Table 4.
The different performances for SCC-DFTB including on-site third-order terms for non-phosphorus compounds and phosphate species.a
| SCC-DFTBb | ||||
|---|---|---|---|---|
| Molecules | G3B3 | |||
| 2nd-order | 3rd-order | Mix-optimized 3rd-order | ||
| Non-phosphorus | ||||
| water | 398.4 | 26.5 | −5.4 (1.3) | 1.0 [−13.9] |
| methanol | 392.6 | 4.5 | −6.3 (−4.0) | −8.3 [−13.1] |
| ethanol | 388.3 | 8.7 | −2.8 (−0.5) | −4.3 [−9.3] |
| propanol | 387.6 | 7.9 | −3.5 (−1.1) | −4.8 [−9.8] |
| 2-propanol | 385.6 | 11.5 | −0.5 (1.8) | −1.4 [−6.5] |
| formic acid | 351.2 | 11.9 | 3.1 (4.2) | −0.9 [−6.8] |
| acetic acid | 355.1 | 11.3 | 1.6 (2.9) | −2.8 [−8.4] |
| propanoic acid | 354.5 | 11.2 | 1.9 (3.1) | −2.5 [−8.0] |
| phenol | 356.7 | 5.5 | 0.2 (1.1) | −2.6 [−5.8] |
| p-methylphenol | 357.9 | 4.6 | −0.4 (0.4) | −3.1 [−6.2] |
| p-nitrophenol | 334.6 | 0.9 | −5.4 (−4.4) | −5.8 [−12.0] |
| CH2(OH)2 | 374.8 | 11.7 | 1.3 (3.4) | −4.7 [−10.1] |
| CH2(OH)(OCH3) | 377.2 | 5.1 | −1.1 (0.0) | −3.4 [−8.4] |
| CH(OH)3 | 361.9 | 18.0 | 3.7 (5.9) | −1.8 [−7.2] |
| CH(OCH3)2OH | 365.7 | 9.5 | 2.5 (3.6) | −0.4 [−5.7] |
| Error Analysis | ||||
| MAXE | 26.5 | −6.3 (5.9) | −8.3 [−13.9] | |
| RMSE | 11.6 | 3.2 (3.0) | 3.8 [9.1] | |
| MUE | 9.9 | 2.6 (2.5) | 3.2 [8.7] | |
| MSE | 9.9 | −0.7 (1.2) | −3.1 [−8.7] | |
| Phosphate | ||||
| H3PO4 | 334.0 | 27.3 | 13.7 | 8.5 [1.6] |
| H2PO4 − | 463.6 | 36.7 | 15.2 | 8.7 [3.7] |
| DMPH | 336.2 | 19.9 | 9.7 | 5.0 [1.7] |
| MMP | 336.7 | 22.2 | 10.3 | 5.2 [−0.1] |
| MMP− | 460.5 | 31.7 | 14.2 | 10.1 [6.1] |
| PH3OH | 201.6 | 1.6 | −2.0 | −2.0 [−3.0] |
| PH2OHOH | 201.6 | 7.4 | 1.6 | 1.6 [−1.0] |
| PHOHOHOH | 200.8 | 14.7 | 6.9 | 6.5 [3.0] |
| PH2(OH)=O | 336.6 | 13.2 | 4.9 | 0.1 [−3.6] |
| PH(OH)(OH)=O | 334.7 | 20.9 | 9.9 | 4.7 [−0.8] |
| Error Analysis | ||||
| MAXE | 36.7 | 15.2 | 10.1 [6.1] | |
| RMSE | 22.1 | 10.0 | 6.1 [3.0] | |
| MUE | 19.6 | 8.8 | 5.2 [2.5] | |
| MSE | 19.6 | 8.4 | 4.8 [0.8] | |
The PA values and errors (in kcal/mol) are defined in the same manner as in Table 3.
See Table 1 for the notations used to label different SCC−DFTB approaches. The values in parentheses are obtained using a third-order approach optimized in Ref. 59 based on 32 non-phosphorus compounds. For the “Mix-optimized 3rd-order” set, both non-phosphorus and phosphate molecules (shown in italics) are included to attempt to optimize a set of third-order parameters that work for both classes of molecules, although the results are not satisfying (see text). The numbers in bracket are based on the phosphate hydrolysis reaction parameter set (SCC−DFTBPR).