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@ -160,14 +160,15 @@ the generally robust $n$-electron valence state perturbation theory ({\NEV}). In
single-reference methods have been found to be unsuitable with MAEs of $0.86$ and $0.42$ eV for {\CCT} and {\CCSDT}, respectively.
In this case, multireference methods are required to obtain accurate results. \cite{Loo19c}
Obviously, a clear limit of our 2018 work\cite{Loo18a} is that we treated only compounds containing 1--3 non-hydrogen atoms, hence introducing a significant chemical bias. Therefore we have decided to go for larger molecules and we consider in the present contribution organic
compounds encompassing 4, 5, and 6 non-hydrogen atoms. For such systems, performing {\CCSDTQ} calculations with large bases remains a dream, and, the convergence of {\SCI} with the number of determinants is slower
as well, so that extrapolating to the {\FCI} limit with a ca.~$0.01$ eV error bar is rarely doable in practice. Consequently, the ``brute-force'' determination of {\FCI}/CBS estimates, as in our earlier work,\cite{Loo18a} is beyond reach.
Anticipating this problem, we have previously demonstrated that one can very accurately estimate such limit by correcting values obtained with a high-level of theory and a double-$\zeta$ basis set by {\CCT} results obtained with a
larger basis, \cite{Loo18a} and we glibally follow such strategy here. In addition, we also performed {\NEV} calculations in an effort to check the consistency of our estimates, especially for ES with intermediate $\%T_1$ values.
Using this protocol, we define a set of more than 200 {\AVTZ} reference transition energies, most being within $\pm 0.03$ eV for the {\FCI} limit. These reference energies are obtained on {\CCT} geometries and further basis set
corrections up to at least quadruple-$\zeta$, are also provided with {\CCT}. Together with the results obtained in our two earlier works, \cite{Loo18a,Loo19c} the present TBE will hopefully contribute to climb a further step
on the ES accuracy staircase.
A clear limit from our 2018 work \cite{Loo18a} was the sizes of the compounds put together in our set.
These were limited to $1$--$3$ non-hydrogen atoms, hence introducing a potential ``chemical'' bias. Therefore, we have decided, in the present contribution, to consider larger molecules with organic
compounds encompassing 4, 5, and 6 non-hydrogen atoms. For such systems, performing {\CCSDTQ} calculations with large one-electron basis sets is elusive. Moreover, the convergence of the {\SCI} energy with respect to the number of determinants is obviously slower for these larger compounds, hence
extrapolating to the {\FCI} limit with an error of $\sim 0.01$ eV is rarely achievable in practice. Consequently, the ``brute-force'' determination of {\FCI}/CBS estimates, as in our earlier work, \cite{Loo18a} is definitely out of reach here.
Anticipating this problem, we have recently investigated bootstrap CBS extrapolation techniques. \cite{Loo18a,Loo19c}
In particular, we have demonstrated that, following an ONIOM-like scheme, \cite{Chu15} one can very accurately estimate such limit by correcting high-level values obtained in a small basis by the difference between {\CCT} results obtained in a larger basis and in the same small basis.\cite{Loo18a}
We globally follow such strategy here. In addition, we also perform {\NEV} calculations in an effort to check the consistency of our estimates. It is especially critical for ES with intermediate $\%T_1$ values.
Using this protocol, we define a set of more than 200 {\AVTZ} reference transition energies, most being within $\pm 0.03$ eV of the {\FCI} limit. These reference energies are obtained on {\CCT}/{\AVTZ} geometries and further basis set
corrections (up to quadruple-$\zeta$ at least) are also provided for {\CCT}. Together with the results obtained in our two earlier works, \cite{Loo18a,Loo19c} the present TBE will hopefully contribute to climb a rung higher on the ES accuracy ladder.
%
% II. Computational Details
@ -304,7 +305,7 @@ their CCSDT counterparts, although all CC estimates of Table \ref{Table-1} come,
{\AVTZ} basis set. All these facts provide strong evidences that the CC estimates can be fully trusted for these three linear systems. The basis set effects are quite significant for the valence excited-states of cyanoacetylene with successive drops of the transition
energies by approximately $0.10$ eV, when going from {\Pop} to {\AVDZ} and from {\AVDZ} to {\AVTZ}. The lowest triplet state appears less basis set sensitive, though. As expected,
extending further the basis set size (to quadruple and quintuple-$\zeta$) leaves the results pretty much unchanged. The same observation holds when adding a second set of diffuse functions, or when correlating the core electrons (see the SI). Obviously,
both cyanogen and diacetylene yield very similar trends, with limited methodological effects and quite large basis set effects, except for the $^1\Sigma_g^+ \ra ^3\Sigma_u^+$ transitions. We note that all CC3 and CCSDT values are, at worst,
both cyanogen and diacetylene yield very similar trends, with limited methodological effects and quite large basis set effects, except for the $^1\Sigma_g^+ \ra {} ^3\Sigma_u^+$ transitions. We note that all CC3 and CCSDT values are, at worst,
within $\pm 0.02$ eV of the {\FCI} window, \ie, all methods presented in Table \ref{Table-1} provide very consistent estimates. For all the states reported in this Table, the average absolute deviation between {\NEV}/{\AVTZ} and {\CCT}/{\AVTZ}
({\CCSDT}/{\AVTZ}) is as small as $0.02$ ($0.03$) eV, the lowest absorption and emission energies of cyanogen being the only two cases showing significant deviations. As a final note, all our vertical absorption (emission) energies are significantly bigger
(smaller) than the experimentally measured 0-0 energies, as it should. We refer the interested reader to previous works, \cite{Fis03,Loo19a} for comparisons between theoretical ({\CASPT} and {\CCT}) and experimental 0-0 energies for these three compounds.
@ -485,31 +486,31 @@ consistently with the typical error sign of these two models. For the two lowest
can be seen in Table S3, the {\AVTZ} basis set delivers excitation energies very close to the CBS limit: the largest variation \titou{when going to {\AVQZ}} ($+0.04$ eV) is obtained for the second $^1A'$ Rydberg ES. As experimental data
are limited to measured UV spectra, \cite{Wal45,Bec70} one has to be cautious in establishing TBE for acrolein (\emph{vide infra}).
The nature and relative energies of the lowest bright $B_u$ and dark $A_g$ ES of butadiene have bamboozled theoretical chemists for many years. It is beyond our scope to provide an exhaustive
list of previous calculations and experimental estimates for these two hallmark ES, and we refer the readers to Refs.~\citenum{Wat12} and \citenum{Shu17} for overviews and references. For the $B_u$ transition
the best previous TBE we are aware of is the $6.21$ eV value obtained by Watson and Chan using a computational strategy similar to ours. \cite{Wat12} Our {\CCSDT}/{\AVTZ} value of $6.24$ eV is obviously compatible
with this reference value, and our TBE value is actually $6.21$ eV as well (\emph{vide infra}). For the $A_g$ state, we believe that our previous basis-corrected {\FCI} estimate of $6.50$ eV \cite{Loo19c} remains
the most accurate available to date. These two values are slightly smaller than the heath-bath CI data obtained by Chien \emph{et al.} with a double-$\zeta$ basis and a slightly different geometry: $6.45$ and $6.58$ eV for $B_u$ and $A_g$,
respectively. \cite{Chi18} One can of course find many other estimates, \eg, at the SAC-CI, \cite{Sah06} {\CCT}, \cite{Sil10c,Sch17} {\CASPT}, \cite{Sil10c} and {\NEV} levels, \cite{Sok17} for these two ES.
More globally, in butadiene, we find an excellent coherence between the {\CCT}, {\CCSDT}, and {\CCSDTQ} estimates, that all fall in a $\pm 0.02$ eV window. Unsurprisingly, this does not apply for the
already mentioned $^1A_g$ ES that is $0.2$ and $0.1$ eV too high with the two former CC methods, consistent with the large electronic reorganization taking place in that state. For all the other butadiene ES listed in
Table \ref{Table-3}, both {\CCT} and {\CCSDT} can be trusted. We also note that the {\NEV} estimates are within $0.1$--$0.2$ eV of the CC values, but for the lowest $B_u$ ES, which is very dependent on the selected
active space (see the SI). Finally, as can be seen in Table S3, {\AVTZ} is sufficient for most ES, but a significant basis set effect exists for the Rydberg $^1B_u (\pi \ra 3p)$ ES with an energy decrease as large as $-0.12$ eV
when going from {\AVTZ} to {\AVQZ}. For the records, we note that the available electron impact data \cite{Mos73,Fli78,Doe81} provide the very same ES ordering value as our calculations.
The nature and relative energies of the lowest bright $B_u$ and dark $A_g$ ES of butadiene have bamboozled theoretical chemists for many years. It is beyond the scope of the present study to provide an exhaustive
list of previous calculations and experimental measurements for these two hallmark ES, and we refer the readers to Refs.~\citenum{Wat12} and \citenum{Shu17} for a general and broader overview and the corresponding references. For the $B_u$ transition,
we believe that the most solid TBE is the $6.21$ eV value obtained by Watson and Chan using a computational strategy similar to ours. \cite{Wat12} Our {\CCSDT}/{\AVTZ} value of $6.24$ eV is obviously compatible
with their reference value, and our TBE value is actually $6.21$ eV as well (\emph{vide infra}). For the $A_g$ state, we believe that our previous basis set corrected {\FCI} estimate of $6.50$ eV \cite{Loo19c} remains
the most accurate available to date. These two values are slightly smaller than the semi-stochastic heath-bath CI data obtained by Chien \emph{et al.} with a double-$\zeta$ basis and a slightly different geometry: $6.45$ and $6.58$ eV for $B_u$ and $A_g$,
respectively. \cite{Chi18} For these two thoroughly studied ES, one can, of course, find many other estimates, \eg, at the SAC-CI, \cite{Sah06} {\CCT}, \cite{Sil10c,Sch17} {\CASPT}, \cite{Sil10c} and {\NEV} \cite{Sok17} levels.
Globally, for butadiene, we find an excellent coherence between the {\CCT}, {\CCSDT}, and {\CCSDTQ} estimates, that all fall in a $\pm 0.02$ eV window. Unsurprisingly, this does not apply to the
already mentioned $^1A_g$ ES that is $0.2$ and $0.1$ eV too high with the two former CC methods, \titou{consistent with the large electronic reorganization taking place in that state.} For all the other butadiene ES listed in
Table \ref{Table-3}, both {\CCT} and {\CCSDT} can be trusted. We also note that the {\NEV} estimates are within $0.1$--$0.2$ eV of the CC values, except for the lowest $B_u$ ES for which the associated excitation energy is highly dependent on the selected
active space (see the SI). Finally, as can be seen in Table S3, {\AVTZ} produces near-CBS excitation energies for most ES.
However, a significant basis set effect exists for the Rydberg $^1B_u (\pi \ra 3p)$ ES with an energy lowering as large as $-0.12$ eV
when going from {\AVTZ} to {\AVQZ}. For the records, we note that the available electron impact data \cite{Mos73,Fli78,Doe81} provide the very same ES ordering as our calculations.
Globally, the conclusions obtained for acrolein and butadiene pertain for glyoxal, \ie, highly consistent CC estimates, reasonable agreement between {\NEV} and {\CCT} estimates, and limited basis set effects beyond {\AVTZ}
but for the considered Rydberg state (see Tables \ref{Table-3} and S3). This Rydberg $^1B_u (n \ra 3p)$ state also hows a comparatively large deviation between {\CCT} and {\CCSDTQ}, that is $0.04$ eV. More interestingly,
glyoxal presents a low-lying ``true'' double ES, $^1A_g (n,n \ra \pis,\pis)$, a transition that is totally unseen by approaches that do not explicitly include double excitations during the calculation of transition energies, \eg, TD-DFT, {\CCSD},
or {\AD}. Compared to the {\FCI} values, the {\CCT} and {\CCSDT} estimates for this transition are too large by ca.~$1.0$ and $0.5$ eV, respectively, whereas both the {\CCSDTQ} and {\NEV} approaches are much closer to the spot, as already
Globally, the conclusions obtained for acrolein and butadiene pertain for glyoxal, \ie, highly consistent CC estimates, reasonable agreement between {\NEV} and {\CCT}, and limited basis set effects beyond {\AVTZ}, except for the $^1B_u (n \ra 3p)$ Rydberg state (see Tables \ref{Table-3} and S3). This Rydberg state also indicates a unexpectedly large deviation of $0.04$ eV between {\CCT} and {\CCSDTQ}. More interestingly,
glyoxal presents a genuine low-lying double ES of $^1A_g$ symmetry. The corresponding $(n,n \ra \pis,\pis)$ transition is totally unseen by approaches that cannot model double excitations, \eg, TD-DFT, {\CCSD},
or {\AD}. Compared to the {\FCI} values, the {\CCT} and {\CCSDT} estimates associated with this transition are too large by $\sim 1.0$ and $\sim 0.5$ eV, respectively, whereas both the {\CCSDTQ} and {\NEV} approaches are much closer, as already
mentioned in our previous work. \cite{Loo19c} For the other transitions, the present {\CCT} estimates are logically coherent with the values of Ref.~\citenum{Sch17} obtained with the same approach on a different
geometry, and remain slightly lower than the SAC-CI estimates of Ref.~\citenum{Sah06}. Once more, the experimental data \cite{Ver80,Rob85b} make an unhelpful guide in view of the targeted accuracy.
geometry, and remain slightly lower than the SAC-CI estimates of Ref.~\citenum{Sah06}. Once more, the experimental data \cite{Ver80,Rob85b} are unhelpful in view of the targeted accuracy.
\subsubsection{Acetone, cyanoformaldehyde, isobutene, propynal, thioacetone, and thiopropynal}
Let us now turn towards six other four-atom compounds. There are several earlier estimates of vertical transition energies for both acetone \cite{Gwa95,Mer96b,Roo96,Wib98,Toz99b,Wib02,Sch08,Sil10c,Car10,Pas12,Ise12,Gua13,Sch17}
and isobutene. \cite{Wib02,Car10,Ise12} To the best of our knowledge, the previous computational efforts were mainly focussed on 0-0 energies of the lowest-lying states for the four other compounds. \cite{Koh03,Hat05c,Sen11b,Loo18b,Loo19a}
There are also a few experimental values available for all six derivatives. \cite{Bir73,Jud83,Bra74,Sta75,Joh79,Jud83,Jud84c,Rob85,Pal87,Kar91b,Xin93} Our main data are reported in Tables \ref{Table-4}
and S4.
Let us now turn towards six other four-atom compounds. There are several earlier studies reporting estimates of the vertical transition energies for both acetone \cite{Gwa95,Mer96b,Roo96,Wib98,Toz99b,Wib02,Sch08,Sil10c,Car10,Pas12,Ise12,Gua13,Sch17}
and isobutene. \cite{Wib02,Car10,Ise12} To the best of our knowledge, for the four other compounds, the previous computational efforts were mainly focussed on the 0-0 energies of the lowest-lying states. \cite{Koh03,Hat05c,Sen11b,Loo18b,Loo19a}
There are also very few experimental data available for these six derivatives. \cite{Bir73,Jud83,Bra74,Sta75,Joh79,Jud83,Jud84c,Rob85,Pal87,Kar91b,Xin93}
Our main results are reported in Tables \ref{Table-4} and S4.
\begin{table}[htp]
\caption{\small Vertical transition energies (in eV) of acetone, cyanonformaldehyde, isobutene, propynal, thioacetone, and thiopropynal.}
@ -579,20 +580,21 @@ $^3A'' (n \ra \pis)$ &1.84&1.82& & &1.83&1.82&1.81 & &1.81 &1.64\
\vspace{-0.5 cm}
\begin{flushleft}
\begin{footnotesize}
$^a${{\CASPT} of Ref.~\citenum{Mer96b};}
$^b${EOM-CCSD of Ref.~\citenum{Gwa95};}
$^a${{\CASPT} results from Ref.~\citenum{Mer96b};}
$^b${EOM-CCSD results from Ref.~\citenum{Gwa95};}
$^c${Two lowest singlet states: various experiments summarized in Ref.~\citenum{Rob85}; three next singlet states: REMPI experiments from Ref.~\citenum{Xin93}; lowest triplet: trapped electron measurements from Ref.~\citenum{Sta75};}
$^d${0-0 energy reported in Ref.~\citenum{Kar91b};}
$^e${EOM-CCSD from Ref.~\citenum{Car10};}
$^e${EOM-CCSD results from Ref.~\citenum{Car10};}
$^f${Energy loss experiment from Ref.~\citenum{Joh79};}
$^g${VUV experiment from Ref.~\citenum{Pal87} (we report the lowest of the $\pi \ra 3p$ state for the $^1A_1$ state)};
$^h${0-0 energies of Refs.~\citenum{Bra74} (singlet) and \citenum{Bir73} (triplet);}
$^h${0-0 energies from Refs.~\citenum{Bra74} (singlet) and \citenum{Bir73} (triplet);}
$^i${0-0 energies from Ref.~\citenum{Jud83};}
$^i${0-0 energies from Ref.~\citenum{Jud84c}.}
\end{footnotesize}
\end{flushleft}
\end{table}
\titou{HERE}
For acetone, one should clearly distinguish the valence ES, for which both methodological and basis set effects are small, and the Rydberg transitions that, not only are very
sensitive to the basis set, but are upshifted by ca.~$0.04$ eV with {\CCSDTQ} as compared to {\CCT} and {\CCSDT}. For this compound, the 1996 {\CASPT} transition energies of Merch\'an and coworkers listed on the
r.h.s. of Table \ref{Table-4} are quite clearly too small, especially for the three valence ES. \cite{Mer96b} As expected, this error can be partially ascribed to the details of the calculations, as the Urban group obtained {\CASPT}

13
Manuscript/biblio-new.bib Executable file → Normal file
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@ -1,7 +1,7 @@
%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/
%% Created for Pierre-Francois Loos at 2019-11-07 23:20:54 +0100
%% Created for Pierre-Francois Loos at 2019-11-10 21:22:21 +0100
%% Saved with string encoding Unicode (UTF-8)
@ -82,6 +82,17 @@
@string{theo = {J. Mol. Struct. (THEOCHEM)}}
@article{Chu15,
Author = {Lung Wa Chung and W. M. C. Sameera and Romain Ramozzi and Alister J. Page and Miho Hatanaka and Galina P. Petrova and Travis V. Harris and Xin Li and Zhuofeng Ke and Fengyi Liu and Hai-Bei Li and Lina Ding and Keiji Morokuma},
Date-Added = {2019-11-10 21:20:50 +0100},
Date-Modified = {2019-11-10 21:22:18 +0100},
Doi = {10.1021/cr5004419},
Journal = {Chem. Rev.},
Pages = {5678--5796},
Title = {The ONIOM Method and Its Applications},
Volume = {115},
Year = {2015}}
@article{Ang02,
Author = {Angeli, Celestino and Cimiraglia, Renzo and Malrieu, Jean-Paul},
Date-Added = {2019-11-07 23:20:49 +0100},