starting correction bench
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@ -51,15 +51,23 @@
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% basis
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\newcommand{\Pop}{6-31+G(d)}
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\newcommand{\AVDZ}{\emph{aug}-cc-pVDZ}
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\newcommand{\AVTZ}{\emph{aug}-cc-pVTZ}
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\newcommand{\DAVTZ}{d-\emph{aug}-cc-pVTZ}
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\newcommand{\AVQZ}{\emph{aug}-cc-pVQZ}
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\newcommand{\AVFZ}{\emph{aug}-cc-pV5Z}
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\newcommand{\DAVQZ}{d-\emph{aug}-cc-pVQZ}
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\newcommand{\TAVQZ}{t-\emph{aug}-cc-pVQZ}
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\newcommand{\AVPZ}{\emph{aug}-cc-pV5Z}
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\newcommand{\DAVPZ}{d-\emph{aug}-cc-pV5Z}
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%\newcommand{\AVDZ}{\emph{aug}-cc-pVDZ}
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%\newcommand{\AVTZ}{\emph{aug}-cc-pVTZ}
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%\newcommand{\DAVTZ}{d-\emph{aug}-cc-pVTZ}
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%\newcommand{\AVQZ}{\emph{aug}-cc-pVQZ}
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%\newcommand{\AVFZ}{\emph{aug}-cc-pV5Z}
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%\newcommand{\DAVQZ}{d-\emph{aug}-cc-pVQZ}
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%\newcommand{\TAVQZ}{t-\emph{aug}-cc-pVQZ}
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%\newcommand{\AVPZ}{\emph{aug}-cc-pV5Z}
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%\newcommand{\DAVPZ}{d-\emph{aug}-cc-pV5Z}
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\newcommand{\AVDZ}{aVDZ}
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\newcommand{\AVTZ}{aVTZ}
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\newcommand{\DAVTZ}{daVTZ}
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\newcommand{\AVQZ}{aVQZ}
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\newcommand{\DAVQZ}{daVQZ}
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\newcommand{\TAVQZ}{taVQZ}
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\newcommand{\AVPZ}{aV5Z}
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\newcommand{\DAVPZ}{dapV5Z}
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% units
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\newcommand{\IneV}[1]{#1 eV}
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@ -105,14 +113,14 @@
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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
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obtained for 27 molecules encompassing 4, 5, and 6 non-hydrogen atoms: acetone, acrolein, benzene, butadiene, cyanoacetylene, cyanoformaldehyde, cyanogen, cyclopentadiene, cyclopropenone, cyclopropenethione,
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diacetylene, furan, glyoxal, imidazole, isobutene, methylenecyclopropene, propynal, pyrazine, pyridazine, pyridine, pyrimidine, pyrrole, tetrazine, thioacetone, thiophene, thiopropynal, and triazine.
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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),
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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),
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as well as the multiconfigurational $n$-electron valence state perturbation theory (NEVPT2) method.
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All these approaches are applied in combination with diffuse-containing atomic basis sets. For all transitions, we report at least {\CCT}/{\AVQZ} vertical excitation
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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.
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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
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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.
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The present contribution gathers a large, diverse and accurate set of more than 200 highly-accurate transition energies for states of various natures
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(valence, Rydberg, singlet, triplet, $n \ra \pis$, $\pi \ra \pis$, \ldots).
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We use this series of theoretical best estimates to benchmark a series of popular methods for excited state calculations: CIS(D), {\AD},
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{\CCD}, {\STEOM}, {\CCSD}, CCSDR(3), CCSDT-3, and {\CCT}. The results of these benchmarks are compared to the available literature data.
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We use this series of theoretical best estimates to benchmark a series of popular methods for excited state calculations: CIS(D), ADC(2),
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CC2, STEOM-CCSD, EOM-CCSD, CCSDR(3), CCSDT-3, and CC3. The results of these benchmarks are compared to the available literature data.
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\end{abstract}
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\clearpage
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@ -179,6 +187,8 @@ corrections (up to quadruple-$\zeta$ at least) are also provided for {\CCT}. Tog
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Unless otherwise stated, all transition energies are computed in the frozen-core approximation (with a large core for the sulfur atoms).
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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.
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In the following, we employ the aVXZ shorthand notations for these diffuse-containing Dunning basis sets.
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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.
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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.
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@ -256,7 +266,7 @@ relevant and are therefore unlikely to change any of our main conclusions.
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\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}}
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\hline
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\mc{14}{c}{Cyanoacetylene}\\
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& \mc{4}{c}{\Pop} & \mc{4}{c}{\AVDZ}& \mc{3}{c}{\AVTZ} & \mc{1}{c}{\AVQZ} & \mc{1}{c}{\AVFZ} & \mc{2}{c}{Litt.}\\
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& \mc{4}{c}{\Pop} & \mc{4}{c}{\AVDZ}& \mc{3}{c}{\AVTZ} & \mc{1}{c}{\AVQZ} & \mc{1}{c}{\AVPZ} & \mc{2}{c}{Litt.}\\
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State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI}& {\CCT} & {\CCSDT} & {\NEV} & {\CCT} & {\CCT}& Th.$^a$ & Exp.$^b$ \\
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\hline
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$^1\Sigma^-$ &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\\
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@ -266,7 +276,7 @@ $^3\Delta$ &5.35&5.34& &5.32$\pm$0.03 &5.28&5.27& &5.20$\pm$0.08 &5.
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$^1A''$[F]$^c$ &3.70&3.72&3.70&3.67$\pm$0.03 &3.60&3.62&3.60&3.59$\pm$0.02 &3.54&3.56&3.50& 3.54 & &&\\
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\hline
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\mc{14}{c}{Cyanogen}\\
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& \mc{4}{c}{\Pop} & \mc{4}{c}{\AVDZ}& \mc{3}{c}{\AVTZ} & \mc{1}{c}{\AVQZ} & \mc{1}{c}{\AVFZ} & \mc{1}{c}{Litt.}\\
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& \mc{4}{c}{\Pop} & \mc{4}{c}{\AVDZ}& \mc{3}{c}{\AVTZ} & \mc{1}{c}{\AVQZ} & \mc{1}{c}{\AVPZ} & \mc{1}{c}{Litt.}\\
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State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI}& {\CCT} & {\CCSDT} & {\NEV}& {\CCT} & {\CCT}& Exp.$^d$ \\
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\hline
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$^1\Sigma_u^-$ &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\\
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@ -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$0.07 &4.9
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$^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$0.09 &5.06&5.07&4.97& 5.05 &5.05 & \\
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\hline
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\mc{14}{c}{Diacetylene}\\
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& \mc{4}{c}{\Pop} & \mc{4}{c}{\AVDZ}& \mc{3}{c}{\AVTZ} & \mc{1}{c}{\AVQZ} & \mc{1}{c}{\AVFZ} & \mc{1}{c}{Litt.}\\
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& \mc{4}{c}{\Pop} & \mc{4}{c}{\AVDZ}& \mc{3}{c}{\AVTZ} & \mc{1}{c}{\AVQZ} & \mc{1}{c}{\AVPZ} & \mc{1}{c}{Litt.}\\
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State & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI} & {\CCT} & {\CCSDT} & {\CCSDTQ} & {\FCI}& {\CCT} & {\CCSDT} & {\NEV}& {\CCT} & {\CCT}& Exp.$^e$ \\
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\hline
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$^1\Sigma_u^-$ &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\\
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@ -389,7 +399,7 @@ results might be slightly too low for the second transition. }
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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
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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
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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,
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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,
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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 (\%$T_1 = 85\%$),
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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
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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
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@ -619,11 +629,11 @@ This is further confirmed by the {\FCI} data.
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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.
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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,
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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
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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
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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
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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
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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
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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),
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one obtains a mean signed deviation of $+0.09$ ($+0.09$) eV and a mean absolute deviation of $0.11$ ($0.12$) eV.
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one obtains a MSE of $+0.09$ ($+0.09$) eV and a MAE of $0.11$ ($0.12$) eV.
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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.
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\subsection{Five-atom molecules}
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@ -1104,7 +1114,7 @@ our previous works indicated that {\CCSDT} tends to overshoot the transition ene
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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
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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
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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-$\zeta$,
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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,
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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,
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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
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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,
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in principle, necessary to add core polarization functions in such ``full'' calculations.
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@ -1137,154 +1147,154 @@ that have always been obtained at the {\CCT} level. Values displayed in italics
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\endfoot
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\hline
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\endlastfoot
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Acetone &$^1A_2 (\Val; n \ra \pis)$ & & 91.1 & 4.47 & B & 4.48 & AVQZ \\
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&$^1B_2 (\mathrm{R}; n \ra 3s)$ &0.000 & 90.5 & 6.46 & B & 6.51 & AVQZ \\
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&$^1A_2 (\mathrm{R}; n \ra 3p)$ & & 90.9 & 7.47 & B & 7.44 & AVQZ \\
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&$^1A_1 (\mathrm{R}; n \ra 3p)$ &0.004 & 90.6 & 7.51 & B & 7.55 & AVQZ \\
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&$^1B_2 (\mathrm{R}; n \ra 3p)$ &0.029 & 91.2 & 7.62 & B & 7.63 & AVQZ \\
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&$^3A_2 (\Val; n \ra \pis)$ & & 97.8 & 4.13 & D & 4.15 & AVQZ \\
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&$^3A_1 (\Val; \pi \ra \pis)$ & & 98.7 & 6.25 & D & 6.27 & AVQZ \\
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Acrolein &$^1A'' (\Val; n \ra \pis)$ &0.000 & 87.6 & 3.73 & {\CCSDT}/AVTZ & 3.74 & AVQZ \\
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&$^1A' (\Val; \pi \ra \pis)$ &0.344 & 91.2 & 6.69 & {\CCSDT}/AVTZ & 6.69 & AVQZ \\
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&$^1A'' (\Val; n \ra \pis)$ &0.000 & 79.4 & \emph{6.72} & D &\emph{6.74} & AVQZ \\
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&$^1A' (\mathrm{R}; n \ra 3s)$ &0.109 & 89.4 & 7.08 & D & 7.12 & AVQZ \\
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&$^3A'' (\Val; n \ra \pis)$ & & 97.0 & 3.44 & D & 3.43 & AVQZ \\
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&$^3A' (\Val; \pi \ra \pis)$ & & 98.6 & 3.94 & D & 3.95 & AVQZ \\
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&$^3A' (\Val; \pi \ra \pis)$ & & 98.4 & 6.18 & D & 6.19 & AVQZ \\
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&$^3A'' (\Val; n \ra \pis)$ & & 92.7 & \emph{6.54} & E & \emph{6.55}& AVQZ \\%remove
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Benzene &$^1B_{2u} (\Val; \pi \ra \pis)$ & & 86.3 & 5.06 & {\CCSDT}/AVTZ & 5.06 &AVQZ \\
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&$^1B_{1u} (\Val; \pi \ra \pis)$ & & 92.9 & 6.45 & {\CCSDT}/AVTZ &6.44 &AVQZ \\
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&$^1E_{1g} (\mathrm{R}; \pi \ra 3s)$ & & 92.8 & 6.52 & {\CCSDT}/AVTZ &6.54 &AVQZ \\
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&$^1A_{2u} (\mathrm{R}; \pi \ra 3p)$ &0.066 & 93.4 & 7.08 & {\CCSDT}/AVTZ &7.10 &AVQZ \\
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&$^1E_{2u} (\mathrm{R}; \pi \ra 3p)$ & & 92.8 & 7.15 & {\CCSDT}/AVTZ &7.16 &AVQZ \\
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&$^3B_{1u} (\Val; \pi \ra \pis)$ & & 98.6 & 4.16 & D &4.17 &AVQZ \\
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&$^3E_{1u}(\Val; \pi \ra \pis)$ & & 97.1 & 4.85 & D &4.86 &AVQZ \\
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&$^3B_{2u} (\Val; \pi \ra \pis)$ & & 98.1 & 5.81 & D & 5.81 &AVQZ \\
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Butadiene &$^1B_u (\Val; \pi \ra \pis)$ &0.664 & 93.3 & 6.22 & B & 6.21 & AVQZ \\
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&$^1B_g (\mathrm{R}; \pi \ra 3s)$ & & 94.1 & 6.33 & B & 6.35 & AVQZ \\
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&$^1A_g (\Val; \pi \ra \pis)$ & & 75.1 & 6.50 & F & 6.50 & AVQZ \\
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&$^1A_u (\mathrm{R}; \pi \ra 3p)$ &0.001 & 94.1 & 6.64 & B & 6.66 & AVQZ \\
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&$^1A_u (\mathrm{R}; \pi \ra 3p)$ &0.049 & 94.1 & 6.80 & B & 6.82 & AVQZ \\
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&$^1B_u (\mathrm{R}; \pi \ra 3p)$ &0.055 & 93.8 & 7.68 & C & 7.54 & AVQZ \\
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&$^3B_u (\Val; \pi \ra \pis)$ & & 98.4 & 3.36 & D & 3.37 & AVQZ \\
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&$^3A_g (\Val; \pi \ra \pis)$ & & 98.7 & 5.20 & D & 5.21 & AVQZ \\
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&$^3B_g (\mathrm{R}; \pi \ra 3s)$ & & 97.9 & 6.29 & D & 6.31 & AVQZ \\
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Cyanoacetylene &$^1\Sigma^- (\Val; \pi \ra \pis)$ & & 94.3 & 5.80 & A & 5.79 & AV5Z\\
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&$^1\Delta (\Val; \pi \ra \pis)$ & & 94.0 & 6.07 & A & 6.05 &AV5Z\\
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&$^3\Sigma^+ (\Val; \pi \ra \pis)$ & & 98.5 & 4.44 & {\CCSDT}/AVTZ & 4.46 &AV5Z \\
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&$^3\Delta (\Val; \pi \ra \pis)$ & & 98.2 & 5.21 & {\CCSDT}/AVTZ & 5.21 & AV5Z\\
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&$^1A'' [\mathrm{F}] (\Val; \pi \ra \pis)$ & 0.004 & 93.6 & 3.54 & A & 3.54 & AVQZ \\
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Cyanoformaldehyde &$^1A'' (\Val; n \ra \pis)$ & 0.001 & 89.8 & 3.81 & {\CCSDT}/AVTZ & 3.82 & AVQZ \\
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&$^1A'' (\Val; \pi \ra \pis)$ & 0.000 & 91.9 & 6.46 & {\CCSDT}/AVTZ & 6.45 & AVQZ \\
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&$^3A'' (\Val; n \ra \pis)$ & & 97.6 & 3.44 & D & 3.45 & AVQZ \\
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&$^3A' (\Val; \pi \ra \pis)$ & & 98.4 & 5.01 & D & 5.02 & AVQZ \\
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Cyanogen & $^1\Sigma_u^- (\Val; \pi \ra \pis)$ & & 94.1 & 6.39 & A & 6.38 & AV5Z\\
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& $^1\Delta_u (\Val; \pi \ra \pis)$ & & 93.4 & 6.66 & A & 6.64 & AV5Z\\
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& $^3\Sigma_u^+ (\Val; \pi \ra \pis)$ & & 98.5 & 4.91 & B & 4.93 & AV5Z \\
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& $^1\Sigma_u^- [\mathrm{F}] (\Val; \pi \ra \pis)$ & & 93.4 & 5.05 & A & 5.03 & AV5Z \\
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Cyclopentadiene &$^1B_2 (\Val; \pi \ra \pis)$ &0.084 & 93.8 & 5.56 & {\CCSDT}/AVTZ & 5.55 & AVQZ \\
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&$^1A_2 (\mathrm{R}; \pi \ra 3s)$ & & 94.0 & 5.78 & {\CCSDT}/AVTZ & 5.80 & AVQZ \\
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&$^1B_1 (\mathrm{R}; \pi \ra 3p)$ &0.037 & 94.2 & 6.41 & {\CCSDT}/AVTZ & 6.42 & AVQZ \\
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&$^1A_2 (\mathrm{R}; \pi \ra 3p)$ & & 93.8 & 6.46 & {\CCSDT}/AVTZ & 6.47 & AVQZ \\
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&$^1B_2 (\mathrm{R}; \pi \ra 3p)$ &0.046 & 94.2 & 6.56 &{\CCSDT}/AVTZ & 6.55 & AVQZ\\
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&$^1A_1 (\Val; \pi \ra \pis)$ &0.001 & 78.9 & \emph{6.51} & D & \emph{6.51} & AVQZ \\
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&$^3B_2 (\Val; \pi \ra \pis)$ & & 98.4 & 3.31 & D & 3.31 & AVQZ \\
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&$^3A_1 (\Val; \pi \ra \pis)$ & & 98.6 & 5.11 & D & 5.12 & AVQZ \\
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&$^3A_2 (\mathrm{R}; \pi \ra 3s)$ & & 97.9 & 5.73 & D & 5.75 & AVQZ \\
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&$^3B_1 (\mathrm{R}; \pi \ra 3p)$ & & 97.9 & 6.36 & D & 6.38 & AVQZ \\
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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}
|
||||
@ -1394,21 +1404,22 @@ 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
|
||||
{\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\\
|
||||
@ -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
|
||||
|
||||
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