.09 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & N \\ +136 & & $^3B_2 (\pi \ra \pi^*)$ & V & 98 & & 2.29 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +137 & & $^3A_2 (n \ra \pi^*)$ & V & 96 & & 2.65 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +138 & & $^3A_1 (\pi \ra \pi^*)$ & V & 98 & & 4.19 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +139 & & $^3B_1 (\text{double})$ & V & 10 & & 4.91 & NEVPT2/AVTZ & N \\ +140 & Cyclopentadienethione & $^1A_2 (n \ra \pi^*)$ & V & 87 & & 1.70 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +141 & & $^1B_2 (\pi \ra \pi^*)$ & V & 85 & 0.000 & 2.63 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +142 & & $^1B_1 (\text{double})$ & V & 1 & 0.000 & 3.16 & NEVPT2/AVTZ & N \\ +143 & & $^1A_1 (\pi \ra \pi^*)$ & V & 89 & 0.378 & 4.96 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +144 & & $^1A_1 (\text{double})$ & V & 51 & 0.003 & 5.43 & NEVPT2/AVTZ & N \\ +145 & & $^3A_2 (n \ra \pi^*)$ & V & 97 & & 1.47 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +146 & & $^3B_2 (\pi \ra \pi^*)$ & V & 97 & & 1.88 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +147 & & $^3A_1 (\pi \ra \pi^*)$ & V & 98 & & 2.51 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +148 & & $^3B_1 (\text{double})$ & V & 4 & & 3.13 & NEVPT2/AVTZ & N \\ +149 & Cyclopropene & $^1B_1 (\sigma \ra \pi^*)$ & V & 92 & 0.001 & 6.68 & CCSDT/AVTZ & Y \\ +150 & & $^1B_2 (\pi \ra \pi^*)$ & V & 95 & 0.071 & 6.79 & FCI/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +151 & & $^3B_2 (\pi \ra \pi^*)$ & V & 98 & & 4.38 & FCI/AVTZ & Y \\ +152 & & $^3B_1 (\sigma \ra \pi^*)$ & V & 98 & & 6.45 & FCI/AVTZ & Y \\ +153 & Cyclopropenone & $^1B_1 (n \ra \pi^*)$ & V & 87 & 0.000 & 4.26 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +154 & & $^1A_2 (n \ra \pi^*)$ & V & 91 & & 5.55 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +155 & & $^1B_2 (n \ra 3s)$ & R & 90 & 0.003 & 6.34 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +156 & & $^1B_2 (\pi \ra \pi^*)$ & V & 86 & 0.047 & 6.54 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +157 & & $^1B_2 (n \ra 3p)$ & R & 91 & 0.018 & 6.98 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +158 & & $^1A_1 (n \ra 3p)$ & R & 91 & 0.003 & 7.02 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +159 & & $^1A_1 (\pi \ra \pi^*)$ & V & 90 & 0.320 & 8.28 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +160 & & $^3B_1 (n \ra \pi^*)$ & V & 96 & & 3.93 & CCSDT/AVTZ & Y \\ +161 & & $^3B_2 (\pi \ra \pi^*)$ & V & 97 & & 4.88 & CCSDT/AVTZ & Y \\ +162 & & $^3A_2 (n \ra \pi^*)$ & V & 97 & & 5.35 & CCSDT/AVTZ & Y \\ +163 & & $^3A_1 (\pi \ra \pi^*)$ & V & 98 & & 6.79 & CCSDT/AVTZ & Y \\ +164 & Cyclopropenethione & $^1A_2 (n \ra \pi^*)$ & V & 89 & & 3.41 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +165 & & $^1B_1 (n \ra \pi^*)$ & V & 84 & 0.000 & 3.45 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +166 & & $^1B_2 (\pi \ra \pi^*)$ & V & 83 & 0.007 & 4.60 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +167 & & $^1B_2 (n \ra 3s)$ & R & 91 & 0.048 & 5.34 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +168 & & $^1A_1 (\pi \ra \pi^*)$ & V & 89 & 0.228 & 5.46 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +169 & & $^1B_2 (n \ra 3p)$ & R & 91 & 0.084 & 5.92 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +170 & & $^3A_2 (n \ra \pi^*)$ & V & 97 & & 3.28 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +171 & & $^3B_1 (n \ra \pi^*)$ & V & 94 & & 3.32 & CCSDT/AVTZ & Y \\ +172 & & $^3B_2 (\pi \ra \pi^*)$ & V & 96 & & 4.01 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +173 & & $^3A_1 (\pi \ra \pi^*)$ & V & 98 & & 4.01 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +174 & Diacetylene & $^1\Sigma_u^- (\pi \ra \pi^*)$ & V & 94 & & 5.33 & CCSDTQ/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +175 & & $^1\Delta_u (\pi \ra \pi^*)$ & V & 94 & & 5.61 & CCSDTQ/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +176 & & $^3\Sigma_u^+ (\pi \ra \pi^*)$ & V & 98 & & 4.10 & CCSDTQ/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +177 & & $^3\Delta_u (\pi \ra \pi^*)$ & V & 98 & & 4.78 & CCSDTQ/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +178 & Diazirine & $^1B_1 (n \ra \pi^*)$ & V & 92 & 0.002 & 4.09 & CCSDTQ/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +179 & & $^1B_2 (\sigma \ra \pi^*)$ & V & 90 & & 7.27 & CCSDTQ/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +180 & & $^1A_2 (n \ra 3s)$ & R & 93 & 0.000 & 7.44 & CCSDTQ/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +181 & & $^1A_1 (n \ra 3p)$ & R & 93 & 0.132 & 8.03 & CCSDTQ/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +182 & & $^3B_1 (n \ra \pi^*)$ & V & 98 & & 3.49 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +183 & & $^3B_2 (\pi \ra \pi^*)$ & V & 98 & & 5.06 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +184 & & $^3A_2 (n \ra \pi^*)$ & V & 98 & & 6.12 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +185 & & $^3A_1 (n \ra 3p)$ & R & 98 & & 6.81 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +186 & Diazomethane & $^1A_2 (\pi \ra \pi^*)$ & V & 90 & & 3.14 & FCI/AVTZ & Y \\ +187 & & $^1B_1 (\pi \ra 3s)$ & R & 93 & 0.016 & 5.54 & FCI/AVTZ & Y \\ +188 & & $^1A_1 (\pi \ra \pi^*)$ & V & 91 & 0.234 & 5.90 & FCI/AVTZ & Y \\ +189 & & $^3A_2 (\pi \ra \pi^*)$ & V & 97 & & 2.79 & FCI/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +190 & & $^3A_1 (\pi \ra \pi^*)$ & V & 98 & & 4.05 & FCI/AVTZ & Y \\ +191 & & $^3B_1 (\pi \ra 3s) $ & R & 98 & & 5.35 & FCI/AVTZ & Y \\ +192 & & $^3A_1 (\pi \ra 3p)$ & R & 98 & & 6.82 & FCI/AVTZ & Y \\ +193 & & $^1A'' [F] (\pi \ra \pi^*)$ & V & 87 & 0.000 & 0.71 & FCI/AVTZ & Y \\ +194 & Difluorodiazirine & $^1B_1 (n \ra \pi^*)$ & V & 93 & 0.002 & 3.74 & CCSDT/AVTZ & Y \\ +195 & & $^1A_2 (\pi \ra \pi^*)$ & V & 91 & & 7.00 & CCSDT/AVTZ & Y \\ +196 & & $^1B_2 (\pi \ra \pi^*)$ & V & 93 & 0.026 & 8.52 & CCSDT/AVTZ & Y \\ +197 & & $^3B_1 (n \ra \pi^*)$ & V & 98 & & 3.03 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +198 & & $^3B_2 (\pi \ra \pi^*)$ & V & 98 & & 5.44 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +199 & & $^3A_2 (\pi \ra \pi^*)$ & V & 98 & & 5.80 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +200 & Dinitrogen & $^1\Pi_g (n \ra \pi^*)$ & V & 92 & & 9.34 & FCI/AVTZ & Y \\ +201 & & $^1\Sigma_u^- (\pi \ra \pi^*)$ & V & 97 & & 9.88 & FCI/AVTZ & Y \\ +202 & & $^1\Delta_u (\pi \ra \pi^*)$ & V & 95 & 0.000 & 10.29 & FCI/AVTZ & Y \\ +203 & & $^1\Sigma_g^+ (\text{n.d.})$ & R & 92 & & 12.98 & FCI/AVTZ & Y \\ +204 & & $^1\Pi_u (\text{n.d.})$ & R & 82 & 0.458 & 13.03 & FCI/AVTZ & Y \\ +205 & & $^1\Sigma_u^+ (\text{n.d.})$ & R & 92 & 0.296 & 13.09 & FCI/AVTZ & Y \\ +206 & & $^1\Pi_u (\text{n.d.})$ & R & 87 & 0.000 & 13.46 & FCI/AVTZ & Y \\ +207 & & $^3\Sigma_u^+ (\pi \ra \pi^*)$ & V & 99 & & 7.70 & FCI/AVTZ & Y \\ +208 & & $^3\Pi_g (n \ra \pi^*)$ & V & 98 & & 8.01 & FCI/AVTZ & Y \\ +209 & & $^3\Delta_u (\pi \ra \pi^*)$ & V & 99 & & 8.87 & FCI/AVTZ & Y \\ +210 & & $^3\Sigma_u^- (\pi \ra \pi^*)$ & V & 98 & & 9.66 & FCI/AVTZ & Y \\ +211 & Ethylene & $^1B_{3u} p3s $ & R & 95 & 0.078 & 7.39 & FCI/AVTZ & Y \\ +212 & & $^1B_{1u} (\pi \ra \pi^*)$ & V & 95 & 0.346 & 7.93 & FCI/AVTZ & Y \\ +213 & & $^1B_{1g} (\pi \ra 3p)$ & R & 95 & & 8.08 & FCI/AVTZ & Y \\ +214 & & $^1A_g (\text{double})$ & V & 20 & & 12.92 & FCI/AVTZ & Y \\ +215 & & $^3B_{1u} (\pi \ra \pi^*)$ & V & 99 & & 4.54 & FCI/AVTZ & Y \\ +216 & & $^3B_{3u} p3s $ & R & 98 & & 7.23 & FCI/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +217 & & $^3B_{1g} (\pi \ra 3p)$ & R & 98 & & 7.98 & FCI/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +218 & Formaldehyde & $^1A_2 (n \ra \pi^*)$ & V & 91 & & 3.98 & FCI/AVTZ & Y \\ +219 & & $^1B_2 (n \ra 3s)$ & R & 91 & 0.021 & 7.23 & FCI/AVTZ & Y \\ +220 & & $^1B_2 (n \ra 3p)$ & R & 92 & 0.037 & 8.13 & FCI/AVTZ & Y \\ +221 & & $^1A_1 (n \ra 3p)$ & R & 91 & 0.052 & 8.23 & FCI/AVTZ & Y \\ +222 & & $^1A_2 (n \ra 3p)$ & R & 91 & & 8.67 & FCI/AVTZ & Y \\ +223 & & $^1B_1 (\text{n.d.})$ & V & 90 & 0.001 & 9.22 & FCI/AVTZ & Y \\ +224 & & $^1A_1 (\pi \ra \pi^*)$ & V & 90 & 0.135 & 9.43 & FCI/AVTZ & Y \\ +225 & & $^1A_1 (\text{double})$ & V & 5 & (\text{n.d.}) & 10.35 & FCI/AVTZ & Y \\ +226 & & $^3A_2 (n \ra \pi^*)$ & V & 98 & & 3.58 & FCI/AVTZ & Y \\ +227 & & $^3A_1 (\pi \ra \pi^*)$ & V & 99 & & 6.06 & FCI/AVTZ & Y \\ +228 & & $^3B_2 (n \ra 3s)$ & R & 97 & & 7.06 & FCI/AVTZ & Y \\ +229 & & $^3B_2 (n \ra 3p)$ & R & 97 & & 7.94 & FCI/AVTZ & Y \\ +230 & & $^3A_1 (n \ra 3p)$ & R & 97 & & 8.10 & FCI/AVTZ & Y \\ +231 & & $^3B_1 (\text{n.d.})$ & R & 97 & & 8.42 & FCI/AVTZ & Y \\ +232 & & $^1A^" [F] (n \ra \pi^*)$ & V & 87 & 0.000 & 2.80 & FCI/AVTZ & Y \\ +233 & Formamide & $^1A'' (n \ra \pi^*)$ & V & 90 & 0.000 & 5.65 & FCI/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +234 & & $^1A' (n \ra 3s)$ & R & 88 & 0.001 & 6.77 & FCI/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & N \\ +235 & & $^1A' (n \ra 3p)$ & R & 89 & 0.111 & 7.38 & CCSDT/AVTZ & N \\ +236 & & $^1A' (\pi \ra \pi^*)$ & V & 89 & 0.251 & 7.63 & FCI/AVTZ & N \\ +237 & & $^3A'' (n \ra \pi^*)$ & V & 97 & & 5.38 & FCI/AVDZ + [CC3/AVTZ - CCS3/AVDZ] & Y \\ +238 & & $^3A' (\pi \ra \pi^*)$ & V & 98 & & 5.81 & FCI/AVDZ + [CC3/AVTZ - CCS3/AVDZ] & Y \\ +239 & Formylfluoride & $^1A'' (n \ra \pi^*)$ & V & 91 & & 5.96 & FCI/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +240 & & $^3A" (n \ra \pi^*)$ & V & 98 & 0.001 & 5.63 & FCI/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +241 & Furan & $^1A_2 (\pi \ra 3s)$ & R & 93 & & 6.09 & CCSDT/AVTZ & Y \\ +242 & & $^1B_2 (\pi \ra \pi^*)$ & V & 93 & 0.163 & 6.37 & CCSDT/AVTZ & Y \\ +243 & & $^1A_1 (\pi \ra \pi^*)$ & V & 92 & 0.000 & 6.56 & CCSDT/AVTZ & Y \\ +244 & & $^1B_1 (\pi \ra 3p)$ & R & 93 & 0.038 & 6.64 & CCSDT/AVTZ & Y \\ +245 & & $^1A_2 (\pi \ra 3p)$ & R & 93 & & 6.81 & CCSDT/AVTZ & Y \\ +246 & & $^1B_2 (\pi \ra 3p)$ & R & 93 & 0.007 & 7.24 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +247 & & $^3B_2 (\pi \ra \pi^*)$ & V & 98 & & 4.20 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +248 & & $^3A_1 (\pi \ra \pi^*)$ & V & 98 & & 5.46 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +249 & & $^3A_2 (\pi \ra 3s)$ & R & 97 & & 6.02 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +250 & & $^3B_1 (\pi \ra 3p)$ & R & 97 & & 6.59 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +251 & Glyoxal & $^1A_u (n \ra \pi^*)$ & V & 91 & 0.000 & 2.88 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +252 & & $^1B_g (n \ra \pi^*)$ & V & 88 & & 4.24 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +253 & & $^1A_g (\text{double})$ & V & 0 & 0.000 & 5.61 & FCI/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +254 & & $^1B_g (n \ra \pi^*)$ & V & 83 & & 6.57 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +255 & & $^1B_u (n \ra 3p)$ & R & 91 & 0.095 & 7.71 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +256 & & $^3A_u (n \ra \pi^*)$ & V & 97 & & 2.49 & CCSDT/AVTZ & Y \\ +257 & & $^3B_g (n \ra \pi^*)$ & V & 97 & & 3.89 & CCSDT/AVTZ & Y \\ +258 & & $^3B_u (\pi \ra \pi^*)$ & V & 98 & & 5.15 & CCSDT/AVTZ & Y \\ +259 & & $^3A_g (\pi \ra \pi^*)$ & V & 98 & & 6.30 & CCSDT/AVTZ & Y \\ +260 & HCCl & $^1A" (\sigma \ra \pi^*)$ & V & 94 & 0.003 & 1.98 & FCI/AVTZ & Y \\ +261 & HCF & $^1A" (\sigma \ra \pi^*)$ & V & 95 & 0.006 & 2.49 & FCI/AVTZ & Y \\ +262 & HCP & $^1\Sigma^- (\pi \ra \pi^*)$ & V & 94 & & 4.84 & FCI/AVTZ & Y \\ +263 & & $^1\Delta (\pi \ra \pi^*)$ & V & 94 & & 5.15 & FCI/AVTZ & Y \\ +264 & & $^3\Sigma^+ (\pi \ra \pi^*)$ & V & 98 & & 3.47 & FCI/AVTZ & Y \\ +265 & & $^3\Delta (\pi \ra \pi^*)$ & V & 98 & & 4.22 & FCI/AVTZ & Y \\ +266 & Hexatriene & $^1B_u (\pi \ra \pi^*)$ & V & 92 & 1.115 & 5.37 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +267 & & $^1A_g (\pi \ra \pi^*)$ & V & 65 & & 5.62 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & N \\ +268 & & $^1A_u (\pi \ra 3s)$ & R & 93 & 0.009 & 5.79 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +269 & & $^1B_g (\pi \ra 3p)$ & R & 93 & & 5.94 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +270 & & $^3B_u (\pi \ra \pi^*)$ & V & 97 & & 2.73 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +271 & & $^3A_g (\pi \ra \pi^*)$ & V & 98 & & 4.36 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +272 & HPO & $^1A'' (n \ra \pi^*)$ & V & 90 & 0.003 & 2.47 & FCI/AVTZ & Y \\ +273 & HPS & $^1A'' (n \ra \pi^*)$ & V & 90 & 0.001 & 1.59 & FCI/AVTZ & Y \\ +274 & HSiF & $^1A'' (\sigma \ra \pi^*)$ & V & 93 & 0.024 & 3.05 & FCI/AVTZ & Y \\ +275 & Hydrogen chloride & $^1\Pi $ & CT & 94 & 0.056 & 7.84 & FCI/AVTZ & Y \\ +276 & Hydrogen sulfide & $^1A_2 (n \ra 3p)$ & R & 94 & & 6.18 & FCI/AVTZ & Y \\ +277 & & $^1B_1 (n \ra 3p)$ & R & 94 & 0.063 & 6.24 & FCI/AVTZ & Y \\ +278 & & $^3A_2 (n \ra 3p)$ & R & 98 & & 5.81 & FCI/AVTZ & Y \\ +279 & & $^3B_1 (n \ra 3p)$ & R & 98 & & 5.88 & FCI/AVTZ & Y \\ +280 & Imidazole & $^1A'' (\pi \ra 3s)$ & R & 93 & 0.001 & 5.71 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +281 & & $^1A' (\pi \ra \pi^*)$ & V & 89 & 0.124 & 6.41 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +282 & & $^1A'' (n \ra \pi^*)$ & V & 93 & 0.028 & 6.50 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +283 & & $^1A' (\pi \ra 3p)$ & R & 88 & 0.035 & 6.83 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & N \\ +284 & & $^3A' (\pi \ra \pi^*)$ & V & 98 & & 4.73 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +285 & & $^3A'' (\pi \ra 3s)$ & R & 97 & & 5.66 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +286 & & $^3A' (\pi \ra \pi^*)$ & V & 97 & & 5.74 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +287 & & $^3A'' (n \ra \pi^*)$ & V & 97 & & 6.31 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +288 & Isobutene & $^1B_1 (\pi \ra 3s)$ & R & 94 & 0.006 & 6.46 & CCSDT/AVTZ & Y \\ +289 & & $^1A_1 (\pi \ra 3p)$ & R & 94 & 0.228 & 7.01 & CCSDT/AVTZ & Y \\ +290 & & $^3A_1 (\pi \ra \pi^*)$ & V & 98 & & 4.53 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +291 & Ketene & $^1A_2 (\pi \ra \pi^*)$ & V & 91 & & 3.85 & FCI/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +292 & & $^1B_1 (n \ra 3s)$ & R & 93 & 0.035 & 6.01 & FCI/AVTZ & Y \\ +293 & & $^1A_1 (\pi \ra \pi^*)$ & V & 92 & 0.154 & 7.25 & CCSDTQ/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +294 & & $^1A_2 (\pi \ra 3p)$ & R & 94 & & 7.18 & FCI/AVTZ & Y \\ +295 & & $^3A_2 (n \ra \pi^*)$ & V & 91 & & 3.77 & FCI/AVTZ & Y \\ +296 & & $^3A_1 (\pi \ra \pi^*)$ & V & 98 & & 5.61 & FCI/AVTZ & Y \\ +297 & & $^3B_1 (n \ra 3p)$ & R & 98 & & 5.79 & FCI/AVTZ & Y \\ +298 & & $^3A_2 (\pi \ra 3p)$ & R & 94 & & 7.12 & FCI/AVTZ & Y \\ +299 & & $^1A^" [F] (\pi \ra \pi^*)$ & V & 87 & 0.000 & 1.00 & FCI/AVTZ & Y \\ +300 & Maleimide & $^1B_1 (n \ra \pi^*)$ & V & 87 & 0.000 & 3.80 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +301 & & $^1A_2 (n \ra \pi^*)$ & V & 85 & & 4.52 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +302 & & $^1B_2 (\pi \ra \pi^*)$ & V & 88 & 0.025 & 4.89 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +303 & & $^1B_2 (\pi \ra \pi^*)$ & V & 89 & 0.373 & 6.21 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +304 & & $^1B_2 (n \ra 3s)$ & R & 89 & 0.034 & 7.20 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +305 & & $^3B_1 (n \ra \pi^*)$ & V & 96 & & 3.57 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +306 & & $^3B_2 (\pi \ra \pi^*)$ & V & 98 & & 3.74 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +307 & & $^3B_2 (\pi \ra \pi^*)$ & V & 96 & & 4.24 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +308 & & $^3A_2 (n \ra \pi^*)$ & V & 96 & & 4.32 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +309 & Methanimine & $^1A^" (n \ra \pi^*)$ & V & 90 & 0.003 & 5.23 & FCI/AVTZ & Y \\ +310 & & $^3A^" (n \ra \pi^*)$ & V & 98 & & 4.65 & FCI/AVTZ & Y \\ +311 & Methylenecyclopropene & $^1B_2 (\pi \ra \pi^*)$ & V & 85 & 0.011 & 4.28 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +312 & & $^1B_1 (\pi \ra 3s)$ & R & 93 & 0.005 & 5.44 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +313 & & $^1A_2 (\pi \ra 3p)$ & R & 93 & & 5.96 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +314 & & $^1A_1 (\pi \ra \pi^*)$ & V & 92 & 0.224 & 6.12 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & N \\ +315 & & $^3B_2 (\pi \ra \pi^*)$ & V & 97 & & 3.49 & CCSDT/AVTZ & Y \\ +316 & & $^3A_1 (\pi \ra \pi^*)$ & V & 98 & & 4.74 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +317 & Naphthalene & $^1B_{3u} (\pi \ra \pi^*)$ & V & 85 & 0.000 & 4.27 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +318 & & $^1B_{2u} (\pi \ra \pi^*)$ & V & 90 & 0.067 & 4.90 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +319 & & $^1A_u (\pi \ra 3s)$ & R & 92 & & 5.65 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +320 & & $^1B_{1g} (\pi \ra \pi^*)$ & V & 84 & & 5.84 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +321 & & $^1A_g (\pi \ra \pi^*)$ & V & 83 & & 5.89 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & N \\ +322 & & $^1B_{3g} (\pi \ra 3p)$ & R & 92 & & 6.07 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +323 & & $^1B_{2g} (\pi \ra 3p)$ & R & 92 & & 6.09 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +324 & & $^1B_{3u} (\pi \ra \pi^*)$ & V & 90 & (\text{n.d.}) & 6.19 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & N \\ +325 & & $^1B_{1u} (\pi \ra 3s)$ & R & 91 & (\text{n.d.}) & 6.33 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +326 & & $^1B_{2u} (\pi \ra \pi^*)$ & V & 90 & (\text{n.d.}) & 6.42 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +327 & & $^1B_{1g} (\pi \ra \pi^*)$ & V & 87 & & 6.48 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +328 & & $^1A_g (\pi \ra \pi^*)$ & V & 71 & & 6.87 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +329 & & $^3B_{2u} (\pi \ra \pi^*)$ & V & 97 & & 3.17 & CC3/AVTZ & N \\ +330 & & $^3B_{3u} (\pi \ra \pi^*)$ & V & 96 & & 4.16 & CC3/AVTZ & N \\ +331 & & $^3B_{1g} (\pi \ra \pi^*)$ & V & 97 & & 4.48 & CC3/AVTZ & N \\ +332 & & $^3B_{2u} (\pi \ra \pi^*)$ & V & 96 & & 4.64 & CC3/AVTZ & N \\ +333 & & $^3B_{3u} (\pi \ra \pi^*)$ & V & 97 & & 4.95 & CC3/AVTZ & N \\ +334 & & $^3A_g (\pi \ra \pi^*)$ & V & 97 & & 5.49 & CC3/AVTZ & N \\ +335 & & $^3B_{1g} (\pi \ra \pi^*)$ & V & 95 & & 6.17 & CC3/AVTZ & N \\ +336 & & $^3A_g (\pi \ra \pi^*)$ & V & 95 & & 6.39 & CC3/AVTZ & N \\ +337 & Nitrosomethane & $^1A'' (n \ra \pi^*)$ & V & 93 & 0.000 & 1.96 & FCI/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +338 & & $^1A' (\text{double})$ & V & 2 & 0.000 & 4.76 & FCI/AVTZ & Y \\ +339 & & $^1A' (\text{n.d.})$ & R & 90 & 0.006 & 6.29 & CCSDTQ/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +340 & & $^3A'' (n \ra \pi^*)$ & V & 98 & & 1.16 & FCI/AVTZ & Y \\ +341 & & $^3A' (\pi \ra \pi^*)$ & V & 98 & & 5.60 & FCI/AVTZ & Y \\ +342 & & $^1A'' [F] (n \ra \pi^*)$ & V & 92 & 0.000 & 1.67 & FCI/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +343 & Nitroxyl (HNO) & $^1A'' (n \ra \pi^*)$ & V & 93 & 0.000 & 1.74 & FCI/AVTZ & Y \\ +344 & & $^1A' (\text{double})$ & V & 0 & 0.000 & 4.33 & FCI/AVTZ & Y \\ +345 & & $^1A' (\text{n.d.})$ & R & 92 & 0.038 & 6.27 & CCSDTQ/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +346 & & $^3A'' (n \ra \pi^*)$ & V & 99 & & 0.88 & FCI/AVTZ & Y \\ +347 & & $^3A' (\pi \ra \pi^*)$ & V & 98 & & 5.61 & FCI/AVTZ & Y \\ +348 & Octatetraene & $^1B_u (\pi \ra \pi^*)$ & V & 91 & (\text{n.d.}) & 4.78 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +349 & & $^1A_g (\pi \ra \pi^*)$ & V & 63 & & 4.90 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & N \\ +350 & & $^3B_u (\pi \ra \pi^*)$ & V & 97 & & 2.36 & CC3/AVTZ & N \\ +351 & & $^3A_g (\pi \ra \pi^*)$ & V & 98 & & 3.73 & CC3/AVTZ & N \\ +352 & Propynal & $ ^1A'' (n \ra \pi^*)$ & V & 89 & 0.000 & 3.80 & CCSDT/AVTZ & Y \\ +353 & & $^1A'' (\pi \ra \pi^*)$ & V & 92 & 0.000 & 5.54 & CCSDT/AVTZ & Y \\ +354 & & $^3A'' (n \ra \pi^*)$ & V & 97 & & 3.47 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +355 & & $^3A' (\pi \ra \pi^*)$ & V & 98 & & 4.47 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +356 & Pyrazine & $^1B_{3u} (n \ra \pi^*)$ & V & 90 & 0.006 & 4.15 & CCSDT/AVTZ & Y \\ +357 & & $^1A_u (n \ra \pi^*)$ & V & 88 & & 4.98 & CCSDT/AVTZ & Y \\ +358 & & $^1B_{2u} (\pi \ra \pi^*)$ & V & 86 & 0.078 & 5.02 & CCSDT/AVTZ & Y \\ +359 & & $^1B_{2g} (n \ra \pi^*)$ & V & 85 & & 5.71 & CCSDT/AVTZ & Y \\ +360 & & $^1A_g (n \ra 3s)$ & R & 91 & & 6.65 & CCSDT/AVTZ & Y \\ +361 & & $^1B_{1g} (n \ra \pi^*)$ & V & 84 & & 6.74 & CCSDT/AVTZ & Y \\ +362 & & $^1B_{1u} (\pi \ra \pi^*)$ & V & 92 & 0.063 & 6.88 & CCSDT/AVTZ & Y \\ +363 & & $^1B_{1g} (\pi \ra 3s)$ & R & 93 & & 7.21 & CCSDT/AVTZ & Y \\ +364 & & $^1B_{2u} (n \ra 3p)$ & R & 90 & 0.037 & 7.24 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +365 & & $^1B_{1u} (n \ra 3p)$ & R & 91 & 0.128 & 7.44 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +366 & & $^1B_{1u} (\pi \ra \pi^*)$ & V & 90 & 0.285 & 7.98 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & N \\ +367 & & $^1A_g (\text{double})$ & V & 12 & & 8.04 & NEVPT2/AVTZ & N \\ +368 & & $^1A_g (\pi \ra \pi^*)$ & V & 71 & & 8.69 & CC3/AVTZ & N \\ +369 & & $^3B_{3u} (n \ra \pi^*)$ & V & 97 & & 3.59 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +370 & & $^3B_{1u} (\pi \ra \pi^*)$ & V & 98 & & 4.35 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +371 & & $^3B_{2u} (\pi \ra \pi^*)$ & V & 97 & & 4.39 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +372 & & $^3A_u (n \ra \pi^*)$ & V & 96 & & 4.93 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +373 & & $^3B_{2g} (n \ra \pi^*)$ & V & 97 & & 5.08 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +374 & & $^3B_{1u} (\pi \ra \pi^*)$ & V & 97 & & 5.28 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +375 & Pyridazine & $^1B_1 (n \ra \pi^*)$ & V & 89 & 0.005 & 3.83 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +376 & & $^1A_2 (n \ra \pi^*)$ & V & 86 & & 4.37 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +377 & & $^1A_1 (\pi \ra \pi^*)$ & V & 85 & 0.016 & 5.26 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +378 & & $^1A_2 (n \ra \pi^*)$ & V & 86 & & 5.72 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +379 & & $^1B_2 (n \ra 3s)$ & R & 88 & 0.001 & 6.17 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +380 & & $^1B_1 (n \ra \pi^*)$ & V & 87 & 0.004 & 6.37 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +381 & & $^1B_2 (\pi \ra \pi^*)$ & V & 90 & 0.010 & 6.75 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +382 & & $^3B_1 (n \ra \pi^*)$ & V & 97 & & 3.19 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +383 & & $^3A_2 (n \ra \pi^*)$ & V & 96 & & 4.11 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +384 & & $^3B_2 (\pi \ra \pi^*)$ & V & 98 & & 4.34 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & N \\ +385 & & $^3A_1 (\pi \ra \pi^*)$ & V & 97 & & 4.82 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +386 & Pyridine & $^1B_1 (n \ra \pi^*)$ & V & 88 & 0.004 & 4.95 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +387 & & $^1B_2 (\pi \ra \pi^*)$ & V & 86 & 0.028 & 5.14 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +388 & & $^1A_2 (n \ra \pi^*)$ & V & 87 & & 5.40 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +389 & & $^1A_1 (\pi \ra \pi^*)$ & V & 92 & 0.010 & 6.62 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +390 & & $^1A_1 (n \ra 3s)$ & R & 89 & 0.011 & 6.76 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +391 & & $^1A_2 (\pi \ra 3s)$ & R & 93 & & 6.82 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +392 & & $^1B_1 (\pi \ra 3p)$ & R & 93 & 0.045 & 7.38 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +393 & & $^1A_1 (\pi \ra \pi^*)$ & V & 90 & 0.291 & 7.39 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +394 & & $^1B_2 (\pi \ra \pi^*)$ & V & 90 & 0.319 & 7.40 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & N \\ +395 & & $^3A_1 (\pi \ra \pi^*)$ & V & 98 & & 4.30 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +396 & & $^3B_1 (n \ra \pi^*)$ & V & 97 & & 4.46 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +397 & & $^3B_2 (\pi \ra \pi^*)$ & V & 97 & & 4.79 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +398 & & $^3A_1 (\pi \ra \pi^*)$ & V & 97 & & 5.04 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +399 & & $^3A_2 (n \ra \pi^*)$ & V & 95 & & 5.36 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +400 & & $^3B_2 (\pi \ra \pi^*)$ & V & 97 & & 6.24 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +401 & Pyrimidine & $^1B_1 (n \ra \pi^*)$ & V & 88 & 0.005 & 4.44 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +402 & & $^1A_2 (n \ra \pi^*)$ & V & 88 & & 4.85 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +403 & & $^1B_2 (\pi \ra \pi^*)$ & V & 86 & 0.028 & 5.38 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +404 & & $^1A_2 (n \ra \pi^*)$ & V & 86 & & 5.92 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +405 & & $^1B_1 (n \ra \pi^*)$ & V & 86 & 0.005 & 6.26 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +406 & & $^1B_2 (n \ra 3s)$ & R & 90 & 0.005 & 6.70 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +407 & & $^1A_1 (\pi \ra \pi^*)$ & V & 91 & 0.036 & 6.88 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +408 & & $^3B_1 (n \ra \pi^*)$ & V & 96 & & 4.09 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +409 & & $^3A_1 (\pi \ra \pi^*)$ & V & 98 & & 4.51 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & N \\ +410 & & $^3A_2 (n \ra \pi^*)$ & V & 96 & & 4.66 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +411 & & $^3B_2 (\pi \ra \pi^*)$ & V & 97 & & 4.96 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +412 & Pyrrole & $^1A_2 (\pi \ra 3s)$ & R & 92 & & 5.24 & CCSDT/AVTZ & Y \\ +413 & & $^1B_1 (\pi \ra 3p)$ & R & 92 & 0.015 & 6.00 & CCSDT/AVTZ & Y \\ +414 & & $^1A_2 (\pi \ra 3p)$ & R & 93 & & 6.00 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +415 & & $^1B_2 (\pi \ra \pi^*)$ & V & 92 & 0.164 & 6.26 & CCSDT/AVTZ & Y \\ +416 & & $^1A_1 (\pi \ra \pi^*)$ & V & 86 & 0.001 & 6.30 & CCSDT/AVTZ & Y \\ +417 & & $^1B_2 (\pi \ra 3p)$ & R & 92 & 0.003 & 6.83 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +418 & & $^3B_2 (\pi \ra \pi^*)$ & V & 98 & & 4.51 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +419 & & $^3A_2 (\pi \ra 3s)$ & R & 97 & & 5.21 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +420 & & $^3A_1 (\pi \ra \pi^*)$ & V & 97 & & 5.45 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +421 & & $^3B_1 (\pi \ra 3p)$ & R & 97 & & 5.91 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +422 & SiCl2 & $^1B_1 (\sigma \ra \pi^*)$ & V & 92 & 0.031 & 3.91 & FCI/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +423 & & $^3B_1 (\sigma \ra \pi^*)$ & V & 98 & & 2.48 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +424 & Silylidene & $^1A_2 (\text{n.d.})$ & R & 92 & & 2.11 & FCI/AVTZ & Y \\ +425 & & $^1B_2 (\text{n.d.})$ & R & 88 & 0.033 & 3.78 & FCI/AVTZ & Y \\ +426 & Streptocyanine-1 & $^1B_2 (\pi \ra \pi^*)$ & V & 88 & 0.347 & 7.13 & FCI/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +427 & & $^3B_2 (\pi \ra \pi^*)$ & V & 98 & & 5.52 & FCI/AVTZ & Y \\ +428 & Streptocyanine-3 & $^1B_2 (\pi \ra \pi^*)$ & V & 87 & 0.755 & 4.82 & FCI/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +429 & & $^3B_2 (\pi \ra \pi^*)$ & V & 98 & & 3.44 & FCI/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +430 & Streptocyanine-5 & $^1B_2 (\pi \ra \pi^*)$ & V & 85 & 1.182 & 3.64 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +431 & & $^3B_2 (\pi \ra \pi^*)$ & V & 97 & & 2.47 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +432 & Tetrazine & $^1B_{3u} (n \ra \pi^*)$ & V & 89 & 0.006 & 2.47 & CCSDT/AVTZ & Y \\ +433 & & $^1A_u (n \ra \pi^*)$ & V & 87 & & 3.69 & CCSDT/AVTZ & Y \\ +434 & & $^1A_g (\text{double})$ & V & 0 & & 4.61 & NEVPT2/AVTZ & N \\ +435 & & $^1B_{1g} (n \ra \pi^*)$ & V & 83 & & 4.93 & CCSDT/AVTZ & Y \\ +436 & & $^1B_{2u} (\pi \ra \pi^*)$ & V & 85 & 0.055 & 5.21 & CCSDT/AVTZ & Y \\ +437 & & $^1B_{2g} (n \ra \pi^*)$ & V & 81 & & 5.45 & CCSDT/AVTZ & Y \\ +438 & & $^1A_u (n \ra \pi^*)$ & V & 87 & & 5.53 & CCSDT/AVTZ & Y \\ +439 & & $^1B_{3g} (\text{double})$ & V & 0 & & 6.15 & NEVPT2/AVTZ & N \\ +440 & & $^1B_{2g} (n \ra \pi^*)$ & V & 80 & & 6.12 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +441 & & $^1B_{1g} (n \ra \pi^*)$ & V & 85 & & 6.91 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +442 & & $^3B_{3u} (n \ra \pi^*)$ & V & 97 & & 1.85 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +443 & & $^3A_u (n \ra \pi^*)$ & V & 96 & & 3.45 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +444 & & $^3B_{1g} (n \ra \pi^*)$ & V & 97 & & 4.20 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +445 & & $^1B_{1u} (\pi \ra \pi^*)$ & V & 98 & & 4.49 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & N \\ +446 & & $^3B_{2u} (\pi \ra \pi^*)$ & V & 97 & & 4.52 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +447 & & $^3B_{2g} (n \ra \pi^*)$ & V & 96 & & 5.04 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +448 & & $^3A_u (n \ra \pi^*)$ & V & 96 & & 5.11 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +449 & & $^3B_{3g} (\text{double})$ & V & 5 & & 5.51 & NEVPT2/AVTZ & N \\ +450 & & $^3B_{1u} (\pi \ra \pi^*)$ & V & 96 & & 5.42 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +451 & Thioacetone & $^1A_2 (n \ra \pi^*)$ & V & 88 & & 2.53 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +452 & & $^1B_2 (n \ra 3s)$ & R & 91 & 0.052 & 5.56 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +453 & & $^1A_1 (\pi \ra \pi^*)$ & V & 90 & 0.242 & 5.88 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +454 & & $^1B_2 (n \ra 3p)$ & R & 92 & 0.028 & 6.51 & CCSDTQ/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +455 & & $^1A_1 (n \ra 3p)$ & R & 91 & 0.023 & 6.61 & CCSDTQ/6-31+G(d) + [CCSDT/AVTZ - CCSDT/6-31+G(d)] & Y \\ +456 & & $^3A_2 (n \ra \pi^*)$ & V & 97 & & 2.33 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +457 & & $^3A_1 (\pi \ra \pi^*)$ & V & 98 & & 3.45 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +458 & Thioacrolein & $^1A'' (n \ra \pi^*)$ & V & 86 & 0.000 & 2.11 & CCSDT/AVTZ & Y \\ +459 & & $^3A'' (n \ra \pi^*)$ & V & 96 & & 1.91 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +460 & Thioformaldehyde & $^1A_2 (n \ra \pi^*)$ & V & 89 & & 2.22 & FCI/AVTZ & Y \\ +461 & & $^1B_2 (n \ra 3s)$ & R & 92 & 0.012 & 5.96 & FCI/AVTZ & Y \\ +462 & & $^1A_1 (\pi \ra \pi^*)$ & V & 90 & 0.178 & 6.38 & CCSDTQ/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +463 & & $^3A_2 (n \ra \pi^*)$ & V & 97 & & 1.94 & FCI/AVTZ & Y \\ +464 & & $^3A_1 (\pi \ra \pi^*)$ & V & 98 & & 3.43 & FCI/AVTZ & Y \\ +465 & & $^3B_2 (n \ra 3s)$ & R & 97 & & 5.72 & FCI/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ] & Y \\ +466 & & $^1A_2 [F] (n \ra \pi^*)$ & V & 87 & & 1.95 & FCI/AVTZ & Y \\ +467 & Thiophene & $^1A_1 (\pi \ra \pi^*)$ & V & 87 & 0.070 & 5.64 & CCSDT/AVTZ & Y \\ +468 & & $^1B_2 (\pi \ra \pi^*)$ & V & 91 & 0.079 & 5.98 & CCSDT/AVTZ & Y \\ +469 & & $^1A_2 (\pi \ra 3s)$ & R & 92 & & 6.14 & CCSDT/AVTZ & Y \\ +470 & & $^1B_1 (\pi \ra 3p)$ & R & 90 & 0.010 & 6.14 & CCSDT/AVTZ & Y \\ +471 & & $^1A_2 (\pi \ra 3p)$ & R & 91 & & 6.21 & CCSDT/AVTZ & Y \\ +472 & & $^1B_1 (\pi \ra 3s)$ & R & 92 & 0.000 & 6.49 & CCSDT/AVTZ & Y \\ +473 & & $^1B_2 (\pi \ra 3p)$ & R & 92 & 0.082 & 7.29 & CCSDT/AVTZ & Y \\ +474 & & $^1A_1 (\pi \ra \pi^*)$ & V & 86 & 0.314 & 7.31 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & N \\ +475 & & $^3B_2 (\pi \ra \pi^*)$ & V & 98 & & 3.97 & FCI/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +476 & & $^3A_1 (\pi \ra \pi^*)$ & V & 97 & & 4.76 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +477 & & $^3B_1 (\pi \ra 3p)$ & R & 96 & & 5.93 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +478 & & $^3A_2 (\pi \ra 3s)$ & R & 97 & & 6.08 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +479 & Thiopropynal & $^1A'' (n \ra \pi^*)$ & V & 87 & 0.000 & 2.03 & CCSDT/AVTZ & Y \\ +480 & & $^3A'' (n \ra \pi^*)$ & V & 97 & & 1.80 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +481 & Triazine & $^1A_1'' (n \ra \pi^*)$ & V & 88 & & 4.72 & CCSDT/AVTZ & Y \\ +482 & & $^1A_2'' (n \ra \pi^*)$ & V & 88 & 0.014 & 4.75 & CCSDT/AVTZ & Y \\ +483 & & $^1E'' (n \ra \pi^*)$ & V & 88 & & 4.78 & CCSDT/AVTZ & Y \\ +484 & & $^1A_2' (\pi \ra \pi^*)$ & V & 85 & & 5.75 & CCSDT/AVTZ & Y \\ +485 & & $^1A_1' (\pi \ra \pi^*)$ & V & 90 & & 7.24 & CCSDT/AVTZ & Y \\ +486 & & $^1E' (n \ra 3s)$ & R & 90 & 0.016 & 7.32 & CCSDT/AVTZ & Y \\ +487 & & $^1E'' (n \ra \pi^*)$ & V & 82 & & 7.78 & CCSDT/AVTZ & Y \\ +488 & & $^1E' (\pi \ra \pi^*)$ & V & 90 & 0.451 & 7.94 & CCSDT/AVTZ & Y \\ +489 & & $^3A_2'' (n \ra \pi^*)$ & V & 96 & & 4.33 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +490 & & $^3E'' (n \ra \pi^*)$ & V & 96 & & 4.51 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +491 & & $^3A_1'' (n \ra \pi^*)$ & V & 96 & & 4.73 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +492 & & $^3A_1' (\pi \ra \pi^*)$ & V & 98 & & 4.85 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +493 & & $^3E' (\pi \ra \pi^*)$ & V & 96 & & 5.59 & CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)] & Y \\ +494 & & $^3A_2' (\pi \ra \pi^*)$ & V & 97 & & 6.62 & CCSDT/AVDZ + [CC3/AVTZ - CC3/AVDZ] & Y \\ +495 & Water & $^1B_1 (n \ra 3s)$ & R & 93 & 0.054 & 7.62 & FCI/AVTZ & Y \\ +496 & & $^1A_2 (n \ra 3p)$ & R & 93 & & 9.41 & FCI/AVTZ & Y \\ +497 & & $^1A_1 (n \ra 3s)$ & R & 93 & 0.100 & 9.99 & FCI/AVTZ & Y \\ +498 & & $^3B_1 (n \ra 3s)$ & R & 98 & & 7.25 & FCI/AVTZ & Y \\ +499 & & $^3A_2 (n \ra 3p)$ & R & 98 & & 9.24 & FCI/AVTZ & Y \\ +500 & & $^3A_1 (n \ra 3s)$ & R & 98 & & 9.54 & FCI/AVTZ & Y \\ +\end{longtable} +\end{ThreePartTable} + +%%% TABLE III %%% +\begin{table}[htp] +\centering +\scriptsize +\caption{Theoretical best estimates TBEs (in eV) for the doublet-doublet transitions of the open-shell molecules belonging to QUEST\#4. +These TBEs are obtained with the aug-cc-pVTZ basis set, and ``Method'' indicates the protocol employed to compute them.} +\label{tab:rad} +\begin{threeparttable} +\begin{tabular}{cllcl} +\headrow +\thead{\#} & \thead{Molecule} & \thead{Transition} & \thead{TBE/aug-cc-pVTZ} & \thead{Method} \\ +1 & Allyl &$^2B_1$ &3.39 & FCI/6-31+G(d) + [CCSDT/aug-cc-pVTZ - CCSDT/6-31+G(d)] \\ +2 & &$^2A_1$ &4.99 & FCI/6-31+G(d) + [CCSDT/aug-cc-pVTZ - CCSDT/6-31+G(d)] \\ +3 & \ce{BeF} &$^2\Pi$ &4.14 & FCI/aug-cc-pVTZ \\ +4 & &$^2\Sigma^+$ &6.21 & FCI/aug-cc-pVTZ \\ +5 & \ce{BeH} &$^2\Pi$ &2.49 & FCI/aug-cc-pVTZ \\ +6 & &$^2\Pi$ &6.46 & FCI/aug-cc-pVTZ \\ +7 & \ce{BH2} &$^2B_1$ &1.18 & FCI/aug-cc-pVTZ \\ +8 & \ce{CH} &$^2\Delta$ &2.91 & FCI/aug-cc-pVTZ \\ +9 & &$^2\Sigma^-$ &3.29 & FCI/aug-cc-pVTZ \\ +10 & &$^2\Sigma^+$ &3.98 & FCI/aug-cc-pVTZ \\ +11 & \ce{CH3} &$^2A_1'$ &5.85 & FCI/aug-cc-pVTZ \\ +12 & &$^2E'$ &6.96 & FCI/aug-cc-pVTZ \\ +13 & &$^2E'$ &7.18 & FCI/aug-cc-pVTZ \\ +14 & &$^2A_2''$ &7.65 & FCI/aug-cc-pVTZ \\ +15 & \ce{CN} &$^2\Pi$ &1.34 & FCI/aug-cc-pVTZ \\ +16 & &$^2\Sigma^+$ &3.22 & FCI/aug-cc-pVTZ \\ +17 & \ce{CNO} &$^2\Sigma^+$ &1.61 & FCI/aug-cc-pVTZ \\ +18 & &$^2\Pi$ &5.49 & FCI/6-31+G(d) + [CCSDT/aug-cc-pVTZ - CCSDT/6-31+G(d)] \\ +19 & \ce{CON} &$^2\Pi$ &3.53 & FCI/aug-cc-pVDZ + [CCSDT/aug-cc-pVTZ - CCSDT/aug-cc-pVDZ] \\ +20 & &$^2\Sigma^+$ &3.86 & CCSDTQ/6-31+G(d) + [CCSDT/aug-cc-pVTZ - CCSDT/6-31+G(d)] \\ +21 & \ce{CO+} &$^2\Pi$ &3.28 & FCI/aug-cc-pVTZ \\ +22 & &$^2\Sigma^+$ &5.81 & FCI/aug-cc-pVTZ \\ +23 & \ce{F2BO} &$^2B_1$ &0.73 & FCI/aug-cc-pVDZ + [CCSDT/aug-cc-pVTZ - CCSDT/aug-cc-pVDZ] \\ +24 & &$^2A_1$ &2.80 & FCI/aug-cc-pVDZ + [CCSDT/aug-cc-pVTZ - CCSDT/aug-cc-pVDZ] \\ +25 & \ce{F2BS} &$^2B_1$ &0.51 & FCI/aug-cc-pVDZ + [CCSDT/aug-cc-pVTZ - CCSDT/aug-cc-pVDZ] \\ +26 & &$^2A_1$ &2.99 & FCI/aug-cc-pVDZ + [CCSDT/aug-cc-pVTZ - CCSDT/aug-cc-pVDZ] \\ +27 & \ce{H2BO} &$^2B_1$ &2.15 & FCI/aug-cc-pVTZ \\ +28 & &$^2A_1$ &3.49 & FCI/aug-cc-pVTZ \\ +29 & \ce{HCO} &$^2A''$ &2.09 & FCI/aug-cc-pVTZ \\ +30 & &$^2A'$ &5.45 & FCI/aug-cc-pVDZ + [CCSDT/aug-cc-pVTZ - CCSDT/aug-cc-pVDZ] \\ +31 & \ce{HOC} &$^2A''$ &0.92 & FCI/aug-cc-pVTZ \\ +32 & \ce{H2PO} &$^2A''$ &2.80 & FCI/aug-cc-pVTZ \\ +33 & &$^2A'$ &4.21 & FCI/aug-cc-pVDZ + [CCSDT/aug-cc-pVTZ - CCSDT/aug-cc-pVDZ] \\ +34 & \ce{H2PS} &$^2A''$ &1.16 & FCI/aug-cc-pVTZ \\ +35 & &$^2A'$ &2.72 & FCI/aug-cc-pVTZ \\ +36 & \ce{NCO} &$^2\Sigma^+$ &2.89 & FCI/aug-cc-pVDZ + [CCSDT/aug-cc-pVTZ - CCSDT/aug-cc-pVDZ] \\ +37 & &$^2\Pi$ &4.73 & FCI/aug-cc-pVDZ + [CCSDT/aug-cc-pVTZ - CCSDT/aug-cc-pVDZ] \\ +38 & \ce{NH2} &$^2A_1$ &2.12 & FCI/aug-cc-pVTZ \\ +39 & Nitromethyl &$^2B_2$ &2.05 & CCSDT/aug-cc-pVTZ \\ +40 & &$^2A_2$ &2.38 & CCSDT/aug-cc-pVTZ \\ +41 & &$^2A_1$ &2.56 & CCSDT/aug-cc-pVTZ \\ +42 & &$^2B_1$ &5.35 & CCSDT/aug-cc-pVTZ \\ +43 & \ce{NO} &$^2\Sigma^+$ &6.13 & FCI/aug-cc-pVTZ \\ +44 & &$^2\Sigma^+$ &7.29 & CCSDTQ/aug-cc-pVTZ \\ +45 & \ce{OH} &$^2\Sigma^+$ &4.10 & FCI/aug-cc-pVTZ \\ +46 & &$^2\Sigma^-$ &8.02 & FCI/aug-cc-pVTZ \\ +47 & \ce{PH2} &$^2A_1$ &2.77 & FCI/aug-cc-pVTZ \\ +48 & Vinyl &$^2A''$ &3.26 & FCI/aug-cc-pVTZ \\ +49 & &$^2A''$ &4.69 & FCI/aug-cc-pVTZ \\ +50 & &$^2A'$ &5.60 & FCI/aug-cc-pVTZ \\ +51 & &$^2A'$ &6.20 & FCI/6-31+G(d) + [CCSDT/aug-cc-pVTZ - CCSDT/6-31+G(d)] \\ +\hline +\end{tabular} +\end{threeparttable} +\end{table} +%%% %%% %%% %%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Benchmarks} +\label{sec:bench} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +In this section, we report a comprehensive benchmark of various lower-order methods on the entire set of closed-shell compounds belonging to the QUEST database. +Statistical quantities are reported in Table \ref{tab:stat} (the entire set of data can be found in the {\SupInf}). +Additionally, we also provide a specific analysis for each type of excited states. +Hence, the statistical values are reported for various types of excited states and molecular sizes for the MSE and MAE. +The distribution of the errors in vertical excitation energies (with respect to the TBE/aug-cc-pVTZ reference values) are represented in Fig.~\ref{fig:QUEST_stat} for all the ``safe'' excitations having a dominant single excitation character (\ie, the double excitations are discarded). +Similar graphs are reported in the {\SupInf} for specific sets of transitions and molecules. + +%%% TABLE IV %%% +\begin{sidewaystable} +\scriptsize +\centering +\caption{Mean signed error (MSE), mean absolute error (MAE), root-mean-square error (RMSE), standard deviation of the errors (SDE), as well as the maximum positive error [Max(+)] and negative error [Max($-$)] with respect to the TBE/aug-cc-pVTZ for the entire QUEST database. +Only the ``safe'' TBEs are considered (see Table \ref{tab:TBE}). +For the MSE and MAE, the statistical values are reported for various types of excited states and molecular sizes. +All quantities are given in eV. +``Count'' refers to the number of transitions considered for each method.} +\label{tab:stat} +\begin{threeparttable} +\begin{tabular}{llccccccccccccccc} +\headrow + & & \thead{CIS(D)} & \thead{CC2} & \thead{EOM-MP2} & \thead{STEOM-CCSD} & \thead{CCSD} & \thead{CCSDR(3)} & \thead{CCCSDT-3} & \thead{CC3} + & \thead{SOS-ADC(2)$^a$} & \thead{SOS-CC2$^a$} & \thead{SCS-CC2$^a$} & \thead{SOS-ADC(2)$^b$} & \thead{ADC(2)} & \thead{ADC(3)} & \thead{ADC(2.5)} \\ +Count & & 429 & 431 & 427 & 360 & 431 & 259 & 251 & 431 & 430 & 430 & 430 & 430 & 426 & 423 & 423 \\ +Max(+) & & 1.06 & 0.63 & 0.80 & 0.59 & 0.80 & 0.43 & 0.26 & 0.19 & 0.87 & 0.84 & 0.76 & 0.73 & 0.64 & 0.60 & 0.24 \\ +Max($-$) & & -0.69 & -0.71 & -0.38 & -0.56 & -0.25 & -0.07 & -0.07 & -0.09 & -0.29 & -0.24 & -0.92 & -0.46 & -0.76 & -0.79 & -0.34 \\ +MSE & & 0.13 & 0.02 & 0.18 & -0.01 & 0.10 & 0.04 & 0.04 & 0.00 & 0.18 & 0.21 & 0.15 & 0.02 & -0.01 & -0.12 & -0.06 \\ + & singlet & 0.10 & -0.02 & 0.22 & 0.03 & 0.14 & 0.04 & 0.04 & 0.00 & 0.18 & 0.20 & 0.13 & 0.00 & -0.04 & -0.08 & -0.06 \\ + & triplet & 0.19 & 0.08 & 0.14 & -0.07 & 0.03 & & & 0.00 & 0.19 & 0.22 & 0.17 & 0.04 & 0.04 & -0.18 & -0.07 \\ + & valence & 0.20 & 0.10 & 0.20 & -0.06 & 0.10 & 0.06 & 0.05 & 0.00 & 0.19 & 0.24 & 0.20 & 0.02 & 0.04 & -0.16 & -0.06 \\ + & Rydberg & -0.04 & -0.17 & 0.15 & 0.09 & 0.08 & 0.01 & 0.03 & -0.01 & 0.16 & 0.12 & 0.01 & 0.02 & -0.13 & -0.02 & -0.07 \\ + & $n \ra \pis$ & 0.16 & 0.02 & 0.24 & -0.03 & 0.17 & 0.07 & 0.07 & 0.00 & 0.26 & 0.32 & 0.22 & 0.05 & -0.05 & -0.01 & -0.03 \\ + & $\pi \ra \pis$& 0.25 & 0.17 & 0.20 & -0.07 & 0.06 & 0.05 & 0.04 & 0.00 & 0.15 & 0.19 & 0.19 & 0.00 & 0.12 & -0.27 & -0.07 \\ + & 1--3 non-H & 0.10 & 0.03 & 0.03 & -0.02 & 0.04 & 0.01 & 0.01 & 0.00 & 0.13 & 0.16 & 0.11 & -0.01 & -0.01 & -0.17 & -0.09 \\ + & 4 non-H & 0.13 & 0.04 & 0.12 & 0.00 & 0.09 & 0.03 & 0.04 & 0.00 & 0.19 & 0.26 & 0.19 & 0.03 & -0.04 & -0.10 & -0.07 \\ + & 5--6 non-H & 0.17 & 0.02 & 0.30 & -0.01 & 0.11 & 0.05 & 0.05 & 0.00 & 0.21 & 0.20 & 0.14 & 0.03 & 0.03 & -0.10 & -0.04 \\ + & 7--10 non-H & 0.15 & -0.03 & 0.42 & -0.05 & 0.22 & 0.10 & 0.08 & -0.01 & 0.26 & 0.29 & 0.19 & 0.05 & -0.06 & -0.02 & -0.04 \\ +SDE & & 0.24 & 0.20 & 0.21 & 0.13 & 0.12 & 0.05 & 0.04 & 0.02 & 0.17 & 0.16 & 0.16 & 0.15 & 0.20 & 0.22 & 0.08 \\ +RMSE & & 0.29 & 0.22 & 0.28 & 0.15 & 0.16 & 0.07 & 0.06 & 0.03 & 0.25 & 0.26 & 0.22 & 0.17 & 0.21 & 0.26 & 0.10 \\ +MAE & & 0.22 & 0.16 & 0.22 & 0.11 & 0.12 & 0.05 & 0.04 & 0.02 & 0.20 & 0.22 & 0.18 & 0.13 & 0.15 & 0.21 & 0.08 \\ + & singlet & 0.22 & 0.16 & 0.25 & 0.10 & 0.14 & 0.05 & 0.04 & 0.02 & 0.21 & 0.22 & 0.17 & 0.14 & 0.16 & 0.20 & 0.09 \\ + & triplet & 0.23 & 0.15 & 0.18 & 0.12 & 0.08 & & & 0.01 & 0.20 & 0.23 & 0.19 & 0.11 & 0.15 & 0.22 & 0.08 \\ + & valence & 0.22 & 0.14 & 0.24 & 0.12 & 0.13 & 0.06 & 0.05 & 0.02 & 0.21 & 0.25 & 0.20 & 0.12 & 0.13 & 0.22 & 0.08 \\ + & Rydberg & 0.22 & 0.21 & 0.19 & 0.10 & 0.08 & 0.03 & 0.03 & 0.02 & 0.20 & 0.15 & 0.13 & 0.14 & 0.21 & 0.18 & 0.09 \\ + & $n \ra \pis$ & 0.18 & 0.08 & 0.28 & 0.08 & 0.17 & 0.07 & 0.07 & 0.01 & 0.26 & 0.32 & 0.22 & 0.11 & 0.10 & 0.14 & 0.07 \\ + & $\pi \ra \pis$& 0.27 & 0.19 & 0.21 & 0.14 & 0.11 & 0.06 & 0.04 & 0.02 & 0.18 & 0.21 & 0.20 & 0.12 & 0.16 & 0.28 & 0.09 \\ + & 1--3 non-H & 0.23 & 0.19 & 0.13 & 0.10 & 0.07 & 0.03 & 0.03 & 0.02 & 0.18 & 0.20 & 0.19 & 0.14 & 0.19 & 0.24 & 0.10 \\ + & 4 non-H & 0.22 & 0.19 & 0.15 & 0.11 & 0.11 & 0.03 & 0.04 & 0.02 & 0.19 & 0.26 & 0.22 & 0.13 & 0.18 & 0.23 & 0.08 \\ + & 5--6 non-H & 0.21 & 0.12 & 0.30 & 0.12 & 0.13 & 0.06 & 0.05 & 0.01 & 0.22 & 0.21 & 0.15 & 0.11 & 0.11 & 0.19 & 0.07 \\ + & 7--10 non-H & 0.24 & 0.11 & 0.42 & 0.12 & 0.23 & 0.10 & 0.08 & 0.02 & 0.27 & 0.29 & 0.19 & 0.12 & 0.14 & 0.16 & 0.07 \\ +\hline +\end{tabular} +\begin{tablenotes} +\item $^a$ Excitation energies computed with TURBOMOLE. +\item $^b$ Excitation energies computed with Q-CHEM. +\end{tablenotes} +\end{threeparttable} +\end{sidewaystable} + +%%% FIGURE 5 %%% +\begin{figure} + \centering + \includegraphics[width=0.9\textwidth]{fig5} + \caption{Distribution of the error (in eV) in excitation energies (with respect to the TBE/aug-cc-pVTZ values) for various methods for the entire QUEST database considering only closed-shell compounds. + Only the ``safe'' TBEs are considered (see Table \ref{tab:TBE}). + See Table \ref{tab:stat} for the values of the corresponding statistical quantities. + QC and TM indicate that Q-CHEM and TURBOMOLE scaling factors are considered, respectively. The SOS-CC2 and SCS-CC2 approaches are obtained with the latter code. + \label{fig:QUEST_stat}} +\end{figure} + +The most striking feature from the statistical indicators gathered in Table \ref{tab:stat} is the overall accuracy of CC3 with MAEs and MSEs systematically below the chemical accuracy threshold (errors $<$ 0.043 eV or 1 kcal/mol), irrespective of the nature of the transition and the size of the molecule. +CCSDR(3) are CCCSDT-3 can also be regarded as excellent performers with overall MAEs below $0.05$ eV, though one would notice a slight degradation of their performances for the $n \ra \pis$ excitations and the largest molecules of the database. +The other third-order method, ADC(3), which enjoys a lower computational cost, is significantly less accurate and does not really improve upon its second-order analog, even for the largest systems considered here, an observation in line with a previous analysis by some of the authors \cite{Loos_2020d}. +Nonetheless, ADC(3)'s accuracy improves in larger compounds, with a MAE of 0.24 eV (0.16 eV) for the subsets of the most compact (extended) compounds considered herein. The ADC(2.5) composite method introduced in Ref.~\cite{Loos_2020d}, which corresponds to grossly average the ADC(2) and ADC(3) +values, yields an appreciable accuracy improvement, as shown in Fig.~\ref{fig:QUEST_stat}. Indeed, we note that the MAE of 0.07 eV obtained for ``large'' compounds is comparable to the one obtained with CCSDR(3) and CCSDT-3 for these molecules. All these third-order methods +are rather equally efficient for valence and Rydberg transitions. + +Concerning the second-order methods (which have the indisputable advantage to be applicable to larger molecules than the ones considered here), we have the following ranking in terms of MAEs: EOM-MP2 $\approx$ CIS(D) $<$ CC2 $\approx$ ADC(2) $<$ CCSD $\approx$ STEOM-CCSD, which fits our previous conclusions on the specific subsets \cite{Loos_2018a,Loos_2019,Loos_2020b,Loos_2020c,Loos_2020d}. +A very similar ranking is obtained when one looks at the MSEs. +It is noteworthy that the performances of EOM-MP2 and CCSD are getting notably worse when the system size increases, while CIS(D) and STEOM-CCSD have a very stable behavior with respect to system size. +Indeed, the EOM-MP2 MAE attains 0.42 eV for molecules containing between 7 and 10 non-hydrogen atoms, whereas the CCSD tendency to overshoot the transition energies yield a MSE of 0.22 eV for the same set (a rather large error). +For CCSD, this conclusion fits benchmark studies published by other groups \cite{Schreiber_2008,Caricato_2010,Watson_2013,Kannar_2014,Kannar_2017,Dutta_2018}. +For example, K\'ann\'ar and Szalay obtained a MAE of 0.18 eV on Thiel's set for the states exhibiting a dominant single excitation character. +The CCSD degradation with system size might partially explain the similar (though less pronounced) trend obtained for CCSDR(3). +Regarding the apparently better performances of STEOM-CCSD as compared to CCSD, we recall that several challenging states have been naturally removed from the STEOM-CCSD statistics because the active character percentage was lower than $98\%$ (see above). +In contrast to EOM-MP2 and CCSD, the overall accuracy of CC2 and ADC(2) does significantly improve for larger molecules, the performances of the two methods being, as expected, similar \cite{Harbach_2014}. +Let us note that these two methods show similar accuracies for singlet and triplet transitions, but are significantly less accurate for Rydberg transitions, as already pointed out previously \cite{Kannar_2017}. +Therefore, both CC2 and ADC(2) offer an appealing cost-to-accuracy ratio for large compounds, which explains their popularity in realistic chemical scenarios \cite{Hattig_2005c,Goerigk_2010a,Send_2011a,Winter_2013,Jacquemin_2015b,Oruganti_2016}. +For the scaled methods [SOS-ADC(2), SOS-CC2, and SCS-CC2], the TURBOMOLE scaling factors do not seem to improve things upon the unscaled versions, while the Q-CHEM scaling factors for ADC(2) provide a small, yet significant improvement for this set of molecules. +Of course, one of the remaining open questions regarding all these methods is their accuracy for even larger systems. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{The QUESTDB website} +\label{sec:website} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +Quite a large number of calculations were required for each of the +QUEST articles \cite{Loos_2018a,Loos_2019,Loos_2020b,Loos_2020c,Loos_2020d}. +Up to now, all the curated data was shared as +supplementary information presented as a file in portable document +format (pdf). This way of sharing data does not require too much +effort for the authors, but it is obviously not optimal from the +user's point of view. +We have now addressed this problem by creating a database which +contains all the vertical and fluorescence transition energies as well +the corresponding molecular geometries. This data can be manipulated via +a web application which allows to plot the statistical indicators (generated with the \texttt{Plotly} library) +computed on selected subsets of molecules, methods and basis sets. +The application also gives the possibility to the user to import +external data files, in order to compare the performance of methods +that are not in our database. +Both the web application and the data are hosted in a single GitHub +repository (\url{https://github.com/LCPQ/QUESTDB_website}) +and available at the following address: \url{https://lcpq.github.io/QUESTDB_website}. +In this way, extending the database is as simple as adding new data files to the +repository, together with the corresponding bibliographic references, +and we strongly encourage users to contribute to enlarge this database +via GitHub pull requests. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Concluding remarks} +\label{sec:ccl} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +In the present review article, we have presented and extended the QUEST database of highly-accurate excitation energies for molecular systems \cite{Loos_2020a,Loos_2018a,Loos_2019,Loos_2020b,Loos_2020c} that we started building +in 2018 and that is now composed by more than 500 vertical excitations, many of which can be reasonably considered as within 1 kcal/mol (or less) of the FCI limit for the considered CC3/aug-cc-pVTZ geometry and basis set (\emph{aug}-cc-pVTZ). +In particular, we have detailed the specificities of our protocol by providing computational details regarding geometries, basis sets, as well as reference and benchmarked computational methods. The content of our five QUEST subsets has +been presented in detail, and for each of them, we have provided the number of reference excitation energies, the nature and size of the molecules, the list of benchmarked methods, as well as other useful specificities. +Importantly, we have proposed a new statistical method that produces much safer estimates of the extrapolation error in SCI calculations. This new method based on Gaussian random variables has been tested by computing additional FCI values for five- and six-membered rings. +After having discussed the generation of our TBEs, we have reported a comprehensive benchmark for a significant number of methods on the entire QUEST set with, in addition, a specific analysis for each type of excited states. +Finally, the main features of the website specifically designed to gather the entire data generated during these past few years have been presented and discussed. + +Paraphrasing Thiel's conclusions \cite{Schreiber_2008}, we hope that not only the QUEST database will be used for further benchmarking and testing, but that other research groups will also improve it, providing not only corrections +(inevitable in such a large data set), but more importantly extensions with both improved estimates for some compounds and states, or new molecules. +In this framework, we provide in the {\SupInf} a file with all our benchmark data. + +Regarding future improvements and extensions, we would like to mention that although our present goal is to produce chemically accurate vertical excitation energies, we are currently devoting great efforts to obtain highly-accurate excited-state properties \cite{Hodecker_2019,Eriksen_2020b} such as dipoles and oscillator strengths for molecules of small and medium sizes \cite{Chrayteh_2021,Sarkar_2021}, so as to complete previous efforts aiming at determining accurate excited-state geometries \cite{Budzak_2017,Jacquemin_2018}. +Reference ground-state properties (such as correlation energies and atomization energies) are also being currently produced \cite{Scemama_2020,Loos_2020e}. +Besides this, because computing 500 (or so) excitation energies can be a costly exercise even with cheap computational methods, we are planning on developing a ``diet set'' (\ie, a much smaller set of excitation energies which can reproduce key results of the full QUEST database, including ranking of approximations) following the philosophy of the ``diet GMTKN55'' set proposed recently by Gould \cite{Gould_2018b}. +We hope to report on this in the near future. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\section*{acknowledgements} +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%AS, MC, and PFL thank the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant agreement No.~863481) for financial support. +%Support from the \textit{``Centre National de la Recherche Scientifique''} is acknowledged. + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section*{research resources} +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +This work was performed using HPC resources from GENCI-TGCC (Grand Challenge 2019-gch0418) and from CALMIP (Toulouse) under allocation 2020-18005. +DJ acknowledges the \textit{R\'egion des Pays de la Loire} for financial support and the CCIPL computational center for ultra-generous allocation of computational time. + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section*{conflict of interest} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +The authors have declared no conflicts of interest for this article. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section*{supporting information} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +Cartesian coordinates of each molecule (in bohr), Python code associated with the algorithm employed to compute the extrapolated FCI excitation energies and their associated error bars (as well as additional examples for smaller systems), a detailed discussion of each molecule of the QUEST\#5 subset including comparisons with literature data, Excel spreadsheet gathering all benchmark data and additional statistical analyses for various molecular and excitation subsets. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\bibliography{QUESTDB} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\newpage + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{biography}[MVeril]{M.~V\'eril} +was born in Toulouse in 1993. +He received his B.Sc.~in Molecular Chemistry from the Universit\'e Paul Sabatier (Toulouse, France) in 2015 and his M.Sc.~in Computational and Theoretical Chemistry and Modeling from the same university in 2018. +Since 2018, he is a Ph.D.~student in the group of Dr.~Pierre-Fran\c{c}ois Loos at the Laboratoire de Chimie et Physique Quantiques in Toulouse. +He is currently developing QUANTUM PACKAGE and the web application linked to the QUEST project. +\end{biography} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{biography}[AScemama]{A.~Scemama} +received his Ph.D.~in Computational and Theoretical Chemistry from the Universit\'e Pierre et Marie Curie (Paris, France) in 2004. +He then moved to the Netherlands for a one-year postdoctoral stay in the group of Claudia Filippi, and came back in France for another year in the group of Eric Canc\`es. +In 2006, he obtained a Research Engineer position from the \textit{``Centre National de la Recherche Scientifique (CNRS)} at the \textit{Laboratoire de Chimie et Physique Quantiques} in Toulouse (France) to work on computational methods and high-performance computing for quantum chemistry. He was awarded the Crystal medal of the CNRS in 2019. +\end{biography} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{biography}[MCaffarel]{M.~Caffarel} +received his Ph.D. in Theoretical Physics and Chemistry from the Universit\'e Pierre et Marie Curie (Paris, France) in 1987, before moving to the University of Illinois at Urbana-Champaign for a two-year postdoctoral stay in the group of Prof.~David Ceperley. +He is currently working as a senior scientist at the ``Centre National de la Recherche Scientifique (CNRS)'' at the Laboratoire de Chimie et Physique Quantiques in Toulouse (France). +His research is mainly focused on the development and application of quantum Monte Carlo methods for theoretical chemistry and condensed-mater physics. +\end{biography} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{biography}[FLipparini]{F.~Lipparini} +got his Ph.D. in Chemistry from Scuola Normale Superiore, Pisa in 2013. He worked as a Postdoc at the Universit\'e Pierre et Marie Curie in Paris and moved to Mainz, Germany, with a fellowship from the Alexander von Humboldt foundation and then as a regular postdoc. Since June 2017 he is assistant professor of Physical Chemistry at the department of Chemistry of the University of Pisa, in Italy. In 2014, he was awarded the ``Eolo Scrocco'' prize for young researcher in theoretical and computational chemistry by the Italian Chemical Society. His research focuses on mathematical methods and algorithms for computational chemistry, with a particular interest to their application to multiscale methods and electronic structure theory. +\end{biography} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{biography}[MBoggioPasqua]{M.~Boggio-Pasqua} +received his PhD in Physical Chemistry from the Universit\'e Bordeaux 1 in 1999. +He then worked as a post-doctoral research associate at King's College London (2000-2003) and at Imperial College London (2004-2007) with M.~Robb and M.~Bearpark. +He was then appointed as a CNRS researcher at the Laboratoire de Chimie et Physique Quantiques at the Universit\'e Paul Sabatier (Toulouse). +His main research interests are focused on the theoretical studies of photochemical processes in complex molecular systems including the description of excited-state reaction mechanisms based on static explorations of potential energy surfaces and simulations of nonadiabatic dynamics. +\end{biography} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{biography}[DJacquemin]{D.~Jacquemin} +received his PhD in Chemistry from the University of Namur in 1998, before moving to the University of Florida for his postdoctoral stay. He is currently full Professor at the University of Nantes (France). +His research is focused on modeling electronically excited-state processes in organic and inorganic dyes as well as photochromes using a large panel of \emph{ab initio} approaches. His group collaborates with many experimental and theoretical groups. +He is the author of more than 500 scientific papers. He has been ERC grantee (2011--2016), member of Institut Universitaire de France (2012--2017) and received the WATOC's Dirac Medal (2014). +\end{biography} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{biography}[PFLoos]{P.-F.~Loos} +received his Ph.D.~in Computational and Theoretical Chemistry from the Universit\'e Henri Poincar\'e (Nancy, France) in 2008. +From 2009 to 2013, He was undertaking postdoctoral research with Peter M.W.~Gill at the Australian National University (ANU). +From 2013 to 2017, he was a \textit{``Discovery Early Career Researcher Award''} recipient and, then, a senior lecturer at the ANU. +Since 2017, he holds a researcher position from the \textit{``Centre National de la Recherche Scientifique (CNRS)} at the \textit{Laboratoire de Chimie et Physique Quantiques} in Toulouse (France), and was awarded, in 2019, an ERC consolidator grant for the development of new excited-state methodologies. +\end{biography} 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