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Pierre-Francois Loos 2020-10-26 21:31:02 +01:00
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Cyclopentadiene "^1 B_2 (\pi \rightarrow \pi^*)" 5.79 5.80 5.80 0.02 5.79 0.02
Cyclopentadiene "^3 B_2 (\pi \rightarrow \pi^*)" 3.33 3.33 3.32 0.04 3.29 0.07
Furan "^1A_2(\pi \rightarrow 3s)" 6.26 6.28 6.31 0.05 6.37 0.01
Furan "^3B_2(\pi \rightarrow \pi^*)" 4.28 4.28 4.26 0.04 4.22 0.07
Imidazole "^1A''(\pi \rightarrow 3s)" 5.77 5.77 5.78 0.05 5.96 0.14
Imidazole "^3A'(\pi \rightarrow \pi^*)" 4.83 4.81 4.82 0.07 4.65 0.22
Pyrrole "^1A_2(\pi \rightarrow 3s)" 5.25 5.25 5.23 0.07 5.31 0.01
Pyrrole "^3B_2(\pi \rightarrow \pi^*)" 4.59 4.58 4.54 0.07 4.37 0.23
Thiophene "^1A_1(\pi \rightarrow \pi^*)" 5.79 5.77 5.75 0.08 5.73 0.09
Thiophene "^3B_2(\pi \rightarrow \pi^*)" 3.95 3.94 3.98 0.01 3.99 0.02
Benzene "^1B_{2u}(\pi \rightarrow \pi^*)" 5.13 5.10 5.06 0.09 5.21 0.07
Benzene "^3B_{1u}(\pi \rightarrow \pi^*)" 4.18 4.16 4.28 0.06 4.17 0.07
Cyclopentadienone "^1A_2(n \rightarrow \pi^*)" 3.03 3.03 3.08 0.02 3.13 0.03
Cyclopentadienone "^3B_2(\pi \rightarrow \pi^*)" 2.30 2.32 2.37 0.05 2.10 0.25
Pyrazine "^1B_{3u}(n \rightarrow \pi^*)" 4.28 4.28 4.26 0.09 4.10 0.25
Pyrazine "^3B_{3u}(n \rightarrow \pi^*)" 3.68 3.68 3.70 0.03 3.70 0.01
Tetrazine "^1B_{3u}(n \rightarrow \pi^*)" 2.53 2.54 2.56 0.05 5.07 0.16
Tetrazine "^3B_{3u}(n \rightarrow \pi^*)" 1.87 1.88 1.91 0.03 4.04 0.49
Pyridazine "^1B_1(n \rightarrow \pi^*)" 3.95 3.95 3.97 0.10 3.60 0.43
Pyridazine "^3B_1(n \rightarrow \pi^*)" 3.27 3.26 3.27 0.15 3.46 0.14
Pyridine "^1B_1(n \rightarrow \pi^*)" 5.12 5.10 5.15 0.12 4.90 0.24
Pyridine "^3A_1(\pi \rightarrow \pi^*)" 4.33 4.31 4.42 0.85 3.68 1.05
Pyrimidine "^1B_1(n \rightarrow \pi^*)" 4.58 4.57 4.64 0.11 2.54 0.05
Pyrimidine "^3B_1(n \rightarrow \pi^*)" 4.20 4.20 4.55 0.37 2.18 0.27
Triazine "^1A_1''(n \rightarrow \pi^*)" 4.85 4.84 4.77 0.13 5.12 0.51
Triazine "^3A_2''(n \rightarrow \pi^*)" 4.40 4.40 4.45 0.39 4.73 0.06

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Manuscript/QUEST_WIREs.tex
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\title{QUESTDB: a database of highly-accurate excitation energies for the electronic structure community}
% List abbreviations here, if any. Please note that it is preferred that abbreviations be defined at the first instance they appear in the text, rather than creating an abbreviations list.
\abbrevs{ABC, a black cat; DEF, doesn't ever fret; GHI, goes home immediately.}
%\abbrevs{ABC, a black cat; DEF, doesn't ever fret; GHI, goes home immediately.}
% Include full author names and degrees, when required by the journal.
% Use the \authfn to add symbols for additional footnotes and present addresses, if any. Usually start with 1 for notes about author contributions; then continuing with 2 etc if any author has a different present address.
@ -224,7 +224,6 @@ Moreover, a renormalized version of the PT2 correction (dubbed rPT2) has been re
We refer the interested reader to Ref.~\cite{Garniron_2019} where one can find all the details regarding the implementation of the CIPSI algorithm.
Note that, all our SCI wave functions are eigenfunctions of the $\Hat{S}^2$ spin operator which is, unlike ground-state calculations, paramount in the case of excited states \cite{Applencourt_2018}.
%------------------------------------------------
\subsubsection{Benchmarked computational methods}
%------------------------------------------------
@ -326,10 +325,11 @@ This strategy has been considered in some of our previous works \cite{Loos_2020b
%%% TABLE I %%%
\begin{table}
\centering
\caption{Singlet and triplet excitation energies obtained at the CC3, CCSDT, and FCI levels of theory with the 6-31+G* basis set for various five- and six-membered rings.}
\caption{Singlet and triplet excitation energies obtained at the CC3, CCSDT, and FCI levels of theory with the 6-31+G* basis set for various five- and six-membered rings.
The error bars reported in parenthesis correspond to one standard deviation.}
\label{tab:cycles}
\begin{threeparttable}
\begin{tabular}{lccrrr}
\begin{tabular}{lccccc}
\headrow
\thead{Molecule} & \thead{Transition} & \thead{CC3} & \thead{CCSDT} & \thead{FCI$^a$} & \thead{FCI$^b$}\\
\mc{6}{c}{Five-membered rings} \\
@ -364,12 +364,21 @@ Triazine & $^1A_1''(n \ra \pis)$ & 4.85 & 4.84 & 4.77(13)& 5.12(51) \\%& 5.1
\hline % Please only put a hline at the end of the table
\end{tabular}
\begin{tablenotes}
\item $^a$ Error bar estimated thanks to the present method (see Sec.~\ref{sec:error}).
\item $^b$ Error bar estimated as the difference in excitation energies obtained with the three-point linear extrapolation and the largest variational wave function.
\item $^a$ Excitation energies and error bars estimated via the present method (see Sec.~\ref{sec:error}).
\item $^b$ Excitation energies obtained via a three-point linear fit using the three largest variational wave functions, and error bars estimated via the extrapolation distance, \ie, the difference in excitation energies obtained with the three-point linear extrapolation and the largest variational wave function.
\end{tablenotes}
\end{threeparttable}
\end{table}
%%% FIGURE 2 %%%
\begin{figure}
\centering
\label{fig:errors}
\includegraphics[width=0.5\linewidth]{errors}
\caption{Deviation from the CCSDT excitation energies of singlet and triplet excitation energies of five- and six-membered rings obtained at the FCI/6-31+G* level of theory. Red dots: excitation energies and error bars estimated via the present method (see Sec.~\ref{sec:error}). Blue dots: excitation energies obtained via a three-point linear fit using the three largest variational wave functions, and error bars estimated via the extrapolation distance, \ie, the difference in excitation energies obtained with the three-point linear extrapolation and the largest variational wave function.
The error bars corresponds to one standard deviation.}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{The QUEST database}
\label{sec:QUEST}
@ -597,34 +606,34 @@ 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)} \\
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 \\
Min($-$) & & -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 \\
MSE & & 0.13 & 0.02 & 0.18 & -0.01 & 0.10 & 0.04 & 0.04 & 0.00 & 0.18 & 0.21 & 0.15 & 0.02 & -0.01 & -0.12 & -0.06 \\
& singlet & 0.10 & -0.02 & 0.22 & 0.03 & 0.14 & 0.04 & 0.04 & 0.00 & 0.18 & 0.20 & 0.13 & 0.00 & -0.04 & -0.08 & -0.06 \\
& triplet & 0.19 & 0.08 & 0.14 & -0.07 & 0.03 & & & 0.00 & 0.19 & 0.22 & 0.17 & 0.04 & 0.04 & -0.18 & -0.07 \\
& valence & 0.20 & 0.10 & 0.20 & -0.06 & 0.10 & 0.06 & 0.05 & 0.00 & 0.19 & 0.24 & 0.20 & 0.02 & 0.04 & -0.16 & -0.06 \\
& Rydberg & -0.04 & -0.17 & 0.15 & 0.09 & 0.08 & 0.01 & 0.03 & -0.01 & 0.16 & 0.12 & 0.01 & 0.02 & -0.13 & -0.02 & -0.07 \\
& $n \ra \pis$ & 0.16 & 0.02 & 0.24 & -0.03 & 0.17 & 0.07 & 0.07 & 0.00 & 0.26 & 0.32 & 0.22 & 0.05 & -0.05 & -0.01 & -0.03 \\
& $\pi \ra \pis$& 0.25 & 0.17 & 0.20 & -0.07 & 0.06 & 0.05 & 0.04 & 0.00 & 0.15 & 0.19 & 0.19 & 0.00 & 0.12 & -0.27 & -0.07 \\
& 1--3 non-H & 0.10 & 0.03 & 0.03 & -0.02 & 0.04 & 0.01 & 0.01 & 0.00 & 0.13 & 0.16 & 0.11 & -0.01 & -0.01 & -0.17 & -0.09 \\
& 4 non-H & 0.13 & 0.04 & 0.12 & 0.00 & 0.09 & 0.03 & 0.04 & 0.00 & 0.19 & 0.26 & 0.19 & 0.03 & -0.04 & -0.10 & -0.07 \\
& 5--6 non-H & 0.17 & 0.02 & 0.30 & -0.01 & 0.11 & 0.05 & 0.05 & 0.00 & 0.21 & 0.20 & 0.14 & 0.03 & 0.03 & -0.10 & -0.04 \\
& \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)} \\
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 \\
Min($-$) & & -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 \\
MSE & & 0.13 & 0.02 & 0.18 & -0.01 & 0.10 & 0.04 & 0.04 & 0.00 & 0.18 & 0.21 & 0.15 & 0.02 & -0.01 & -0.12 & -0.06 \\
& singlet & 0.10 & -0.02 & 0.22 & 0.03 & 0.14 & 0.04 & 0.04 & 0.00 & 0.18 & 0.20 & 0.13 & 0.00 & -0.04 & -0.08 & -0.06 \\
& triplet & 0.19 & 0.08 & 0.14 & -0.07 & 0.03 & & & 0.00 & 0.19 & 0.22 & 0.17 & 0.04 & 0.04 & -0.18 & -0.07 \\
& valence & 0.20 & 0.10 & 0.20 & -0.06 & 0.10 & 0.06 & 0.05 & 0.00 & 0.19 & 0.24 & 0.20 & 0.02 & 0.04 & -0.16 & -0.06 \\
& Rydberg & -0.04 & -0.17 & 0.15 & 0.09 & 0.08 & 0.01 & 0.03 & -0.01 & 0.16 & 0.12 & 0.01 & 0.02 & -0.13 & -0.02 & -0.07 \\
& $n \ra \pis$ & 0.16 & 0.02 & 0.24 & -0.03 & 0.17 & 0.07 & 0.07 & 0.00 & 0.26 & 0.32 & 0.22 & 0.05 & -0.05 & -0.01 & -0.03 \\
& $\pi \ra \pis$& 0.25 & 0.17 & 0.20 & -0.07 & 0.06 & 0.05 & 0.04 & 0.00 & 0.15 & 0.19 & 0.19 & 0.00 & 0.12 & -0.27 & -0.07 \\
& 1--3 non-H & 0.10 & 0.03 & 0.03 & -0.02 & 0.04 & 0.01 & 0.01 & 0.00 & 0.13 & 0.16 & 0.11 & -0.01 & -0.01 & -0.17 & -0.09 \\
& 4 non-H & 0.13 & 0.04 & 0.12 & 0.00 & 0.09 & 0.03 & 0.04 & 0.00 & 0.19 & 0.26 & 0.19 & 0.03 & -0.04 & -0.10 & -0.07 \\
& 5--6 non-H & 0.17 & 0.02 & 0.30 & -0.01 & 0.11 & 0.05 & 0.05 & 0.00 & 0.21 & 0.20 & 0.14 & 0.03 & 0.03 & -0.10 & -0.04 \\
& 7--10 non-H & 0.15 & -0.03 & 0.42 & -0.05 & 0.22 & 0.10 & 0.08 & -0.01 & 0.26 & 0.29 & 0.19 & 0.05 & -0.06 & -0.02 & -0.04 \\
MSE & & 0.13 & 0.02 & 0.18 & -0.01 & 0.10 & 0.04 & 0.04 & 0.00 & 0.18 & 0.21 & 0.15 & 0.02 & -0.01 & -0.12 & -0.06 \\
SDE & & 0.24 & 0.20 & 0.21 & 0.13 & 0.12 & 0.05 & 0.04 & 0.02 & 0.17 & 0.16 & 0.16 & 0.15 & 0.20 & 0.22 & 0.08 \\
RMSE & & 0.29 & 0.22 & 0.28 & 0.15 & 0.16 & 0.07 & 0.06 & 0.03 & 0.25 & 0.26 & 0.22 & 0.17 & 0.21 & 0.26 & 0.10 \\
MAE & & 0.22 & 0.16 & 0.22 & 0.11 & 0.12 & 0.05 & 0.04 & 0.02 & 0.20 & 0.22 & 0.18 & 0.13 & 0.15 & 0.21 & 0.08 \\
& singlet & 0.22 & 0.16 & 0.25 & 0.10 & 0.14 & 0.05 & 0.04 & 0.02 & 0.21 & 0.22 & 0.17 & 0.14 & 0.16 & 0.20 & 0.09 \\
& triplet & 0.23 & 0.15 & 0.18 & 0.12 & 0.08 & & & 0.01 & 0.20 & 0.23 & 0.19 & 0.11 & 0.15 & 0.22 & 0.08 \\
& valence & 0.22 & 0.14 & 0.24 & 0.12 & 0.13 & 0.06 & 0.05 & 0.02 & 0.21 & 0.25 & 0.20 & 0.12 & 0.13 & 0.22 & 0.08 \\
& Rydberg & 0.22 & 0.21 & 0.19 & 0.10 & 0.08 & 0.03 & 0.03 & 0.02 & 0.20 & 0.15 & 0.13 & 0.14 & 0.21 & 0.18 & 0.09 \\
& $n \ra \pis$ & 0.18 & 0.08 & 0.28 & 0.08 & 0.17 & 0.07 & 0.07 & 0.01 & 0.26 & 0.32 & 0.22 & 0.11 & 0.10 & 0.14 & 0.07 \\
& $\pi \ra \pis$& 0.27 & 0.19 & 0.21 & 0.14 & 0.11 & 0.06 & 0.04 & 0.02 & 0.18 & 0.21 & 0.20 & 0.12 & 0.16 & 0.28 & 0.09 \\
& 1--3 non-H & 0.23 & 0.19 & 0.13 & 0.10 & 0.07 & 0.03 & 0.03 & 0.02 & 0.18 & 0.20 & 0.19 & 0.14 & 0.19 & 0.24 & 0.10 \\
& 4 non-H & 0.22 & 0.19 & 0.15 & 0.11 & 0.11 & 0.03 & 0.04 & 0.02 & 0.19 & 0.26 & 0.22 & 0.13 & 0.18 & 0.23 & 0.08 \\
& 5--6 non-H & 0.21 & 0.12 & 0.30 & 0.12 & 0.13 & 0.06 & 0.05 & 0.01 & 0.22 & 0.21 & 0.15 & 0.11 & 0.11 & 0.19 & 0.07 \\
MSE & & 0.13 & 0.02 & 0.18 & -0.01 & 0.10 & 0.04 & 0.04 & 0.00 & 0.18 & 0.21 & 0.15 & 0.02 & -0.01 & -0.12 & -0.06 \\
SDE & & 0.24 & 0.20 & 0.21 & 0.13 & 0.12 & 0.05 & 0.04 & 0.02 & 0.17 & 0.16 & 0.16 & 0.15 & 0.20 & 0.22 & 0.08 \\
RMSE & & 0.29 & 0.22 & 0.28 & 0.15 & 0.16 & 0.07 & 0.06 & 0.03 & 0.25 & 0.26 & 0.22 & 0.17 & 0.21 & 0.26 & 0.10 \\
MAE & & 0.22 & 0.16 & 0.22 & 0.11 & 0.12 & 0.05 & 0.04 & 0.02 & 0.20 & 0.22 & 0.18 & 0.13 & 0.15 & 0.21 & 0.08 \\
& singlet & 0.22 & 0.16 & 0.25 & 0.10 & 0.14 & 0.05 & 0.04 & 0.02 & 0.21 & 0.22 & 0.17 & 0.14 & 0.16 & 0.20 & 0.09 \\
& triplet & 0.23 & 0.15 & 0.18 & 0.12 & 0.08 & & & 0.01 & 0.20 & 0.23 & 0.19 & 0.11 & 0.15 & 0.22 & 0.08 \\
& valence & 0.22 & 0.14 & 0.24 & 0.12 & 0.13 & 0.06 & 0.05 & 0.02 & 0.21 & 0.25 & 0.20 & 0.12 & 0.13 & 0.22 & 0.08 \\
& Rydberg & 0.22 & 0.21 & 0.19 & 0.10 & 0.08 & 0.03 & 0.03 & 0.02 & 0.20 & 0.15 & 0.13 & 0.14 & 0.21 & 0.18 & 0.09 \\
& $n \ra \pis$ & 0.18 & 0.08 & 0.28 & 0.08 & 0.17 & 0.07 & 0.07 & 0.01 & 0.26 & 0.32 & 0.22 & 0.11 & 0.10 & 0.14 & 0.07 \\
& $\pi \ra \pis$& 0.27 & 0.19 & 0.21 & 0.14 & 0.11 & 0.06 & 0.04 & 0.02 & 0.18 & 0.21 & 0.20 & 0.12 & 0.16 & 0.28 & 0.09 \\
& 1--3 non-H & 0.23 & 0.19 & 0.13 & 0.10 & 0.07 & 0.03 & 0.03 & 0.02 & 0.18 & 0.20 & 0.19 & 0.14 & 0.19 & 0.24 & 0.10 \\
& 4 non-H & 0.22 & 0.19 & 0.15 & 0.11 & 0.11 & 0.03 & 0.04 & 0.02 & 0.19 & 0.26 & 0.22 & 0.13 & 0.18 & 0.23 & 0.08 \\
& 5--6 non-H & 0.21 & 0.12 & 0.30 & 0.12 & 0.13 & 0.06 & 0.05 & 0.01 & 0.22 & 0.21 & 0.15 & 0.11 & 0.11 & 0.19 & 0.07 \\
& 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}