WTMAD-4: A Fair Weighting Scheme for GMTKN55

Abstract: The GMTKN55 data set is a collection of standard benchmarks used in molecular quantum chemistry that spans small- and large-molecule thermochemistry, reaction barriers, and non-covalent interactions. Herein, we identify a flaw in the weighted mean absolute deviation (WTMAD) definitions commonly used to quantify performance of various electronic-structure methods for the GMTKN55 set, which under-weight some of its component benchmarks by orders of magnitude. A new WTMAD-4 metric is proposed, based on typical errors observed for well-behaved density-functional approximations (DFAs), ensuring fair treatment across all benchmarks. The performance of 135 dispersion-corrected DFAs is assessed by combining literature data with new results for 20 minimally empirical methods, primarily involving the exchange-hole dipole moment and many-body dispersion corrections, available in the FHI-aims code. Lastly, we highlight a literature example where a DFA parametrised by minimising WTMAD-2 underperforms for benchmarks marginalised by that metric.