Judging density-functional approximations: Some pitfalls of statistics

Abstract

Density-functional theory (DFT) methods have achieved widespread popularity for thermochemical predictions, which has lead to extensive benchmarking of functionals. While the use of statistics to judge the quality of various density-functional approximations is valuable and even seems unavoidable, the present chapter suggests some pitfalls of statistical analyses. Several illustrative examples, focusing on analysis of thermochemistry and intermolecular interactions, are presented to show that conclusions can be heavily influenced by both the data-set size and the choice of the criterion used to assess an approximation’s quality. Even with reliable approximations, the risk of publishing inaccurate results naturally increases with the number of calculations reported.