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Manuscript/FCI2.tex
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@ -139,7 +139,7 @@ available. \cite{Lau13}
While several of these benchmarks rely on experimental data as reference (typically band shapes \cite{Die04,Die04b,Avi13,Cha13,Lat15b,Mun15,Vaz15,San16b} or 0-0 energies While several of these benchmarks rely on experimental data as reference (typically band shapes \cite{Die04,Die04b,Avi13,Cha13,Lat15b,Mun15,Vaz15,San16b} or 0-0 energies
\cite{Die04b,Goe10a,Jac12d,Chi13b,Win13,Fan14b,Jac14a,Jac15b,Loo19b}), references from theoretical best estimates (TBE) based on state-of-the-art computational methods \cite{Sch08,Sau09,Sil10b,Sil10c,Sch17,Loo18a} \cite{Die04b,Goe10a,Jac12d,Chi13b,Win13,Fan14b,Jac14a,Jac15b,Loo19b}), references from theoretical best estimates (TBE) based on state-of-the-art computational methods \cite{Sch08,Sau09,Sil10b,Sil10c,Sch17,Loo18a}
are advantageous as they allow comparisons on a perfectly equal footing (same geometry, vertical transitions, no environmental effects, etc). In such a case, the challenge is in fact to obtain accurate TBE, as these top-notch theoretical models are advantageous as they allow comparisons on a perfectly equal footing (same geometry, vertical transitions, no environmental effects, etc). In such a case, the challenge is in fact to obtain accurate TBE, as these top-notch theoretical models
generally come with a dreadful scaling with system size and, in addition, typically require large atomic basis sets to deliver transition energies close to the complete basis set (CBS) limit. generally come with a dreadful scaling with system size and, in addition, typically require large atomic basis sets to deliver transition energies close to the complete basis set (CBS) limit. \cite{Gin19}
More than 20 years ago, Serrano-Andr\`es, Roos, and collaborators compiled an impressive series of reference transition energies for several typical conjugated organic molecules (butadiene, furan, pyrrole, tetrazine, \ldots). More than 20 years ago, Serrano-Andr\`es, Roos, and collaborators compiled an impressive series of reference transition energies for several typical conjugated organic molecules (butadiene, furan, pyrrole, tetrazine, \ldots).
\cite{Ful92,Ser93,Ser93b,Ser93c,Lor95b,Mer96,Mer96b,Roo96,Ser96b} To this end, they relied on experimental GS geometries and the complete-active-space second-order perturbation theory ({\CASPT}) approach with the largest active spaces and basis sets \cite{Ful92,Ser93,Ser93b,Ser93c,Lor95b,Mer96,Mer96b,Roo96,Ser96b} To this end, they relied on experimental GS geometries and the complete-active-space second-order perturbation theory ({\CASPT}) approach with the largest active spaces and basis sets
@ -246,14 +246,14 @@ Default program settings were applied. We note that for {\STEOM} we only report
\section{Main results} \section{Main results}
\label{sec-res} \label{sec-res}
In the following, we present the results obtained for molecules containing four, five, and six (non-hydrogen) atoms. In all cases, we test several atomic basis sets and push the CC excitation order as high as technically possible. In the following, we present results obtained for molecules containing four, five, and six (non-hydrogen) atoms. In all cases, we test several atomic basis sets and push the CC excitation order as high as technically possible.
Given that the {\SCI} results converges rather slowly for these larger systems, we provide an estimated error bar for these extrapolated {\FCI} values (\emph{vide supra}). In most cases, these extrapolated FCI reference data are used as a safety net to demonstrate the Given that the {\SCI} energy converges rather slowly for these larger systems, we provide an estimated error bar for these extrapolated {\FCI} values (\emph{vide supra}). In most cases, these extrapolated FCI reference data are used as a ``safety net'' to demonstrate the overall
consistency of the approaches rather than as definitive TBE (see next Section). We also show the results of {\NEV}/{\AVTZ} calculations for all relevant states to have a further consistency check. We underline that, except consistency of the various approaches rather than as definitive reference values (see next Section). As a further consistency check, we also report {\NEV}/{\AVTZ} excitation energies for all states. We underline that, except
when specifically discussed, all ES present a dominant single-excitation character (see also next Section), so that we do not expect serious CC breakdowns. This is especially true for the triplet ES that are known to show when specifically discussed, all ES present a dominant single-excitation character (see also next Section), so that we do not expect serious CC breakdowns. This is especially true for triplet ES that are known to be characterized by
very large $\Td$ for the vast majority of states, \cite{Sch08} and we consequently put our maximal computational effort on determining accurate transition energies for singlet states. To assign the different ES, we use literature data, as well as very large $\Td$ values in the vast majority of the cases. \cite{Sch08} Consequently, we concentrate most of our computational effort on the obtention of accurate transition energies for singlet states. To assign the different ES, we use literature data, as well as
usual criteria, \ie, relative energies, symmetries and compositions of the underlying MOs, as well as oscillator strengths. This allows clear-cut assignment for the vast majority of the cases. There are however some the usual criteria, \ie, relative energies, spatial and spin symmetries, compositions from the underlying molecular orbitals, and oscillator strengths. This allows clear-cut assignments for the vast majority of the cases. There are however some
state/method combination for which strong mixing between ES of the same symmetry makes unambiguous assignments beyond reach, which is a typical problem in such works. Such cases are however not statistically state/method combinations for which strong mixing between ES of the same symmetry makes unambiguous assignments almost impossible.
relevant and are therefore unlikely to change any of our main conclusions. \titou{Such cases are therefore discarded from our benchmark set.}
\subsection{Four-atom molecules} \subsection{Four-atom molecules}
@ -962,19 +962,19 @@ This feature is likely due to the use of distinct geometries in the two studies.
\subsubsection{Pyridazine, pyridine, pyrimidine, and triazine} \subsubsection{Pyridazine, pyridine, pyrimidine, and triazine}
\titou{HERE} Those four azabenzenes with $C_{2v}$ and $D_{3h}$ spatial symmetry are also popular molecules in terms of ES calculations. \cite{Pal91,Ful92,Wal92,Lor95,Del97b,Noo97,Noo99,Fis00,Cai00b,Wan01b,Sch08,Sil10b,Sil10c,Car10,Lea12,Kan14,Sch17,Dut18}
Those four azabenzenes, of $C_{2v}$ and $D_{3h}$ symmetry, are also popular molecules for ES calculations. \cite{Pal91,Ful92,Wal92,Lor95,Del97b,Noo97,Noo99,Fis00,Cai00b,Wan01b,Sch08,Sil10b,Sil10c,Car10,Lea12,Kan14,Sch17,Dut18}
Our results for pyridazine and pyridine are gathered in Tables \ref{Table-9} and S9. For the former compound, the available wavefunction results \cite{Pal91,Ful92,Del97b,Noo99,Fis00,Sch08,Sil10b,Sil10c,Kan14,Sch17,Dut18} Our results for pyridazine and pyridine are gathered in Tables \ref{Table-9} and S9. For the former compound, the available wavefunction results \cite{Pal91,Ful92,Del97b,Noo99,Fis00,Sch08,Sil10b,Sil10c,Kan14,Sch17,Dut18}
only considered singlet transitions, at the exception of a rather old MRCI, \cite{Pal91} and {\CASPT} investigations. \cite{Fis00} Again, the $\Td$ values are larger than $85\%$ ($95\%$) for the singlet (triplet) transitions, only considered singlet transitions, at the exception of a rather old MRCI, \cite{Pal91} and {\CASPT} investigations. \cite{Fis00} Again, the $\Td$ values are larger than $85\%$ ($95\%$) for the singlet (triplet) transitions,
and the only state for which there is a variation larger than $0.03$ eV between the {\CCT}/{\AVDZ} and {\CCSDT}/{\AVDZ} energies, but for the $^3B_2 (\pi \ra \pis)$ transition. \hl{BASIS SETS} For the valence singlet and the only state for which there is a variation larger than $0.03$ eV between the {\CCT}/{\AVDZ} and {\CCSDT}/{\AVDZ} energies is the $^3B_2 (\pi \ra \pis)$ transition. \hl{BASIS SETS}
ES, we find again a quite good agreement with previous {\STEOM} \cite{Noo99} and CC \cite{Del97b,Sil10c} estimates, but are again significantly higher than {\CASPT} estimates. \cite{Ful92,Sil10c} For the triplets, the For the singlet valence ES, we find again a rather good agreement with previous {\STEOM} \cite{Noo99} and CC \cite{Del97b,Sil10c} estimates, which are again significantly higher than the {\CASPT} estimates reported in Refs.~\citenum{Ful92,Sil10c} For the triplets, the
present data represents the best published to date. Interestingly, beyond the usually cited experiments, \cite{Inn88,Pal91} there is a very recent experimental EEL analysis for pyridazine, \cite{Lin19} that localized present data represents the best published to date. Interestingly, beyond the usually cited experiments, \cite{Inn88,Pal91} there is a very recent experimental EEL analysis for pyridazine, \cite{Lin19} that locates
almost all ES. The transition energies reported in this very recent effort are systematically smaller than our CC estimates, by ca.~$-0.20$ eV, but remarkably show exactly the exact same ranking. almost all ES. The transition energies reported in this very recent work are systematically smaller than our CC estimates by approximately $-0.20$ eV.
Nonetheless, this study provides exactly the same ES ranking as our theoretical protocol.
For pyridine, that has been more thoroughly investigated with wavefunction approaches, \cite{Ful92,Lor95,Del97b,Noo97,Noo99,Cai00b,Wan01b,Sch08,Sil10b,Sil10c,Car10,Kan14,Sch17,Dut18} and for which we could found two Pyridine has been more scrutinized with various wavefunction approaches. \cite{Ful92,Lor95,Del97b,Noo97,Noo99,Cai00b,Wan01b,Sch08,Sil10b,Sil10c,Car10,Kan14,Sch17,Dut18} Beside, we have found two detailed EEL experiments. \cite{Wal90,Lin16}
detailed EEL experiments, \cite{Wal90,Lin16} the general trends described for pyridazine pertain: i) large $\Td$ and good CC consistency for all transitions listed in Table \ref{Table-9}; ii) \hl{basis}; iii) good agreement with previous For pyridine, the general trends described above for pyridazine pertain: i) large $\Td$ values and consistency between our various CC estimates for all transitions listed in Table \ref{Table-9}; ii) \hl{basis}; iii) qualitative agreement with past
CC estimates; and iv) same ranking of the ES as in the most recent measurements. \cite{Lin16} Beyond those aspects, it is worth to underline that the second $^1B_2 (\pi \ra \pis)$ ES is strongly mixed with a nearby CC results; and iv) same ES ranking as in the most recent measurements. \cite{Lin16} Beyond these aspects, it is worth mentioning that the second $^1B_2 (\pi \ra \pis)$ ES is strongly mixed with a nearby
Rydberg transition that is separated by only $0.03$ eV at the {\CCT}/{AVTZ} level, making the analysis particularly challenging for that specific transition. \hl{Keep or not A1 transitiion} Rydberg transition that is separated by only $0.03$ eV at the {\CCT}/{AVTZ} level. This obviously makes the analysis particularly challenging for that specific transition. \hl{Keep or not A1 transitiion}
\begin{table}[htp] \begin{table}[htp]
\caption{\small Vertical transition energies (in eV) of pyridazine and pyridine.} \caption{\small Vertical transition energies (in eV) of pyridazine and pyridine.}
@ -1037,13 +1037,12 @@ $^j${Significant state mixing with a close-lying Rydberg transition, rendering u
\end{flushleft} \end{flushleft}
\end{table} \end{table}
The results obtained for both pyrimidine and triazine are listed in Tables \ref{Table-10} and S10. For the former derivative previous theoretical \cite{Ful92,Del97b,Ser97b,Noo99,Ohr01,Fis03b,Li07b,Sch08,Sil10b,Sil10c,Car10,Kan14,Sch17,Dut18} The results obtained for both pyrimidine and triazine are listed in Tables \ref{Table-10} and S10. For the former derivative, previous theoretical \cite{Ful92,Del97b,Ser97b,Noo99,Ohr01,Fis03b,Li07b,Sch08,Sil10b,Sil10c,Car10,Kan14,Sch17,Dut18}
and experimental \cite{Bol84,Pal90,Lin15} studies are rather extensive, as it can be viewed as the smallest model of DNA bases. For triazine, which does not have an abelian point group, one finds less theoretical studies, and experimental \cite{Bol84,Pal90,Lin15} studies are rather extensive, as it can be viewed as the smallest model of DNA bases. For triazine, which does not have an abelian point group, theoretical studies are scarcer,
\cite{Ful92,Wal92,Pal95,Del97b,Noo99,Oli05,Sch08,Sil10b,Sil10c,Kan14,Sch17,Dut18}, especially for the triplet transitions. \cite{Wal92,Pal95,Oli05} The experimental data are also less numerous. \cite{Bol84,Wal92} \cite{Ful92,Wal92,Pal95,Del97b,Noo99,Oli05,Sch08,Sil10b,Sil10c,Kan14,Sch17,Dut18}, especially for the triplet transitions. \cite{Wal92,Pal95,Oli05} Experimental data are also limited. \cite{Bol84,Wal92}
As in pyridazine and pyridine, all the ES listed in Table \ref{Table-10} show $\Td$ larger than $85\%$ for singlet and $95\%$ for triplet, so that {\CCT} and {\CCSDT} are highly coherent, but possibly in one case, the As in pyridazine and pyridine, all the ES listed in Table \ref{Table-10} show $\Td$ values larger than $85\%$ for singlets and $95\%$ for triplets, so that {\CCT} and {\CCSDT} are highly coherent, except maybe for the $^3A_1 (\pi \ra \pis)$ transitions in pyrimidine.
$^3A_1 (\pi \ra \pis)$ transitions in pyrimidine. The basis set effects are also small, with no variations larger than $0.10$ ($0.03$) eV between double-$\zeta$ and triple-$\zeta$ (triple-$\zeta$ and quadruple-$\zeta$) and only The basis set effects are also small, with no variation larger than $0.10$ ($0.03$) eV between double-$\zeta$ and triple-$\zeta$ (triple-$\zeta$ and quadruple-$\zeta$) and only
slightly larger variations for the two Rydberg transitions. For both compounds, the current values are almost systematically larger than most previously published data. For the triplets of triazine, the three lowest ES estimated slightly larger variations for the two Rydberg transitions. For both compounds, the current values are almost systematically larger than previously published data. For the triplets of triazine, the three lowest ES previously estimated by {\CASPT} are too low by roughly half an eV.
by {\CASPT} previously are too low by ca.~$-0.5$ eV.
\begin{table}[htp] \begin{table}[htp]
\caption{\small Vertical transition energies (in eV) of pyrimidine and triazine.} \caption{\small Vertical transition energies (in eV) of pyrimidine and triazine.}

23
Manuscript/biblio-new.bib
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@ -1,7 +1,7 @@
%% This BibTeX bibliography file was created using BibDesk. %% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/ %% http://bibdesk.sourceforge.net/
%% Created for Pierre-Francois Loos at 2019-11-10 21:22:21 +0100 %% Created for Pierre-Francois Loos at 2019-11-11 20:28:33 +0100
%% Saved with string encoding Unicode (UTF-8) %% Saved with string encoding Unicode (UTF-8)
@ -82,6 +82,16 @@
@string{theo = {J. Mol. Struct. (THEOCHEM)}} @string{theo = {J. Mol. Struct. (THEOCHEM)}}
@article{Gin19,
Author = {E. Giner and A. Scemama and J. Toulouse and P. F. Loos},
Date-Added = {2019-11-11 20:26:47 +0100},
Date-Modified = {2019-11-11 20:28:33 +0100},
Journal = {J. Chem. Phys.},
Pages = {144118},
Title = {Chemically Accurate Excitation Energies With Small Basis Sets},
Volume = {151},
Year = {2019}}
@article{Chu15, @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}, 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-Added = {2019-11-10 21:20:50 +0100},
@ -91,7 +101,8 @@
Pages = {5678--5796}, Pages = {5678--5796},
Title = {The ONIOM Method and Its Applications}, Title = {The ONIOM Method and Its Applications},
Volume = {115}, Volume = {115},
Year = {2015}} Year = {2015},
Bdsk-Url-1 = {https://doi.org/10.1021/cr5004419}}
@article{Ang02, @article{Ang02,
Author = {Angeli, Celestino and Cimiraglia, Renzo and Malrieu, Jean-Paul}, Author = {Angeli, Celestino and Cimiraglia, Renzo and Malrieu, Jean-Paul},
@ -5122,10 +5133,6 @@
Year = {2018}, Year = {2018},
Bdsk-Url-1 = {http://dx.doi.org/10.1039/C8QM00171E}} Bdsk-Url-1 = {http://dx.doi.org/10.1039/C8QM00171E}}
@article{cite-key,
Date-Added = {2018-06-08 10:10:38 +0000},
Date-Modified = {2018-06-08 10:10:38 +0000}}
@article{Che05e, @article{Che05e,
Author = {Chen, Zhongfang and Wannere, Chaitanya S and Corminboeuf, Cl{\'e}mence and Puchta, Ralph and Schleyer, Paul von Ragu{\'e}}, Author = {Chen, Zhongfang and Wannere, Chaitanya S and Corminboeuf, Cl{\'e}mence and Puchta, Ralph and Schleyer, Paul von Ragu{\'e}},
Date-Added = {2018-06-06 08:50:59 +0000}, Date-Added = {2018-06-06 08:50:59 +0000},
@ -5276,10 +5283,6 @@
Year = {2017}, Year = {2017},
Bdsk-Url-1 = {http://dx.doi.org/10.1039/C7CP02600E}} Bdsk-Url-1 = {http://dx.doi.org/10.1039/C7CP02600E}}
@article{cite-key,
Date-Added = {2018-06-04 13:29:00 +0000},
Date-Modified = {2018-06-04 13:29:00 +0000}}
@article{Har97b, @article{Har97b,
Author = {Harper,Warren W. and Waddell,Kevin W. and Clouthier,Dennis J.}, Author = {Harper,Warren W. and Waddell,Kevin W. and Clouthier,Dennis J.},
Date-Added = {2018-06-04 07:56:57 +0000}, Date-Added = {2018-06-04 07:56:57 +0000},