Conclusions
A simple encoding procedure borrowed from data science was used to show that the number of parameters of a fitted exchange–correlation functional (or in a general sense, its degrees of freedom) are not representative of transferability across different chemical systems. In section \ref{816226}, more than 300 functionals from the LibXC DFT library are represented using one single parameter. This exercise disentangles the arbitrary measurement “number of parameter” from the fundamental concept of transferability of the results, and validates the proposition of Yu and Truhlar \cite{yu_perspective:_2016} reading: “Counting parameters in a density functional is a little bit like evaluating the quality of a research program by counting the publications it produces—the number of publications is hardly irrelevant, but it is far from the whole story, and usually it is not the decisive measure of quality.”
To compensate for this lack of a “decisive measure of quality”, three new criteria based on the statistical analysis of the recently proposed ASCDB database of chemical data were developed in section \ref{898228} for the assessment of exchange–correlation functional approximations. These criteria are the Akaike information criterion (AIC), the Vapnik–Chervonenkis criterion (VCC), and the cross-validation criterion (CVC). While the criteria mostly provide similar rankings, some differences between them do exist, and the average ranking across the three criteria is the most unambiguous measurement for the evaluation of functionals.
Preliminary results of the average ranking with 60 functionals show that the best ones are those that carefully use a flexible mathematical form with a modest number of appropriately fitted parameters (5–12). In the debate between different functional development philosophies, occupying the middle ground seems to be the current winning strategy.