Table 1.
The calculated relative energies (in kcal/mol) between the optimized and partially optimized structures of H5O2+, CH3OH…H+…OH2 and CH3COOH…OH2 and mean unsigned errors (in kcal/mol).
| Methods | H5O2+ | CH3OH…H+…OH2 | CH3COOH…OH2 | MUE(3)a | MUE(8)b | |||||
|---|---|---|---|---|---|---|---|---|---|---|
|
| ||||||||||
| (Ec − Eb) | (Ec − Ea) | (Eb − Ea) | (EC − EB) | (EC − EA) | (EB − EA) | ΔE1 | ΔE2 | |||
| Wave function theory | ||||||||||
| CCSD(T)-F12a/jun-cc-pVTZ//M | 5.27 | 9.99 | 4.72 | 9.85 | 11.93 | 2.09 | 183.43 | -10.61 | 0.00 | 0.00 |
| MP2/MG3S | 5.15 | 9.97 | 4.82 | 9.48 | 11.82 | 2.34 | 182.87 | -10.68 | 0.08 | 0.20 |
| CCSD(T)/MG3S//M | 5.59 | 10.12 | 4.53 | 10.25 | 12.12 | 1.87 | 184.50 | -10.70 | 0.21 | 0.33 |
| CCSD(T)/MG3S//C | 5.61 | 10.12 | 4.51 | 10.23 | 12.32 | 2.09 | 186.47 | -10.68 | 0.23 | 0.83 |
| CCSD/MG3S | 6.42 | 10.60 | 4.17 | 11.28 | 13.18 | 1.89 | 185.48 | -9.99 | 0.77 | 0.91 |
| HF/MG3S | 10.43 | 13.20 | 2.78 | 16.41 | 17.40 | 0.99 | 187.19 | -7.61 | 3.44 | 3.77 |
| HF/STO-3G | 3.18 | 24.22 | 21.05 | 6.64 | 24.06 | 17.42 | 249.33 | -10.86 | 10.89 | 16.18 |
| Hybrid density functional theory | ||||||||||
| M06/MG3S | 5.07 | 10.21 | 5.14 | 9.37 | 11.32 | 1.95 | 182.85 | -11.10 | 0.28 | 0.29 |
| PW6B95/MG3S | 4.78 | 9.79 | 5.01 | 9.35 | 11.64 | 2.30 | 183.60 | -10.09 | 0.33 | 0.33 |
| M08-HX/MG3S | 5.42 | 9.73 | 4.31 | 9.81 | 12.03 | 2.22 | 181.93 | -11.57 | 0.27 | 0.44 |
| M08-SO/MG3S | 5.25 | 9.75 | 4.49 | 9.75 | 11.56 | 1.81 | 181.92 | -11.73 | 0.16 | 0.48 |
| M05/MG3S | 4.37 | 9.75 | 5.38 | 9.13 | 10.80 | 1.67 | 183.21 | -10.47 | 0.60 | 0.49 |
| PBE0/MG3S | 4.03 | 9.99 | 5.96 | 8.29 | 11.35 | 3.06 | 183.15 | -10.73 | 0.83 | 0.75 |
| M06-2X/MG3S | 3.94 | 10.25 | 6.31 | 8.30 | 11.73 | 3.43 | 183.73 | -11.29 | 1.06 | 0.91 |
| B3LYP/MG3S | 3.82 | 8.94 | 5.12 | 8.33 | 10.67 | 2.34 | 183.06 | -9.59 | 0.97 | 0.92 |
| PWB6K/MG3S | 6.38 | 11.55 | 5.17 | 11.15 | 13.65 | 2.50 | 184.62 | -10.81 | 1.04 | 0.99 |
| M05-2X/MG3S | 3.41 | 9.75 | 6.34 | 8.05 | 11.35 | 3.30 | 183.65 | -11.19 | 1.24 | 1.02 |
| Density functional theory without HF exchange | ||||||||||
| M06-L/MG3S | 4.06 | 8.80 | 4.75 | 8.31 | 10.32 | 2.01 | 184.80 | -10.83 | 0.81 | 0.72 |
| VSXC/MG3S | 4.18 | 7.67 | 3.49 | 9.82 | 10.92 | 1.10 | 182.90 | -12.32 | 1.55 | 1.11 |
| SOGGA11/MG3S | 3.17 | 9.43 | 6.26 | 7.19 | 10.27 | 3.08 | 179.84 | -6.49 | 1.40 | 2.15 |
| PBE/MG3S | 1.96 | 7.56 | 5.60 | 5.67 | 8.43 | 2.76 | 181.24 | -11.04 | 2.21 | 2.20 |
| BLYP/MG3S | 2.14 | 6.82 | 4.68 | 6.24 | 8.27 | 2.03 | 169.35 | -8.87 | 2.11 | 3.68 |
| Semiempirical molecular orbital theory including overlap | ||||||||||
| SCC-DFTB | 4.07 | 9.26 | 5.19 | 6.22 | 8.96 | 2.74 | 185.36 | -7.97 | 0.80 | 1.78 |
| NDDO Methods | ||||||||||
| PMO | 4.32 | 8.40 | 4.07 | … | … | … | … | … | 1.06 | … |
| PDDG/PM3 | 8.28 | 9.90 | 1.62 | 8.93 | 10.17 | 1.24 | 192.07 | -5.01 | 2.06 | 3.00 |
| RM1 | 2.44 | 10.69 | 8.25 | 2.51 | 9.34 | 6.83 | 185.39 | -3.85 | 2.36 | 3.81 |
| AM1 | 9.60 | 7.43 | -2.18 | 12.97 | 10.13 | -2.84 | 190.29 | -7.44 | 4.60 | 4.21 |
| PM3 | 12.67 | 8.84 | -3.84 | 13.81 | 14.13 | 0.32 | 194.85 | -5.97 | 5.70 | 5.14 |
| PM6 | 0.00 | 3.41 | 3.41 | 0.89 | 3.34 | 2.45 | 166.44 | -8.90 | 4.38 | 6.22 |
| PDDG/MNDO | 13.15 | 14.53 | 1.38 | 14.98 | 14.51 | -0.47 | 166.38 | -1.17 | 5.25 | 6.56 |
| MNDO | 20.63 | 21.45 | 0.82 | 21.64 | 23.40 | 1.76 | 186.19 | -0.88 | 10.24 | 8.35 |
a
MUE(3) is the unsigned error averaged over the three energy differences of H5O2+.
b
MUE(8) is the unsigned error averaged over all eight relative energies.