Fig. 5. Performance of HF-r²SCAN-DC4 and other conventional functionals.

a The mean absolute error (MAE) for the water-based reactions appear in this work (hexamer isomer energies, water 20-mers isomer energies, WATER27 binding energies, water-small organic molecule interaction energies, and water dimer interaction energies) versus the weighted-mean-absolute-deviation-2 (WTMAD-2) for the GMTKN55 database for selected functionals. For a further description of the reactions used in the y-axis, see Supplementary Note 8. HF-SCAN-D4 functional used here is from ref. ⁷⁴. b The hexagon plot with MAEs for selected water-based datasets and WTMAD-2 values for the whole GMTKN55 databases (for WTMAD-2 values for other GMTKN55 database, see Supplementary Fig. 10). Abbreviations of isomerization (I), binding (B), and interaction (T) energy are noted in the vertex caption. MAEs of HF-r²SCAN-DC4 for individual GMTKN55 datasets are shown in Supplementary Table 1. In Supplementary Fig. 11, we give further details about the interaction energies used in the water-small organic molecule dataset.