Cover_Letter/CoverLetter.tex

@@ -1,33 +0,0 @@
-\documentclass[10pt]{letter}
-\usepackage{UPS_letterhead,xcolor,mhchem,mathpazo,ragged2e,url}
-\newcommand{\alert}[1]{\textcolor{red}{#1}}
-\definecolor{darkgreen}{HTML}{009900}
-
-
-\begin{document}
-
-\begin{letter}%
-{To the Editors of WIREs Comput. Mol. Sci.}
-
-\opening{Dear Cl\'emence,}
-
-\justifying
-Please find enclosed our manuscript entitled \textit{``QUESTDB: a database of highly-accurate excitation energies for the electronic structure community''}, which we would like you to consider as an Advanced Review in \textit{WIREs Comput. Mol. Sci.}.
-
-The present review summarises and extends our effort to build a comprehensive database of highly-accurate vertical excitation energies for small- and medium-sized molecules that we have named the QUEST database.
-In order to gather the huge amount of data produced during the QUEST project, we have specifically created for the present article a brand new website [\url{https://lcpq.github.io/QUESTDB_ website}] where one can easily test and compare various theoretical methods.
-We hope that the present review will provide a useful summary of our effort so far and foster new developments around excited-state methods.
-
-We look forward to hearing from you.
-
-\closing{Sincerely, the authors.}
-
-
-\end{letter}
-\end{document}
-
-
-
-
-
-

Cover_Letter/UPS_letterhead.sty

@@ -1,70 +0,0 @@
-%ANU etterhead Yves
-%version 1.0	12/06/08
-%need to be improved
-
-
-\RequirePackage{graphicx}
-
-%%%%%%%%%%%%%%%%%%%%% DEFINE USER-SPECIFIC MACROS BELOW %%%%%%%%%%%%%%%%%%%%%
-\def\Who     {Pierre-Fran\c{c}ois Loos}
-\def\What    {Dr}
-\def\Where   {Universit\'e Paul Sabatier}
-\def\Address {Laboratoire de Chimie et Physique Quantiques}
-\def\CityZip {Toulouse, France}
-\def\Email   {loos@irsamc.ups-tlse.fr}
-\def\TEL     {+33 5 61 55 73 39}
-\def\URL     {} % NOTE: use $\sim$ for tilde
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% MARGINS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\textwidth       6in
-\textheight      9.25in
-\oddsidemargin   0.25in
-\evensidemargin  0.25in
-\topmargin       -1.50in
-\longindentation 0.50\textwidth
-\parindent       5ex
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%% ADDRESS MACRO BELOW %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\address{
-    \includegraphics[height=0.7in]{CNRS_logo.pdf}     \hspace*{\fill}\includegraphics[height=0.7in]{UPS_logo.pdf}
-	\\
-	\hrulefill
-	\\
-	{\small \What~\Who\hspace*{\fill} Telephone:\ \TEL
-	\\
-	\Where\hspace*{\fill}  Email:\ \Email
-	\\
-	\Address\hspace*{\fill}
-	\\
-	\CityZip\hspace*{\fill} \URL}
-	 }
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%% OTHER MACROS BELOW %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%\signature{\What~\Who}
-
-\def\opening#1{\ifx\@empty\fromaddress
- \thispagestyle{firstpage}
- \hspace*{\longindendation}\today\par
- \else \thispagestyle{empty}
- {\centering\fromaddress \vspace{5\parskip} \\
-\today\hspace*{\fill}\par}
- \fi
- \vspace{3\parskip}
- {\raggedright \toname \\ \toaddress \par}\vspace{3\parskip}
- \noindent #1\par\raggedright\parindent 5ex\par
- }
-
-%I do not know what does the macro below
-
-%\long\def\closing#1{\par\nobreak\vspace{\parskip}
- %\stopbreaks
- %\noindent
- %\ifx\@empty\fromaddress\else
- %\hspace*{\longindentation}\fi
- %\parbox{\indentedwidth}{\raggedright
- %\ignorespaces #1\vskip .65in
- %\ifx\@empty\fromsig
- %\else \fromsig \fi\strut}
- %\vspace*{\fill}
-% \par}

Manuscript/QUESTDB.bib

@@ -1,35 +1,24 @@
 %% This BibTeX bibliography file was created using BibDesk.
 %% http://bibdesk.sourceforge.net/
 
-%% Created for Pierre-Francois Loos at 2021-01-01 21:49:37 +0100 
+%% Created for Pierre-Francois Loos at 2020-11-27 22:23:32 +0100 
 
 
 %% Saved with string encoding Unicode (UTF-8) 
 
 
 
-@article{Mardirossian_2017,
-	author = {Narbe Mardirossian and Martin Head-Gordon},
-	date-added = {2021-01-01 21:49:17 +0100},
-	date-modified = {2021-01-01 21:49:36 +0100},
-	doi = {10.1080/00268976.2017.1333644},
-	journal = {Mol. Phys.},
-	number = {19},
-	pages = {2315-2372},
-	title = {Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals},
-	volume = {115},
-	year = {2017},
-	Bdsk-Url-1 = {https://doi.org/10.1080/00268976.2017.1333644}}
-
 @book{Robb_2018,
 	author = {Robb, Michael A},
 	date-added = {2020-11-27 22:23:19 +0100},
-	date-modified = {2020-11-29 21:13:13 +0100},
+	date-modified = {2020-11-27 22:23:27 +0100},
 	doi = {10.1039/9781788013642},
+	isbn = {978-1-78262-864-4},
 	pages = {P001-225},
 	publisher = {The Royal Society of Chemistry},
 	series = {Theoretical and Computational Chemistry Series},
 	title = {Theoretical Chemistry for Electronic Excited States},
+	url = {http://dx.doi.org/10.1039/9781788013642},
 	year = {2018},
 	Bdsk-Url-1 = {http://dx.doi.org/10.1039/9781788013642}}
 

Manuscript/QUEST_WIREs.tex

@@ -73,9 +73,7 @@
 
 %\presentadd[\authfn{2}]{Department, Institution, City, State or Province, Postal Code, Country}
 
-\fundinginfo{European Research Council (ERC), European Union's Horizon 2020 research and innovation programme, Grant agreement No.~863481.
-%This work benefited from the support of the ANR in the framework of the PIA program ANR-18-EURE-0012.
-}
+\fundinginfo{European Research Council (ERC), European Union's Horizon 2020 research and innovation programme, Grant agreement No.~863481}
 
 % Include the name of the author that should appear in the running header
 \runningauthor{V\'eril et al.}
@@ -94,6 +92,7 @@ the complete basis set limit) for some of them. The TBEs/aug-cc-pVTZ have been e
 STEOM-CCSD, CCSD, CCSDR(3), CCSDT-3, ADC(3), CC3,  NEVPT2, and others (including spin-scaled variants). In order to gather the huge amount of data produced during the QUEST
 project, we have created a website [\url{https://lcpq.github.io/QUESTDB_website}] where one can easily test and compare the accuracy of a given method with respect to various variables
 such as the molecule size or its family,  the nature of the excited states, the type of basis set, etc.
+%Add website address here
 We hope that the present review will provide a useful summary of our effort so far and foster new developments around excited-state methods.
 % Please include a maximum of seven keywords
 \keywords{excited states, benchmark, database, full configuration interaction, coupled cluster theory, excitation energies}
@@ -130,8 +129,8 @@ of Hobza and collaborators which provides benchmark interaction energies for wea
 systems \cite{vanSetten_2013,Bruneval_2016,Caruso_2016,Govoni_2018}. The extrapolated ab initio thermochemistry (HEAT) set designed to achieve high accuracy for enthalpies of formation
 of atoms and small molecules (without experimental data) is yet another successful example of benchmark set \cite{Tajti_2004,Bomble_2006,Harding_2008}. More recently, let us mention the benchmark datasets
 of the \textit{Simons Collaboration on the Many-Electron Problem} providing, for example, highly-accurate ground-state energies for
-hydrogen chains \cite{Motta_2017} as well as transition metal atoms and their ions and monoxides \cite{Williams_2020}. 
-Let us also mention the set of Zhao and Truhlar for small transition metal complexes employed to compare the accuracy of density-functional methods \cite{ParrBook} for $3d$ transition-metal chemistry \cite{Zhao_2006}, \alert{the MGCDB84 molecular database of Mardirossian and Head-Gordon that they use to benchmark a total of 200 density functionals and design (using a combinatorial approach) the $\omega$B97M-V functional \cite{Mardirossian_2017},} and finally the popular GMTKN24 \cite{Goerigk_2010},
+hydrogen chains \cite{Motta_2017} as well as transition metal atoms and their ions and monoxides \cite{Williams_2020}. Let us also mention the set of Zhao and Truhlar for small transition metal complexes
+employed to compare the accuracy of density-functional methods \cite{ParrBook} for $3d$ transition-metal chemistry \cite{Zhao_2006}, and finally the popular GMTKN24 \cite{Goerigk_2010},
 GMTKN30 \cite{Goerigk_2011a,Goerigk_2011b} and GMTKN55 \cite{Goerigk_2017} databases for general main group thermochemistry, kinetics, and non-covalent interactions developed by Goerigk, Grimme and
 their coworkers.
 
@@ -240,7 +239,6 @@ This has the advantage to produce a smoother and faster convergence of the SCI e
 The CIPSI energy $E_\text{CIPSI}$ is defined as the sum of the variational energy $E_\text{var}$ (computed via diagonalization of the CI matrix in the reference space) and a PT2 correction $E_\text{PT2}$ which estimates the contribution of the determinants not included in the CI space \cite{Garniron_2017b}.
 By linearly extrapolating this second-order correction to zero, one can efficiently estimate the FCI limit for the total energies.
 These extrapolated total energies (simply labeled as $E_\text{FCI}$ in the remainder of the paper) are then used to compute vertical excitation energies.
-
 Depending on the set, we estimated the extrapolation error via different techniques.
 For example, in Ref.~\cite{Loos_2020b}, we estimated the extrapolation error by the difference between the transition energies obtained with the largest SCI wave function and the FCI extrapolated value.
 This definitely cannot be viewed as a true error bar, but it provides an idea of the quality of the FCI extrapolation and estimate.
@@ -248,7 +246,7 @@ Below, we provide a much cleaner way of estimating the extrapolation error in SC
 The particularity of the current implementation is that the selection step and the PT2 correction are computed \textit{simultaneously} via a hybrid semistochastic algorithm \cite{Garniron_2017,Garniron_2019}.
 Moreover, a renormalized version of the PT2 correction (dubbed rPT2) has been recently implemented for a more efficient extrapolation to the FCI limit \cite{Garniron_2019}.
 We refer the interested reader to Ref.~\cite{Garniron_2019} where one can find all the details regarding the implementation of the CIPSI algorithm.
-\alert{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}. In the case of ground-state calculations, this constraint can be relaxed without altering the final result (see, for example, Ref.~\cite{Loos_2020e}).}
+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}
@@ -296,91 +294,96 @@ For the $m$th excited state (where $m = 0$ corresponds to the ground state), we
   E_{\text{var}}^{(m)} \approx E_\text{FCI}^{(m)} - \alpha^{(m)} E_{\text{rPT2}}^{(m)},
   \label{eqx}
 \end{equation}
-where $E_{\text{var}}^{(m)}$ and $E_{\text{rPT2}}^{(m)}$ are calculated with CIPSI and $E_\text{FCI}^{(m)}$ is the FCI energy to be extrapolated. 
-This relation is valid in the regime of a sufficiently large number of determinants where the second-order perturbational correction largely dominates.
-In theory, the coefficient $\alpha^{(m)}$ should be equal to one but, in practice, due to the residual higher-order terms, it deviates slightly from unity.
-
-For the largest systems considered here, $\abs{E_{\text{rPT2}}}$ can be as large as 2~eV and, thus,
-the accuracy of the excitation energy estimates strongly depends on our ability to compensate the errors in the calculations.
-Here, we greatly enhance the compensation of errors by making use of
-our selection procedure ensuring that the rPT2 values of both states
-match as well as possible (a trick known as PT2 matching
-\cite{Dash_2018,Dash_2019}), i.e. $E_{\text{rPT2}}^{(0)} \approx E_{\text{rPT2}}^{(m)}$, and
-by using a common set of state-averaged natural orbitals with equal weights for the ground and excited states.
-%This last feature tends to make the values of $\alpha^{(0)}$ and $\alpha^{(m)}$ very close to each other, such that the error on the energy difference is decreased.
+where $E_{\text{var}}^{(m)}$ and $E_{\text{rPT2}}^{(m)}$ are calculated with CIPSI and $E_\text{FCI}^{(m)}$ is the FCI energy
+to be extrapolated. This relation is valid in the regime of a sufficiently large number of determinants where the second-order perturbational
+correction largely dominates.
+However, in practice, due to the residual higher-order terms, the coefficient $\alpha^{(m)}$ deviates slightly from unity.
 
 Using Eq.~\eqref{eqx} the estimated error on the CIPSI energy is calculated as
 \begin{equation}
   E_{\text{CIPSI}}^{(m)} - E_{\text{FCI}}^{(m)}
   = \qty(E_\text{var}^{(m)}+E_{\text{rPT2}}^{(m)}) - E_{\text{FCI}}^{(m)}
-  = \qty(1-\alpha^{(m)}) E_{\text{rPT2}}^{(m)}
+  = \qty(1-\alpha^{(m)}) E_{\text{rPT2}}^{(m)},
 \end{equation}
-and thus the extrapolated excitation energy associated with the $m$th excited state is given by
+and thus the extrapolated excitation energy associated with the $m$th
+state is given by
 \begin{equation}
   \Delta E_{\text{FCI}}^{(m)}
- = \qty[ E_\text{var}^{(m)} + E_{\text{rPT2}}^{(m)} + \qty(\alpha^{(m)}-1) E_{\text{rPT2}}^{(m)} ]
- - \qty[ E_\text{var}^{(0)} + E_{\text{rPT2}}^{(0)} + \qty(\alpha^{(0)}-1) E_{\text{rPT2}}^{(0)} ].
+  = \qty[ E_\text{var}^{(m)} + E_{\text{rPT2}} + \qty(\alpha^{(m)}-1) E_{\text{rPT2}} ]
+  - \qty[ E_\text{var}^{(0)} + E_{\text{rPT2}} + \qty(\alpha^{(0)}-1) E_{\text{rPT2}} ]
+  + \mathcal{O}\qty[{E_{\text{rPT2}}^2 }],
 \end{equation}
-The slopes $\alpha^{(m)}$ and $\alpha^{(0)}$ deviating only slightly from the unity, the error in
-$\Delta E_{\text{FCI}}^{(m)}$ can be expressed at leading order as $\qty(\alpha^{(m)}-\alpha^{(0)}) {\bar E}_{\text{rPT2}} + \mathcal{O}\qty[{{\bar E}_{\text{rPT2}}^2}]$, where ${\bar E}_{\text{rPT2}}=\qty(E_{\text{rPT2}}^{(m)} +E_{\text{rPT2}}^{(0)})/2$ is the averaged second-order correction.
+which evidences that the error in $\Delta E_{\text{FCI}}^{(m)}$ can be expressed as $\qty(\alpha^{(m)}-\alpha^{(0)}) E_{\text{rPT2}} + \mathcal{O}\qty[{E_{\text{rPT2}}^2}]$.
 
-In the ideal case where one is able to fully correlate the CIPSI calculations associated with the ground and excited states, the fluctuations of
-$\Delta E_\text{CIPSI}^{(m)}(n)$ as a function of the iteration number $n$ would completely vanish and the exact excitation energy would be obtained from the first CIPSI iterations.
+Now, for the largest systems considered here, $\abs{E_{\text{rPT2}}}$ can be as large as 2~eV and, thus,
+the accuracy of the excitation energy estimates strongly depends on our ability to compensate the errors in the calculations.
+Here, we greatly enhance the compensation of errors by making use of
+our selection procedure ensuring that the PT2 values of both states
+match as well as possible (a trick known as PT2 matching
+\cite{Dash_2018,Dash_2019}), i.e. $E_{\text{rPT2}} =
+E_{\text{rPT2}}^{(0)} \approx E_{\text{rPT2}}^{(m)}$, and
+by using a common set of state-averaged natural orbitals with equal weights for the ground and excited states.
+This last feature tends to make the values of $\alpha^{(0)}$ and $\alpha^{(m)}$ very close to each other, such that the error on the energy difference
+is decreased.
+In the ideal case where we would be able to fully correlate the CIPSI calculations associated with the ground and excited states, the fluctuations of
+$\Delta E_\text{CIPSI}^{(m)}(n)$ as a function of $n$ would completely vanish and the exact excitation energy would be obtained from the first CIPSI iterations.
 Quite remarkably, in practice, numerical experience shows that the fluctuations with respect to the extrapolated value $\Delta E_\text{FCI}^{(m)}$ are small,
-zero-centered, and display a Gaussian-like distribution.
-In addition, as evidenced in Fig.~\ref{fig:histo}, these fluctuations are found to be (very weakly) dependent on the iteration number $n$ (as far as not too close $n$ values are considered). 
-Hence, this weak dependency does not significantly alter our results and will not be considered here.
-
+zero-centered, almost independent of $n$ when not too close iteration
+numbers are considered, and display a Gaussian-like distribution.
+In addition, as stated just above, the fluctuations are found to be (very weakly) dependent on the iteration number $n$ (see Fig.~\ref{fig:histo}), so
+this dependence will not significantly alter our results and will not be considered here.
 We thus introduce the following random variable
 \begin{equation}
-\label{eq:X}
 X^{(m)}= \frac{\Delta E_\text{CIPSI}^{(m)}(n)- \Delta E_\text{FCI}^{(m)}}{\sigma(n)}
 \end{equation}
 where
 \begin{equation}
   \Delta E_\text{CIPSI}^{(m)}(n) = \qty[ E_\text{var}^{(m)}(n) +
   E_{\text{rPT2}}^{(m)}(n) ]
-  - \qty[ E_\text{var}^{(0)}(n) + E_{\text{rPT2}}^{(0)}(n) ]
+  - \qty[ E_\text{var}^{(0)}(n) + E_{\text{rPT2}}^{(0)}(n) ],
 \end{equation}
 and
 ${\sigma(n)}$ is a quantity proportional to the average fluctuations of $\Delta E_\text{CIPSI}^{(m)}$.
 A natural choice for $\sigma^2(n)$, playing here the role of a variance, is
 \begin{equation}
-\sigma^2(n) \propto \qty[E_{\text{rPT2}}^{(m)}(n)]^2 + \qty[E_{\text{rPT2}}^{(0)}(n)]^2
+\sigma^2(n) \propto \qty[E_{\text{rPT2}}^{(m)}(n)]^2 + \qty[E_{\text{rPT2}}^{(0)}(n)]^2,
 \end{equation}
-which vanishes in the large-$n$ limit (as it should).
+which vanishes in the large-$n$ limit as it should.
 
 %%% FIGURE 2 %%%
 \begin{figure}
 \centering
 \includegraphics[width=0.9\linewidth]{fig2/fig2}
-\caption{Histogram of the random variable $X^{(m)}$ [see Eq.~\eqref{eq:X} in the main text for its definition]. 
-About 200 values of singlet and triplet excitation energies taken at various iteration number $n$ for the 13 five- and six-membered ring molecules have been considered to build the present histogram.
-The number $M$ of iterations kept at each calculation is chosen according to the statistical test presented in the text.}
+\caption{Histogram of the random variable $X^{(m)}$ (see, text). About 200 values of the transition energies
+for the 13 five- and six-membered ring molecules, both for the singlet and triplet transitions and for a number of CIPSI iterations, are used.
+The number $M$ of iterations kept is chosen according to the statistical test presented in the text.}
 \label{fig:histo}
 \end{figure}
 
-The histogram of $X^{(m)}$ resulting from the singlet and triplet excitation energies obtained at various iteration number $n$ for the 13 five- and six-membered ring molecules is shown in Fig.~\ref{fig:histo}. 
-To avoid transient effects, only excitation energies at sufficiently large $n$ are retained in the data set.
-The statistical criterion used to decide from which precise value of $n$ the data should be kept is presented below. 
-In the present example, the total number of values employed to construct the histogram of Fig.~\ref{fig:histo} is about 200. 
-The dashed line represents the best (in a least-squares sense) Gaussian fit reproducing the data.
-As clearly seen from Fig.~\ref{fig:histo}, the distribution can be fairly well described by a Gaussian probability distribution
+The histogram of $X^{(m)}$ resulting from the excitation energies
+obtained at different values of the CIPSI iterations $n$
+and for the 13 five- and six-membered ring molecules, both for the singlet and triplet transitions,
+is shown in Fig.~\ref{fig:histo}. To avoid transient effects, only excitation energies at sufficiently large $n$ are retained in the data set.
+The criterion used to decide from which precise value of $n$ the data should be kept will be presented below. In our application, the total number
+of values employed to make the histogram is about 200. The dashed line of Fig.~\ref{fig:histo} represents the best Gaussian fit
+(in the sense of least-squares) reproducing the data.
+As seen, the distribution can be described by the Gaussian probability
 \begin{equation}
 P\qty[X^{(m)}] \propto \exp[-\frac{{X^{(m)}}^2} {2{\sigma^{*}}^2} ]
 \end{equation}
-where $\sigma^{*2}$ is some ``universal'' variance depending only on the way the correlated selection of both states is done, not on the molecule considered in our set.
+where $\sigma^{*2}$ is some "universal" variance depending only
+on the way the correlated selection of both states is done, not on the molecule considered in our set.
 
-For each CIPSI calculation, an estimate of $\Delta E_{\text{FCI}}^{(m)}$ is thus
-\begin{equation}
-	\Delta E_\text{FCI}^{(m)} = \frac{ \sum_{n=1}^M  \frac{\Delta E_\text{CIPSI}^{(m)}(n)} {\sigma(n)} }
-            { \sum_{n=1}^M  \frac{1}{\sigma(n)} }
-\end{equation}
-where $M$ is the number of iterations that has been retained to compute the statistical quantities.
-Regarding the estimate of the error on $\Delta E_\text{FCI}^{(m)}$ some caution is required since, although the distribution is globally Gaussian-like
-(see Fig.~\ref{fig:histo}), there exists some significant deviation from it and we must to take this feature into account.
+An estimate of $\Delta E_{\text{FCI}}^{(m)}$ as the average excitation energy of $\Delta E_\text{CIPSI}^{(m)}$ is thus
+$$\Delta E_\text{FCI}^{(m)} = \frac{ \sum_{n=1}^M  \frac{\Delta E_\text{CIPSI}^{(m)}(n)} {\sigma(n)} }
+            { \sum_{n=1}^M  \frac{1}{\sigma(n)} },
+$$
+where $M$ is the number of data kept.
+Now, regarding the estimate of the error on $\Delta E_\text{FCI}^{(m)}$ some caution is required since, although the distribution is globally Gaussian-like
+(see Fig.~\ref{fig:histo}) there exists
+some significant departure from it and we need to take this feature into account.
 
-More precisely, we search for a confidence interval $\mathcal{I}$ such that the true value of the excitation energy $\Delta E_{\text{FCI}}^{(m)}$ lies within one standard deviation of $\Delta E_\text{CIPSI}^{(m)}$, i.e., $P\qty( \Delta E_{\text{FCI}}^{(m)} \in \qty[ \Delta E_\text{CIPSI}^{(m)} \pm \sigma ] \; \Big| \; \mathcal{G}) = p = 0.6827$.
+More precisely, we search for a confidence interval $\mathcal{I}$ such that the true value of the excitation energy $\Delta E_{\text{FCI}}^{(m)}$ lies within one standard deviation of $\Delta E_\text{CIPSI}^{(m)}$, i.e., $P\qty( \Delta E_{\text{FCI}}^{(m)} \in \qty[ \Delta E_\text{CIPSI}^{(m)} \pm \sigma ] \; \Big| \; \mathcal{G}) = 0.6827$.
 In a Bayesian framework, the probability that $\Delta E_{\text{FCI}}^{(m)}$ is in an interval $\mathcal{I}$ is
 \begin{equation}
    P\qty( \Delta E_{\text{FCI}}^{(m)} \in \mathcal{I} ) = P\qty( \Delta E_{\text{FCI}}^{(m)} \in I \Big| \mathcal{G}) \times P\qty(\mathcal{G})
@@ -397,7 +400,7 @@ The inverse of the cumulative distribution function of the $t$-distribution, $t_
    \beta = t_{\text{CDF}}^{-1} \qty[
    \frac{1}{2} \qty( 1 + \frac{0.6827}{P(\mathcal{G})}), M ]
 \end{equation}
-such that $P\qty( \Delta E_{\text{FCI}}^{(m)} \in \qty[ \Delta E_{\text{CIPSI}}^{(m)} \pm \beta \sigma ] ) = p $.
+such that $P\qty( \Delta E_{\text{FCI}}^{(m)} \in \qty[ \Delta E_{\text{CIPSI}}^{(m)} \pm \beta \sigma ] ) = p = 0.6827$.
 Only the last $M>2$ computed transition energies are considered. $M$ is chosen such that $P(\mathcal{G})>0.8$ and such that the error bar is minimal.
 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}.
@@ -408,7 +411,6 @@ states a very good agreement between the CC3 and CCSDT values, indicating that t
 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 and error bars estimated via the extrapolation distance.
 These results contain a good balance between well-behaved and ill-behaved cases.
 For example, cyclopentadiene and furan correspond to well-behaved scenarios where the two flavors of extrapolations yield nearly identical estimates and the error bars associated with these two methods nicely overlap.
@@ -460,9 +462,9 @@ Triazine			&	$^1A_1''(n \ra \pis)$			&	4.85	&	4.84	&	4.77(13)&	5.12(51)	\\
 \hline  % Please only put a hline at the end of the table
 \end{tabular}
 \begin{tablenotes}
-\item $^a$ Excitation energies and error bars \alert{(in eV)} estimated via the novel statistical method based on Gaussian random variables (see Sec.~\ref{sec:error}).
+\item $^a$ Excitation energies and error bars estimated via the novel statistical method based on Gaussian random variables (see Sec.~\ref{sec:error}).
 The error bars reported in parenthesis correspond to one standard deviation.
-\item $^b$ Excitation energies obtained via a three-point linear fit using the three largest CIPSI variational wave functions, and error bars \alert{(in eV)} estimated via the extrapolation distance, \ie, the difference in excitation energies obtained with the three-point linear extrapolation and the largest CIPSI wave function.
+\item $^b$ Excitation energies obtained via a three-point linear fit using the three largest CIPSI 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 CIPSI wave function.
 \end{tablenotes}
 \end{threeparttable}
 \end{table}
@@ -579,8 +581,9 @@ In addition, QUEST is composed by 24 open-shell molecules with a single unpaired
 Amongst these excited states, 485 of them are considered as ``safe'', \ie, chemically-accurate for the considered basis set and geometry.
 Besides this energetic criterion, we consider as ``safe'' transitions that are either: i) computed with FCI or CCSDTQ, or ii) in which the difference between CC3 and CCSDT excitation energies is small (\ie, around $0.03$--$0.04$ eV) with a large $\%T_1$ value.
 
-\begin{center}
+\begin{ThreePartTable}
 \scriptsize
+\centering
 \begin{longtable}{clccccclc}
 \caption{Theoretical best estimates TBEs (in eV), oscillator strengths $f$, percentage of single excitations $\%T_1$ involved in the transition (computed at the CC3 level) for the full set of closed-shell compounds of the QUEST database.
 ``Method'' provides the protocol employed to compute the TBEs.
@@ -949,7 +952,7 @@ AVXZ stands for aug-cc-pVXZ.
 345	&		&	$^1A'    (\text{n.d.})$	&	R	&	92	&	0.038	&	6.27	&	CCSDTQ/AVDZ + [CCSDT/AVTZ - CCSDT/AVDZ]	&	Y	\\
 346	&		&	$^3A''    (n \ra \pi^*)$	&	V	&	99	&		&	0.88	&	FCI/AVTZ	&	Y	\\
 347	&		&	$^3A'    (\pi \ra \pi^*)$	&	V	&	98	&		&	5.61	&	FCI/AVTZ	&	Y	\\
-348	&	Octatetraene	&	$^1B_u    (\pi \ra \pi^*)$	&	V	&	91	&	1.557	&	4.78	&	CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)]	&	Y	\\
+348	&	Octatetraene	&	$^1B_u    (\pi \ra \pi^*)$	&	V	&	91	&	(\text{n.d.})	&	4.78	&	CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)]	&	Y	\\
 349	&		&	$^1A_g (\pi \ra \pi^*)$	&	V	&	63	&		&	4.90	&	CCSDT/6-31+G(d) + [CC3/AVTZ - CC3/6-31+G(d)]	&	N	\\
 350	&		&	$^3B_u (\pi \ra \pi^*)$	&	V	&	97	&		&	2.36	&	CC3/AVTZ	&	N	\\
 351	&		&	$^3A_g (\pi \ra \pi^*)$	&	V	&	98	&		&	3.73	&	CC3/AVTZ	&	N	\\
@@ -1103,7 +1106,7 @@ AVXZ stands for aug-cc-pVXZ.
 499	&	                              	&	$^3A_2    (n \ra 3p)$	&	R	&	98	&		&	9.24	&	FCI/AVTZ	&	Y	\\
 500	&		&	$^3A_1    (n \ra 3s)$	&	R	&	98	&		&	9.54	&	FCI/AVTZ	&	Y	\\
 \end{longtable}
-\end{center}
+\end{ThreePartTable}
 
 %%% TABLE III %%%
 \begin{table}[htp]
@@ -1183,8 +1186,6 @@ Additionally, we also provide a specific analysis for each type of excited state
 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 ``safe'' excitations having a dominant single excitation character (\ie, the double excitations are discarded).
 Similar graphs are reported in the {\SupInf} for specific sets of transitions and molecules.
-\alert{The comparison between methods presented here is performed for Franck-Condon geometries only.
-Then, it is important to stress that the present method ranking might change significantly when moving away from the Franck-Condon region as most excited-state methods do not provide a uniform description of potential energy surfaces.}
 
 %%% TABLE IV %%%
 \begin{sidewaystable}
@@ -1259,12 +1260,10 @@ Concerning the second-order methods (which have the indisputable advantage to be
 A very similar ranking is obtained when one looks at the MSEs.
 It is noteworthy that the performances of EOM-MP2 and CCSD are getting notably worse when the system size increases, while CIS(D) and STEOM-CCSD have a very stable behavior with respect to system size.
 Indeed, the EOM-MP2 MAE attains 0.42 eV for molecules containing between 7 and 10 non-hydrogen atoms, whereas the CCSD tendency to overshoot the transition energies yield a MSE of 0.22 eV for the same set (a rather large error).
-
 For CCSD, this conclusion fits benchmark studies published by other groups \cite{Schreiber_2008,Caricato_2010,Watson_2013,Kannar_2014,Kannar_2017,Dutta_2018}.
 For example, K\'ann\'ar and Szalay obtained a MAE of 0.18 eV on Thiel's set for the states exhibiting a dominant single excitation character.
 The CCSD degradation with system size might partially explain the similar (though less pronounced) trend obtained for CCSDR(3).
 Regarding the apparently better performances of STEOM-CCSD as compared to CCSD, we recall that several challenging states have been naturally removed from the STEOM-CCSD statistics because the active character percentage was lower than $98\%$ (see above).
-
 In contrast to EOM-MP2 and CCSD, the overall accuracy of CC2 and ADC(2) does significantly improve for larger molecules, the performances of the two methods being, as expected, similar \cite{Harbach_2014}.
 Let us note that these two methods show similar accuracies for singlet and triplet transitions, but are significantly less accurate for Rydberg transitions, as already pointed out previously \cite{Kannar_2017}.
 Therefore, both CC2 and ADC(2) offer an appealing cost-to-accuracy ratio for large compounds, which explains their popularity in realistic chemical scenarios \cite{Hattig_2005c,Goerigk_2010a,Send_2011a,Winter_2013,Jacquemin_2015b,Oruganti_2016}.
@@ -1316,28 +1315,18 @@ Paraphrasing Thiel's conclusions \cite{Schreiber_2008}, we hope that not only th
 In this framework, we provide in the {\SupInf} a file with all our benchmark data.
 
 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 \cite{Hodecker_2019,Eriksen_2020b} such as dipoles and oscillator strengths for molecules of small and medium sizes \cite{Chrayteh_2021,Sarkar_2021}, so as to complete previous efforts aiming at determining accurate excited-state geometries \cite{Budzak_2017,Jacquemin_2018}.
-\alert{In this context, methods for which one has access to analytic nuclear gradients [\eg, ADC(2) and CC2] and frequencies [\eg, EOM-CCSD] have an indisputable edge.}
 Reference ground-state properties (such as correlation energies and atomization energies) are also being currently produced \cite{Scemama_2020,Loos_2020e}.
-\alert{Additional reference energies for charge-transfer excited states \cite{Kozma_2020} and transition metal compounds \cite{Zhao_2006,Williams_2020} would be a valuable addition to the present database.}
 Besides this, because computing 500 (or so) excitation energies can be a costly exercise even with cheap computational methods, we are planning on developing a ``diet set'' (\ie, a much smaller set of excitation energies which can reproduce key results of the full QUEST database, including ranking of approximations) following the philosophy of the ``diet GMTKN55'' set proposed recently by Gould \cite{Gould_2018b}.
 We hope to report on this in the near future.
 
-
-
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%\section*{acknowledgements}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%AS, MC, and PFL thank the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant agreement No.~863481) for financial support.
-%Support from the \textit{``Centre National de la Recherche Scientifique''} is acknowledged.
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section*{research resources}
+\section*{acknowledgements}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%
 This work was performed using HPC resources from GENCI-TGCC (Grand Challenge 2019-gch0418) and from CALMIP (Toulouse) under allocation 2020-18005.
+AS, MC, and PFL thank the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant agreement No.~863481) for financial support.
+Funding from the \textit{``Centre National de la Recherche Scientifique''} is also acknowledged.
 DJ acknowledges the \textit{R\'egion des Pays de la Loire} for financial support and the CCIPL computational center for ultra-generous allocation of computational time.
 
-
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section*{conflict of interest}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Manuscript/SI/QUEST_WIREs-SI.tex

@@ -203,7 +203,7 @@ For the dipole-allowed transitions, we provide the corresponding values of the o
 \headrow			&	 Nature	 		& $f$		& \%$T_1$& {\Pop} 	& {\AVDZ} & {\AVTZ}& {\Pop} 	& {\AVDZ}  	&Th.$^a$	&Th.$^b$	&Th.$^c$	&Exp.$^d$	&Exp.$^e$&Exp.$^f$		&Exp.$^g$\\	
 Benzoquinone		&$^1B_{1g}  (n \ra \pis)$	&		&85.3	&2.85	&2.81	&2.79	&2.87	&2.84		&2.50	&2.39	&2.74	&			&		&2.52		&2.49	\\
 				&$^1A_u	 (n \ra \pis)$	&		&84.1	&2.99	&2.95	&2.94	&3.01	&2.97		&2.50	&2.43	&2.86	&			&		&2.49		&2.48	\\
-				&$^1A_g (n,n  \ra \pis,\pis)$ &		&0.0		&5.92	&5.94	&6.02	&5.79	&5.83		&4.41	&4.36	&		&			&		&			&\\
+				&$^1A_g (n,n  \ra \pis,\pis)$ &		&0.0		&5.92	&5.94	&6.02	&5.79	&5.84		&4.41	&4.36	&		&			&		&			&\\
 				&$^1B_{3g} (\pi \ra \pis)$	&		&88.6	&4.66	&4.58	&4.53	&4.71	&4.63		&4.19	&4.01	&4.44	&4.3			&4.09	&4.07		&\\
 				&$^1B_{1u} (\pi \ra \pis)$	&0.471	&88.4	&5.71	&5.63	&5.58	&5.75	&5.67		&5.15	&5.09	&5.47	&5.38--5.70	&5.08	&5.12		&\\
 				&$^1B_{3u} (n \ra \pis)$	&0.001	&79.8	&5.95	&5.77	&5.75	&5.96	&5.81		&5.15	&4.91	&5.71	&			&		&			&\\

Response_Letter/Response_Letter.tex

@@ -1,154 +0,0 @@
-\documentclass[10pt]{letter}
-\usepackage{UPS_letterhead,xcolor,mhchem,mathpazo,ragged2e,hyperref}
-\newcommand{\alert}[1]{\textcolor{red}{#1}}
-\definecolor{darkgreen}{HTML}{009900}
-
-
-\begin{document}
-
-\begin{letter}%
-{To the Editors of WIREs Comput. Mol. Sci.}
-
-\opening{Dear Editors,}
-
-\justifying
-Please find attached a revised version of the manuscript entitled 
-\begin{quote}
-	\textit{``QUESTDB: a database of highly-accurate excitation energies for the electronic structure community''}.
-\end{quote}
-We thank the reviewers for their constructive comments.
-Our detailed responses to their comments can be found below.
-For convenience, changes are highlighted in red in the revised version of the manuscript. 
-
-We look forward to hearing from you.
-
-\closing{Sincerely, the authors.}
-
-%%% REVIEWER 1 %%%
-\noindent \textbf{\large Authors' answer to Reviewer \#1}
-
-\begin{itemize}
-
-	\item 
-	{This focus article by V\'eril et al. proposes a detailed analysis of the performances of current electronic structure methods to describe excitation energies. 
-	This review is based on the authors' past and current efforts to develop a large dataset of accurate vertical excitation energies for various types of molecules, to which the result of other methods can be compared. 
-	This last point is particularly crucial as the use of experimental data to benchmark electronic transitions can be quite challenging (as experimental values do not only reflect the change of electronic character but also encodes contribution from the nuclear degrees of freedom). 
-	In this work, the authors summarize their detailed benchmark and introduce a very exciting web platform that allows any user to test and compare the different methods for specific properties, as they want. 
-	This web platform allows moving beyond the typical benchmark proposed in articles and doing way more with the data collected. 
-	I warmly welcome such a contribution in the field and recommend this work for publication in WIRES Comput. Mol. Sci.
-	I have a few comments/suggestions that the authors may want to consider.}
-	\\
-	\alert{We thank the reviewer for his/her kind comments.}
-
-	\item 
-	{For any benchmark presentation, I believe that the limits of validity should be identified and made clear to the reader to prevent any misuse or misunderstanding. 
-	In this review, I feel that some more points might need to be stressed to achieve this. 
-	The comparison between methods presented here is performed for Franck-Condon (ground-state) geometries only. 
-	It is then essential to stress that the ranking of the electronic structure methods (as nicely illustrated in Fig. 5) might change significantly when moving away from the Franck-Condon region. 
-	Most electronic structure methods for excited states cannot provide a uniform description of potential energy surfaces, being more accurate in certain regions than in others.}
-	\\
-	\alert{We have added a comment in the benchmarks section.}
-	
-	\item 
-	{The discussion is based on electronic energies. 
-	While electronic energies are important, investigation of excited electronic state often requires additional quantities due to the importance played by nuclear motion and coordinates. 
-	Some of this is already discussed in substance in the last paragraph of the conclusion, but offering some information about which methods can provide nuclear gradients or Hessians would be valuable for the reader.}
-	\\
-	\alert{A sentence has been added to clarity this point in the concluding section.}
- 
-	\item 
-	{While many different molecules are discussed in this work, I think that a caveat about the performance of some of the methods presented for other families of molecules might be welcome. 
-	(The authors mention a few different types of molecules in the introduction, but it might be interesting to stress them at the end of this work too.)}
-	\\
-	\alert{Another comment has been added in the concluding section.}
-	
-\end{itemize}
-
-%%% REVIEWER 2 %%%
-\noindent \textbf{\large Authors' answer to Reviewer \#2}
-
-\begin{itemize}
-
-	\item 
-	{It is my pleasure to review "QUESTDB: a database of highly-accurate excitation energies for the electronic structure community" by V\'eril et al for consideration in WIREs as a Focus Article. 
-	The manuscript is easy to follow and very comprehensive. 
-	I have no hesitation in recommend it for publication.
-
-	Firstly, I have to commend the authors on making their paper easy to follow. 
-	I am only passingly familiar with many of the methods they test. 
-	Despite this, I gained a good understanding of why they had made the choices they made, and why they should be right. 
-	That is not a minor undertaking.
-
-	The manuscript is also structured exceedingly well with a logical path from start to finish. 
-	It explains why the QUEST work is important, how it was done, and what remains to be done.
-
-	I do have a number of minor suggestions, identified below. 
-	Once these are addressed, I would argue that the paper is more than ready for publication and will make an outstanding contribution to the field.}
-	\\
-	\alert{We would like to thank the reviewer for his/her support.}
-
-	\item 
-	{MGCDB84 by Madirossian and Head-Gordon [10.1080/00268976.2017.1333644] seems to be missing (or at least not highlighted) from the list of ground state benchmark sets despite being one of the largest.}
-	\\
-	\alert{The reviewer is right. The work of Madirossian and Head-Gordon is now mentioned and cited in the Introduction.}
-	
-	\item 
-	{p6: The third paragraph is a lot to take in and should probably be split into two or three paragraphs to make reading a bit easier.}
-	\\
-	\alert{This paragraph has been split.}
- 
-	\item 
-	{p7 line 47-48: The wording of the final sentence on this page makes spin-symmetry breaking sound acceptable. 
-	While I don't disagree that some (perhaps most) quantum chemists would agree, for those of us on the opposing side I'd like to see a caveat (e.g. which is, unlike common wisdom about).}
-	\\
-	\alert{This comment has been reworded accordingly.}
-
-	\item 
-	{p10-11: Final/start paragraph of p10/p11 should probably be split into two or three.}
-	\\
-	\alert{These paragraphs have been split.}
-	
-	\item 
-	{Table 1: Are the error bars in eV? This does not seem to be stated.}
-	\\
-	\alert{Yes, they are and it is now mentioned. Thank you for spotting this.}
-	
-	\item 
-	{Table 2: I would suggest to use italic numbers for "unsafe" TBE so that readers can easily identify them.}
-	\\
-	\alert{There is already a label Y/N to identify the unsafe TBEs, so we would prefer to leave it as it is.
-	Moreover, these data can be also extracted from the website (there is a box to select only the safe TBEs) or the excel spreadsheet provided as supplementary material.}
-		
-	\item 
-	{Table 4: This is purely a matter of taste and 100\% optional given that the authors provide online access to data. 
-	But, I think readers might benefit from having the table reported as two horizontal panels, with one reporting up to CC3 and the other the rest. 
-	The reason being that many people now read on a screen, where rotation is more annoying than on paper.}
-	\\
-	\alert{Again, these data are also reported as supplementary material, so we propose to leave Table 4 as it is.}
-		
-	\item 
-	{Figure 5: This is an excellent figure!}
-	\\
-	\alert{Thank you!}
-		
-	\item 
-	{p27: the second full paragraph should probable by split in two or three (yes, this is a theme).}
-	\\
-	\alert{Not a problem. This paragraph has been split.}
-		
-	\item 
-	{Finally, on a technical note I suspect that the authors may need to test some more (lower quality) methods to get sufficient statistical accuracy for dieting. 
-	The distributions in Figure 5 suggest quite a lot of correlation between the lower accuracy methods tested so far (e.g. CIS(D), CC2 and ADC(2) have very similar error distributions).}
-	\\
-	\alert{Yes, we are aware of this. We would like to thank the reviewer for pointing this out.}
-%	We have added a sentence at the end of the manuscript to mention it.}	
-\end{itemize}
- 
-\end{letter}
-\end{document}
-
-
-
-
-
-

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-\changefontsizes[13\p@]{8\p@}
-
-% sectional headings
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-  \newcommand{\allcaps}[2][10.0]{\addfontfeature{LetterSpace=#1}\MakeTextUppercase{#2}}
-  %% Fake small caps
-  \renewcommand{\textsc}[1]{{\addfontfeature{LetterSpace=10.0,Scale=0.8}\MakeTextUppercase{#1}}}
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-  \ifpdf
-    \newcommand{\allcaps}[2][]{\textls*[#1]{\MakeTextUppercase{#2}}}
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-    \newcommand{\allcaps}[2][]{\MakeTextUppercase{#2}}
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-
-\titleformat{\section}
-  {\fontsize{10pt}{13\p@}\bfseries}
-  {\thesection}{1em}{\textmd{|}\quad\allcaps{#1}}
-
-\newcommand{\backmatter}{%
-  \titleformat{\section}
-    {\fontsize{10pt}{13\p@}\bfseries}
-    {}{0pt}{\allcaps{##1}}%
-  \titlespacing*{\section}{0pt}{ 1.5\baselineskip}{0.5\baselineskip}
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-\ifxetexorluatex
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-    {\fontsize{10pt}{13\p@}\scshape\bfseries}
-    {}{0pt}{#1}
-  \fi
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-\titleformat{\subsection}
-  {\fontsize{10pt}{13\p@}\bfseries}
-  {\thesubsection}{1em}{\textmd{|}\quad#1}
-
-\titlespacing*{\subsection}{0pt}{1.5\baselineskip}{0.5\baselineskip}
-
-\titleformat{\subsubsection}
-  {\fontsize{10pt}{13\p@}\bfseries}
-  {\thesubsubsection}{1em}{\textmd{|}\quad#1}
-\titlespacing*{\subsubsection}{0pt}{1.5\baselineskip}{0.5\baselineskip}
-
-\ifxetexorluatex
-  \titleformat{\paragraph}[hang]
-    {\fontsize{8.5\p@}{13\p@}\fontspec{Lato Black}\color{black!75}}
-    {\theparagraph}{0pt}{#1}
-  \titleformat{name=\paragraph,numberless}[hang]
-    {\fontsize{8.5\p@}{13\p@}\fontspec{Lato Black}}
-    {}{0pt}{#1}
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-  \titleformat{\paragraph}[hang]
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-    {\theparagraph}{0pt}{#1}
-  \titleformat{name=\paragraph,numberless}[hang]
-    {\fontsize{8.5\p@}{13\p@}\fontseries{eb}\selectfont}
-    {}{0pt}{#1}
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-\titlespacing*{\paragraph}{0pt}{\baselineskip}{0pt}
-
-\ifxetex
-  \titleformat{\subparagraph}[runin]
-    {\normalsize\fontspec{Lato Black}\color{black!75}}
-    {\thesubparagraph}{0pt}{#1}
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-    {\normalsize\fontseries{eb}\selectfont\color{black!75}}
-    {\thesubparagraph}{0pt}{#1}
-\fi
-\titlespacing*{\subparagraph}{0pt}{\baselineskip}{1em}
-
-
-% Formatting of footer for first page
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-\def\blfootnote{\gdef\@thefnmark{}\@footnotetext}
-\appto{\footnotelayout}{\fontsize{6\p@}{9\p@}\selectfont}
-\renewcommand{\footnoterule}{\noindent\textcolor{black!50}{\rule{\textwidth}{0.5\p@}}\vskip2\p@}
-
-
-%% Headers
-\RequirePackage{fancyhdr}
-\fancyhf{}
-\renewcommand{\headrule}{}
-\fancyhead[LO]{{\fontsize{7\p@}{13\p@}\selectfont%
-  \setlength{\arrayrulewidth}{.5\p@}%
-  \arrayrulecolor{black}%
-  \begin{tabularx}{\textwidth}{@{}X r | r @{}}%
-  \textsc{\@runningauthor} & & \thepage\\\hline
-  %& %\multicolumn{1}{r}{%
-    %\raisebox{0pt}[0pt][0pt]{\includegraphics[height=2.5em]{\@jlogo}}%
-    %\quad%
-    %\raisebox{0.25em}[0pt][0pt]{\colorbox{white}{\includegraphics[height=2em]{Wiley_Wordmark_black}}}} & \\
-\end{tabularx}%
-}}
-
-\fancyhead[LE]{{\fontsize{7\p@}{13\p@}\selectfont%
-  \setlength{\arrayrulewidth}{.5\p@}%
-  \arrayrulecolor{black}%
-  \begin{tabularx}{\textwidth}{@{}l | l >{\raggedleft\arraybackslash}X @{}}%
-  \thepage & & \textsc{\@runningauthor}\\\hline
-%   \multicolumn{1}{@{}c}{} &
-%   \raisebox{0.25em}[0pt][0pt]{\colorbox{white}{\includegraphics[height=2em]{Wiley_Wordmark_black}}}%
-%   \quad%
-%   \raisebox{0pt}[0pt][0pt]{\includegraphics[height=2.5em]{\@jlogo}}\\
-  \end{tabularx}%
-}}
-
-%% First page header + footer
-\fancypagestyle{firstpage}{
-%   \renewcommand{\footrule}{\hdashrule{\textwidth}{0.5\p@}{2\p@}\\[-2\p@]}
-
-  \fancyhead[L]{\fontsize{7\p@}{13\p@}\selectfont%
-  \setlength{\arrayrulewidth}{.5\p@}%
-  \arrayrulecolor{black}%
-  \begin{tabularx}{\textwidth}{@{}l | l | X @{}}%
-  \ifdefempty{\@paperreceived}
-    {\multicolumn{3}{l}{}}
-    {Received: \@paperreceived &
-  Revised: \@paperrevised &
-  Accepted: \@paperaccepted}
-  \\\hline
-  \ifdefempty{\@paperdoi}{}{\multicolumn{3}{@{}l}{DOI: \@paperdoi}}
-  \end{tabularx}}
-
-  \fancyfoot[L]{%\fontsize{7\p@}{10pt}\selectfont%
-%   \setlength{\arrayrulewidth}{.5\p@}%
-%   \arrayrulecolor{black}\raggedright%
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-%   \begingroup
-  \fontsize{7\p@}{13\p@}\selectfont%
-  \begin{tabularx}{\textwidth}{@{}X  >{\centering\arraybackslash}X  r | r @{}}%
-  \hline
-  \ifdefempty{\@paperreceived}{& & & }{%
-  \textit{\@jname}~\@jyear; \@jvolume: \@jpages &
-  \@jwebsite &
-  \textcopyright~\@jyear\space Wiley Periodicals, Inc. &
-  }
-  \thepage
-  \end{tabularx}%
-%   \endgroup
-  }
-}
-
-% For adding notes about author contributions
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-  \blfootnote{\textsuperscript{#1}#2}%
-}
-
-
-% Author and affiliation fonts
-\setcounter{Maxaffil}{1}
-\renewcommand{\Authsep}{\quad|\quad}
-\renewcommand{\Authand}{\quad|\quad}
-\renewcommand{\Authands}{\quad|\quad}
-\renewcommand{\Authfont}{\fontsize{12\p@}{20pt}\bfseries\raggedright}
-\renewcommand{\Affilfont}{\fontsize{7\p@}{10pt}\selectfont\raggedright}
-\renewcommand\AB@authnote[1]{\textsuperscript{#1}}
-\patchcmd{\AB@affilsepx}{\\}{\\[3\p@]}{}{}
-
-\patchcmd{\@author}{\AB@authlist\\[\affilsep]\AB@affillist}{\AB@authlist}{}{}
-
-% % \AtBeginDocument{
-%   \if@blindreview
-%     \let\oldauthor\author
-%     \let\oldaffil\affil
-%     \renewcommand{\author}[2][]{\oldauthor{Author}}
-%     \renewcommand{\affil}[2][]{\oldaffil{An affiliation}}
-% % %     \def\AB@authors{Anonymous Authors}
-% %     \def\AB@affillist{Anonymous Affiliations}
-%   \fi
-% % }
-
-% Title
-\renewcommand{\maketitle}{%
-  \if@blindreview
-    \def\AB@authlist{\Authfont Anonymous Authors}
-    \def\AB@affillist{\Affilfont Anonymous Affiliations}
-    \def\@runningauthor{Authors (Anon)}
-    \def\@corraddress{Anonymous correspoundence}
-    \def\@corremail{anon@example.com}
-    \def\@presentaddress{Anonymous present address}
-    \def\@fundinginfo{Anonymous funders}
-  \fi
-  \vspace*{\dimexpr 27\p@-2\baselineskip}%
-  \noindent\begingroup%
-  \setul{3\p@}{1\p@}%
-  \ifxetexorluatex\fontspec{Lato Heavy}\else\fontseries{eb}\selectfont\fi
-  {\fontsize{9\p@}{15\p@}\allcaps[\ifxetexorluatex 20\else 200\fi]{\ul{\@papertype}}}
-  \ifdefempty{\@jlogo}{\rule{0pt}{2em}}{%
-  \hfill%
-%   \includegraphics[height=1.5em]{Wiley_Wordmark_black}%
-%   \quad%
-  \includegraphics[height=2em]{\@jlogo}}
-  \\[2\p@]%
-  {\fontsize{8\p@}{15\p@}%
-  \ifxetexorluatex
-    \addfontfeature{LetterSpace=20.0}\@paperfield%
-  \else
-    \ifpdf
-    \textls*[150]{\@paperfield}%
-    \else
-    \@paperfield
-    \fi
-  \fi}
-  \endgroup%
-  \vskip13\p@%
-  {\fontsize{18\p@}{23\p@}\bfseries\raggedright\@title\par}
-  \vskip27\p@%
-  \noindent\begin{minipage}{0.8\textwidth}\@author\end{minipage}%
-  \vskip21\p@%
-  \thispagestyle{firstpage}
-}
-
-% Affiliation + other metadata
-\newcommand{\wiley@affilmetadata}{%
-  \AB@affillist\par%
-  \vskip10pt%
-  \textbf{Correspondence}\\
-  \@corraddress\\
-  Email: \@corremail\par
-  \ifx\empty\@presentaddress
-  \else%
-    \vskip10pt%
-    \textbf{Present address}\\
-    \@presentaddress\par
-  \fi%
-  \vskip10pt%
-  \textbf{Funding information}\\
-  \@fundinginfo\par
-  \ifdefempty{\@papereditor}{}
-  {\vskip10pt Editor: \@papereditor\par}
-}
-
-%% Abbreviations in the footnote
-\newcommand{\abbrevs}[1]{\blfootnote{\textbf{Abbreviations:} #1\\[-3\p@]}}
-
-%% Abstract and affiliation in the margin
-\RequirePackage{changepage}
-\RequirePackage{environ}
-\reversemarginpar
-\newlength{\wiley@affilmetadataheight}
-\newlength{\wiley@abstractheight}
-\NewEnviron{wiley@abstract}{%
-  \newcommand{\keywords}[1]{%
-    \vskip8\p@%
-    \noindent{\bfseries\fontsize{7\p@}{13\p@}\allcaps[\ifxetexorluatex 20\else 200\fi]{keywords}\par}
-    \noindent{\raggedright\fontsize{8\p@}{13\p@}\selectfont ##1\par}
-  }%
-  \strictpagecheck%
-  \begin{adjustwidth*}{\dimexpr 54.9mm-6.5\p@}{}%
-  \setlength{\marginparsep}{-47mm}%
-  \setlength{\marginparwidth}{47mm}%
-  %% Measure the height of the affil metadata in the sidebar
-  \settototalheight{\wiley@affilmetadataheight}{\parbox{\marginparwidth}{\wiley@affilmetadata}}%
-  \newsavebox{\wiley@abstractbox}%
-  %% Save the abstract text in a box
-  \savebox{\wiley@abstractbox}{%
-    \parbox{\linewidth}{%
-    \begin{mdframed}[font=\fontsize{9\p@}{15\p@}\selectfont,
-      topline=false,bottomline=false,
-      leftline=true,rightline=false,
-      backgroundcolor=black!10,
-      middlelinewidth=6\p@,middlelinecolor=white,
-      outerlinewidth=0.5\p@]
-      \BODY
-    \end{mdframed}}%
-  }%
-  \settototalheight{\wiley@abstractheight}{\usebox{\wiley@abstractbox}}%
-  \marginpar{\wiley@affilmetadata}\vskip-1.5em%
-  \begin{mdframed}[font=\fontsize{9\p@}{15\p@}\selectfont,
-  topline=false,bottomline=false,
-  leftline=true,rightline=false,
-  backgroundcolor=black!10,
-  middlelinewidth=6\p@,middlelinecolor=white,
-  outerlinewidth=0.5\p@]%
-  \BODY
-  \end{mdframed}%
-  %% If the affildata is taller than the abstract, add vskip
-  \ifdimgreater
-    {\wiley@affilmetadataheight}
-    {\wiley@abstractheight}
-    {\vskip\dimexpr\wiley@affilmetadataheight-\wiley@abstractheight+\baselineskip\relax}{}
-}[\end{adjustwidth*}]%
-
-\renewcommand{\abstract}{\wiley@abstract}
-\renewcommand{\endabstract}{\endwiley@abstract}
-
-% quotes and epigraphs
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-\quotingsetup{vskip=\baselineskip,indentfirst=false,font={itshape,RaggedRight,normalsize},leftmargin=26\p@,rightmargin=26\p@}
-
-\renewenvironment{quote}{\begin{quoting}}{\end{quoting}}
-
-\renewenvironment{quotation}{\begin{quoting}}{\end{quoting}}
-
-\newenvironment{epigraph}[1]
-{\begin{quoting}\def\@quotesource{#1}}
-{\par\hfill\@quotesource\end{quoting}}
-
-\newenvironment{pullquote}
-{\begin{quoting}[vskip=\dimexpr 39\p@-23\p@\relax,leftmargin=12\p@,rightmargin=12\p@,font+={raggedright},begintext={\fontsize{18\p@}{23\p@}\selectfont\color{black!50}}]}
-{\end{quoting}}
-
-% Enum/itemized
-\RequirePackage[inline]{enumitem}
-\setlist{nosep,font=\bfseries,leftmargin=*,align=left}
-\setlist[1]{topsep=\baselineskip,leftmargin=\parindent,labelsep=*,labelwidth=*}
-\setlist[enumerate,2]{label={\alph*.},}
-
-% Space above/below equations
-\g@addto@macro\normalsize{%
-  \setlength\abovedisplayskip{\baselineskip}%
-  \setlength\belowdisplayskip{\baselineskip}%
-  \setlength\abovedisplayshortskip{\baselineskip}%
-  \setlength\belowdisplayshortskip{\baselineskip}%
-}
-
-% All the popular math environments
-\newtheorem{theorem}{Theorem}
-\newtheorem{lemma}[theorem]{Lemma}
-\newtheorem{proposition}[theorem]{Proposition}
-\newtheorem{corollary}[theorem]{Corollary}
-
-\newenvironment{proof}[1][Proof]{\begin{trivlist}
-\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}
-\newenvironment{definition}[1][Definition]{\begin{trivlist}
-\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}
-\newenvironment{example}[1][Example]{\begin{trivlist}
-\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}
-\newenvironment{remark}[1][Remark]{\begin{trivlist}
-\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}
-
-\newcommand{\qed}{\nobreak \ifvmode \relax \else
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-      \hskip1.5em plus0em minus0.5em \fi \nobreak
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-
-% Captions
-\RequirePackage[tableposition=top]{caption}
-\DeclareCaptionFont{captionfont}{\fontsize{8\p@}{11\p@}\selectfont}
-\DeclareCaptionFont{boxcaption}{\fontsize{9\p@}{13\p@}\selectfont}
-\ifxetexorluatex
-  \DeclareCaptionFont{heavy}{\fontspec{Lato Black}}
-  \DeclareCaptionLabelFormat{allcaps}{\addfontfeature{LetterSpace=15.0}{\MakeTextUppercase{#1}~#2}}
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-  \DeclareCaptionFont{heavy}{\fontseries{eb}}
-  \ifpdf
-  \DeclareCaptionLabelFormat{allcaps}{\textls[150]{\MakeTextUppercase{#1}~#2}}
-  \else
-  \DeclareCaptionLabelFormat{allcaps}{\MakeTextUppercase{#1}~#2}
-  \fi
-\fi
-\captionsetup*{justification=raggedright,singlelinecheck=false,font=captionfont,labelformat=allcaps,labelfont={heavy},labelsep=quad}
-\captionsetup*[table]{skip=0.5ex}
-
-% Tables
-\AtBeginEnvironment{table}{%
-  \fontsize{7.5\p@}{10.5\p@}\selectfont%
-  \rowcolors*{3}{black!10}{}%
-  \renewcommand{\arraystretch}{1.25}%
-  \arrayrulecolor{black!20}%
-  \setlength{\arrayrulewidth}{1\p@}%
-}
-
-\RequirePackage{threeparttable}
-\renewcommand{\TPTnoteSettings}{\leftmargin=0pt}
-\newcommand{\headrow}{\rowcolor{black!20}}
-\newcommand{\thead}[1]{\multicolumn{1}{l}{\bfseries #1\rule[-1.2ex]{0pt}{2em}}}
-
-%% Boxes!
-\RequirePackage{newfloat}
-\DeclareFloatingEnvironment[placement=bt,name=box]{featurebox}
-\captionsetup*[featurebox]{skip=1em,labelformat={default},font={heavy,boxcaption},labelfont={sc,color=black!75}}
-\AtBeginEnvironment{featurebox}{%
-  \setlist*{topsep=0pt}%
-}
-\apptocmd{\featurebox}{%
-  \begin{mdframed}[linewidth=5\p@,linecolor=black!20,
-  innerleftmargin=12\p@,innerrightmargin=12\p@,
-  innertopmargin=12\p@,innerbottommargin=12\p@]
-}{}{}
-\pretocmd{\endfeaturebox}{\end{mdframed}}{}{}
-
-
-% Skips for floats
-\setlength{\floatsep}{1.5\baselineskip}
-\setlength{\intextsep}{\baselineskip}
-\setlength{\textfloatsep}{1.5\baselineskip}
-
-% The endnotes
-\RequirePackage{enotez}
-\newlist{enotezlist}{itemize}{1}
-\setlist[enotezlist,1]{leftmargin=*,label=\arabic*,labelsep=0.25em,itemsep=0pt,topsep=0.5\baselineskip}
-\EditInstance{enotez-list}{itemize}
-{list-type=enotezlist}
-\setenotez{list-name={endnotes},list-style=itemize}
-\EditInstance{enotez-list}{itemize}{
-  format=\fontsize{7.5\p@}{10.5\p@}\selectfont,
-  number = \textsuperscript{#1}
-}
-
-% References
-\if@numrefs
-  \RequirePackage[numbers]{natbib}
-  \bibliographystyle{vancouver-authoryear}
-\fi
-\if@alpharefs
-    \RequirePackage{natbib}
-    \bibliographystyle{rss}
-\fi
-\if@amsrefs
-  \RequirePackage{amsrefs}
-  \let\citep\cite
-  \let\citet\ocite
-  \renewcommand{\biblistfont}{\fontsize{7.5\p@}{10.5\p@}\selectfont}
-\fi
-
-\AtBeginDocument{
-  \@ifpackageloaded{natbib}{
-    \setlength{\bibhang}{1.5em}
-    \renewcommand{\bibfont}{\fontsize{7.5\p@}{10.5\p@}\selectfont}
-    \renewcommand{\refname}{references}
-    \renewcommand{\bibname}{references}
-  }{}
-
-  \@ifpackageloaded{amsrefs}{
-    \renewcommand{\biblistfont}{\fontsize{7.5\p@}{10.5\p@}\selectfont}
-	\renewcommand{\refname}{references}
-	\renewcommand{\bibname}{references}
-  }{}
-}
-
-% Author biography
-\RequirePackage{lettrine}
-\newenvironment{biography}[2][]
-{\begin{mdframed}
-  [linewidth=0.5\p@,skipabove=1.5\baselineskip,%nobreak,
-    innerleftmargin=6\p@,innerrightmargin=6\p@,
-    innertopmargin=6\p@,innerbottommargin=6\p@]
-  \ifstrequal{#1}{}{}
-  {\lettrine[image,lines=5,findent=1em,nindent=0pt]{#1}{}}%
-  {\bfseries\scshape #2}}
-{\end{mdframed}}
-
-\newcommand{\otherinfo}[2][]{%
-  \backmatter%
-  \ifstrequal{#1}{suppinfo}
-  {\section{Supporting Information}
-  Additional Supporting Information may be found online in the supporting information for this article.}
-  {}
-
-  \begin{mdframed}
-  [linewidth=1\p@,linecolor=black!40,nobreak,
-    innerleftmargin=12\p@,innerrightmargin=12\p@,
-    innertopmargin=12\p@,innerbottommargin=12\p@,
-    skipabove=\baselineskip]
-  \textbf{How to cite this article:} #2
-  \end{mdframed}
-}
-
-\newenvironment{graphicalabstract}[1]{%
-  \backmatter
-  \section{graphical abstract}
-  \lettrine[image,lines=10,findent=1em,nindent=0pt]{#1}{}%
-}{}
-
-% Here we go!
-\normalsize
-\pagestyle{fancy}