TABLE 1.
Proton affinity (left column) and gas-phase basicity (right column) error analysis. All quantities are in kcal/mol. Experimental values are from ref. 67 with error estimates given in parentheses. Error is given as quantum model chemistry minus experimental value (error = calculated - experiment). Error metrics of maximum error (MAXE), root-mean-squared error (RMSE), mean unsigned error (MUE), and mean signed error (MSE) are given below.
| Moleculea |
CBS |
G3B3 |
G3MP2 |
PBE0 |
B1B95 |
B3LYP |
QCRNA |
Experiment |
||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| water | 1.7 | 1.7 | 1.2 | 1.2 | 1.3 | 1.3 | 3.2 | 3.2 | 3.3 | 3.3 | 0.1 | 0.1 | 0.1 | 0.1 | 390.3 (0.2) | 383.7 (0.2) |
| hydronium | −1.0 | −1.1 | −0.3 | −0.4 | −0.4 | −0.5 | 0.6 | 0.5 | 0.5 | 0.3 | −1.1 | −1.2 | −1.1 | −1.2 | 165.0 (1.0) | 157.7 (0.1) |
| methanol | 1.1 | 1.3 | 2.2 | 2.4 | 2.2 | 2.3 | −0.5 | −0.3 | −0.1 | 0.1 | −2.3 | −2.0 | −2.3 | −2.1 | 381.5 (1.0) | 374.8 (0.7) |
| ethanol | 0.7 | 0.4 | 1.5 | 1.3 | 1.7 | 1.4 | −0.3 | −0.5 | 0.3 | −0.0 | −2.2 | −2.5 | −2.2 | −2.4 | 378.2 (0.8) | 371.3 (1.0) |
| propanol | 1.1 | 0.7 | 2.0 | 1.6 | 2.2 | 1.8 | 0.4 | −0.1 | 0.9 | 0.4 | −1.2 | −1.8 | −1.2 | −1.7 | 376.0 (1.1) | 369.4 (1.1) |
| 2−propanol | 0.8 | 0.3 | 1.4 | 1.0 | 1.7 | 1.3 | 0.7 | 0.3 | 1.2 | 0.8 | −1.4 | −1.8 | −1.3 | −1.7 | 375.7 (0.8) | 368.8 (1.0) |
| DMPHb | −2.4 | −1.7 | −1.8 | −1.2 | −1.3 | −0.7 | −0.6 | 0.2 | −0.7 | 0.3 | −1.6 | −0.8 | −1.5 | −0.9 | 331.6 (4.1) | 324.6 (4.0) |
| phosphoric acid | −2.6 | −2.5 | −2.2 | −2.2 | −1.8 | −1.8 | −0.5 | −0.3 | −0.6 | −0.4 | −2.4 | −2.2 | −2.3 | −2.2 | 330.5 (5.0) | 323.2 (4.9) |
| formic acid | −0.4 | −1.3 | 0.4 | −0.6 | 0.9 | −0.1 | −0.2 | −1.1 | 0.1 | −0.8 | −2.0 | −2.9 | −2.0 | −2.9 | 344.0 (1.6) | 337.9 (1.2) |
| acetic acid | 0.2 | −2.0 | 1.0 | −1.2 | 1.4 | −0.8 | 0.4 | −0.1 | 0.7 | 0.1 | −1.4 | −1.9 | −0.8 | −3.1 | 347.2 (1.1) | 341.4 (1.2) |
| propanoic acid | −1.2 | −0.3 | −0.4 | 0.6 | −0.0 | 1.0 | 0.4 | −1.2 | 0.5 | −0.5 | −1.3 | −2.8 | −1.9 | −1.0 | 347.4 (1.8) | 340.4 (1.4) |
| glycine | 1.5 | −0.4 | 2.3 | 0.5 | 2.7 | 0.8 | 2.7 | 0.7 | 2.9 | 0.9 | 1.2 | −0.9 | 1.2 | −0.8 | 340.3 (1.1) | 335.1 (1.4) |
| proline | −0.2 | −0.9 | 0.7 | −0.0 | 0.9 | 0.2 | 1.8 | 1.0 | 1.8 | 1.0 | 0.1 | −0.8 | 0.1 | −0.8 | 340.3 (3.1) | 333.4 (3.0) |
| phenol | −0.8 | −0.6 | −0.6 | −0.5 | −0.6 | −0.5 | −1.4 | −1.3 | −0.7 | −0.7 | −2.4 | −2.3 | −2.5 | −2.4 | 350.1 (1.1) | 342.9 (1.4) |
| o-chlorophenol | 0.7 | −0.7 | 1.0 | −0.4 | 1.0 | −0.4 | 0.4 | −1.1 | 1.0 | −0.5 | −1.0 | −2.4 | −1.0 | −2.4 | 343.4 (2.3) | 337.1 (2.0) |
| m-chlorophenol | −0.5 | −1.2 | −0.2 | −0.9 | −0.2 | −0.9 | −1.2 | −1.8 | −0.6 | −1.2 | −2.4 | −3.0 | −2.3 | −2.9 | 342.1 (3.1) | 335.2 (1.4) |
| p-chlorophenol | −0.5 | −0.9 | −0.2 | −0.5 | −0.2 | −0.5 | −1.0 | −1.3 | −0.5 | −0.7 | −2.2 | −2.4 | −2.3 | −2.6 | 343.4 (1.6) | 336.5 (1.4) |
| p-methylphenol | −0.3 | −0.6 | 0.0 | −0.4 | 0.0 | −0.4 | −0.7 | −1.0 | −0.1 | −0.6 | −1.8 | −2.0 | −1.8 | −2.2 | 350.7 (1.3) | 343.8 (1.2) |
| p-nitrophenol | −0.2 | −0.1 | 0.2 | 0.2 | 0.7 | 0.7 | −2.3 | −2.3 | −1.7 | −1.8 | −4.1 | −4.1 | −4.1 | −4.2 | 327.8 (2.1) | 320.9 (2.0) |
| hydrogen sulfide | −0.5 | −0.5 | −0.1 | 0.0 | 0.2 | 0.2 | 0.5 | 0.5 | 0.8 | 0.8 | −0.3 | −0.3 | −0.4 | −0.4 | 351.3 (0.8) | 344.9 (2.0) |
| methanethiol | −0.5 | −0.2 | 0.1 | 0.2 | 0.4 | 0.7 | 0.9 | 1.2 | 1.4 | 1.7 | 0.0 | 0.4 | −0.0 | 0.3 | 357.3 (1.2) | 350.6 (2.0) |
| ethanethiol | −1.2 | −1.5 | −0.5 | −0.0 | −0.2 | −0.6 | 0.3 | −0.1 | 1.0 | 0.7 | −0.4 | −0.9 | −0.4 | −0.8 | 355.4 (1.5) | 348.9 (2.0) |
| propanethiol | −1.0 | −1.0 | −0.4 | 0.4 | −0.1 | −0.2 | 0.6 | 0.5 | 1.2 | 1.0 | 0.2 | −0.2 | 0.2 | −0.2 | 354.2 (2.2) | 347.9 (2.0) |
| 2-propanethiol | −0.5 | −1.2 | 0.1 | −0.9 | 0.4 | −0.3 | 1.4 | 0.6 | 2.0 | 1.2 | 0.6 | −0.1 | 0.6 | −0.1 | 353.4 (2.2) | 347.1 (2.0) |
| ammonium | 0.2 | 0.3 | 0.5 | −0.5 | 0.3 | 0.3 | 0.6 | 0.7 | 0.2 | 0.3 | −1.1 | −1.0 | −1.1 | −1.0 | 204.0 (0.5) | 195.7 (0.5) |
| methylammonium | 0.1 | 0.2 | 0.6 | −0.6 | 0.4 | 0.6 | 0.5 | 0.5 | 0.2 | 0.3 | −0.6 | −0.6 | −0.6 | −0.6 | 214.9 (0.5) | 206.6 (0.5) |
| ethylammonium | 0.1 | 0.6 | 0.6 | 0.6 | 0.5 | 1.0 | 0.9 | 1.4 | 0.5 | 1.0 | −0.1 | 0.3 | −0.1 | 0.3 | 218.0 (0.5) | 210.0 (5.0) |
| propanammonium | −0.1 | 0.5 | 0.4 | 0.7 | 0.2 | 0.9 | 0.9 | 1.5 | 0.7 | 1.3 | −0.0 | 0.5 | −0.1 | 0.6 | 219.4 (0.5) | 211.3 (0.5) |
| 2-propanammonium | −0.6 | 0.2 | −0.1 | 1.1 | −0.2 | 0.6 | 1.0 | 1.8 | 0.7 | 1.5 | −0.1 | 0.8 | −0.1 | 0.7 | 220.8 (0.5) | 212.5 (0.5) |
| 1H-3H–imidazolium | −0.0 | −0.5 | 0.7 | 1.0 | 0.4 | −0.1 | 1.9 | 1.4 | 1.8 | 1.2 | 1.3 | 0.8 | 1.3 | 0.8 | 225.3 (0.5) | 217.7 (0.5) |
| 4-methyl-imidazolium | 1.3 | 1.1 | 1.9 | 0.7 | 1.7 | 1.5 | 3.6 | 3.5 | 3.5 | 3.4 | 3.0 | 2.9 | 3.0 | 2.9 | 227.7 (2.0) | 220.1 (2.0) |
| pyridinium | −0.4 | −0.8 | 0.3 | 0.1 | 0.0 | −0.3 | 2.0 | 1.7 | 1.8 | 1.5 | 1.8 | 1.5 | 1.9 | 1.5 | 222.0 (5.0) | 214.7 (0.5) |
| pyrrolidinium | 0.1 | 0.4 | 0.8 | 1.7 | 0.7 | 1.2 | 1.0 | 1.3 | 0.8 | 1.1 | 0.6 | 0.9 | 0.6 | 1.0 | 226.6 (0.5) | 218.8 (0.5) |
| glycinium | −0.0 | 0.4 | 0.4 | −0.0 | 0.3 | 0.7 | 1.7 | 1.7 | 1.3 | 1.5 | 0.1 | 0.3 | 0.1 | 0.5 | 211.9 (0.5) | 203.7 (0.5) |
| MAXE | −2.6 | −2.5 | 2.3 | 2.4 | 2.7 | 2.3 | 3.6 | 3.5 | 3.5 | 3.4 | −4.1 | −4.1 | −4.1 | −4.2 | ||
| RMSE | 1.0 | 1.0 | 1.1 | 1.0 | 1.1 | 0.9 | 1.4 | 1.3 | 1.4 | 1.2 | 1.6 | 1.8 | 1.6 | 1.8 | ||
| MUE | 0.7 | 0.8 | 0.8 | 0.8 | 0.8 | 0.8 | 1.1 | 1.1 | 1.1 | 1.0 | 1.2 | 1.5 | 1.2 | 1.5 | ||
| MSE | −0.2 | −0.4 | 0.4 | 0.2 | 0.5 | 0.3 | 0.6 | 0.3 | 0.8 | 0.5 | −0.7 | −0.9 | −0.7 | −0.9 | ||
a
”Molecule” refers to AH in Eq. 1.
b
hydrogen dimethyl phosphate.