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\begin{document}
\title{}
\author[1]{Anonymous IJQC Reviewer}%
\affil[1]{Affiliation not available}%
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\date{\today}
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\begin{abstract}
In this manuscript, the authors present, discuss, and assess several
criteria to evaluate the transferability of approximations to the
exchange-correlation functional of density functional theory (DFT). In
the first part of the paper they demonstrate that one criteria often
used to assess such transferability -~ the number of parameters in a
given functional - is clearly inadequate for the task. In the second
part of the paper, the authors introduce three statistical criteria with
roots in statistics and machine learning and apply them to a selection
of existing density functional approximations.
Considering that the choice of the functional can have a profound impact
on the quality and computational cost of DFT calculations and that there
are hundreds of functionals available in the literature, this is clearly
a topic of importance for a large number of researchers.
The work presented here is, to the best of my knowledge, scientifically
sound and original. I therefore recommend that the manuscript be
accepted for publication in IJQC after the authors have taken the
comments bellow under consideration.%
\end{abstract}%
\sloppy
\section{Referee Report}
{\label{933329}}
I would like to thank the authors for this well written,
thought-provoking manuscript. It made for a very enjoyable read and I
believe it is an important addition to the literature on the design and
benchmarking of exchange-correlation functionals of DFT. I would also
like to congratulate IJQC for this new article format where the computer
code and the data used to generate plots are only a few clicks away.
This is definitely a step forward in ensuring that scientific results
are readily available and reproducible.
For the last 15 years I have followed closely, albeit mainly as an
outsider, what the authors call the "\emph{two philosophies at war in
the world of functional development}". It's good to see that there is
nowadays a greater focus on the issue of how to properly assess the
transferability of functional approximations. In the end, regardless of
how they are constructed, functionals should be assessed against the
same data using sound and well justified criteria. From this point of
view, the work presented in this manuscript is a clear step forward. I
believe the manuscript could be published as is, but the authors might
want to take into account the following comments first.
1. In the first part of the manuscript the authors present their
one-parameter fit of exchange-correlation functionals. Although I
appreciate the point the authors are trying to make, the fact that Eq. 5
cannot be used in practice to evaluate the functional for arbitrary
values of the density seems problematic to me. A functional cannot be
reduced to a finite set of points. As a simple example, one can look at
the existing approximations to the LDA correlation, as most of them are
fits to the same set of points (the Monte Carlo data of Ceperley-Alder).
These functionals are clearly not equivalent, as they give close, but
different results. The authors do point out that a spline interpolation
can be used, but in that case it's hard to argue that such interpolation
is a one parameter fit. I guess one could instead make the point that in
the limit of infinite number of points (and infinite number of
significant digits in the parameter), Eq. 5 is able to represent a given
functional for arbitrary densities. Would this be correct? Maybe the
authors could comment further on this?
2. Another question that is not entirely clear to me regarding the
one-parameter fit is if or how such procedure could be carried over to
hybrid functionals and in particular to range-separated hybrids. I
understand that this goes beyond the scope of the paper, but considering
the popularity and importance of such functionals, I would appreciate if
the authors could share any ideas they might have on this subject.
3. Looking at Table 3, there's a somewhat obvious connection that could
be made between Sections 2 and 3. At first glance, there seems to be no
correlation between the ranking of the functionals and the number of
degrees of freedom. This would be further proof of the inadequacy of
counting parameters as a proxy for functional transferability.
4. I couldn't find the ASCDB\_UE\_C.csv file that is used in the Jupyter
notebook to generate Table 1 in the associated data. Also, it seems that
the weights defined in Eq. 11 are hard-coded in the notebook. The
manuscript explains how they should be calculated, but it is not
possible to check the values without further data.
5.Finally, a very minor point. Although it has become customary to cite
Ref. 53 of the manuscript when referring to the PW91 GGA, the functional
was first described in~\hyperref[csl:1]{(Perdew, 1991)}.~I mention this because I've
seen a few times people mixing up the PW91 GGA with the PW92 LDA as they
assume (correctly!) that the year appearing in the functional
abbreviation corresponds to the year in which the corresponding paper
was first published.
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\section*{References}\sloppy
\phantomsection
\label{csl:1}Ziesche, P., \& Eschrig, H. (Eds.). (1991). {}. In \textit{Proceedings of the 75. WE-Heraeus-Seminar and 21st Annual International Symposium on Electronic Structure of Solids} (p. 11). Akademie Verlag.
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