Table 1. Dataset Sizes, Number of Calculated False Metals, Mean Absolute Errors (MAE, in eV), Mean Absolute Percentage Errors (MAPE), Mean Percentage Errors (MPE), Mean Errors (ME, in eV), Variance (σ2, in eV2), Median Error (MnE, in eV), Median Absolute Deviation from the Median (MADM, in eV), Interquartile Range (IQR, in eV), Linear Fit (y = ax + b) Coefficients, Pearson’s Correlation Coefficient (r), and Kendall’s Rank Correlation Coefficient (τ) for Calculations of the Kohn–Sham Band Gap for All Considered Functionalsa.
| LDA | LDA (SOC) | PBE | PBE (SOC) | PBEsol | HLE16 | HLE16 (SOC) | BJ | mBJ | SCAN | HSE06 | HSE14 | HSEmix | PBE0 | PBE0mix | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| sp | set size | 220 | 220 | 220 | 220 | 220 | 220 | 220 | 220 | 220 | 220 | 220 | 220 | 220 | 220 | 220 |
| false metals | 13 | 14 | 11 | 13 | 11 | 6 | 8 | 9 | 4 | 8 | 4 | 4 | 2 | 2 | 2 | |
| Kendall τ | 0.76 | 0.77 | 0.76 | 0.78 | 0.76 | 0.77 | 0.80 | 0.78 | 0.79 | 0.79 | 0.79 | 0.79 | 0.79 | 0.79 | 0.77 | |
| Pearson r | 0.95 | 0.95 | 0.95 | 0.95 | 0.95 | 0.95 | 0.96 | 0.96 | 0.97 | 0.95 | 0.95 | 0.95 | 0.96 | 0.95 | 0.95 | |
| a | 0.59 | 0.60 | 0.62 | 0.62 | 0.61 | 0.78 | 0.80 | 0.70 | 0.88 | 0.68 | 0.75 | 0.84 | 0.97 | 0.76 | 1.01 | |
| b (eV) | 0.06 | –0.05 | 0.13 | 0.01 | 0.07 | 0.37 | 0.13 | 0.20 | 0.21 | 0.24 | 0.55 | 0.47 | 0.30 | 1.09 | 0.39 | |
| MAE (eV) | 1.3 | 1.4 | 1.2 | 1.3 | 1.3 | 0.7 | 0.6 | 0.9 | 0.6 | 0.9 | 0.7 | 0.6 | 0.7 | 0.8 | 0.8 | |
| ME (eV) | –1.3 | –1.4 | –1.2 | –1.3 | –1.2 | –0.4 | –0.5 | –0.8 | –0.2 | –0.8 | –0.3 | –0.1 | 0.2 | 0.3 | 0.4 | |
| σ2 (eV2) | 1.9 | 1.8 | 1.7 | 1.7 | 1.8 | 1.0 | 0.8 | 1.2 | 0.6 | 1.4 | 1.1 | 0.9 | 0.8 | 1.1 | 1.0 | |
| MnE (eV) | –0.9 | –1.0 | –0.8 | –0.9 | –0.9 | –0.1 | –0.3 | –0.5 | –0.1 | –0.5 | –0.1 | 0.0 | 0.2 | 0.5 | 0.4 | |
| IQR (eV) | 1.3 | 1.2 | 1.2 | 1.1 | 1.2 | 0.9 | 0.8 | 1.1 | 0.8 | 1.0 | 0.8 | 0.8 | 0.8 | 0.8 | 1.2 | |
| MADM (eV) | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.4 | 0.3 | 0.4 | 0.4 | 0.4 | 0.4 | 0.4 | 0.4 | 0.4 | 0.6 | |
| MAPE (%) | 43.8 | 47.4 | 40.0 | 43.0 | 42.1 | 33.8 | 25.5 | 32.9 | 29.0 | 33.0 | 28.9 | 30.4 | 32.9 | 52.6 | 42.2 | |
| MPE (%) | –40.8 | –45.7 | –34.7 | 41.8 | –38.5 | 4.4 | –14.1 | –19.6 | 3.4 | –22.2 | 4.1 | 9.0 | 16.1 | 42.4 | 25.5 | |
| d | set size | 244 | 244 | 244 | 244 | 244 | 244 | 244 | 244 | 244 | 244 | 244 | 244 | 244 | 244 | 244 |
| false metals | 22 | 20 | 19 | 17 | 24 | 8 | 7 | 11 | 7 | 10 | 5 | 4 | 2 | 3 | 2 | |
| Kendall τ | 0.61 | 0.62 | 0.63 | 0.64 | 0.62 | 0.67 | 0.68 | 0.72 | 0.71 | 0.66 | 0.72 | 0.73 | 0.73 | 0.72 | 0.73 | |
| Pearson r | 0.87 | 0.87 | 0.88 | 0.88 | 0.87 | 0.81 | 0.81 | 0.91 | 0.90 | 0.89 | 0.91 | 0.91 | 0.90 | 0.90 | 0.88 | |
| a | 0.66 | 0.65 | 0.67 | 0.67 | 0.67 | 0.65 | 0.65 | 0.73 | 0.82 | 0.75 | 0.90 | 1.02 | 1.14 | 0.92 | 1.20 | |
| b (eV) | –0.31 | –0.36 | –0.24 | –0.29 | –0.28 | 0.34 | 0.27 | –0.10 | 0.14 | –0.14 | 0.28 | 0.35 | 0.24 | 0.80 | 0.33 | |
| MAE (ev) | 1.0 | 1.1 | 0.9 | 1.0 | 1.0 | 0.5 | 0.6 | 0.7 | 0.4 | 0.7 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | |
| ME (ev) | –1.0 | –1.1 | –0.9 | –1.0 | –1.0 | –0.4 | –0.5 | –0.6 | –0.2 | –0.7 | 0.1 | 0.4 | 0.5 | 0.6 | 0.8 | |
| σ2 (eV2) | 0.5 | 0.5 | 0.4 | 0.4 | 0.5 | 0.6 | 0.6 | 0.3 | 0.4 | 0.4 | 0.3 | 0.4 | 0.6 | 0.4 | 0.8 | |
| MnE (eV) | –0.9 | –1.0 | –0.9 | –0.9 | –0.9 | –0.2 | –0.3 | –0.6 | –0.2 | –0.6 | 0.0 | 0.3 | 0.4 | 0.6 | 0.6 | |
| IQR (eV) | 0.8 | 0.8 | 0.8 | 0.8 | 0.8 | 0.6 | 0.6 | 0.6 | 0.6 | 0.7 | 0.5 | 0.6 | 0.7 | 0.6 | 0.8 | |
| MADM (eV) | 0.4 | 0.4 | 0.4 | 0.4 | 0.4 | 0.3 | 0.3 | 0.3 | 0.3 | 0.4 | 0.3 | 0.3 | 0.3 | 0.3 | 0.4 | |
| MAPE (%) | 56.7 | 59.1 | 51.7 | 54.1 | 54.6 | 30.3 | 31.3 | 39.8 | 30.2 | 42.2 | 32.6 | 41.4 | 46.4 | 69.6 | 58.2 | |
| MPE (%) | –52.6 | –56.3 | –46.2 | –50.4 | –49.8 | –15.1 | –20.4 | –32.9 | –6.4 | –31.5 | 15.8 | 32.7 | 39.5 | 64.1 | 52.0 | |
| f | set size | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 8 |
| false metals | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | |
| Kendall τ | 0.90 | 0.90 | 0.71 | 0.71 | 0.64 | 0.71 | 0.71 | 0.90 | 0.81 | 0.64 | 0.71 | 0.71 | 0.71 | 0.71 | 0.71 | |
| Pearson r | 0.99 | 0.99 | 0.97 | 0.98 | 0.98 | 0.92 | 0.93 | 0.99 | 0.99 | 0.96 | 0.95 | 0.96 | 0.96 | 0.93 | 0.97 | |
| a | 0.92 | 0.91 | 0.95 | 0.94 | 0.96 | 0.63 | 0.63 | 0.97 | 1.04 | 1.00 | 1.22 | 1.37 | 1.44 | 1.23 | 1.53 | |
| b (eV) | –1.02 | –1.05 | –1.11 | –1.14 | –1.18 | –0.33 | –0.53 | –0.77 | –0.62 | –0.93 | –0.94 | –1.14 | –1.23 | –0.45 | –1.33 | |
| MAE (eV) | 1.2 | 1.3 | 1.2 | 1.3 | 1.3 | 1.2 | 1.5 | 0.9 | 0.5 | 0.9 | 0.5 | 0.5 | 0.6 | 0.6 | 0.6 | |
| ME (eV) | –1.2 | –1.3 | –1.2 | –1.3 | –1.3 | –1.2 | –1.5 | –0.9 | –0.5 | –0.9 | –0.4 | –0.2 | –0.2 | 0.1 | –0.0 | |
| σ2 (eV2) | 0.0 | 0.1 | 0.1 | 0.1 | 0.1 | 0.4 | 0.4 | 0.0 | 0.0 | 0.1 | 0.4 | 0.6 | 0.7 | 0.5 | 0.8 | |
| MnE (eV) | –1.2 | –1.2 | –1.2 | –1.2 | –1.3 | –1.0 | –1.3 | –0.9 | –0.6 | –0.8 | –0.3 | –0.1 | –0.1 | 0.3 | –0.0 | |
| IQR (eV) | 0.3 | 0.2 | 0.3 | 0.3 | 0.3 | 0.5 | 0.3 | 0.3 | 0.2 | 0.2 | 0.4 | 0.5 | 0.5 | 0.4 | 0.6 | |
| MADM (eV) | 0.2 | 0.0 | 0.2 | 0.1 | 0.2 | 0.2 | 0.1 | 0.1 | 0.2 | 0.1 | 0.3 | 0.3 | 0.3 | 0.2 | 0.4 | |
| MAPE (%) | 57.3 | 59.8 | 59.0 | 61.6 | 62.2 | 53.7 | 64.2 | 40.4 | 25.4 | 44.9 | 25.9 | 25.8 | 25.6 | 25.3 | 26.7 | |
| MPE (%) | –57.3 | –59.8 | –59.0 | –61.6 | –62.2 | –53.7 | –64.2 | –40.4 | –25.4 | –44.9 | –24.1 | –18.9 | –16.1 | 1.4 | –12.0 | |
| all | set size | 471 | 471 | 472 | 472 | 472 | 472 | 472 | 471 | 471 | 472 | 472 | 472 | 472 | 472 | 472 |
| false metals | 35 | 34 | 31 | 31 | 36 | 15 | 16 | 20 | 11 | 19 | 10 | 9 | 5 | 5 | 4 | |
| Kendall τ | 0.68 | 0.69 | 0.69 | 0.70 | 0.68 | 0.71 | 0.73 | 0.74 | 0.75 | 0.72 | 0.75 | 0.75 | 0.75 | 0.75 | 0.74 | |
| Pearson r | 0.93 | 0.94 | 0.94 | 0.94 | 0.94 | 0.93 | 0.94 | 0.95 | 0.96 | 0.94 | 0.94 | 0.94 | 0.94 | 0.94 | 0.93 | |
| a | 0.62 | 0.62 | 0.64 | 0.64 | 0.63 | 0.78 | 0.78 | 0.72 | 0.88 | 0.70 | 0.78 | 0.86 | 0.98 | 0.78 | 1.03 | |
| b (eV) | –0.14 | –0.21 | –0.07 | –0.16 | –0.12 | 0.21 | 0.07 | 0.03 | 0.10 | 0.05 | 0.49 | 0.55 | 0.41 | 1.04 | 0.51 | |
| MAE (eV) | 1.2 | 1.2 | 1.1 | 1.1 | 1.1 | 0.6 | 0.6 | 0.8 | 0.5 | 0.8 | 0.5 | 0.6 | 0.6 | 0.8 | 0.8 | |
| ME (eV) | –1.2 | –1.2 | –1.0 | –1.1 | –1.1 | –0.4 | –0.5 | –0.7 | –0.2 | –0.7 | –0.1 | 0.2 | 0.4 | 0.5 | 0.6 | |
| σ2 (eV2) | 1.1 | 1.1 | 1.0 | 1.0 | 1.1 | 0.8 | 0.7 | 0.8 | 0.5 | 0.8 | 0.7 | 0.7 | 0.7 | 0.8 | 0.9 | |
| MnE (eV) | –0.9 | –1.0 | –0.8 | –0.9 | –0.9 | –0.2 | –0.3 | –0.5 | –0.1 | –0.6 | –0.0 | 0.2 | 0.3 | 0.6 | 0.5 | |
| IQR (eV) | 0.9 | 0.9 | 0.9 | 0.9 | 0.9 | 0.8 | 0.7 | 0.8 | 0.7 | 0.8 | 0.7 | 0.7 | 0.8 | 0.6 | 0.9 | |
| MADM (eV) | 0.5 | 0.5 | 0.4 | 0.4 | 0.5 | 0.4 | 0.3 | 0.4 | 0.4 | 0.4 | 0.3 | 0.3 | 0.4 | 0.3 | 0.4 | |
| MAPE (%) | 50.7 | 53.7 | 46.4 | 49.0 | 48.9 | 32.4 | 29.1 | 36.6 | 29.6 | 38.0 | 30.8 | 36.0 | 39.7 | 60.9 | 50.2 | |
| MPE (%) | –47.2 | –51.4 | –41.1 | –46.6 | –44.8 | –6.7 | –18.2 | –26.8 | –2.1 | –27.4 | 9.6 | 20.8 | 27.7 | 52.9 | 38.6 |
a
Averages are done over the total dataset (all) and over the partial sets sp, d, and f, defined in the main text. A material is classified as a false metal if the calculated band gap is smaller than 0.01 eV.