From 987f517ce04a44ffccf525c856bcf3ace4e7e730 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Mon, 11 Nov 2019 12:39:54 +0100 Subject: [PATCH] starting correction bench --- Manuscript/FCI2.tex | 506 +++++++++++++++++++++++--------------------- 1 file changed, 259 insertions(+), 247 deletions(-) diff --git a/Manuscript/FCI2.tex b/Manuscript/FCI2.tex index 27a1f77..6526594 100644 --- a/Manuscript/FCI2.tex +++ b/Manuscript/FCI2.tex @@ -51,15 +51,23 @@ % basis \newcommand{\Pop}{6-31+G(d)} -\newcommand{\AVDZ}{\emph{aug}-cc-pVDZ} -\newcommand{\AVTZ}{\emph{aug}-cc-pVTZ} -\newcommand{\DAVTZ}{d-\emph{aug}-cc-pVTZ} -\newcommand{\AVQZ}{\emph{aug}-cc-pVQZ} -\newcommand{\AVFZ}{\emph{aug}-cc-pV5Z} -\newcommand{\DAVQZ}{d-\emph{aug}-cc-pVQZ} -\newcommand{\TAVQZ}{t-\emph{aug}-cc-pVQZ} -\newcommand{\AVPZ}{\emph{aug}-cc-pV5Z} -\newcommand{\DAVPZ}{d-\emph{aug}-cc-pV5Z} +%\newcommand{\AVDZ}{\emph{aug}-cc-pVDZ} +%\newcommand{\AVTZ}{\emph{aug}-cc-pVTZ} +%\newcommand{\DAVTZ}{d-\emph{aug}-cc-pVTZ} +%\newcommand{\AVQZ}{\emph{aug}-cc-pVQZ} +%\newcommand{\AVFZ}{\emph{aug}-cc-pV5Z} +%\newcommand{\DAVQZ}{d-\emph{aug}-cc-pVQZ} +%\newcommand{\TAVQZ}{t-\emph{aug}-cc-pVQZ} +%\newcommand{\AVPZ}{\emph{aug}-cc-pV5Z} +%\newcommand{\DAVPZ}{d-\emph{aug}-cc-pV5Z} +\newcommand{\AVDZ}{aVDZ} +\newcommand{\AVTZ}{aVTZ} +\newcommand{\DAVTZ}{daVTZ} +\newcommand{\AVQZ}{aVQZ} +\newcommand{\DAVQZ}{daVQZ} +\newcommand{\TAVQZ}{taVQZ} +\newcommand{\AVPZ}{aV5Z} +\newcommand{\DAVPZ}{dapV5Z} % units \newcommand{\IneV}[1]{#1 eV} @@ -105,14 +113,14 @@ Following our previous work focussing on compounds containing up to 3 non-hydrogen atoms [\emph{J. Chem. Theory Comput.} {\bfseries 14} (2018) 4360--4379], we present here highly-accurate vertical transition energies obtained for 27 molecules encompassing 4, 5, and 6 non-hydrogen atoms: acetone, acrolein, benzene, butadiene, cyanoacetylene, cyanoformaldehyde, cyanogen, cyclopentadiene, cyclopropenone, cyclopropenethione, diacetylene, furan, glyoxal, imidazole, isobutene, methylenecyclopropene, propynal, pyrazine, pyridazine, pyridine, pyrimidine, pyrrole, tetrazine, thioacetone, thiophene, thiopropynal, and triazine. -To obtain these energies, we use equation-of-motion coupled cluster theory up to the highest technically possible excitation order for these systems ({\CCT}, {\CCSDT}, and {\CCSDTQ}), selected configuration interaction ({\SCI}) calculations (with tens of millions of determinants in the reference space), +To obtain these energies, we use equation-of-motion coupled cluster theory up to the highest technically possible excitation order for these systems (CCT3, EOM-CCSDT, and EOM-CCSDTQ), selected configuration interaction (SCI) calculations (with tens of millions of determinants in the reference space), as well as the multiconfigurational $n$-electron valence state perturbation theory (NEVPT2) method. -All these approaches are applied in combination with diffuse-containing atomic basis sets. For all transitions, we report at least {\CCT}/{\AVQZ} vertical excitation -energies as well as {\CCT}/{\AVTZ} oscillator strengths for each dipole-allowed transition. We show that {\CCT} almost systematically delivers transition energies in agreement with higher-level theoretical methods with a typically deviation of $\pm 0.04$ eV, except for transitions with a dominant double excitation character where the error is much larger. +All these approaches are applied in combination with diffuse-containing atomic basis sets. For all transitions, we report at least CC3/aug-cc-pVQZ vertical excitation +energies as well as CC3/aug-cc-pVTZ oscillator strengths for each dipole-allowed transition. We show that CC3 almost systematically delivers transition energies in agreement with higher-level theoretical methods with a typically deviation of $\pm 0.04$ eV, except for transitions with a dominant double excitation character where the error is much larger. The present contribution gathers a large, diverse and accurate set of more than 200 highly-accurate transition energies for states of various natures (valence, Rydberg, singlet, triplet, $n \ra \pis$, $\pi \ra \pis$, \ldots). -We use this series of theoretical best estimates to benchmark a series of popular methods for excited state calculations: CIS(D), {\AD}, -{\CCD}, {\STEOM}, {\CCSD}, CCSDR(3), CCSDT-3, and {\CCT}. The results of these benchmarks are compared to the available literature data. +We use this series of theoretical best estimates to benchmark a series of popular methods for excited state calculations: CIS(D), ADC(2), +CC2, STEOM-CCSD, EOM-CCSD, CCSDR(3), CCSDT-3, and CC3. The results of these benchmarks are compared to the available literature data. \end{abstract} \clearpage @@ -179,6 +187,8 @@ corrections (up to quadruple-$\zeta$ at least) are also provided for {\CCT}. Tog Unless otherwise stated, all transition energies are computed in the frozen-core approximation (with a large core for the sulfur atoms). Pople's {\Pop} and Dunning's \emph{aug}-cc-pVXZ (X $=$ D, T, Q, and 5) atomic basis sets are systematically employed in our excited-state calculations. +In the following, we employ the aVXZ shorthand notations for these diffuse-containing Dunning basis sets. +Various statistical quantities are reported in the remaining of this paper: the mean signed error (MSE), mean absolute error (MAE), root mean square error (RMSE), standard deviation of the errors (SDE), as well as the positive [\MaxP] and negative [\MaxN] maximum errors. Here, we globally follow the same procedure as in Ref.~\citenum{Loo18a}, so that we only briefly outline the various theoretical methods that we have employed in the subsections below. @@ -256,7 +266,7 @@ relevant and are therefore unlikely to change any of our main conclusions. \begin{tabular}{l|p{.5cm}p{1.0cm}p{1.2cm}p{1.4cm}|p{.5cm}p{1.0cm}p{1.2cm}p{1.4cm}|p{.5cm}p{1.0cm}p{1.2cm}|p{.5cm}|p{.5cm}|p{.6cm}p{.6cm}} \hline \mc{14}{c}{Cyanoacetylene}\\ - & \mc{4}{c}{\Pop} & \mc{4}{c}{\AVDZ}& \mc{3}{c}{\AVTZ} & \mc{1}{c}{\AVQZ} & \mc{1}{c}{\AVFZ} & \mc{2}{c}{Litt.}\\ + & \mc{4}{c}{\Pop} & \mc{4}{c}{\AVDZ}& \mc{3}{c}{\AVTZ} & \mc{1}{c}{\AVQZ} & \mc{1}{c}{\AVPZ} & \mc{2}{c}{Litt.}\\ State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI}& {\CCT} & {\CCSDT} & {\NEV} & {\CCT} & {\CCT}& Th.$^a$ & Exp.$^b$ \\ \hline $^1\Sigma^-$ &6.02&6.04&6.02&6.02$\pm$0.01 &5.92&5.92&5.91&5.84$\pm$0.09 &5.80&5.81&5.78& 5.79 &5.79 &5.46&4.77\\ @@ -266,7 +276,7 @@ $^3\Delta$ &5.35&5.34& &5.32$\pm$0.03 &5.28&5.27& &5.20$\pm$0.08 &5. $^1A''$[F]$^c$ &3.70&3.72&3.70&3.67$\pm$0.03 &3.60&3.62&3.60&3.59$\pm$0.02 &3.54&3.56&3.50& 3.54 & &&\\ \hline \mc{14}{c}{Cyanogen}\\ - & \mc{4}{c}{\Pop} & \mc{4}{c}{\AVDZ}& \mc{3}{c}{\AVTZ} & \mc{1}{c}{\AVQZ} & \mc{1}{c}{\AVFZ} & \mc{1}{c}{Litt.}\\ + & \mc{4}{c}{\Pop} & \mc{4}{c}{\AVDZ}& \mc{3}{c}{\AVTZ} & \mc{1}{c}{\AVQZ} & \mc{1}{c}{\AVPZ} & \mc{1}{c}{Litt.}\\ State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI}& {\CCT} & {\CCSDT} & {\NEV}& {\CCT} & {\CCT}& Exp.$^d$ \\ \hline $^1\Sigma_u^-$ &6.62&6.63&6.62&6.58$\pm$0.03 &6.52&6.52&6.51&6.44$\pm$0.08 &6.39&6.40&6.32& 6.38 &6.38 &5.63\\ @@ -275,7 +285,7 @@ $^3\Sigma_u^+$ &4.92&4.92&4.94&4.91$\pm$0.06 &4.89&4.89& &4.87$\pm$0.07 &4.9 $^1\Sigma_u^-$[F]$^c$ &5.27&5.28&5.26&5.31$\pm$0.05 &5.19&5.20&5.18&5.26$\pm$0.09 &5.06&5.07&4.97& 5.05 &5.05 & \\ \hline \mc{14}{c}{Diacetylene}\\ - & \mc{4}{c}{\Pop} & \mc{4}{c}{\AVDZ}& \mc{3}{c}{\AVTZ} & \mc{1}{c}{\AVQZ} & \mc{1}{c}{\AVFZ} & \mc{1}{c}{Litt.}\\ + & \mc{4}{c}{\Pop} & \mc{4}{c}{\AVDZ}& \mc{3}{c}{\AVTZ} & \mc{1}{c}{\AVQZ} & \mc{1}{c}{\AVPZ} & \mc{1}{c}{Litt.}\\ State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI}& {\CCT} & {\CCSDT} & {\NEV}& {\CCT} & {\CCT}& Exp.$^e$ \\ \hline $^1\Sigma_u^-$ &5.57&5.58&5.56&5.52$\pm$0.06 &5.44&5.45&5.43&5.47$\pm$0.02 &5.34&5.35&5.33& 5.33 &5.33 &4.81\\ @@ -389,7 +399,7 @@ results might be slightly too low for the second transition. } Our results are listed in Tables \ref{Table-2} and S2. As above, considering the {\Pop} basis set, we notice very small differences between {\CCT}, {\CCSDT}, and {\CCSDTQ}, the latter method giving transition energies systematically falling within the {\FCI} extrapolation incertitude, except in one case (the lowest totally symmetric state of methylenecyclopropene for which the {\CCSDTQ} value is ``off'' by $0.02$ eV only). Depending on the state, it is -either {\CCT} or {\CCSDT} that is closest to {\CCSDTQ}. In fact, considering the {\CCSDTQ}/{\Pop} data listed in Table \ref{Table-2} as reference, the mean absolute deviation of {\CCT} and {\CCSDT} is $0.019$ and $0.016$ eV, respectively, +either {\CCT} or {\CCSDT} that is closest to {\CCSDTQ}. In fact, considering the {\CCSDTQ}/{\Pop} data listed in Table \ref{Table-2} as reference, the MAE of {\CCT} and {\CCSDT} is $0.019$ and $0.016$ eV, respectively, hinting that the improvement brought by the latter, more expensive method is limited for this set of compounds. For the lowest $B_2$ state of methylenecyclopropene, one of the most challenging cases (\%$T_1 = 85\%$), it is clear from the {\FCI} value that only {\CCSDTQ} is close, the {\CCT} and {\CCSDT} results being slightly too large by $\sim 0.05$ eV. It seems reasonable to believe that the same observation can be made for the corresponding state of cyclopropenethione, although in that case the FCI error bar is too large to prevent any definitive conclusion. Interestingly, at the {\CCT} level of theory, the rather small {\Pop} basis set provides data within $0.10$ eV of the CBS limit for 80\%\ of @@ -619,11 +629,11 @@ This is further confirmed by the {\FCI} data. As we have seen for the 15 four-atom molecules considered here, we found extremely consistent transition energies between CC and {\FCI} estimates in the vast majority of the cases. Importantly, we confirm our previous conclusions obtained on smaller compounds: \cite{Loo18a} i) {\CCSDTQ} values systematically fall within (or are extremely close to) the {\FCI} error bar, ii) both {\CCT} and {\CCSDT} are also highly trustable when the considered ES does not exhibit a strong double excitation character. Indeed, considering the 54 ``single'' excitations -for which {\CCSDTQ} estimates could be obtained (only excluding the lowest $^1A_g$ ES of butadiene and glyoxal), we determined negligible mean signed errors (MSE of $0.00$ eV), tiny +for which {\CCSDTQ} estimates could be obtained (only excluding the lowest $^1A_g$ ES of butadiene and glyoxal), we determined negligible MSE of $0.00$ eV, tiny MAE ($0.01$ and $0.02$ eV), and small maximal deviations ($0.05$ and $0.04$ eV) for {\CCT} and {\CCSDT}, respectively. This clearly indicates that these two approaches provide chemically-accurate estimates (errors below $1$ kcal.mol$^{-1}$ or $0.043$ eV) for most electronic transitions. Interestingly, some of us have shown that {\CCT} also provides chemically-accurate 0-0 energies as compared to experimental values for most valence transitions. \cite{Loo18b,Loo19a,Sue19} When comparing the {\NEV} and {\CCT} ({\CCSDT}) results obtained with {\AVTZ} for the 91 (65) ES for which comparisons are possible (again excluding only the lowest $^1A_g$ states of butadiene and glyoxal), -one obtains a mean signed deviation of $+0.09$ ($+0.09$) eV and a mean absolute deviation of $0.11$ ($0.12$) eV. +one obtains a MSE of $+0.09$ ($+0.09$) eV and a MAE of $0.11$ ($0.12$) eV. This seems to indicate that {\NEV}, as applied here, has a slight tendency to overestimate the transition energies. This contrasts with {\CASPT} that is known to generally underestimate transition energies, as further illustrated and discussed above. \subsection{Five-atom molecules} @@ -1104,14 +1114,14 @@ our previous works indicated that {\CCSDT} tends to overshoot the transition ene results are unavailable, it is hard to make the final call. For the other transitions, we relied either on the current or previous FCI or the {\NEV} values as reference. We indicate some transition energies in italics in Table \ref{Table-tbe} to stress that they are (relatively) less accurate. This is the case when: i) {\NEV} results have to be selected; ii) the affordable CC calculations yield quite large changes from one expansion order to another despite large $\Td$; and iii) there is a very large ES mixing making hard to follow a specific transition from one method (or one basis) to another. To determine the basis set corrections beyond augmented triple-$\zeta$, -we use the {\CCT}/{\AVQZ} or {\CCT}/{\AVFZ} results. For several compounds, we also provide in the SI, {\CCT}/{\DAVQZ} transition energies. However, we are not using these values as reference. This is because, +we use the {\CCT}/{\AVQZ} or {\CCT}/{\AVPZ} results. For several compounds, we also provide in the SI, {\CCT}/{\DAVQZ} transition energies. However, we are not using these values as reference. This is because, the addition of a second set of diffuse orbitals tends to modify the computed transition energies significantly only when it induces a more complex state mixing. We also stick to the frozen-core approximation for two reasons: i) the corrections brought by ``full-correlation'' are generally trifling (typically $\pm 0.02$ eV) for the compounds under study (see the SI for many examples); and ii) it would be, in principle, necessary to add core polarization functions in such ``full'' calculations. Table \ref{Table-tbe} encompasses 238 ES, all at least obtained at the {\CCSDT} level. This set that can be decomposed as follows: 144 singlet and 94 triplet transitions, or 174 valence (99 $\pi \ra \pis$, 71 $n \ra \pis$ and 4 double excitation) and 64 Rydberg transitions. Amongst the reported transition energies, fifteen can be considered as ``unsafe''. This is a significant extension of all previously -proposed ES datasets (see Introduction). The Table also reports 90 oscillator strengths, $f$ which is, to our knowledge, the largest set of {\CCT}/{\AVTZ} $f$ reported to date, the previous effort being mostly performed +proposed ES datasets (see Introduction). The Table also reports 90 oscillator strengths, $f$ which is, to our knowledge, the largest set of {\CCT}/{\AVTZ} $f$ reported to date, the previous effort being mostly performed at the {\CCT}/TZVP level for Thiel's set. \cite{Kan14} It should also be recalled that all these data are obtained on {\CCT}/{\AVTZ} geometries, consistently with our previous works. \cite{Loo18a,Loo19c} Taken together they offer a consistent ensemble of transition energies of ca. 350 electronic transitions of various natures in small and medium-sized organic compounds. @@ -1137,154 +1147,154 @@ that have always been obtained at the {\CCT} level. Values displayed in italics \endfoot \hline \endlastfoot -Acetone &$^1A_2 (\Val; n \ra \pis)$ & & 91.1 & 4.47 & B & 4.48 & AVQZ \\ - &$^1B_2 (\mathrm{R}; n \ra 3s)$ &0.000 & 90.5 & 6.46 & B & 6.51 & AVQZ \\ - &$^1A_2 (\mathrm{R}; n \ra 3p)$ & & 90.9 & 7.47 & B & 7.44 & AVQZ \\ - &$^1A_1 (\mathrm{R}; n \ra 3p)$ &0.004 & 90.6 & 7.51 & B & 7.55 & AVQZ \\ - &$^1B_2 (\mathrm{R}; n \ra 3p)$ &0.029 & 91.2 & 7.62 & B & 7.63 & AVQZ \\ - &$^3A_2 (\Val; n \ra \pis)$ & & 97.8 & 4.13 & D & 4.15 & AVQZ \\ - &$^3A_1 (\Val; \pi \ra \pis)$ & & 98.7 & 6.25 & D & 6.27 & AVQZ \\ -Acrolein &$^1A'' (\Val; n \ra \pis)$ &0.000 & 87.6 & 3.73 & {\CCSDT}/AVTZ & 3.74 & AVQZ \\ - &$^1A' (\Val; \pi \ra \pis)$ &0.344 & 91.2 & 6.69 & {\CCSDT}/AVTZ & 6.69 & AVQZ \\ - &$^1A'' (\Val; n \ra \pis)$ &0.000 & 79.4 & \emph{6.72} & D &\emph{6.74} & AVQZ \\ - &$^1A' (\mathrm{R}; n \ra 3s)$ &0.109 & 89.4 & 7.08 & D & 7.12 & AVQZ \\ - &$^3A'' (\Val; n \ra \pis)$ & & 97.0 & 3.44 & D & 3.43 & AVQZ \\ - &$^3A' (\Val; \pi \ra \pis)$ & & 98.6 & 3.94 & D & 3.95 & AVQZ \\ - &$^3A' (\Val; \pi \ra \pis)$ & & 98.4 & 6.18 & D & 6.19 & AVQZ \\ - &$^3A'' (\Val; n \ra \pis)$ & & 92.7 & \emph{6.54} & E & \emph{6.55}& AVQZ \\%remove -Benzene &$^1B_{2u} (\Val; \pi \ra \pis)$ & & 86.3 & 5.06 & {\CCSDT}/AVTZ & 5.06 &AVQZ \\ - &$^1B_{1u} (\Val; \pi \ra \pis)$ & & 92.9 & 6.45 & {\CCSDT}/AVTZ &6.44 &AVQZ \\ - &$^1E_{1g} (\mathrm{R}; \pi \ra 3s)$ & & 92.8 & 6.52 & {\CCSDT}/AVTZ &6.54 &AVQZ \\ - &$^1A_{2u} (\mathrm{R}; \pi \ra 3p)$ &0.066 & 93.4 & 7.08 & {\CCSDT}/AVTZ &7.10 &AVQZ \\ - &$^1E_{2u} (\mathrm{R}; \pi \ra 3p)$ & & 92.8 & 7.15 & {\CCSDT}/AVTZ &7.16 &AVQZ \\ - &$^3B_{1u} (\Val; \pi \ra \pis)$ & & 98.6 & 4.16 & D &4.17 &AVQZ \\ - &$^3E_{1u}(\Val; \pi \ra \pis)$ & & 97.1 & 4.85 & D &4.86 &AVQZ \\ - &$^3B_{2u} (\Val; \pi \ra \pis)$ & & 98.1 & 5.81 & D & 5.81 &AVQZ \\ -Butadiene &$^1B_u (\Val; \pi \ra \pis)$ &0.664 & 93.3 & 6.22 & B & 6.21 & AVQZ \\ - &$^1B_g (\mathrm{R}; \pi \ra 3s)$ & & 94.1 & 6.33 & B & 6.35 & AVQZ \\ - &$^1A_g (\Val; \pi \ra \pis)$ & & 75.1 & 6.50 & F & 6.50 & AVQZ \\ - &$^1A_u (\mathrm{R}; \pi \ra 3p)$ &0.001 & 94.1 & 6.64 & B & 6.66 & AVQZ \\ - &$^1A_u (\mathrm{R}; \pi \ra 3p)$ &0.049 & 94.1 & 6.80 & B & 6.82 & AVQZ \\ - &$^1B_u (\mathrm{R}; \pi \ra 3p)$ &0.055 & 93.8 & 7.68 & C & 7.54 & AVQZ \\ - &$^3B_u (\Val; \pi \ra \pis)$ & & 98.4 & 3.36 & D & 3.37 & AVQZ \\ - &$^3A_g (\Val; \pi \ra \pis)$ & & 98.7 & 5.20 & D & 5.21 & AVQZ \\ - &$^3B_g (\mathrm{R}; \pi \ra 3s)$ & & 97.9 & 6.29 & D & 6.31 & AVQZ \\ -Cyanoacetylene &$^1\Sigma^- (\Val; \pi \ra \pis)$ & & 94.3 & 5.80 & A & 5.79 & AV5Z\\ - &$^1\Delta (\Val; \pi \ra \pis)$ & & 94.0 & 6.07 & A & 6.05 &AV5Z\\ - &$^3\Sigma^+ (\Val; \pi \ra \pis)$ & & 98.5 & 4.44 & {\CCSDT}/AVTZ & 4.46 &AV5Z \\ - &$^3\Delta (\Val; \pi \ra \pis)$ & & 98.2 & 5.21 & {\CCSDT}/AVTZ & 5.21 & AV5Z\\ - &$^1A'' [\mathrm{F}] (\Val; \pi \ra \pis)$ & 0.004 & 93.6 & 3.54 & A & 3.54 & AVQZ \\ -Cyanoformaldehyde &$^1A'' (\Val; n \ra \pis)$ & 0.001 & 89.8 & 3.81 & {\CCSDT}/AVTZ & 3.82 & AVQZ \\ - &$^1A'' (\Val; \pi \ra \pis)$ & 0.000 & 91.9 & 6.46 & {\CCSDT}/AVTZ & 6.45 & AVQZ \\ - &$^3A'' (\Val; n \ra \pis)$ & & 97.6 & 3.44 & D & 3.45 & AVQZ \\ - &$^3A' (\Val; \pi \ra \pis)$ & & 98.4 & 5.01 & D & 5.02 & AVQZ \\ -Cyanogen & $^1\Sigma_u^- (\Val; \pi \ra \pis)$ & & 94.1 & 6.39 & A & 6.38 & AV5Z\\ - & $^1\Delta_u (\Val; \pi \ra \pis)$ & & 93.4 & 6.66 & A & 6.64 & AV5Z\\ - & $^3\Sigma_u^+ (\Val; \pi \ra \pis)$ & & 98.5 & 4.91 & B & 4.93 & AV5Z \\ - & $^1\Sigma_u^- [\mathrm{F}] (\Val; \pi \ra \pis)$ & & 93.4 & 5.05 & A & 5.03 & AV5Z \\ -Cyclopentadiene &$^1B_2 (\Val; \pi \ra \pis)$ &0.084 & 93.8 & 5.56 & {\CCSDT}/AVTZ & 5.55 & AVQZ \\ - &$^1A_2 (\mathrm{R}; \pi \ra 3s)$ & & 94.0 & 5.78 & {\CCSDT}/AVTZ & 5.80 & AVQZ \\ - &$^1B_1 (\mathrm{R}; \pi \ra 3p)$ &0.037 & 94.2 & 6.41 & {\CCSDT}/AVTZ & 6.42 & AVQZ \\ - &$^1A_2 (\mathrm{R}; \pi \ra 3p)$ & & 93.8 & 6.46 & {\CCSDT}/AVTZ & 6.47 & AVQZ \\ - &$^1B_2 (\mathrm{R}; \pi \ra 3p)$ &0.046 & 94.2 & 6.56 &{\CCSDT}/AVTZ & 6.55 & AVQZ\\ - &$^1A_1 (\Val; \pi \ra \pis)$ &0.001 & 78.9 & \emph{6.51} & D & \emph{6.51} & AVQZ \\ - &$^3B_2 (\Val; \pi \ra \pis)$ & & 98.4 & 3.31 & D & 3.31 & AVQZ \\ - &$^3A_1 (\Val; \pi \ra \pis)$ & & 98.6 & 5.11 & D & 5.12 & AVQZ \\ - &$^3A_2 (\mathrm{R}; \pi \ra 3s)$ & & 97.9 & 5.73 & D & 5.75 & AVQZ \\ - &$^3B_1 (\mathrm{R}; \pi \ra 3p)$ & & 97.9 & 6.36 & D & 6.38 & AVQZ \\ -Cyclopropenone &$^1B_1 (\Val; n \ra \pis)$ &0.000 & 87.7 & 4.26 & B & 4.28 & AV5Z \\ - &$^1A_2 (\Val; n \ra \pis)$ & & 91.0 & 5.55 & B & 5.56 &AV5Z \\ - &$^1B_2 (\mathrm{R}; n \ra 3s)$ &0.003 & 90.8 & 6.34 & B & 6.40 & AV5Z \\ - &$^1B_2 (\Val; \pi \ra \pis$) &0.047 & 86.5 & 6.54 & B & 6.56 & AV5Z\\ - &$^1B_2 (\mathrm{R}; n \ra 3p)$ &0.018 & 91.1 & 6.98 & B & 7.01 & AV5Z \\ - &$^1A_1 (\mathrm{R}; n \ra 3p)$ &0.003 & 91.2 & 7.02 & B & 7.08 &AV5Z \\ - &$^1A_1 (\Val; \pi \ra \pis)$ &0.320 & 90.8 & 8.28 & B & 8.26 &AV5Z \\ - &$^3B_1 (\Val; n \ra \pis)$ & & 96.0 & 3.93 & {\CCSDT}/AVTZ & 3.96 & AV5Z \\ - &$^3B_2 (\Val; \pi \ra \pis)$ & & 97.9 & 4.88 & {\CCSDT}/AVTZ & 4.91 & AV5Z \\ - &$^3A_2 (\Val; n \ra \pis)$ & & 97.5 & 5.35 & {\CCSDT}/AVTZ & 5.37 & AV5Z \\ - &$^3A_1 (\Val; \pi \ra \pis)$ & & 98.1 & 6.79 & {\CCSDT}/AVTZ & 6.81 & AV5Z\\ -Cyclopropenethione &$^1A_2 (\Val; n \ra \pis)$ & & 89.6 & 3.41 & B & 3.41 & AV5Z \\ - &$^1B_1 (\Val; n \ra \pis)$ &0.000 & 84.8 & 3.45 & B & 3.48 & AV5Z \\ - &$^1B_2 (\Val; \pi \ra \pis)$ &0.007 & 83.0 & 4.60 & B & 4.62 & AV5Z \\ - &$^1B_2 (\mathrm{R}; n \ra 3s)$ &0.048 & 91.8 & 5.34 & B & 5.40 & AV5Z \\ - &$^1A_1 (\Val; \pi \ra \pis)$ &0.228 & 89.0 & 5.46 & B & 5.46 & AV5Z \\ - &$^1B_2 (\mathrm{R}; n \ra 3p)$ &0.084 & 91.3 & 5.92 & B & 5.94 & AV5Z \\ - &$^3A_2 (\Val; n \ra \pis)$ & & 97.2 & 3.28 & D & 3.28 & AV5Z \\ - &$^3B_1 (\Val; n \ra \pis)$ & & 94.5 & 3.32 & {\CCSDT}/AVTZ & 3.36 & AV5Z \\ - &$^3B_2 (\Val; \pi \ra \pis)$ & & 96.5 & 4.01 & D & 4.04 & AV5Z \\ - &$^3A_1 (\Val; \pi \ra \pis)$ & & 98.2 & 4.01 & D & 4.01 & AV5Z \\ -Diacetylene &$^1\Sigma_u^- (\Val; \pi \ra \pis)$ & & 94.4 & 5.33 & A & 5.32 & AV5Z \\ - &$^1\Delta_u (\Val; \pi \ra \pis)$ & & 94.1 & 5.61 & A & 5.60 & AV5Z \\ - &$^3\Sigma_u^+ (\Val; \pi \ra \pis)$ & & 98.5 & 4.10 & C & 4.13 & AV5Z \\ - &$^3\Delta_u (\Val; \pi \ra \pis)$ & & 98.2 & 4.78 & B & 4.78 &AV5Z \\ -Furan &$^1A_2 (\mathrm{R}; \pi \ra 3s)$ & & 93.8 & 6.09 &{\CCSDT}/AVTZ & 6.11 &AVQZ \\ - &$^1B_2 (\Val; \pi \ra \pis)$ &0.163 & 93.0 & 6.37 &{\CCSDT}/AVTZ & 6.37 &AVQZ \\ - &$^1A_1 (\Val; \pi \ra \pis)$ &0.000 & 92.4 & 6.56 &{\CCSDT}/AVTZ & 6.56 &AVQZ \\ - &$^1B_1 (\mathrm{R}; \pi \ra 3p)$ &0.038 & 93.9 & 6.64 &{\CCSDT}/AVTZ & 6.66 &AVQZ \\ - &$^1A_2 (\mathrm{R}; \pi \ra 3p)$ & & 93.6 & 6.81 &{\CCSDT}/AVTZ & 6.83 &AVQZ \\ - &$^1B_2 (\mathrm{R}; \pi \ra 3p)$ &0.008 & 93.5 & 7.24 & D & 7.14 &AVQZ \\ - &$^3B_2 (\Val; \pi \ra \pis)$ & & 98.4 & 4.20 & D & 4.20 &AVQZ \\ - &$^3A_1 (\Val; \pi \ra \pis)$ & & 98.1 & 5.46 & D & 5.47 &AVQZ \\ - &$^3A_2 (\mathrm{R}; \pi \ra 3s)$ & & 97.9 & 6.02 & D & 6.05 &AVQZ \\ - &$^3B_1 (\mathrm{R}; \pi \ra 3p)$ & & 97.9 & 6.59 & D & 6.61 &AVQZ \\ -Glyoxal &$^1A_u (\Val; n \ra \pis)$ & 0.000 & 91.0 & 2.88 & B & 2.88 & AV5Z \\ - &$^1B_g (\Val; n \ra \pis)$ & & 88.3 & 4.24 & B & 4.24 & AVQZ \\ - &$^1A_g (\Val; n,n \ra \pis,\pis)$ & & 0.5 & 5.61 & F & 5.60 & AV5Z \\%to be remade with CCSDT correction ?? - &$^1B_g (\Val; n \ra \pis)$ & & 83.9 & 6.57 & B & 6.58 & AVQZ \\ - &$^1B_u (\mathrm{R}; n \ra 3p)$ & 0.095 & 91.7 & 7.71 & B & 7.78 & AV5Z \\ - &$^3A_u (\Val; n \ra \pis)$ & & 97.6 & 2.49 & {\CCSDT}/AVTZ & 2.50 & AV5Z \\ - &$^3B_g (\Val; n \ra \pis)$ & & 97.4 & 3.89 & {\CCSDT}/AVTZ & 3.90 & AVQZ \\ - &$^3B_u (\Val; \pi \ra \pis)$ & & 98.5 & 5.15 & {\CCSDT}/AVTZ & 5.17 & AV5Z \\ - &$^3A_g (\Val; \pi \ra \pis)$ & & 98.8 & 6.30 & {\CCSDT}/AVTZ & 6.31 & AV5Z \\ -Imidazole &$^1A'' (\mathrm{R}; \pi \ra 3s)$ & 0.001 & 93.0 & 5.71 & D & 5.73 & AVQZ \\ - &$^1A' (\Val; \pi \ra \pis)$ & 0.124 & 89.6 & 6.41 & D & 6.41s & AVQZ \\ - &$^1A'' (\Val; n \ra \pis)$ & 0.028 & 93.6 & 6.50 & D & 6.53 & AVQZ \\ - &$^1A' (\mathrm{R};\pi \ra 3p)$ & 0.035 & 88.9 & \emph{6.83} & D &\emph{6.82} & AVQZ \\ - &$^3A' (\Val; \pi \ra \pis)$ & & 98.3 & 4.73 & E & 4.74 & AVQZ \\ - &$^3A'' (\mathrm{R};(\pi \ra 3s)$ & & 97.6 & 5.66 & D & 5.69 & AVQZ \\ - &$^3A' (\Val; \pi \ra \pis)$ & & 97.9 & 5.74 & E & 5.75 & AVQZ \\ - &$^3A'' (\Val; n \ra \pis)$ & & 97.3 & 6.31 & D & 6.31 & AVQZ \\ -Isobutene &$^1B_1 (\mathrm{R}; \pi \ra 3s)$ & 0.006 & 94.1 & 6.46 & {\CCSDT}/AVTZ & 6.48 & AVQZ \\ - &$^1A_1 (\mathrm{R}; \pi \ra 3p)$ & 0.228 & 94.2 & 7.01 & {\CCSDT}/AVTZ & 7.00 & AVQZ \\ - &$^3A_1 (\Val; (\pi \ra \pis)$ & & 98.9 & 4.53 & D & 4.54 & AVQZ \\ -Methylenecyclopropene& $^1B_2 (\Val; \pi \ra \pis)$ & 0.011 & 85.4 & 4.28 & B & 4.29 & AV5Z \\ - &$^1B_1 (\mathrm{R}; \pi \ra 3s)$ & 0.005 & 93.6 & 5.44 & B & 5.47 & AV5Z \\ - &$^1A_2 (\mathrm{R}; \pi \ra 3p)$ & & 93.3 & 5.96 & B & 5.99 & AVQZ \\ - &$^1A_1(\Val; \pi \ra \pis)$ & 0.224 & 92.8 & \emph{6.12} & B & \emph{6.03} & AV5Z \\ - &$^3B_2 (\Val; \pi \ra \pis)$ & & 97.2 & 3.49 & {\CCSDT}/AVTZ & 3.49 & AVQZ \\ - &$^3A_1 (\Val; \pi \ra \pis)$ & & 98.6 & 4.74 & D & 4.75 & AV5Z \\ -Propynal & $^1A'' (\Val; n \ra \pis)$ & 0.000 & 89.0 & 3.80 & {\CCSDT}/AVTZ & 3.81 & AVQZ \\ - &$^1A'' (\Val; \pi \ra \pis)$ & 0.000 & 92.9 & 5.54 & {\CCSDT}/AVTZ & 5.53 & AVQZ \\ - &$^3A'' (\Val; n \ra \pis)$ & & 97.4 & 3.47 & D & 3.48 & AVQZ \\ - &$^3A' (\Val; \pi \ra \pis)$ & & 98.3 & 4.47 & D & 4.48 & AVQZ \\ -Pyrazine &$^1B_{3u} (\Val; n \ra \pis)$ &0.006 & 90.1 & 4.15 & {\CCSDT}/AVTZ & 4.15 & AVQZ \\ - &$^1A_{u} (\Val; n \ra \pis)$ & & 88.6 & 4.98 & {\CCSDT}/AVTZ & 4.99 & AVQZ \\ - &$^1B_{2u} (\Val; \pi \ra \pis)$ &0.078 & 86.9 & 5.02 & {\CCSDT}/AVTZ & 5.01 & AVQZ \\ - &$^1B_{2g} (\Val; n \ra \pis)$ & & 85.6 & 5.71 & {\CCSDT}/AVTZ & 5.71 & AVQZ \\ - &$^1A_{g} (\mathrm{R};n \ra 3s)$ & & 91.1 & 6.65 & {\CCSDT}/AVTZ & 6.69 & AVQZ \\ - &$^1B_{1g} (\Val; n \ra \pis)$ & & 84.2 & 6.74 & {\CCSDT}/AVTZ & 6.74 & AVQZ \\ - &$^1B_{1u} (\Val; \pi \ra \pis)$ &0.063 & 92.8 & 6.88 & {\CCSDT}/AVTZ & 6.87 & AVQZ \\ - &$^1B_{1g} (\mathrm{R};n \ra 3p)$ & & 93.8 & 7.21 & {\CCSDT}/AVTZ & 7.24 & AVQZ \\ - &$^1B_{2u} (\mathrm{R};n \ra 3p)$ &0.037 & 90.8 & 7.24 & D & 7.28 &AVQZ \\ - &$^1B_{1u} (\mathrm{R};\pi \ra 3s)$ &0.128 & 91.4 & 7.44 & D & 7.47 &AVQZ \\ - &$^1B_{1u} (\Val; \pi \ra \pis)$ &0.285 & 90.5 & \emph{7.98}& D & \emph{7.97} &AVQZ \\ - &$^3B_{3u} (\Val; n \ra \pis)$ & & 97.3 & 3.59 & D & 3.59 & AVQZ \\ - &$^3B_{1u} (\Val; \pi \ra \pis)$ & & 98.5 & 4.35 & D & 4.36 & AVQZ \\ - &$^3B_{2u} (\Val; (\pi \ra \pis)$ & & 97.6 & 4.39 & D & 4.39 & AVQZ \\ - &$^3A_{u} (\Val; n \ra \pis)$ & & 96.1 & 4.93 & D & 4.94 & AVQZ \\ - &$^3B_{2g} (\Val; n \ra \pis)$ & & 97.0 & 5.08 & D & 5.09 & AVQZ \\ - &$^3B_{1u} (\Val; \pi \ra \pis)$ & & 97.0 & 5.28 & D & 5.28 & AVQZ \\ +Acetone &$^1A_2 (\Val; n \ra \pis)$ & & 91.1 & 4.47 & B & 4.48 & \AVQZ \\ + &$^1B_2 (\mathrm{R}; n \ra 3s)$ &0.000 & 90.5 & 6.46 & B & 6.51 & \AVQZ \\ + &$^1A_2 (\mathrm{R}; n \ra 3p)$ & & 90.9 & 7.47 & B & 7.44 & \AVQZ \\ + &$^1A_1 (\mathrm{R}; n \ra 3p)$ &0.004 & 90.6 & 7.51 & B & 7.55 & \AVQZ \\ + &$^1B_2 (\mathrm{R}; n \ra 3p)$ &0.029 & 91.2 & 7.62 & B & 7.63 & \AVQZ \\ + &$^3A_2 (\Val; n \ra \pis)$ & & 97.8 & 4.13 & D & 4.15 & \AVQZ \\ + &$^3A_1 (\Val; \pi \ra \pis)$ & & 98.7 & 6.25 & D & 6.27 & \AVQZ \\ +Acrolein &$^1A'' (\Val; n \ra \pis)$ &0.000 & 87.6 & 3.73 & {\CCSDT}/\AVTZ & 3.74 & \AVQZ \\ + &$^1A' (\Val; \pi \ra \pis)$ &0.344 & 91.2 & 6.69 & {\CCSDT}/\AVTZ & 6.69 & \AVQZ \\ + &$^1A'' (\Val; n \ra \pis)$ &0.000 & 79.4 & \emph{6.72} & D &\emph{6.74} & \AVQZ \\ + &$^1A' (\mathrm{R}; n \ra 3s)$ &0.109 & 89.4 & 7.08 & D & 7.12 & \AVQZ \\ + &$^3A'' (\Val; n \ra \pis)$ & & 97.0 & 3.44 & D & 3.43 & \AVQZ \\ + &$^3A' (\Val; \pi \ra \pis)$ & & 98.6 & 3.94 & D & 3.95 & \AVQZ \\ + &$^3A' (\Val; \pi \ra \pis)$ & & 98.4 & 6.18 & D & 6.19 & \AVQZ \\ + &$^3A'' (\Val; n \ra \pis)$ & & 92.7 & \emph{6.54} & E & \emph{6.55}& \AVQZ \\%remove +Benzene &$^1B_{2u} (\Val; \pi \ra \pis)$ & & 86.3 & 5.06 & {\CCSDT}/\AVTZ & 5.06 &\AVQZ \\ + &$^1B_{1u} (\Val; \pi \ra \pis)$ & & 92.9 & 6.45 & {\CCSDT}/\AVTZ &6.44 &\AVQZ \\ + &$^1E_{1g} (\mathrm{R}; \pi \ra 3s)$ & & 92.8 & 6.52 & {\CCSDT}/\AVTZ &6.54 &\AVQZ \\ + &$^1A_{2u} (\mathrm{R}; \pi \ra 3p)$ &0.066 & 93.4 & 7.08 & {\CCSDT}/\AVTZ &7.10 &\AVQZ \\ + &$^1E_{2u} (\mathrm{R}; \pi \ra 3p)$ & & 92.8 & 7.15 & {\CCSDT}/\AVTZ &7.16 &\AVQZ \\ + &$^3B_{1u} (\Val; \pi \ra \pis)$ & & 98.6 & 4.16 & D &4.17 &\AVQZ \\ + &$^3E_{1u}(\Val; \pi \ra \pis)$ & & 97.1 & 4.85 & D &4.86 &\AVQZ \\ + &$^3B_{2u} (\Val; \pi \ra \pis)$ & & 98.1 & 5.81 & D & 5.81 &\AVQZ \\ +Butadiene &$^1B_u (\Val; \pi \ra \pis)$ &0.664 & 93.3 & 6.22 & B & 6.21 & \AVQZ \\ + &$^1B_g (\mathrm{R}; \pi \ra 3s)$ & & 94.1 & 6.33 & B & 6.35 & \AVQZ \\ + &$^1A_g (\Val; \pi \ra \pis)$ & & 75.1 & 6.50 & F & 6.50 & \AVQZ \\ + &$^1A_u (\mathrm{R}; \pi \ra 3p)$ &0.001 & 94.1 & 6.64 & B & 6.66 & \AVQZ \\ + &$^1A_u (\mathrm{R}; \pi \ra 3p)$ &0.049 & 94.1 & 6.80 & B & 6.82 & \AVQZ \\ + &$^1B_u (\mathrm{R}; \pi \ra 3p)$ &0.055 & 93.8 & 7.68 & C & 7.54 & \AVQZ \\ + &$^3B_u (\Val; \pi \ra \pis)$ & & 98.4 & 3.36 & D & 3.37 & \AVQZ \\ + &$^3A_g (\Val; \pi \ra \pis)$ & & 98.7 & 5.20 & D & 5.21 & \AVQZ \\ + &$^3B_g (\mathrm{R}; \pi \ra 3s)$ & & 97.9 & 6.29 & D & 6.31 & \AVQZ \\ +Cyanoacetylene &$^1\Sigma^- (\Val; \pi \ra \pis)$ & & 94.3 & 5.80 & A & 5.79 & \AVPZ\\ + &$^1\Delta (\Val; \pi \ra \pis)$ & & 94.0 & 6.07 & A & 6.05 &\AVPZ\\ + &$^3\Sigma^+ (\Val; \pi \ra \pis)$ & & 98.5 & 4.44 & {\CCSDT}/\AVTZ & 4.46 &\AVPZ \\ + &$^3\Delta (\Val; \pi \ra \pis)$ & & 98.2 & 5.21 & {\CCSDT}/\AVTZ & 5.21 & \AVPZ\\ + &$^1A'' [\mathrm{F}] (\Val; \pi \ra \pis)$ & 0.004 & 93.6 & 3.54 & A & 3.54 & \AVQZ \\ +Cyanoformaldehyde &$^1A'' (\Val; n \ra \pis)$ & 0.001 & 89.8 & 3.81 & {\CCSDT}/\AVTZ & 3.82 & \AVQZ \\ + &$^1A'' (\Val; \pi \ra \pis)$ & 0.000 & 91.9 & 6.46 & {\CCSDT}/\AVTZ & 6.45 & \AVQZ \\ + &$^3A'' (\Val; n \ra \pis)$ & & 97.6 & 3.44 & D & 3.45 & \AVQZ \\ + &$^3A' (\Val; \pi \ra \pis)$ & & 98.4 & 5.01 & D & 5.02 & \AVQZ \\ +Cyanogen & $^1\Sigma_u^- (\Val; \pi \ra \pis)$ & & 94.1 & 6.39 & A & 6.38 & \AVPZ\\ + & $^1\Delta_u (\Val; \pi \ra \pis)$ & & 93.4 & 6.66 & A & 6.64 & \AVPZ\\ + & $^3\Sigma_u^+ (\Val; \pi \ra \pis)$ & & 98.5 & 4.91 & B & 4.93 & \AVPZ \\ + & $^1\Sigma_u^- [\mathrm{F}] (\Val; \pi \ra \pis)$ & & 93.4 & 5.05 & A & 5.03 & \AVPZ \\ +Cyclopentadiene &$^1B_2 (\Val; \pi \ra \pis)$ &0.084 & 93.8 & 5.56 & {\CCSDT}/\AVTZ & 5.55 & \AVQZ \\ + &$^1A_2 (\mathrm{R}; \pi \ra 3s)$ & & 94.0 & 5.78 & {\CCSDT}/\AVTZ & 5.80 & \AVQZ \\ + &$^1B_1 (\mathrm{R}; \pi \ra 3p)$ &0.037 & 94.2 & 6.41 & {\CCSDT}/\AVTZ & 6.42 & \AVQZ \\ + &$^1A_2 (\mathrm{R}; \pi \ra 3p)$ & & 93.8 & 6.46 & {\CCSDT}/\AVTZ & 6.47 & \AVQZ \\ + &$^1B_2 (\mathrm{R}; \pi \ra 3p)$ &0.046 & 94.2 & 6.56 &{\CCSDT}/\AVTZ & 6.55 & \AVQZ\\ + &$^1A_1 (\Val; \pi \ra \pis)$ &0.001 & 78.9 & \emph{6.51} & D & \emph{6.51} & \AVQZ \\ + &$^3B_2 (\Val; \pi \ra \pis)$ & & 98.4 & 3.31 & D & 3.31 & \AVQZ \\ + &$^3A_1 (\Val; \pi \ra \pis)$ & & 98.6 & 5.11 & D & 5.12 & \AVQZ \\ + &$^3A_2 (\mathrm{R}; \pi \ra 3s)$ & & 97.9 & 5.73 & D & 5.75 & \AVQZ \\ + &$^3B_1 (\mathrm{R}; \pi \ra 3p)$ & & 97.9 & 6.36 & D & 6.38 & \AVQZ \\ +Cyclopropenone &$^1B_1 (\Val; n \ra \pis)$ &0.000 & 87.7 & 4.26 & B & 4.28 & \AVPZ \\ + &$^1A_2 (\Val; n \ra \pis)$ & & 91.0 & 5.55 & B & 5.56 &\AVPZ \\ + &$^1B_2 (\mathrm{R}; n \ra 3s)$ &0.003 & 90.8 & 6.34 & B & 6.40 & \AVPZ \\ + &$^1B_2 (\Val; \pi \ra \pis$) &0.047 & 86.5 & 6.54 & B & 6.56 & \AVPZ\\ + &$^1B_2 (\mathrm{R}; n \ra 3p)$ &0.018 & 91.1 & 6.98 & B & 7.01 & \AVPZ \\ + &$^1A_1 (\mathrm{R}; n \ra 3p)$ &0.003 & 91.2 & 7.02 & B & 7.08 &\AVPZ \\ + &$^1A_1 (\Val; \pi \ra \pis)$ &0.320 & 90.8 & 8.28 & B & 8.26 &\AVPZ \\ + &$^3B_1 (\Val; n \ra \pis)$ & & 96.0 & 3.93 & {\CCSDT}/\AVTZ & 3.96 & \AVPZ \\ + &$^3B_2 (\Val; \pi \ra \pis)$ & & 97.9 & 4.88 & {\CCSDT}/\AVTZ & 4.91 & \AVPZ \\ + &$^3A_2 (\Val; n \ra \pis)$ & & 97.5 & 5.35 & {\CCSDT}/\AVTZ & 5.37 & \AVPZ \\ + &$^3A_1 (\Val; \pi \ra \pis)$ & & 98.1 & 6.79 & {\CCSDT}/\AVTZ & 6.81 & \AVPZ\\ +Cyclopropenethione &$^1A_2 (\Val; n \ra \pis)$ & & 89.6 & 3.41 & B & 3.41 & \AVPZ \\ + &$^1B_1 (\Val; n \ra \pis)$ &0.000 & 84.8 & 3.45 & B & 3.48 & \AVPZ \\ + &$^1B_2 (\Val; \pi \ra \pis)$ &0.007 & 83.0 & 4.60 & B & 4.62 & \AVPZ \\ + &$^1B_2 (\mathrm{R}; n \ra 3s)$ &0.048 & 91.8 & 5.34 & B & 5.40 & \AVPZ \\ + &$^1A_1 (\Val; \pi \ra \pis)$ &0.228 & 89.0 & 5.46 & B & 5.46 & \AVPZ \\ + &$^1B_2 (\mathrm{R}; n \ra 3p)$ &0.084 & 91.3 & 5.92 & B & 5.94 & \AVPZ \\ + &$^3A_2 (\Val; n \ra \pis)$ & & 97.2 & 3.28 & D & 3.28 & \AVPZ \\ + &$^3B_1 (\Val; n \ra \pis)$ & & 94.5 & 3.32 & {\CCSDT}/\AVTZ & 3.36 & \AVPZ \\ + &$^3B_2 (\Val; \pi \ra \pis)$ & & 96.5 & 4.01 & D & 4.04 & \AVPZ \\ + &$^3A_1 (\Val; \pi \ra \pis)$ & & 98.2 & 4.01 & D & 4.01 & \AVPZ \\ +Diacetylene &$^1\Sigma_u^- (\Val; \pi \ra \pis)$ & & 94.4 & 5.33 & A & 5.32 & \AVPZ \\ + &$^1\Delta_u (\Val; \pi \ra \pis)$ & & 94.1 & 5.61 & A & 5.60 & \AVPZ \\ + &$^3\Sigma_u^+ (\Val; \pi \ra \pis)$ & & 98.5 & 4.10 & C & 4.13 & \AVPZ \\ + &$^3\Delta_u (\Val; \pi \ra \pis)$ & & 98.2 & 4.78 & B & 4.78 &\AVPZ \\ +Furan &$^1A_2 (\mathrm{R}; \pi \ra 3s)$ & & 93.8 & 6.09 &{\CCSDT}/\AVTZ & 6.11 &\AVQZ \\ + &$^1B_2 (\Val; \pi \ra \pis)$ &0.163 & 93.0 & 6.37 &{\CCSDT}/\AVTZ & 6.37 &\AVQZ \\ + &$^1A_1 (\Val; \pi \ra \pis)$ &0.000 & 92.4 & 6.56 &{\CCSDT}/\AVTZ & 6.56 &\AVQZ \\ + &$^1B_1 (\mathrm{R}; \pi \ra 3p)$ &0.038 & 93.9 & 6.64 &{\CCSDT}/\AVTZ & 6.66 &\AVQZ \\ + &$^1A_2 (\mathrm{R}; \pi \ra 3p)$ & & 93.6 & 6.81 &{\CCSDT}/\AVTZ & 6.83 &\AVQZ \\ + &$^1B_2 (\mathrm{R}; \pi \ra 3p)$ &0.008 & 93.5 & 7.24 & D & 7.14 &\AVQZ \\ + &$^3B_2 (\Val; \pi \ra \pis)$ & & 98.4 & 4.20 & D & 4.20 &\AVQZ \\ + &$^3A_1 (\Val; \pi \ra \pis)$ & & 98.1 & 5.46 & D & 5.47 &\AVQZ \\ + &$^3A_2 (\mathrm{R}; \pi \ra 3s)$ & & 97.9 & 6.02 & D & 6.05 &\AVQZ \\ + &$^3B_1 (\mathrm{R}; \pi \ra 3p)$ & & 97.9 & 6.59 & D & 6.61 &\AVQZ \\ +Glyoxal &$^1A_u (\Val; n \ra \pis)$ & 0.000 & 91.0 & 2.88 & B & 2.88 & \AVPZ \\ + &$^1B_g (\Val; n \ra \pis)$ & & 88.3 & 4.24 & B & 4.24 & \AVQZ \\ + &$^1A_g (\Val; n,n \ra \pis,\pis)$ & & 0.5 & 5.61 & F & 5.60 & \AVPZ \\%to be remade with CCSDT correction ?? + &$^1B_g (\Val; n \ra \pis)$ & & 83.9 & 6.57 & B & 6.58 & \AVQZ \\ + &$^1B_u (\mathrm{R}; n \ra 3p)$ & 0.095 & 91.7 & 7.71 & B & 7.78 & \AVPZ \\ + &$^3A_u (\Val; n \ra \pis)$ & & 97.6 & 2.49 & {\CCSDT}/\AVTZ & 2.50 & \AVPZ \\ + &$^3B_g (\Val; n \ra \pis)$ & & 97.4 & 3.89 & {\CCSDT}/\AVTZ & 3.90 & \AVQZ \\ + &$^3B_u (\Val; \pi \ra \pis)$ & & 98.5 & 5.15 & {\CCSDT}/\AVTZ & 5.17 & \AVPZ \\ + &$^3A_g (\Val; \pi \ra \pis)$ & & 98.8 & 6.30 & {\CCSDT}/\AVTZ & 6.31 & \AVPZ \\ +Imidazole &$^1A'' (\mathrm{R}; \pi \ra 3s)$ & 0.001 & 93.0 & 5.71 & D & 5.73 & \AVQZ \\ + &$^1A' (\Val; \pi \ra \pis)$ & 0.124 & 89.6 & 6.41 & D & 6.41s & \AVQZ \\ + &$^1A'' (\Val; n \ra \pis)$ & 0.028 & 93.6 & 6.50 & D & 6.53 & \AVQZ \\ + &$^1A' (\mathrm{R};\pi \ra 3p)$ & 0.035 & 88.9 & \emph{6.83} & D &\emph{6.82} & \AVQZ \\ + &$^3A' (\Val; \pi \ra \pis)$ & & 98.3 & 4.73 & E & 4.74 & \AVQZ \\ + &$^3A'' (\mathrm{R};(\pi \ra 3s)$ & & 97.6 & 5.66 & D & 5.69 & \AVQZ \\ + &$^3A' (\Val; \pi \ra \pis)$ & & 97.9 & 5.74 & E & 5.75 & \AVQZ \\ + &$^3A'' (\Val; n \ra \pis)$ & & 97.3 & 6.31 & D & 6.31 & \AVQZ \\ +Isobutene &$^1B_1 (\mathrm{R}; \pi \ra 3s)$ & 0.006 & 94.1 & 6.46 & {\CCSDT}/\AVTZ & 6.48 & \AVQZ \\ + &$^1A_1 (\mathrm{R}; \pi \ra 3p)$ & 0.228 & 94.2 & 7.01 & {\CCSDT}/\AVTZ & 7.00 & \AVQZ \\ + &$^3A_1 (\Val; (\pi \ra \pis)$ & & 98.9 & 4.53 & D & 4.54 & \AVQZ \\ +Methylenecyclopropene& $^1B_2 (\Val; \pi \ra \pis)$ & 0.011 & 85.4 & 4.28 & B & 4.29 & \AVPZ \\ + &$^1B_1 (\mathrm{R}; \pi \ra 3s)$ & 0.005 & 93.6 & 5.44 & B & 5.47 & \AVPZ \\ + &$^1A_2 (\mathrm{R}; \pi \ra 3p)$ & & 93.3 & 5.96 & B & 5.99 & \AVQZ \\ + &$^1A_1(\Val; \pi \ra \pis)$ & 0.224 & 92.8 & \emph{6.12} & B & \emph{6.03} & \AVPZ \\ + &$^3B_2 (\Val; \pi \ra \pis)$ & & 97.2 & 3.49 & {\CCSDT}/\AVTZ & 3.49 & \AVQZ \\ + &$^3A_1 (\Val; \pi \ra \pis)$ & & 98.6 & 4.74 & D & 4.75 & \AVPZ \\ +Propynal & $^1A'' (\Val; n \ra \pis)$ & 0.000 & 89.0 & 3.80 & {\CCSDT}/\AVTZ & 3.81 & \AVQZ \\ + &$^1A'' (\Val; \pi \ra \pis)$ & 0.000 & 92.9 & 5.54 & {\CCSDT}/\AVTZ & 5.53 & \AVQZ \\ + &$^3A'' (\Val; n \ra \pis)$ & & 97.4 & 3.47 & D & 3.48 & \AVQZ \\ + &$^3A' (\Val; \pi \ra \pis)$ & & 98.3 & 4.47 & D & 4.48 & \AVQZ \\ +Pyrazine &$^1B_{3u} (\Val; n \ra \pis)$ &0.006 & 90.1 & 4.15 & {\CCSDT}/\AVTZ & 4.15 & \AVQZ \\ + &$^1A_{u} (\Val; n \ra \pis)$ & & 88.6 & 4.98 & {\CCSDT}/\AVTZ & 4.99 & \AVQZ \\ + &$^1B_{2u} (\Val; \pi \ra \pis)$ &0.078 & 86.9 & 5.02 & {\CCSDT}/\AVTZ & 5.01 & \AVQZ \\ + &$^1B_{2g} (\Val; n \ra \pis)$ & & 85.6 & 5.71 & {\CCSDT}/\AVTZ & 5.71 & \AVQZ \\ + &$^1A_{g} (\mathrm{R};n \ra 3s)$ & & 91.1 & 6.65 & {\CCSDT}/\AVTZ & 6.69 & \AVQZ \\ + &$^1B_{1g} (\Val; n \ra \pis)$ & & 84.2 & 6.74 & {\CCSDT}/\AVTZ & 6.74 & \AVQZ \\ + &$^1B_{1u} (\Val; \pi \ra \pis)$ &0.063 & 92.8 & 6.88 & {\CCSDT}/\AVTZ & 6.87 & \AVQZ \\ + &$^1B_{1g} (\mathrm{R};n \ra 3p)$ & & 93.8 & 7.21 & {\CCSDT}/\AVTZ & 7.24 & \AVQZ \\ + &$^1B_{2u} (\mathrm{R};n \ra 3p)$ &0.037 & 90.8 & 7.24 & D & 7.28 &\AVQZ \\ + &$^1B_{1u} (\mathrm{R};\pi \ra 3s)$ &0.128 & 91.4 & 7.44 & D & 7.47 &\AVQZ \\ + &$^1B_{1u} (\Val; \pi \ra \pis)$ &0.285 & 90.5 & \emph{7.98}& D & \emph{7.97} &\AVQZ \\ + &$^3B_{3u} (\Val; n \ra \pis)$ & & 97.3 & 3.59 & D & 3.59 & \AVQZ \\ + &$^3B_{1u} (\Val; \pi \ra \pis)$ & & 98.5 & 4.35 & D & 4.36 & \AVQZ \\ + &$^3B_{2u} (\Val; (\pi \ra \pis)$ & & 97.6 & 4.39 & D & 4.39 & \AVQZ \\ + &$^3A_{u} (\Val; n \ra \pis)$ & & 96.1 & 4.93 & D & 4.94 & \AVQZ \\ + &$^3B_{2g} (\Val; n \ra \pis)$ & & 97.0 & 5.08 & D & 5.09 & \AVQZ \\ + &$^3B_{1u} (\Val; \pi \ra \pis)$ & & 97.0 & 5.28 & D & 5.28 & \AVQZ \\ Pyridazine &$^1B_1 (\Val; n \ra \pis)$ & & 89.0 & 3.83 & D &\hl{XXXX} & \hl{XXXXX} \\ &$^1A_2 (\Val; n \ra \pis)$ & & 86.9 & 4.37 & D &\hl{XXXX} & \hl{XXXXX} \\ - &$^1A_1 (\Val; \pi \ra \pis)$ & & 85.8 & 5.26 & D & 5.26 & AVQZ \\ + &$^1A_1 (\Val; \pi \ra \pis)$ & & 85.8 & 5.26 & D & 5.26 & \AVQZ \\ &$^1A_2 (\Val; n \ra \pis)$ & & 86.2 & 5.72 & D &\hl{XXXX} & \hl{XXXXX} \\ &$^1B_2 (\mathrm{R}; n \ra 3s)$ & & 88.5 & 6.17 & D &\hl{XXXX} & \hl{XXXXX} \\ &$^1B_1 (\Val; n \ra \pis)$ & & 87.0 & 6.37 & D &\hl{XXXX} & \hl{XXXXX} \\ &$^1B_2 (\Val; \pi \ra \pis)$ & & 90.6 & 6.75 & D &\hl{XXXX} & \hl{XXXXX} \\ - &$^3B_1 (\Val; n \ra \pis)$ & & 97.1 & 3.19 & D &3.20 & AVQZ \\ + &$^3B_1 (\Val; n \ra \pis)$ & & 97.1 & 3.19 & D &3.20 & \AVQZ \\ &$^3A_2 (\Val; n \ra \pis)$ & & 96.2 & 4.11 & D &\hl{XXXX} & \hl{XXXXX} \\ &$^3B_2 (\Val; \pi \ra \pis)$ & & 98.5 & \emph{4.34} & D &\hl{XXXX} & \hl{XXXXX} \\ - &$^3A_1 (\Val; \pi \ra \pis)$ & & 97.3 & 4.82 & D & 4.81 & AVQZ \\ + &$^3A_1 (\Val; \pi \ra \pis)$ & & 97.3 & 4.82 & D & 4.81 & \AVQZ \\ Pyridine &$^1B_1 (\Val; n \ra \pis)$ & & 88.4 & 4.95 & D &\hl{XXXX} & \hl{XXXXX} \\ &$^1B_2 (\Val; \pi \ra \pis)$ & & 86.5 & 5.14 & D &\hl{XXXX} & \hl{XXXXX} \\ &$^1A_2 (\Val; n \ra \pis)$ & & 87.9 & 5.40 & D &\hl{XXXX} & \hl{XXXXX} \\ @@ -1305,76 +1315,76 @@ Pyrimidine &$^1B_1 (\Val; n \ra \pis)$ & 0.005 & 88.6 & 4.44 & D &\hl &$^1B_2 (\Val; \pi \ra \pis)$ &0.028 & 86.3 & 5.38 & D &\hl{XXXX} & \hl{XXXXX} \\ &$^1A_2 (\Val; n \ra \pis)$ & & 86.7 & 5.92 & D &\hl{XXXX} & \hl{XXXXX} \\ &$^1B_1 (\Val; n \ra \pis)$ &0.005 & 86.7 & 6.26 & D &\hl{XXXX} & \hl{XXXXX} \\ - &$^1B_2 (\mathrm{R} ;n \ra 3s)$ &0.005 & 90.3 & 6.70 & D &6.74 & AVQZ \\ - &$^1A_1 (\Val; \pi \ra \pis)$ &0.036 & 91.5 & 6.88 & D &6.87 & AVQZ \\ - &$^3B_1 (\Val; n \ra \pis)$ & & 96.8 & 4.09 & D &4.10 & AVQZ \\ - &$^3A_1 (\Val; \pi \ra \pis)$ & & 98.3 & \emph{4.51} & D &\emph{4.52} & AVQZ \\ - &$^3A_2 (\Val; n \ra \pis)$ & & 96.5 & 4.66 & D &4.67 & AVQZ \\ - &$^3B_2 (\Val; \pi \ra \pis)$ & & 97.4 & 4.96 & D &4.96 & AVQZ \\ - Pyrrole &$^1A_2 (\mathrm{R}; \pi \ra 3s)$ & & 92.9 & 5.24 & {\CCSDT}/AVTZ & 5.27 & AVQZ \\ - &$^1B_1 (\mathrm{R};\pi \ra 3p)$ &0.015 & 92.4 & 6.00 & {\CCSDT}/AVTZ & 6.03 & AVQZ \\ - &$^1A_2 (\mathrm{R};\pi \ra 3p)$ & & 93.0 & 6.00 & D & 6.02 & AVQZ \\ - &$^1B_2 (\Val; (\pi \ra \pis)$ &0.164 & 92.5 & 6.26 & {\CCSDT}/AVTZ & 6.23 & AVQZ \\ - &$^1A_1 (\Val; \pi \ra \pis)$ &0.001 & 86.3 & 6.30 & {\CCSDT}/AVTZ & 6.29 & AVQZ \\ - &$^1B_2 (\mathrm{R};\pi \ra 3p)$ &0.003 & 92.6 & 6.83 & D & 6.74 & AVQZ \\ - &$^3B_2 (\Val; \pi \ra \pis)$ & & 98.3 & 4.51 & D & 4.51 & AVQZ \\ - &$^3A_2 (\mathrm{R};\pi \ra 3s)$ & & 97.6 & 5.21 & D & 5.24 & AVQZ \\ - &$^3A_1 (\Val; \pi \ra \pis)$ & & 97.8 & 5.45 & D & 5.46 & AVQZ \\ - &$^3B_1 (\mathrm{R};\pi \ra 3p)$ & & 97.4 & 5.91 & D & 5.94 & AVQZ \\ -Tetrazine &$^1B_{3u} (\Val; n \ra \pis)$ & 0.006 & 89.8 & 2.47 & {\CCSDT}/AVTZ & 2.46 & AVQZ \\ - &$^1A_{u} (\Val; n \ra \pis)$ & & 87.9 & 3.69 & {\CCSDT}/AVTZ & 3.70 & AVQZ \\ - &$^1A_{g} (\Val; n,n \ra \pis, \pis)$ & & 0.7 & \emph{4.61} & {\NEV}/AVTZ & \emph{4.59} & AVQZ\\%to be remade with CCSDT correction ??? - &$^1B_{1g} (\Val; n \ra \pis)$ & & 83.1 & 4.93 & {\CCSDT}/AVTZ & 4.92 & AVQZ \\ - &$^1B_{2u} (\Val; \pi \ra \pis)$ & 0.055 & 85.4 & 5.21 & {\CCSDT}/AVTZ & 5.20 & AVQZ \\ - &$^1B_{2g} (\Val; n \ra \pis)$ & & 81.7 & 5.45 & {\CCSDT}/AVTZ & 5.45 & AVQZ \\ - &$^1A_{u} (\Val; n \ra \pis)$ & & 87.7 & 5.53 & {\CCSDT}/AVTZ & 5.53 & AVQZ \\ - &$^1B_{3g} (\Val; n,n \ra \pis, \pis)$ & & 0.7 & \emph{6.15} & {\NEV}/AVTZ & \emph{6.13} & AVQZ\\ - &$^1B_{2g} (\Val; n \ra \pis)$ & & 80.2 & 6.12 & D & 6.12 & AVQZ \\ - &$^1B_{1g} (\Val; n \ra \pis)$ & & 85.1 & 6.91 & D & 6.91 & AVQZ \\ - &$^3B_{3u} (\Val; n \ra \pis)$ & & 97.1 & 1.85 & D & 1.86 & AVQZ \\ - &$^3A_{u} (\Val; n \ra \pis)$ & & 96.3 & 3.45 & D & 3.46 & AVQZ \\ - &$^3B_{1g} (\Val; n \ra \pis)$ & & 97.0 & 4.20 & D & 4.21 & AVQZ \\ - &$^3B_{1u} (\Val; \pi \ra \pis)$ & & 98.5 & \emph{4.49} & D & \emph{4.49} & AVQZ \\ - &$^3B_{2u} (\Val; \pi \ra \pis)$ & & 97.5 & 4.52 & D & 4.52 & AVQZ \\ - &$^3B_{2g} (\Val; n \ra \pis)$ & & 96.4 & 5.04 & D & 5.04 & AVQZ \\ - &$^3A_{u} (\Val; n \ra \pis)$ & & 96.6 & 5.11 & D & 5.11 & AVQZ \\ - &$^3B_{3g} (\Val; n,n \ra \pis, \pis)$ & & 5.7 & \emph{5.51} &{\NEV}/AVTZ & \emph{5.50} & AVQZ\\ - &$^3B_{1u} (\Val; \pi \ra \pis)$ & & 96.6 & 5.42 & D & 5.43 & AVQZ \\ -Thioacetone &$^1A_2 (\Val; n \ra \pis)$ & & 88.9 & 2.53 & B & 2.54 & AVQZ \\ - &$^1B_2 (\mathrm{R}; n \ra 4s)$ & 0.052 & 91.3 & 5.56 & B & 5.61 & AVQZ \\ - &$^1A_1 (\Val; \pi \ra \pis)$ & 0.242 & 90.6 & 5.88 & B & 5.86 & AVQZ \\ - &$^1B_2 (\mathrm{R}; n \ra 4p)$ & 0.028 & 92.4 & 6.51 & C & 6.52 & AVQZ \\ - &$^1A_1 (\mathrm{R}; n \ra 4p)$ & 0.023 & 91.6 & 6.61 &B & 6.64 & AVQZ \\ - &$^3A_2 (\Val; n \ra \pis)$ & & 97.4 & 2.33 & D & 2.34 & AVQZ \\ - &$^3A_1 (\Val; \pi \ra \pis)$ & & 98.7 & 3.45 & D & 3.46 & AVQZ \\ -Thiophene &$^1A_1 (\Val; \pi \ra \pis)$ &0.070 & 87.6 & 5.64 & {\CCSDT}/AVTZ & 5.63 & AVQZ \\ - &$^1B_2 (\Val; \pi \ra \pis)$ &0.079 & 91.5 & 5.98 & {\CCSDT}/AVTZ & 5.96 & AVQZ \\ - &$^1A_2 (\mathrm{R}; \pi \ra 3s)$ & & 92.6 & 6.14 & {\CCSDT}/AVTZ & 6.16 & AVQZ \\ - &$^1B_1 (\mathrm{R}; \pi \ra 3p)$ &0.010 & 90.1 & 6.14 & {\CCSDT}/AVTZ & 6.11 & AVQZ \\ - &$^1A_2 (\mathrm{R}; \pi \ra 3p)$ & & 91.8 & 6.21 & {\CCSDT}/AVTZ & 6.18 & AVQZ \\ - &$^1B_1 (\mathrm{R}; \pi \ra 3s)$ &0.000 & 92.8 & 6.49 & {\CCSDT}/AVTZ & 6.52 & AVQZ \\ - &$^1B_2 (\mathrm{R}; \pi \ra 3p)$ &0.082 & 92.4 & 7.29 & {\CCSDT}/AVTZ & 7.18 & AVQZ \\ - &$^1A_1 (\Val; \pi \ra \pis)$ &0.314 & 86.5 & \emph{7.31}& E & \emph{7.29} & AVQZ \\ - &$^3B_2 (\Val; \pi \ra \pis)$ & & 98.2 & 3.92 & D & 3.91 & AVQZ \\ - &$^3A_1 (\Val; \pi \ra \pis)$ & & 97.7 & 4.76 & D & 4.76 & AVQZ \\ - &$^3B_1 (\mathrm{R}; \pi \ra 3p)$ & & 96.6 & 5.93 & D & 5.90 & AVQZ \\ - &$^3A_2 (\mathrm{R}; \pi \ra 3s)$ & & 97.5 & 6.08 & D & 5.98 & AVQZ \\ -Thiopropynal &$^1A'' (\Val; n \ra \pis)$ & 0.000 & 87.5 & 2.03 & {\CCSDT}/AVTZ & 2.04 & AVQZ \\ - &$^3A'' (\Val; n \ra \pis)$ & & 97.2 & 1.80 & D & 1.81 & AVQZ \\ -Triazine &$^1A_1'' (\Val; n \ra \pis)$ & & 88.3 & 4.72 & {\CCSDT}/AVTZ & 4.72 & AVQZ \\ - &$^1A_2'' (\Val; n \ra \pis)$ &0.014 & 88.3 & 4.75 & {\CCSDT}/AVTZ & 4.74 & AVQZ \\ - &$^1E'' (\Val; n \ra \pis)$ & & 88.3 & 4.78 & {\CCSDT}/AVTZ & 4.78 & AVQZ \\ - &$^1A_2' (\Val; \pi \ra \pis)$ & & 85.7 & 5.75 & {\CCSDT}/AVTZ &5.75 &AVQZ\\ - &$^1A_1' (\Val; \pi \ra \pis)$ & & 90.4 & 7.24 & {\CCSDT}/AVTZ & 7.23 & AVQZ \\ - &$^1E' (\mathrm{R}; n \ra 3s)$ &0.016 & 90.9 & 7.32 & {\CCSDT}/AVTZ & 7.36 & AVQZ \\ - &$^1E'' (\Val; n \ra \pis)$ & & 82.6 & 7.78 & {\CCSDT}/AVTZ & 7.76 & AVQZ \\ - &$^1E' (\Val; \pi \ra \pis)$ &0.451 & 90.0 & 7.94 & {\CCSDT}/AVTZ & 7.93 & AVQZ \\ - &$^3A_2'' (\Val; n \ra \pis)$ & & 96.7 & 4.33 & D & 4.34 & AVQZ \\ - &$^3E'' (\Val; n \ra \pis)$ & & 96.6 & 4.51 & D & 4.51 & AVQZ \\ - &$^3A_1'' (\Val; n \ra \pis)$ & & 96.2 & 4.73 & D & 4.74 & AVQZ \\ - &$^3A_1' (\Val; \pi \ra \pis)$ & & 98.2 & 4.85 & D & 4.86 & AVQZ \\ - &$^3E' (\Val; \pi \ra \pis)$ & & 96.9 & 5.59 & E & 5.59 & AVQZ \\ - &$^3A_2' (\Val; (\pi \ra \pis)$ & & 97.6 & 6.62 & D & 6.61 & AVQZ \\ + &$^1B_2 (\mathrm{R} ;n \ra 3s)$ &0.005 & 90.3 & 6.70 & D &6.74 & \AVQZ \\ + &$^1A_1 (\Val; \pi \ra \pis)$ &0.036 & 91.5 & 6.88 & D &6.87 & \AVQZ \\ + &$^3B_1 (\Val; n \ra \pis)$ & & 96.8 & 4.09 & D &4.10 & \AVQZ \\ + &$^3A_1 (\Val; \pi \ra \pis)$ & & 98.3 & \emph{4.51} & D &\emph{4.52} & \AVQZ \\ + &$^3A_2 (\Val; n \ra \pis)$ & & 96.5 & 4.66 & D &4.67 & \AVQZ \\ + &$^3B_2 (\Val; \pi \ra \pis)$ & & 97.4 & 4.96 & D &4.96 & \AVQZ \\ + Pyrrole &$^1A_2 (\mathrm{R}; \pi \ra 3s)$ & & 92.9 & 5.24 & {\CCSDT}/\AVTZ & 5.27 & \AVQZ \\ + &$^1B_1 (\mathrm{R};\pi \ra 3p)$ &0.015 & 92.4 & 6.00 & {\CCSDT}/\AVTZ & 6.03 & \AVQZ \\ + &$^1A_2 (\mathrm{R};\pi \ra 3p)$ & & 93.0 & 6.00 & D & 6.02 & \AVQZ \\ + &$^1B_2 (\Val; (\pi \ra \pis)$ &0.164 & 92.5 & 6.26 & {\CCSDT}/\AVTZ & 6.23 & \AVQZ \\ + &$^1A_1 (\Val; \pi \ra \pis)$ &0.001 & 86.3 & 6.30 & {\CCSDT}/\AVTZ & 6.29 & \AVQZ \\ + &$^1B_2 (\mathrm{R};\pi \ra 3p)$ &0.003 & 92.6 & 6.83 & D & 6.74 & \AVQZ \\ + &$^3B_2 (\Val; \pi \ra \pis)$ & & 98.3 & 4.51 & D & 4.51 & \AVQZ \\ + &$^3A_2 (\mathrm{R};\pi \ra 3s)$ & & 97.6 & 5.21 & D & 5.24 & \AVQZ \\ + &$^3A_1 (\Val; \pi \ra \pis)$ & & 97.8 & 5.45 & D & 5.46 & \AVQZ \\ + &$^3B_1 (\mathrm{R};\pi \ra 3p)$ & & 97.4 & 5.91 & D & 5.94 & \AVQZ \\ +Tetrazine &$^1B_{3u} (\Val; n \ra \pis)$ & 0.006 & 89.8 & 2.47 & {\CCSDT}/\AVTZ & 2.46 & \AVQZ \\ + &$^1A_{u} (\Val; n \ra \pis)$ & & 87.9 & 3.69 & {\CCSDT}/\AVTZ & 3.70 & \AVQZ \\ + &$^1A_{g} (\Val; n,n \ra \pis, \pis)$ & & 0.7 & \emph{4.61} & {\NEV}/\AVTZ & \emph{4.59} & \AVQZ\\%to be remade with CCSDT correction ??? + &$^1B_{1g} (\Val; n \ra \pis)$ & & 83.1 & 4.93 & {\CCSDT}/\AVTZ & 4.92 & \AVQZ \\ + &$^1B_{2u} (\Val; \pi \ra \pis)$ & 0.055 & 85.4 & 5.21 & {\CCSDT}/\AVTZ & 5.20 & \AVQZ \\ + &$^1B_{2g} (\Val; n \ra \pis)$ & & 81.7 & 5.45 & {\CCSDT}/\AVTZ & 5.45 & \AVQZ \\ + &$^1A_{u} (\Val; n \ra \pis)$ & & 87.7 & 5.53 & {\CCSDT}/\AVTZ & 5.53 & \AVQZ \\ + &$^1B_{3g} (\Val; n,n \ra \pis, \pis)$ & & 0.7 & \emph{6.15} & {\NEV}/\AVTZ & \emph{6.13} & \AVQZ\\ + &$^1B_{2g} (\Val; n \ra \pis)$ & & 80.2 & 6.12 & D & 6.12 & \AVQZ \\ + &$^1B_{1g} (\Val; n \ra \pis)$ & & 85.1 & 6.91 & D & 6.91 & \AVQZ \\ + &$^3B_{3u} (\Val; n \ra \pis)$ & & 97.1 & 1.85 & D & 1.86 & \AVQZ \\ + &$^3A_{u} (\Val; n \ra \pis)$ & & 96.3 & 3.45 & D & 3.46 & \AVQZ \\ + &$^3B_{1g} (\Val; n \ra \pis)$ & & 97.0 & 4.20 & D & 4.21 & \AVQZ \\ + &$^3B_{1u} (\Val; \pi \ra \pis)$ & & 98.5 & \emph{4.49} & D & \emph{4.49} & \AVQZ \\ + &$^3B_{2u} (\Val; \pi \ra \pis)$ & & 97.5 & 4.52 & D & 4.52 & \AVQZ \\ + &$^3B_{2g} (\Val; n \ra \pis)$ & & 96.4 & 5.04 & D & 5.04 & \AVQZ \\ + &$^3A_{u} (\Val; n \ra \pis)$ & & 96.6 & 5.11 & D & 5.11 & \AVQZ \\ + &$^3B_{3g} (\Val; n,n \ra \pis, \pis)$ & & 5.7 & \emph{5.51} &{\NEV}/\AVTZ & \emph{5.50} & \AVQZ\\ + &$^3B_{1u} (\Val; \pi \ra \pis)$ & & 96.6 & 5.42 & D & 5.43 & \AVQZ \\ +Thioacetone &$^1A_2 (\Val; n \ra \pis)$ & & 88.9 & 2.53 & B & 2.54 & \AVQZ \\ + &$^1B_2 (\mathrm{R}; n \ra 4s)$ & 0.052 & 91.3 & 5.56 & B & 5.61 & \AVQZ \\ + &$^1A_1 (\Val; \pi \ra \pis)$ & 0.242 & 90.6 & 5.88 & B & 5.86 & \AVQZ \\ + &$^1B_2 (\mathrm{R}; n \ra 4p)$ & 0.028 & 92.4 & 6.51 & C & 6.52 & \AVQZ \\ + &$^1A_1 (\mathrm{R}; n \ra 4p)$ & 0.023 & 91.6 & 6.61 &B & 6.64 & \AVQZ \\ + &$^3A_2 (\Val; n \ra \pis)$ & & 97.4 & 2.33 & D & 2.34 & \AVQZ \\ + &$^3A_1 (\Val; \pi \ra \pis)$ & & 98.7 & 3.45 & D & 3.46 & \AVQZ \\ +Thiophene &$^1A_1 (\Val; \pi \ra \pis)$ &0.070 & 87.6 & 5.64 & {\CCSDT}/\AVTZ & 5.63 & \AVQZ \\ + &$^1B_2 (\Val; \pi \ra \pis)$ &0.079 & 91.5 & 5.98 & {\CCSDT}/\AVTZ & 5.96 & \AVQZ \\ + &$^1A_2 (\mathrm{R}; \pi \ra 3s)$ & & 92.6 & 6.14 & {\CCSDT}/\AVTZ & 6.16 & \AVQZ \\ + &$^1B_1 (\mathrm{R}; \pi \ra 3p)$ &0.010 & 90.1 & 6.14 & {\CCSDT}/\AVTZ & 6.11 & \AVQZ \\ + &$^1A_2 (\mathrm{R}; \pi \ra 3p)$ & & 91.8 & 6.21 & {\CCSDT}/\AVTZ & 6.18 & \AVQZ \\ + &$^1B_1 (\mathrm{R}; \pi \ra 3s)$ &0.000 & 92.8 & 6.49 & {\CCSDT}/\AVTZ & 6.52 & \AVQZ \\ + &$^1B_2 (\mathrm{R}; \pi \ra 3p)$ &0.082 & 92.4 & 7.29 & {\CCSDT}/\AVTZ & 7.18 & \AVQZ \\ + &$^1A_1 (\Val; \pi \ra \pis)$ &0.314 & 86.5 & \emph{7.31}& E & \emph{7.29} & \AVQZ \\ + &$^3B_2 (\Val; \pi \ra \pis)$ & & 98.2 & 3.92 & D & 3.91 & \AVQZ \\ + &$^3A_1 (\Val; \pi \ra \pis)$ & & 97.7 & 4.76 & D & 4.76 & \AVQZ \\ + &$^3B_1 (\mathrm{R}; \pi \ra 3p)$ & & 96.6 & 5.93 & D & 5.90 & \AVQZ \\ + &$^3A_2 (\mathrm{R}; \pi \ra 3s)$ & & 97.5 & 6.08 & D & 5.98 & \AVQZ \\ +Thiopropynal &$^1A'' (\Val; n \ra \pis)$ & 0.000 & 87.5 & 2.03 & {\CCSDT}/\AVTZ & 2.04 & \AVQZ \\ + &$^3A'' (\Val; n \ra \pis)$ & & 97.2 & 1.80 & D & 1.81 & \AVQZ \\ +Triazine &$^1A_1'' (\Val; n \ra \pis)$ & & 88.3 & 4.72 & {\CCSDT}/\AVTZ & 4.72 & \AVQZ \\ + &$^1A_2'' (\Val; n \ra \pis)$ &0.014 & 88.3 & 4.75 & {\CCSDT}/\AVTZ & 4.74 & \AVQZ \\ + &$^1E'' (\Val; n \ra \pis)$ & & 88.3 & 4.78 & {\CCSDT}/\AVTZ & 4.78 & \AVQZ \\ + &$^1A_2' (\Val; \pi \ra \pis)$ & & 85.7 & 5.75 & {\CCSDT}/\AVTZ &5.75 &\AVQZ\\ + &$^1A_1' (\Val; \pi \ra \pis)$ & & 90.4 & 7.24 & {\CCSDT}/\AVTZ & 7.23 & \AVQZ \\ + &$^1E' (\mathrm{R}; n \ra 3s)$ &0.016 & 90.9 & 7.32 & {\CCSDT}/\AVTZ & 7.36 & \AVQZ \\ + &$^1E'' (\Val; n \ra \pis)$ & & 82.6 & 7.78 & {\CCSDT}/\AVTZ & 7.76 & \AVQZ \\ + &$^1E' (\Val; \pi \ra \pis)$ &0.451 & 90.0 & 7.94 & {\CCSDT}/\AVTZ & 7.93 & \AVQZ \\ + &$^3A_2'' (\Val; n \ra \pis)$ & & 96.7 & 4.33 & D & 4.34 & \AVQZ \\ + &$^3E'' (\Val; n \ra \pis)$ & & 96.6 & 4.51 & D & 4.51 & \AVQZ \\ + &$^3A_1'' (\Val; n \ra \pis)$ & & 96.2 & 4.73 & D & 4.74 & \AVQZ \\ + &$^3A_1' (\Val; \pi \ra \pis)$ & & 98.2 & 4.85 & D & 4.86 & \AVQZ \\ + &$^3E' (\Val; \pi \ra \pis)$ & & 96.9 & 5.59 & E & 5.59 & \AVQZ \\ + &$^3A_2' (\Val; (\pi \ra \pis)$ & & 97.6 & 6.62 & D & 6.61 & \AVQZ \\ \end{longtable} \end{footnotesize} \begin{flushleft}\begin{footnotesize}\begin{singlespace} @@ -1393,28 +1403,29 @@ Method F: {\FCI}/{\AVDZ} value (from Ref.~\citenum{Loo19c}) corrected by the dif \section{Benchmarks} -Having at hand such a large set of accurate transition energies, it seems natural to pursue previous benchmarking efforts. More specifically, we assess here the performances of eight popular wavefunction approaches, namely, CIS(D), {\AD}, -{\CCD}, {\STEOM}, {\CCSD}, CCSDR(3), CCSDT-3 and {\CCT}. The complete list of results can be found in Table \hl{SXXX} in the SI. As all these approaches are single-reference methods, we have removed from the -benchmark not only the unsafe transition energies (in italics in Table \ref{Table-tbe}), but also the four transitions with a dominant double excitation character ($\Td < 50\%$ listed in Table \ref{Table-tbe}). -Our global results are collected in Table \ref{Table-bench} that presents the MSE, MAE, root mean square deviation (RMS), standard deviation (SD), as well as the positive [\MaxP] and negative [\MaxN] maximum deviations. -Figure \ref{Fig-1} shows histograms of the error distributions for all eight methods. Before discussing the obtained results, let us underline two obvious bias of this benchmark: i) it encompasses only conjugated organic molecules +Having at hand such a large set of accurate transition energies, it seems natural to pursue previous benchmarking efforts. More specifically, we assess here the performances of eight popular wavefunction approaches, namely, CIS(D), {\AD}, +{\CCD}, {\STEOM}, {\CCSD}, CCSDR(3), CCSDT-3 and {\CCT}. The complete list of results can be found in Table \hl{SXXX} of the SI. Because all these approaches are single-reference methods, we have removed from the +reference set the ``unsafe'' transition energies (in italics in Table \ref{Table-tbe}), as well as the four transitions with a dominant double excitation character (with $\Td < 50\%$ as listed in Table \ref{Table-tbe}). +A comprehensive list of results are collected in Table \ref{Table-bench} which, more specifically, gathers the MSE, MAE, RMSE, SDE, \MaxP, and \MaxN. +Figure \ref{Fig-1} shows histograms of the error distributions for these eight methods. Before discussing these, let us stress two obvious biases of this benchmark set: i) it encompasses only conjugated organic molecules containing 4 to 6 non-hydrogen atoms; and ii) we mainly used {\CCSDTQ} (4 atoms) or {\CCSDT} (5--6 atoms) reference values. As discussed in Section \ref{sec-ic} and in our previous work, \cite{Loo18a} the MAE obtained -with these two methods are of the order of $0.01$ and $0.03$ eV, respectively. This means that any deviation (or difference of deviations) smaller than ca.~$0.02$--$0.03$ eV is likely irrelevant. +with these two methods are of the order of $0.01$ and $0.03$ eV, respectively. This means that any statistical quantity smaller than $\sim 0.02$--$0.03$ eV is very likely to be irrelevant. \renewcommand*{\arraystretch}{1.0} \begin{table}[htp] -\caption{Mean signed error (MSE), mean absolute error (MAE), root-mean square deviation (RMS), standard deviation (SD), positive [\MaxP] and negative [\MaxN] maximal deviations with respect to the TBE. -All values are in eV and have been obtained with the {\AVTZ} basis set.} +\caption{Mean signed error (MSE), mean absolute error (MAE), root-mean square error (RMSE), standard deviation of the errors (SDE), as well as the positive [\MaxP] and negative [\MaxN] maximal errors with respect to the TBE. +All these statistical quantities are reported in eV and have been obtained with the {\AVTZ} basis set. +``Count'' refers to the number of states.} \label{Table-bench} \begin{tabular}{lccccccc} \hline -Method & Nb. States & MSE &MAE &RMS &SD &\MaxP &\MaxN \\ +Method & Count & MSE &MAE &RMSE &SDE &\MaxP &\MaxN \\ \hline CIS(D) &220 &0.16 &0.23 &0.29 &0.24 &0.96 &-0.69\\ -{\AD} &217 &0.01 &0.14 &0.20 &0.19 &0.64 &-0.73\\ +{\AD} &217 &0.01 &0.14 &0.20 &0.19 &0.64 &-0.73\\ {\CCD} &222 &0.02 &0.15 &0.21 &0.20 &0.59 &-0.68\\ -{\STEOM} &190 &0.00 &0.12 &0.15 &0.14 &0.59 &-0.42\\ - {\CCSD} &222 &0.11 &0.13 &0.16 &0.12 &0.62 &-0.16\\ +{\STEOM} &190 &0.00 &0.12 &0.15 &0.14 &0.59 &-0.42\\ + {\CCSD} &222 &0.11 &0.13 &0.16 &0.12 &0.62 &-0.16\\ CCSDR(3) &133 &0.05 &0.05 &0.07 &0.05 &0.36 &-0.03\\ CCSDT-3 &126 &0.05 &0.05 &0.07 &0.04 &0.26 &0.00\\ {\CCT} &222 &0.00 &0.01 &0.02 &0.02 &0.17 &-0.05\\ @@ -1424,7 +1435,8 @@ CCSDT-3 &126 &0.05 &0.05 &0.07 &0.04 &0.26 &0.00\\ \begin{figure}[htp] \includegraphics[scale=0.98,viewport=2cm 14.5cm 19cm 27.5cm,clip]{Figure-1.pdf} - \caption{Histograms of the error patterns obtained with various leveles of theory, taking the TBE/{\AVTZ} of Table \ref{Table-bench} as references. Note the different $Y$ scales.} + \caption{Histograms of the error patterns obtained with various levels of theory, taking the TBE/{\AVTZ} of Table \ref{Table-bench} as references. + Note the difference of scaling in the vertical axes.} \label{Fig-1} \end{figure} @@ -1443,7 +1455,7 @@ of being too large, an error sign likely inherited from the parent {\CCSD} model are considered. The {\CCSD} MAE ($0.13$ eV) is much smaller than the one reported by Thiel in its original work ($0.49$ eV) \cite{Sch08} but of the same order of magnitude as in the more recent study of Kannar and Szalay performed on Thiel's set ($0.18$ eV for transitions with $\Td > 90\%$ ). \cite{Kan14} In retrospect, the much larger value obtained by Thiel is likely related to the use of {\CASPT} reference values in the 2008 work. Indeed, as we have shown in many of the proposed examples, {\CASPT} transitions energies tend to be significantly too low, therefore exacerbating {\CCSD}'s overestimation. The {\STEOM} approach, which received relatively less attention to date -- we are -aware of one detailed benchmark \cite{Dut18} only -- provides a smaller MSE than {\CCSD} and comparable MAE and RMS. The spread of the error is however slightly larger as can be seen in Figure \ref{Fig-1} and from the SD values +aware of one detailed benchmark \cite{Dut18} only -- provides a smaller MSE than {\CCSD} and comparable MAE and RMSE. The spread of the error is however slightly larger as can be seen in Figure \ref{Fig-1} and from the SD values in Table \ref{Table-bench}. These trends are the same as for smaller compounds. \cite{Loo18a} For Thiel's set using {\CCT}/TZVP results as references, Dutta and coworkers also reported a rather good performance of {\STEOM}, though in that case a slightly negative MSE is obtained, \cite{Dut18} which could possibly be due to the different basis sets used. It should be nevertheless stressed that we consider here only ``clean'' {\STEOM} results (see Computational details), therefore removing several difficult cases that are included in the {\CCSD} statistics, \eg, the $A_g$ excitation in butadiene, which can slightly bias the relative accuracies when comparing the two models. Finally, for the three @@ -1491,7 +1503,7 @@ We have computed highly-accurate vertical transition energies for a set of 27 me However, most of our theoretical best estimates are based on {\CCSDTQ} (4 atoms) or {\CCSDT} (5 and 6 atoms) excitation energies. For the vast majority of the listed excited states, the present contribution is the very first to disclose (sometimes basis-set extrapolated) {\CCSDT}/{\AVTZ} and (true) {\CCT}/{\AVQZ} transition energies as well as {\CCT}/{\AVTZ} oscillator strengths for each dipole-allowed transition. Our set contains a total of 238 transition energies and 90 oscillator strengths, with a reasonably good balance between singlet, triplet, valence, -and Rydberg states. Amongst these 238 transitions, we believe that 224 are ``solid'' TBE, \ie, they are chemically accurate (mean error below $0.043$ eV or $1$ kcal.mol$^{-1}$) for the considered geometry. +and Rydberg states. Amongst these 238 transitions, we believe that 224 are ``solid'' TBE, \ie, they are chemically accurate (MAE below $0.043$ eV or $1$ kcal.mol$^{-1}$) for the considered geometry. It allows us to establish a reasonable error bar for several popular ES models with lower computational cost: CIS(D), {\AD}, {\CCD}, {\STEOM}, {\CCSD}, CCSDR(3), CCSDT-3, and {\CCT}. It turns out that the latter approach is extremely accurate, and, very likely should be considered as more robust and trustworthy than {\CASPT} or {\NEV}, except for ES with a predominant double excitation character. Other methods including corrections for the triples yield a mean absolute deviation around $0.05$ eV, whereas none of the second-order approach has been found to be chemically accurate with MAE