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Pierre-Francois Loos 2020-10-27 09:59:26 +01:00
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Manuscript/QUEST_WIREs.tex
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@ -315,20 +315,20 @@ Only the last $M>2$ computed energy differences are considered. $M$ is chosen su
If all the values of $P(\mathcal{G})$ are below $0.8$, $M$ is chosen such that $P(\mathcal{G})$ is maximal.
A Python code associated with this procedure is provided in the {\SupInf}.
The singlet and triplet excitation energies obtained at the FCI/6-31+G(d) level are reported in Table \ref{tab:cycles} alongside the computed error bars estimated with the method presented above based on Gaussian random variables.
The singlet and triplet FCI/6-31+G(d) excitation energies and their corresponding error bars estimated with the method presented above based on Gaussian random variables are reported in Table \ref{tab:cycles}.
For the sake of comparison, we also report the CC3 and CCSDT vertical energies from Ref.~\cite{Loos_2020b} computed in the same basis.
The estimated values of the excitation energies obtained via a three-point linear extrapolation considering the three largest CIPSI wave functions are also gathered in Table \ref{tab:cycles}.
In this case, the error bar is estimated via the extrapolation distance, \ie, the difference in excitation energies obtained with the three-point linear extrapolation and the largest CIPSI wave function.
This strategy has been considered in some of our previous works \cite{Loos_2020b,Loos_2020c,Loos_2020e}.
The deviation from the CCSDT excitation energies for the same set of excitations are depicted in Fig.~\ref{fig:errors}, where the red dots correspond to the excitation energies and error bars estimated via the present method, and the blue dots correspond to the excitation energies obtained via a three-point linear fit using the three largest CIPSI wave functions, and error bars estimated via the extrapolation distance.
These results are a good balance between well-behaved and ill-behaved cases.
For example, cyclopentadiene and furan correspond to well-behaved cases where the two flavor of excitation energy estimates are nearly identical and the error bars associated with these two methods overlap nicely.
The deviation from the CCSDT excitation energies for the same set of excitations are depicted in Fig.~\ref{fig:errors}, where the red dots correspond to the excitation energies and error bars estimated via the present method, and the blue dots correspond to the excitation energies obtained via a three-point linear fit and error bars estimated via the extrapolation distance.
These results contains a good balance between well-behaved and ill-behaved cases.
For example, cyclopentadiene and furan correspond to well-behaved scenarios where the two flavor of excitation energy estimates are nearly identical and the error bars associated with these two methods nicely overlap.
In these cases, one can observe that our method based on Gaussian random variables provides almost systematically smaller error bars.
Even in less idealistic situations (like in imidazole, pyrrole, and thiophene), the results are very satisfactory.
The six-membered rings correspond to much more challenging cases for SCI methods, and even for these systems the newly-developed method provides realistic error bars.
The present scheme has also been tested on much smaller systems when one can easily tightly converged the CIPSI calculations.
In these cases, the agreement is nearly perfect in every cases.
Some of these results can be found in the {\SupInf}.
Even in less idealistic situations (like in imidazole, pyrrole, and thiophene), the results are very satisfactory and stable.
The six-membered rings represent much more challenging cases for SCI methods, and even for these systems the newly-developed method provides realistic error bars, and allows to easily detect problematic events (like pyridine for instance).
The present scheme has also been tested on smaller systems when one can tightly converged the CIPSI calculations.
In such cases, the agreement is nearly perfect in every scenario that we have encountered.
A selection of these results can be found in the {\SupInf}.
%%% TABLE I %%%
\begin{table}
@ -615,7 +615,7 @@ All quantities are given in eV. ``Count'' refers to the number of transitions co
\begin{tabular}{llccccccccccccccc}
\headrow
& & \thead{CIS(D)} & \thead{CC2} & \thead{CCSD(2)} & \thead{STEOM-CCSD} & \thead{CCSD} & \thead{CCSDR(3)} & \thead{CCCSDT-3} & \thead{CC3}
& \thead{SOS-ADC(2)[TM]} & \thead{SOS-CC2[TM]} & \thead{SCS-CC2[TM]} & \thead{SOS-ADC(2) [QC]} & \thead{ADC(2)} & \thead{ADC(3)} & \thead{ADC(2.5)} \\
& \thead{SOS-ADC(2)$^a$} & \thead{SOS-CC2$^a$} & \thead{SCS-CC2$^a$} & \thead{SOS-ADC(2)$^b$} & \thead{ADC(2)} & \thead{ADC(3)} & \thead{ADC(2.5)} \\
Count & & 429 & 431 & 427 & 360 & 431 & 259 & 251 & 431 & 430 & 430 & 430 & 430 & 426 & 423 & 423 \\
Max(+) & & 1.06 & 0.63 & 0.80 & 0.59 & 0.80 & 0.43 & 0.26 & 0.19 & 0.87 & 0.84 & 0.76 & 0.73 & 0.64 & 0.60 & 0.24 \\
Max($-$) & & -0.69 & -0.71 & -0.38 & -0.56 & -0.25 & -0.07 & -0.07 & -0.09 & -0.29 & -0.24 & -0.92 & -0.46 & -0.76 & -0.79 & -0.34 \\
@ -646,6 +646,10 @@ MAE & & 0.22 & 0.16 & 0.22 & 0.11 & 0.12 & 0.05 & 0.04 & 0.02 & 0.20 & 0.22
& 7--10 non-H & 0.24 & 0.11 & 0.42 & 0.12 & 0.23 & 0.10 & 0.08 & 0.02 & 0.27 & 0.29 & 0.19 & 0.12 & 0.14 & 0.16 & 0.07 \\
\hline
\end{tabular}
\begin{tablenotes}
\item $^a$ Excitation energies compute with TURBOMOLE.
\item $^b$ Excitation energies compute with Q-CHEM.
\end{tablenotes}
\end{threeparttable}
\end{sidewaystable}
@ -667,7 +671,6 @@ Thanks to this website, one can easily test and compare the accuracy of a given
Because computing 450 excitation energies can be a costly exercise, we are planning on developing a ``diet set'' following the philosophy of the ``diet GMTKN55'' set \cite{Goerigk_2017} proposed recently by Gould \cite{Gould_2018b}.
Although our present goal is to produce chemically accurate vertical excitation energies, we are currently devoting great efforts to obtain of highly-accurate excited-state properties as such dipoles and oscillator strengths for molecules of small and medium sizes \cite{Chrayteh_2020}.
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\section*{acknowledgements}
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