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Manuscript/QUESTDB.bib
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@ -1,13 +1,123 @@
%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/
%% Created for Pierre-Francois Loos at 2020-10-26 13:47:35 +0100
%% Created for Pierre-Francois Loos at 2020-11-04 21:18:12 +0100
%% Saved with string encoding Unicode (UTF-8)
@misc{Eriksen_2021,
Archiveprefix = {arXiv},
Author = {Janus J. Eriksen},
Date-Added = {2020-11-04 21:15:49 +0100},
Date-Modified = {2020-11-04 21:15:58 +0100},
Eprint = {2010.12304},
Primaryclass = {physics.chem-ph},
Title = {The Shape of FCI to Come},
Year = {2020}}
@article{Scemama_2020,
Author = {Scemama,Anthony and Giner,Emmanuel and Benali,Anouar and Loos,Pierre-Fran{\c c}ois},
Date-Added = {2020-11-04 21:14:14 +0100},
Date-Modified = {2020-11-04 21:14:34 +0100},
Doi = {10.1063/5.0026324},
Eprint = {https://doi.org/10.1063/5.0026324},
Journal = {The Journal of Chemical Physics},
Number = {17},
Pages = {174107},
Title = {Taming the fixed-node error in diffusion Monte Carlo via range separation},
Url = {https://doi.org/10.1063/5.0026324},
Volume = {153},
Year = {2020},
Bdsk-Url-1 = {https://doi.org/10.1063/5.0026324}}
@article{Loos_2020f,
Author = {Loos,Pierre-Fran{\c c}ois and Damour,Yann and Scemama,Anthony},
Date-Added = {2020-11-04 21:14:08 +0100},
Date-Modified = {2020-11-04 21:14:48 +0100},
Doi = {10.1063/5.0027617},
Eprint = {https://doi.org/10.1063/5.0027617},
Journal = {The Journal of Chemical Physics},
Number = {17},
Pages = {176101},
Title = {The performance of CIPSI on the ground state electronic energy of benzene},
Url = {https://doi.org/10.1063/5.0027617},
Volume = {153},
Year = {2020},
Bdsk-Url-1 = {https://doi.org/10.1063/5.0027617}}
@article{Chrayteh_2021,
Author = {A. Chrayte and A. Blondel and P. F. Loos and D. Jacquemin},
Date-Added = {2020-11-04 21:07:34 +0100},
Date-Modified = {2020-11-04 21:07:34 +0100},
Journal = {J. Chem. Theory Comput.},
Title = {A mountaineering strategy to excited states: highly-accurate oscillator strengths and dipole moments of small molecules},
Year = {submitted}}
@article{Rowe_1968,
Author = {ROWE, D. J.},
Date-Added = {2020-11-04 16:29:58 +0100},
Date-Modified = {2020-11-04 16:30:08 +0100},
Doi = {10.1103/RevModPhys.40.153},
Issue = {1},
Journal = {Rev. Mod. Phys.},
Month = {Jan},
Numpages = {0},
Pages = {153--166},
Publisher = {American Physical Society},
Title = {Equations-of-Motion Method and the Extended Shell Model},
Url = {https://link.aps.org/doi/10.1103/RevModPhys.40.153},
Volume = {40},
Year = {1968},
Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/RevModPhys.40.153},
Bdsk-Url-2 = {https://doi.org/10.1103/RevModPhys.40.153}}
@article{Blase_2020,
Author = {X. Blase and I. Duchemin and D. Jacquemin and P. F. Loos},
Date-Added = {2020-11-04 16:27:28 +0100},
Date-Modified = {2020-11-04 16:27:28 +0100},
Doi = {10.1021/acs.jpclett.0c01875},
Journal = {J. Phys. Chem. Lett.},
Pages = {7371},
Title = {The Bethe-Salpeter Formalism: From Physics to Chemistry},
Volume = {11},
Year = {2020},
Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpclett.0c01875}}
@article{Krylov_2006,
Author = {Krylov, Anna I.},
Date-Added = {2020-11-04 16:23:34 +0100},
Date-Modified = {2020-11-04 16:23:44 +0100},
Doi = {10.1021/ar0402006},
Eprint = {https://doi.org/10.1021/ar0402006},
Journal = {Accounts of Chemical Research},
Note = {PMID: 16489727},
Number = {2},
Pages = {83-91},
Title = {Spin-Flip Equation-of-Motion Coupled-Cluster Electronic Structure Method for a Description of Excited States, Bond Breaking, Diradicals, and Triradicals},
Url = {https://doi.org/10.1021/ar0402006},
Volume = {39},
Year = {2006},
Bdsk-Url-1 = {https://doi.org/10.1021/ar0402006}}
@article{Piecuch_2002,
Author = {Piotr Piecuch and Karol Kowalski and Ian S. O. Pimienta and Michael J. Mcguire},
Date-Added = {2020-11-04 16:22:51 +0100},
Date-Modified = {2020-11-04 16:22:58 +0100},
Doi = {10.1080/0144235021000053811},
Eprint = {https://doi.org/10.1080/0144235021000053811},
Journal = {International Reviews in Physical Chemistry},
Number = {4},
Pages = {527-655},
Publisher = {Taylor & Francis},
Title = {Recent advances in electronic structure theory: Method of moments of coupled-cluster equations and renormalized coupled-cluster approaches},
Url = {https://doi.org/10.1080/0144235021000053811},
Volume = {21},
Year = {2002},
Bdsk-Url-1 = {https://doi.org/10.1080/0144235021000053811}}
@article{Dunning_1989a,
Author = {Dunning, Thom H.},
Date-Added = {2020-10-26 13:47:31 +0100},
@ -224,12 +334,12 @@
Year = {1987},
Bdsk-Url-1 = {https://doi.org/10.1002/jcc.540080807}}
@article{Chrayteh_2020,
Author = {A. Chrayte and A. Blondel and P. F. Loos and D. Jacquemin},
@article{Sarkar_2021,
Author = {R. Sarkar and M. Boggio-Pasqua and P. F. Loos and D. Jacquemin},
Date-Added = {2020-10-26 13:24:43 +0100},
Date-Modified = {2020-10-26 13:25:32 +0100},
Date-Modified = {2020-11-04 21:08:59 +0100},
Journal = {J. Chem. Theory Comput.},
Title = {A mountaineering strategy to excited states: highly-accurate oscillator strengths and dipole moments of small molecules},
Title = {Benchmark of TD-DFT and Wavefunction Methods for Oscillator Strengths and Excited-State Dipoles},
Year = {submitted}}
@article{Lei_2017,
@ -1027,16 +1137,6 @@
Title = {Towards a Systematic Improvement of the Fixed-Node Approximation in Diffusion Monte Carlo for Solids},
Year = {2020}}
@misc{Scemama_2020,
Archiveprefix = {arXiv},
Author = {Anthony Scemama and Emmanuel Giner Anouar Benali and Pierre-Fran{\c c}ois Loos},
Date-Added = {2020-09-04 09:59:46 +0200},
Date-Modified = {2020-09-04 10:00:38 +0200},
Eprint = {2008.10088},
Primaryclass = {physics.chem-ph},
Title = {Taming the fixed-node error in diffusion Monte Carlo via range separation},
Year = {2020}}
@article{Li_2020,
Author = {Li, Junhao and Yao, Yuan and Holmes, Adam A. and Otten, Matthew and Sun, Qiming and Sharma, Sandeep and Umrigar, C. J.},
Date-Added = {2020-09-04 09:50:25 +0200},
@ -4369,18 +4469,6 @@
Year = {1964},
Bdsk-Url-1 = {https://doi.org/10.1103/PhysRev.135.A932}}
@article{Rowe_1968,
Author = {D. J. Rowe},
Date-Added = {2020-01-04 20:11:46 +0100},
Date-Modified = {2020-01-04 20:12:50 +0100},
Doi = {10.1103/PhysRev.175.1283},
Journal = {Phys. Rev.},
Pages = {1283},
Title = {Methods for Calculating Ground-State Correlations of Vibrational Nuclei},
Volume = {175},
Year = {1968},
Bdsk-Url-1 = {https://doi.org/10.1103/PhysRev.175.1283}}
@article{Salpeter_1951,
Author = {E. E. Salpeter and H. A. Bethe},
Date-Added = {2020-01-04 19:53:01 +0100},

92
Manuscript/QUEST_WIREs.tex
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@ -100,10 +100,10 @@ We hope that the present review will provide a useful summary of our work so far
Nowadays, there exists a very large number of electronic structure computational approaches, more or less expensive depending on their overall accuracy, able to quantitatively predict the absolute and/or relative energies of electronic states in molecular systems \cite{SzaboBook,JensenBook,CramerBook,HelgakerBook}.
One important aspect of some of these theoretical methods is their ability to access the energies of electronic excited states, i.e., states that have higher total energies than the so-called ground (that is, lowest-energy) state.
The faithful description of excited states is particularly challenging from a theoretical point of view \cite{Gonzales_2012,Ghosh_2018,Loos_2020a} and is key to a deeper understanding of photochemical and photophysical processes like absorption, fluorescence, or even chemoluminescence \cite{Bernardi_1996,Olivucci_2010,Robb_2007,Navizet_2011}.
The faithful description of excited states is particularly challenging from a theoretical point of view \cite{Piecuch_2002,Dreuw_2005,Krylov_2006,Gonzales_2012,Ghosh_2018,Blase_2020,Loos_2020a,Eriksen_2021} and is key to a deeper understanding of photochemical and photophysical processes like absorption, fluorescence, or even chemoluminescence \cite{Bernardi_1996,Olivucci_2010,Robb_2007,Navizet_2011}.
For a given level of theory, ground-state methods are usually more accurate than their excited-state analogs.
The reasons behind this are (at least) twofold: i) one might lack a proper variational principle for excited-state energies, and ii) excited states are often very close in energy from each other but they can have very different natures ($\pi \to \pis$, $n \to \pis$, charge transfer, double excitation, valence, Rydberg, singlet, doublet, triplet, etc).
Designing excited-state methods able to tackle on the same footing all these types of excited states at an affordable cost remain an open challenge in theoretical computational chemistry \cite{Gonzales_2012,Ghosh_2018,Loos_2020a}.
The reasons behind this are (at least) threefold: i) one might lack a proper variational principle for excited-state energies and one may have to rely on response theory formalisms which inherently introduce a ground-state ``bias'', iii) accurately modeling the electronic structure of excited states usually requires larger one-electron basis sets (including diffuse functions most of the times) than their ground-state counterpart, and iii) excited states can be governed by different amounts of dynamic/static correlations, have very different physical natures ($\pi \to \pis$, $n \to \pis$, charge transfer, double excitation, valence, Rydberg, singlet, doublet, triplet, etc), yet been very close in energy from each other.
Hence, designing excited-state methods able to tackle simultaneously and on an equal footing all these types of excited states at an affordable cost remain an open challenge in theoretical computational chemistry \cite{Piecuch_2002,Dreuw_2005,Krylov_2006,Gonzales_2012,Ghosh_2018,Blase_2020,Loos_2020a,Eriksen_2021}.
When one designs a new theoretical model, the first feature that one might want to test is its overall accuracy, i.e., its ability to reproduce reference (or benchmark) values for a given system with well-defined setup (same geometry, basis set, etc).
These values can be absolute or relative energies, geometrical parameters, physical or chemical properties extracted from experiments, high-level theoretical calculations, or a combination of both.
@ -122,12 +122,11 @@ Benchmark datasets of excited-state energies and/or properties are less numerous
Below, we provide a short description for some of them.
One of the most characteristic example is the benchmark set of vertical excitations proposed by Thiel and coworkers \cite{Schreiber_2008,Silva-Junior_2008,Silva-Junior_2010,Silva-Junior_2010b,Silva-Junior_2010c}.
The so-called Thiel (or M\"ulheim) set of excitation energies gathers a large number of excitation energies determined in 28 medium-size organic molecules with a total of 223 valence excited states (152 singlet and 71 triplet states) for which theoretical best estimates (TBEs) were defined.
In their first study, Thiel and collaborators performed CC2 \cite{Christiansen_1995a,Hattig_2000}, EOM-CCSD \cite{Koch_1990,Stanton_1993,Koch_1994}, CC3 \cite{Christiansen_1995b,Koch_1997}, and CASPT2 \cite{Andersson_1990,Andersson_1992,Roos,Roos_1996} calculations (with the TZVP basis) on MP2/6-31G(d) geometries in order to provide (based on additional high-quality literature data) TBEs for these transitions.
In their first study, Thiel and collaborators performed CC2 \cite{Christiansen_1995a,Hattig_2000}, EOM-CCSD \cite{Rowe_1968,Koch_1990,Stanton_1993,Koch_1994}, CC3 \cite{Christiansen_1995b,Koch_1997}, and CASPT2 \cite{Andersson_1990,Andersson_1992,Roos,Roos_1996} calculations (with the TZVP basis) on MP2/6-31G(d) geometries in order to provide (based on additional high-quality literature data) TBEs for these transitions.
These TBEs were quickly refined with the larger aug-cc-pVTZ basis set, highlighting the importance of diffuse functions in the faithful description of excited states (especially for Rydberg states) \cite{Silva-Junior_2010b,Silva-Junior_2010c}.
In the same spirit, it is also worth mentioning Gordon's set of vertical transitions (based on experimental values) \cite{Leang_2012} used to benchmark the performance of time-dependent density-functional theory (TD-DFT) \cite{Runge_1984,Casida_1995,Casida_2012,Ulrich_2012}, as well as its extended version by Goerigk and coworkers who decided to replace the experimental reference values by CC3 excitation energies instead \cite{Schwabe_2017,Casanova-Paez_2019,Casanova_Paes_2020}.
Let us also mention the new benchmark set of charge-transfer excited states recently introduced by Szalay and coworkers [based on equation-of-motion coupled cluster (EOM-CC) methods] \cite{Kozma_2020} as well as the Gagliardi-Truhlar set employed to compare the accuracy of multiconfiguration pair-density functional theory \cite{Ghosh_2018} against the well-established CASPT2 method \cite{Hoyer_2016}.
Following a similar philosophy and striving for chemical accuracy, we have recently reported in several studies highly-accurate vertical excitations for small- and medium-sized molecules \cite{Loos_2020a,Loos_2018a,Loos_2019,Loos_2020b,Loos_2020c}.
The so-called QUEST dataset of vertical excitations which we will describe in details in the present review article is composed by 5 subsets (see Fig.~\ref{fig:scheme}): i) a subset of excitations in small molecules containing from 1 to 3 non-hydrogen atoms known as QUEST\#1, ii) a subset of double excitations for molecules of small and medium sizes known as QUEST\#2, iii) a subset of excitation energies for medium-sized molecules containing from 4 to 6 non-hydrogen atoms known as QUEST\#3, iv) a subset composed by more ``exotic'' molecules and radicals labeled as QUEST\#4, and v) a subset known as QUEST\#5, specifically designed for the present article, gathering excitation energies in larger molecules as well as additional smaller molecules.
One of the key aspect of the QUEST dataset is that it does not rely on any experimental values, avoiding potential biases inherently linked to experiments and facilitating in the process theoretical comparisons.
@ -383,7 +382,7 @@ Triazine & $^1A_1''(n \ra \pis)$ & 4.85 & 4.84 & 4.77(13)& 5.12(51) \\
%%% FIGURE 2 %%%
\begin{figure}
\centering
\includegraphics[width=0.6\linewidth]{errors}
\includegraphics[width=\linewidth]{errors}
\caption{Deviation from the CCSDT excitation energies for singlet and triplet excitation energies (in eV) 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 CIPSI 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 CIPSI wave function.
The error bars corresponds to one standard deviation.}
\label{fig:errors}
@ -404,7 +403,7 @@ Throughout the present article, we report several statistical indicators: the me
%%% FIGURE 2 %%%
\begin{figure}
\centering
\includegraphics[width=0.8\linewidth]{fig2}
\includegraphics[width=\linewidth]{fig2}
\caption{Molecules each of the five subsets making up the present QUEST dataset of highly-accurate vertical excitation energies:
QUEST\#1 (red), QUEST\#2 (magenta and/or underlined), QUEST\#3 (black), QUEST\#4 (green), and QUEST\#5 (blue).}
\label{fig:molecules}
@ -461,9 +460,53 @@ Likewise, the excitation energies obtained with CCSD are much less satisfying fo
%=======================
The QUEST\#5 subset is composed by additional accurate excitation energies that we have produced for the present article.
This new set gathers 13 new systems composed by small molecules as well as larger molecules (aza-naphthalene, benzoquinone, cyclopentadienone, cyclopentadienethione, diazirine, hexatriene, maleimide, naphthalene, nitroxyl, octatetraene, streptocyanine-C3, streptocyanine-C5, and thioacrolein).
For these new transitions, we report at least CCSDT/aug-cc-pVTZ vertical energies.
This new set gathers 13 new systems composed by small molecules as well as larger molecules (see blue molecules in Fig.~\ref{fig:molecules}): aza-naphthalene, benzoquinone, cyclopentadienone, cyclopentadienethione, diazirine, hexatriene, maleimide, naphthalene, nitroxyl, octatetraene, streptocyanine-C3, streptocyanine-C5, and thioacrolein.
For these new transitions, we report at least CCSDT/aug-cc-pVTZ vertical energies, and we consider that, out of these \alert{80} new transitions, \alert{55} of them can be labeled as ``safe'', \ie, considered as chemically accurate.
The interested reader will find in the {\SupInf} a detailed discussion for each of these molecules in which comparisons are made with literature data.
Statistical quantities related to the benchmark of various methods for the QUEST5 subset are reported in Table \ref{tab:QUEST5} and depicted in Fig.~\ref{fig:QUEST5_stat}.
\begin{table}[bt]
\centering
\caption{Mean signed error (MSE), mean absolute error (MAE), root-mean-square error (RMSE), standard deviation of the errors (SDE), as well as the maximum positive [Max(+)] and negative [Max($-$)] errors with respect to the TBE/aug-cc-pVTZ for the QUEST5 subset.
For the MSE and MAE, the statistical values are reported for various types of excited states and molecular sizes.
All quantities are given in eV. ``Count'' refers to the number of transitions considered for each method.
\label{tab:QUEST5}}
\begin{threeparttable}
\begin{tabular}{lccccccc}
\headrow
\thead{Method} & \thead{Count} & \thead{Max($+$)} & \thead{Max($-$)} & \thead{MSE}& \thead{SDE} & \thead{RMSE} & \thead{MAE}\\
CIS(D) & 55 & 0.60 & -0.55 & 0.16 & 0.23 & 0.28 & 0.23 \\
ADC(2) & 55 & 0.33 & -0.49 & -0.03 & 0.16 & 0.16 & 0.13 \\
ADC(2.5) & 53 & 0.13 & -0.34 & -0.06 & 0.10 & 0.11 & 0.09 \\
ADC(3) & 53 & 0.60 & -0.53 & -0.10 & 0.22 & 0.24 & 0.20 \\
SOS-ADC(2)$^a$ & 55 & 0.40 & -0.19 & 0.06 & 0.12 & 0.14 & 0.11 \\
SCS-CC2 & 46 & 0.46 & -0.03 & 0.19 & 0.12 & 0.22 & 0.19 \\
SOS-ADC(2)$^b$ & 46 & 0.69 & -0.02 & 0.24 & 0.13 & 0.27 & 0.24 \\
SOS-CC2 & 46 & 0.77 & 0.02 & 0.28 & 0.16 & 0.32 & 0.28 \\
CCSD(2) & 55 & 0.80 & -0.13 & 0.33 & 0.22 & 0.40 & 0.34 \\
CCSD & 55 & 0.80 & -0.25 & 0.17 & 0.17 & 0.24 & 0.19 \\
STEOM-CCSD & 30 & 0.13 & -0.36 & -0.07 & 0.14 & 0.16 & 0.12 \\
CCSDR(3) & 37 & 0.43 & 0.00 & 0.09 & 0.08 & 0.12 & 0.09 \\
CCSDT-3 & 37 & 0.23 & -0.01 & 0.07 & 0.05 & 0.09 & 0.07 \\
CC2 & 55 & 0.29 & -0.54 & -0.01 & 0.15 & 0.15 & 0.11 \\
CC3 & 46 & 0.04 & -0.03 & -0.00 & 0.02 & 0.02 & 0.02 \\
\hline % Please only put a hline at the end of the table
\end{tabular}
\begin{tablenotes}
\item $^a$ Excitation energies computed with Q-CHEM.
\item $^b$ Excitation energies computed with TURBOMOLE.
\end{tablenotes}
\end{threeparttable}
\end{table}
\begin{figure}
\includegraphics[width=\textwidth]{QUEST5_stat}
\caption{Error (in eV) in excitation energies (with respect to TBE/aug-cc-pVTZ values) for various methods for the single excitations of the QUEST\#5 set.
The boxes contain the data between first and third quartiles, and the line in the box represents the median.
The outliers are shown as dots.
\label{fig:QUEST5_stat}}
\end{figure}
%\begin{table}[bt]
%\centering
@ -605,11 +648,12 @@ In this section, we report a comprehensive benchmark of various lower-order meth
Statistical quantities are reported in Table \ref{tab:stat}.
Additionally, we also provide a specific analysis for each type of excited states.
Hence, the statistical values are reported for various types of excited states and molecular sizes for the MSE and MAE.
The distribution of the errors in vertical excitation energies (with respect to the TBE/aug-cc-pVTZ reference values) are represented in Fig.~\ref{fig:QUEST_stat} for all the single excitations of the entire QUEST database.
\begin{sidewaystable}
\scriptsize
\centering
\caption{Mean signed error (MSE), mean absolute error (MAE), root-mean-square error (RMSE), standard deviation of the errors (SDE), as well as the maximum positive [Max(+)] and negative [Max($-$)] errors with respect to the TBE/aug-cc-pVTZ.
\caption{Mean signed error (MSE), mean absolute error (MAE), root-mean-square error (RMSE), standard deviation of the errors (SDE), as well as the maximum positive [Max(+)] and negative [Max($-$)] errors with respect to the TBE/aug-cc-pVTZ for the entire QUEST database.
For the MSE and MAE, the statistical values are reported for various types of excited states and molecular sizes.
All quantities are given in eV. ``Count'' refers to the number of transitions considered for each method.}
\label{tab:stat}
@ -632,7 +676,6 @@ MSE & & 0.13 & 0.02 & 0.18 & -0.01 & 0.10 & 0.04 & 0.04 & 0.00 & 0.18 & 0.2
& 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 \\
@ -649,13 +692,12 @@ MAE & & 0.22 & 0.16 & 0.22 & 0.11 & 0.12 & 0.05 & 0.04 & 0.02 & 0.20 & 0.22
\hline
\end{tabular}
\begin{tablenotes}
\item $^a$ Excitation energies compute with TURBOMOLE.
\item $^b$ Excitation energies compute with Q-CHEM.
\item $^a$ Excitation energies computed with TURBOMOLE.
\item $^b$ Excitation energies computed with Q-CHEM.
\end{tablenotes}
\end{threeparttable}
\end{sidewaystable}
\begin{figure}
\includegraphics[width=\textwidth]{QUEST_stat}
\caption{Error (in eV) in excitation energies (with respect to TBE/aug-cc-pVTZ values) for various methods for the single excitations of the entire QUEST database.
@ -664,14 +706,6 @@ MAE & & 0.22 & 0.16 & 0.22 & 0.11 & 0.12 & 0.05 & 0.04 & 0.02 & 0.20 & 0.22
\label{fig:QUEST_stat}}
\end{figure}
\begin{figure}
\includegraphics[width=\textwidth]{QUEST5_stat}
\caption{Error (in eV) in excitation energies (with respect to TBE/aug-cc-pVTZ values) for various methods for the single excitations of the QUEST\#5 set.
The boxes contain the data between first and third quartiles, and the line in the box represents the median.
The outliers are shown as dots.
\label{fig:QUEST5_stat}}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{The QUESTDB website}
\label{sec:website}
@ -770,8 +804,18 @@ and the value is considered as not safe when one or more value as not safe
\section{Concluding remarks}
\label{sec:ccl}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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}.
In the present review article, we have presented and extended the QUEST database of highly-accurate excitation energies for molecules systems \cite{Loos_2020a,Loos_2018a,Loos_2019,Loos_2020b,Loos_2020c} that we started building in 2018 and that is now composed by more than \alert{470} vertical excitations.
In particular, we have detailed the specificities of our protocol by providing computational details regarding geometries, basis sets, as well as reference and benchmarked computational methods.
The content of our five QUEST subsets has been presented in details, and for each of the them, we have provided the number of reference excitation energies, the nature and size of the molecules, the list of benchmarked methods, as well as other specificities.
Importantly, we have proposed a new method to faithfully estimate the extrapolation error in SCI calculations.
This new method based on Gaussian random variables has been tested by computing additional FCI values for five- and six-membered rings.
After having discussed the generation of our TBEs, we have reported a comprehensive benchmark of a significant number of methods on the entire QUEST set with, in addition, a specific analysis for each type of excited states.
Finally, the main features of the website specifically designed to gather the entire data generated during these last few years have been presented and discussed.
Regarding future improvements and extensions, we would like to mention that although our present goal is to produce chemically accurate vertical excitation energies, we are currently devoting great efforts to obtain highly-accurate excited-state properties as such dipoles and oscillator strengths for molecules of small and medium sizes \cite{Chrayteh_2021,Sarkar_2021}.
Reference ground-state properties (such as correlation energies and atomization energies) are also being currently produced \cite{Scemama_2020,Loos_2020f}.
Besides this, because computing 450 (or so) 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}.
We hope to report on this in the new future.
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\section*{acknowledgements}