Table 4. Mean Absolute Errors (kJ/mol for the Energies, E, and kJ/(mol nm) for the Forces, F) in the Prediction of the Quantities Indicated in the First Column, Using as Training Set the Data Indicated in the First Row and the 12b-1 Modela.
| training set |
|||||||
|---|---|---|---|---|---|---|---|
| test set | F(Zn, 6H2O) | F(Zn, 16H2O) | F(Zn, 32H2O) | F(Zn, 64H2O) | F(Zn, 128H2O) | Li et al. | HF |
| E(6H2O) | 761.97 | 530.02 | 551.62 | 559.56 | 576.14 | 116.71 | 153.47 |
| E(16H2O) | 949.67 | 650.46 | 691.86 | 703.52 | 726.39 | 68.36 | 146.89 |
| E(32H2O) | 998.71 | 669.10 | 719.59 | 732.93 | 758.65 | 74.38 | 136.58 |
| E(64H2O) | 1060.05 | 702.01 | 761.09 | 776.03 | 804.42 | 69.96 | 129.74 |
| E(128H2O) | 1083.49 | 706.46 | 771.29 | 787.29 | 817.46 | 77.10 | 113.38 |
| F(Zn, 6H2O) | 92.95 | 117.31 | 113.81 | 111.44 | 111.08 | 627.34 | 65.13 |
| F(Zn, 16H2O) | 191.20 | 175.86 | 177.88 | 178.36 | 179.11 | 604.13 | 71.97 |
| F(Zn, 32H2O) | 168.91 | 160.55 | 159.70 | 159.41 | 159.70 | 603.82 | 74.96 |
| F(Zn, 64H2O) | 167.94 | 162.12 | 161.04 | 160.58 | 160.79 | 605.57 | 73.59 |
| F(Zn, 128H2O) | 165.53 | 160.95 | 159.46 | 158.92 | 158.96 | 604.22 | 73.81 |
| F(6O, 6H2O) | 312.62 | 284.89 | 269.23 | 261.93 | 252.14 | 1650.26 | 767.28 |
| F(6O, 16H2O) | 302.87 | 357.11 | 338.21 | 329.26 | 316.50 | 1727.30 | 808.86 |
| F(6O, 32H2O) | 286.98 | 370.51 | 349.89 | 340.15 | 325.87 | 1752.40 | 807.00 |
| F(6O, 64H2O) | 285.65 | 363.77 | 343.25 | 333.63 | 319.68 | 1745.70 | 808.01 |
| F(6O, 128H2O) | 285.94 | 362.59 | 342.19 | 332.58 | 318.42 | 1744.27 | 808.02 |
| F(12H, 6H2O) | 259.02 | 301.66 | 285.63 | 282.95 | 278.63 | 356.05 | 527.17 |
| F(12H, 16H2O) | 298.62 | 347.19 | 329.60 | 326.57 | 403.66 | 403.66 | 617.26 |
| F(12H, 32H2O) | 293.34 | 348.17 | 329.14 | 325.80 | 408.32 | 408.32 | 630.00 |
| F(12H, 64H2O) | 296.21 | 349.11 | 330.48 | 327.21 | 407.67 | 407.67 | 629.47 |
| F(12H, 128H2O) | 296.36 | 349.04 | 330.52 | 327.29 | 322.08 | 407.36 | 629.30 |
| optimized charge | 1.529 | 1.787 | 1.709 | 1.694 | 1.670 | ||
a
The values of the errors for the same data set used in the training process are marked in bold. F(6O, nH2O) are the forces on the six oxygen atoms closest to the zinc ion for the cluster with n water molecules. F(12H, nH2O) are the forces on the 12 hydrogen atoms closest to the zinc ion for the cluster with n water molecules.