Erratum: Probabilistic performance estimators for computational chemistry methods: The empirical cumulative distribution function of absolute errors (Journal of Chemical Physics (2018) 148 (241707) DOI: 10.1063/1.5016248)

Abstract

A coding error of Eq. (26) in Ref. 1 was recently discovered2 in the source code we made publicly available for the reproducibility of our results (https://doi.org/10.5281/zenodo.1200153). The variance term was mistyped as σ2 = u11 + u22 instead of σ2 = u21 + u22. This error affects the inversion probabilities reported in Table III of Ref. 1. The corrected version of Table III is presented here (Table I). (Table Presented) Some inversion probabilities are significantly reduced, and the commentary of Table III should be reformulated: "There is a neat segregation of the DFAs in two groups: (1) B97-1, CAM-B3LYP, PBE0, among which the inversion risk is medium to very high, and (2) the remaining DFAs, which have vanishing chances to outperform any DFA of the first group. In the second group, the MUE ranking of PW86PBE and BLYP is not statistically significant." There is no further impact of this error on the remainder of the published results.