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. Recent work in data science, however, has demonstrated that the number of parameters of a fitted model is not related to the complexity of the model itself, nor to its eventual overfitting. Using similar arguments, we show here that it is possible to represent every modern exchange–correlation functional approximation using just one single parameter. This procedure proves the futility of the number of parameters as a measure of transferability. To counteract this shortcoming, we introduce and analyze the performance of three statistical criteria for the evaluation of the transferability of exchange–correlation functionals. The three criteria are called Akaike information criterion (AIC), Vapnik–Chervonenkis criterion (VCC), and cross-validation criterion (CVC) and are used in a preliminary assessment to rank 60 exchange–correlation functional approximations using the ASCDB database of chemical data.
Dear Dr. Cavalleri, I hereby resubmit my paper entitled “Fitting Elephants in the Density Functionals Zoo: Statistical Criteria for the Evaluation of DFT methods as a Suitable Replacement for Counting Parameters” with modifications that address all the concerns raised by the Referees. As such, I believe the manuscript is now ready for publication in the Authorea special issue of the International Journal of Quantum Chemistry. I want to thank the Referees for the clear and very useful remarks. For your convenience, I report below a point-by-point reply to each of the concerns raised by the Referees, and how I've addressed them in the new manuscript:
Density functional theory, or DFT, has become ubiquitous for chemical applications in research and in education. The exact functional at the foundation of DFT is unfortunately unknown, and issues arise when choosing an approximation for a specific application. With this tutorial review, we tackle the selection problem and many related ones, such as the choices of a basis set and of an integration grid, that are often overlooked by occasional practitioners and by more experienced users as well. We offer a practical approach in the form of a commented notebook containing 12 experiments that can be run on a simple computer in just a few hours. We propose this review as a primary source for those who are willing to include DFT in their everyday research or teaching activities in a way that reflects the research advances of the field in the last couple of decades