Fig. 3

Experimental vs. theoretical formation enthalpies (Type 1) a A comparison of experimentally obtained and DFT-calculated ΔH_f for all 1012 compounds analyzed (PBE above; SCAN below) showing that SCAN significantly improves the prediction of ΔH_f over PBE. MAD is the mean absolute difference; RMSD is the root-mean-square difference; R² is the correlation coefficient; N is the number of compounds shown; μ is the mean difference; σ is the standard deviation. A normal distribution constructed from μ and σ is shown as a solid curve. b For the same compounds, a comparison of PBE and SCAN with experiment using fitted elemental reference energies for the calculation of ΔH_f (PBE+ above; SCAN+ below) showed that for Type 1 reactions fitted elemental reference energies significantly improve the prediction of ΔH_f, especially predictions by PBE. These results are provided in Supplementary Table 1 (for elemental energies) and Supplementary Table 2 (for compound data). c The chemical dependence of the MAD between theory and experiment for formation enthalpies. The subscript, calc, refers to the functional shown in the legend. The data is partitioned by: all – all compounds considered; diatomics—compounds that contain one or more element of H, N, O, F, Cl; TMs—compounds that contain one or more group 3–11 element; oxides—compounds that contain oxygen; halides—compounds that contain one or more element of F, Cl, Br, I; chalcogenides—compounds that contain one or more element of S, Se, Te; pnictides—compounds that contain one or more element of N, P, As, Sb, Bi. The numbers in parentheses above each set of bars indicate the number of compounds in that subset. Error bars are the standard error of the mean. The dashed black line at 30 meV/atom indicates the approximate uncertainty of ΔH_f,exp (Supplementary Figure 2). The distribution of ΔH_f,exp is provided in Supplementary Figure 4a