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\begin{document}

\title{}



\author[1]{Anonymous IJQC Reviewer}%
\affil[1]{Affiliation not available}%


\vspace{-1em}



  
  \date{March 14, 2025}


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\selectlanguage{english}
\begin{abstract}
In his present contribution, Peverati addresses whether the number of
degrees of freedom influence the accuracy and applicability of a density
functional. Overall, this question is of interest, particularly to DFT
developers and Peverati answers it appropriately. Therefore, I find this
work suitable for IJQC. That being said, I have to raise two major
points and a couple of minor ones that should be addressed before this
manuscript can be accepted for publication. I therefore recommend a
revision.

Note that I prefer to remain anonymous. While I appreciate that referee
reports are published alongside a paper, making the reviewer public may
actually have the undesired effect that reviewers are reluctant to be
honest in their assessment, which ultimately hampers the production of
high-quality publications.%
\end{abstract}%



\sloppy




\section{Referee Report}

{\label{933329}}

As I mentioned in the abstract of this reviewer form, this manuscript is
suitable for IJQC. However, I have to raise major and minor points for a
revision, which are listed below:

\textbf{Major points:}

\textbf{1)} Multiple times (particularly in the abstract and
introduction), the author alludes to an ongoing discussion in the DFT
community that is biased towards seeing DFT methods that rely on a large
number of fitted parameters as non-transferable to different systems
compared to methods that rely on a smaller number of parameters. At
times, the statements made about this seem rather anecdotal, as they
lack any scientific citation. Some examples are:

\emph{``Counting parameters has become customary in the density
functional theory community as a way to infer the transferability of
popular approximations to the exchange--correlation functionals.''}

\emph{``Among this latter school of thoughts, fitting~xc}
\emph{functionals has achieved a somehow bad reputation, because
parameters have been associated to overfitting and poor
transferability''}

\emph{``A corresponding frequently asked question in the DFT community
is: ``how many parameters does this functional have?'', implying that
functionals with more than four or five fitted parameters are barely
useful elephants in the DFT zoo. ``}

\emph{``Instead of playing the game of counting fitted parameters in
``parametrized functionals'' and compare them to~hidden parameters in
``zero-parameter'' functionals, \ldots{}''}

\emph{``The fight between counting parameters and analytical fits,
\ldots{}''}

\par\null

The author needs to provide some references to support his statements.
In addition, very strong wording is used in the article that in my
opinion is not appropriate for scientific publications and seems a bit
exaggerated, such as \emph{``treacherous'', ``war'', ``fight''.} I
advise to adjust that type of language.

\par\null

\textbf{2)} A large portion of the article, namely Section 2, feels very
disconnected to the main core of this work in Section 3, which answers
the main question of this article and provides a statistical analysis
based on calculated data.

Instead, the article fits a function with a single parameter to
reproduce enhancement factors of popular DFT methods. It turns out that
that parameter needs to rely on an immensely large number of decimals to
achieve appropriate reproduction of the training function. Maybe I
misunderstood this section, but while it looks like an interesting
exercise, I do not see the relevance and the scientific insight.
Expressing an enhancement factor of a complicated functional---which by
itself may depend on a large number of parameters---through a fit
function with one parameter does not really mean that that functional
has now become dependent on just one parameter. Ultimately, the
enhancement factor it was fitted against had been developed with
multiple parameters. Regardless of whether the number of parameters in
that original enhancement factor causes problems in applications or not,
the new single-parameter fit still inherits the virtues and problems of
the original method. In addition, the large number of decimals also
makes me question how easy it is to use that parameter on a different
machine and to reproduce exactly the same function. Is it not possible
that some of those decimals already contain numerical noise? Finally, I
called this section ``disconnected'' because the final important part of
the manuscript never refers back to Section 2.

My recommendation is to shorten Section 2 and to mention it as an
interesting ``fun fact'' with most information being moved to a
Supporting Information.

\textbf{Minor points:}

\textbf{3)} Table 1 presents a ranking of functionals and supports the
author's main point, namely that the number of degrees of freedom does
not tell us anything about a method's applicability. The ranked
functionals closely resemble previous recommendations based on
traditional benchmarking, which complements those previous works nicely.
The database used by the author relies heavily on existing databases and
benchmark sets, with most of them also addressing noncovalent
interactions.~ Indeed, one can see an improvement when some form of
London dispersion correction is used. Therefore, I feel that some
functionals are misrepresented, in particular methods such as revTPSS,
M11, N12, M06 etc. Dispersion corrections for those methods have been
put forward and they have been shown to work. This is also the case for
Truhlar's methods, as shown by different groups, e.g. Goerigk in J. Phys
Chem. Lett in 2015\hyperref[csl:1]{(Goerigk, 2015)}, or Head-Gordon et al in JCTC in
2016. I recommend to also show results for those dispersion-corrected
versions. In fact, including those numbers will do the author a favour.
The number of parameters will increase, but the results improve, further
evidence supporting this paper's main message.

\textbf{4)} Given that this is a full paper without page limitations, I
feel it is not appropriate to refer to the supporting information of a
previous paper for references of functionals or benchmark sets. That
would be a disfavour to all the authors that developed and wrote those
articles. They should be cited in this paper too.

\textbf{5)}~I also find that referring to Morgante
2019\hyperref[csl:2]{(Morgante \& Peverati, 2019)} for technical details is not appropriate. The
readers do not want to look up a different paper for important
information.

\textbf{6)} Where the author cites previous benchmark studies by Goerigk
et al and Head-Gordon et al., he may also want to include Jan Martin's
latest contributions published in the recently published Journal of
Physical Chemistry Festschrift in honour of Leo Radom\hyperref[csl:3]{(Santra et al., 2019)}
and in the Israel Journal of Chemistry\hyperref[csl:4]{(Martin \& Santra, 2019)}.

\par\null

In summary, while this list may look long, I liked reading this work and
I am certain that it will be well received. I hope my comments can
assist the author to improve it further.

\selectlanguage{english}
\FloatBarrier
\section*{References}\sloppy
\phantomsection
\label{csl:1}{Treating London-Dispersion Effects with the Latest Minnesota Density Functionals: Problems and Possible Solutions}. (2015). \textit{The Journal of Physical Chemistry Letters}, \textit{6}(19), 3891–3896. \url{https://doi.org/10.1021/acs.jpclett.5b01591}

\phantomsection
\label{csl:2}{Statistically representative databases for density functional theory via data science}. (2019). \textit{Physical Chemistry Chemical Physics}, \textit{21}(35), 19092–19103. \url{https://doi.org/10.1039/c9cp03211h}

\phantomsection
\label{csl:3}{Minimally Empirical Double-Hybrid Functionals Trained against the {GMTKN}55 Database: {revDSD}-{PBEP}86-D4 {revDOD}-{PBE}-D4, and {DOD}-{SCAN}-D4}. (2019). \textit{The Journal of Physical Chemistry A}, \textit{123}(24), 5129–5143. \url{https://doi.org/10.1021/acs.jpca.9b03157}

\phantomsection
\label{csl:4}{Empirical Double-Hybrid Density Functional Theory: A `Third Way' in Between {WFT} and {DFT}}. (2019). \textit{Israel Journal of Chemistry}. \url{https://doi.org/10.1002/ijch.201900114}

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