When a Few Trees Dominate the Forest: Outlier Analysis on Thermochemical Benchmarks
\(^{1}\) Department of Chemistry, Dalhousie University, 6243 Alumni Crescent, Halifax, Nova Scotia, B3H 4R2, Canada.
\(^{2}\) Department of Physics and Atmospheric Science, Dalhousie University, 6310 Coburg Road, Halifax, Nova Scotia, B3H 4R2, Canada.
\(^{3}\) Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, United Kingdom.
The GMTKN55 data set is a collection of standard benchmarks in molecular quantum chemistry that spans small- and large-molecule thermochemistry, reaction barriers, and non-covalent interactions. The error across this collection of benchmarks is reported as a weighted mean absolute deviation (WTMAD). We identify a flaw in the canonical WTMAD definitions, which weight some benchmarks orders of magnitude more heavily than others, with the top 3 benchmarks contributing as much to the total WTMAD-2 as the bottom 36. A new WTMAD-4 metric is proposed, and assessed on hundreds of DFAs from the literature, including the DM21 and Skala machine-learned functionals that have garnered recent attention. We highlight literature examples where DFAs parameterized by minimising WTMAD-2 underperform on benchmarks marginalised by that metric, and perform outlier analysis for all functionals, providing insight into both performance and consistency across the dataset. We then test the exchange-hole dipole moment (XDM) dispersion correction (and many-body dispersion, MBD) in combination with minimally-empirical DFAs for the first time on GMTKN55. XDM shows excellent performance on both GMTKN55 and molecular crystals when paired with minimally empirical functionals such as revPBE0 and B86bPBE0 and Becke’s recently proposed Z-damping function.
