Fitting Elephants in the Density Functionals Zoo: Statistical
Criteria for the Evaluation of DFT methods as a Suitable Replacement for
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.