Table 1. Calculated Interaction Energies Are Compared to “Gold Standard” CCSD(T) Binding Energies for 10 Methods Using 8 Different Data Sets, Which All Probe Different Types of Interactionsa.
| S22 |
S66 |
S66 (disp)c |
L7 |
|||||
|---|---|---|---|---|---|---|---|---|
| method | RMSD | MSD | RMSD | MSD | RMSD | MSD | RMSD | MSD |
| DFTB3b | 4.1 | 3.4 | 3.0 | 2.7 | 3.4 | 3.1 | 15.9 | 14.1 |
| DFTB3-D3b | 1.5 | 0.7 | 1.1 | 0.4 | 0.6 | –0.4 | 2.3 | –1.4 |
| DFTB3-D3H4b | 1.2 | 0.5 | 0.9 | 0.3 | 0.5 | 0.3 | 2.6 | 0.8 |
| DFTB3/CPE(q)-D3b | 1.1 | 0.5 | 0.6 | 0.0 | 0.7 | –0.3 | 2.1 | –0.6 |
| PM6b | 4.2 | 3.4 | 3.0 | 2.7 | 2.8 | 2.6 | 12.8 | 10.9 |
| PM6-D3H4b | 0.8 | 0.4 | 0.6 | 0.2 | 0.4 | 0.1 | 3.4 | –1.1 |
| OM2 | 3.7 | 3.1 | 2.9 | 2.6 | 3.2 | 3.1 | 16.1 | 14.0 |
| OM2-D3 | 1.4 | 0.9 | 1.1 | 0.6 | 0.4 | 0.1 | 2.6 | 0.6 |
| B3LYP/6-31G(d) | 3.7 | 1.6 | 2.7 | 1.3 | 4.0 | 3.8 | 18.7 | 15.6 |
| B3LYP-D3/6-31G(d) | 2.9 | –2.4 | 2.3 | –2.1 | 1.6 | –1.5 | 7.9 | –7.5 |
| B3LYP/def2-QZVP | 5.0 | 3.7 | 3.8 | 3.2 | 5.4 | 5.2 | 22.7 | 20.1 |
| B3LYP-D3/def2-QZVP | 0.6 | –0.3 | 0.4 | –0.3 | 0.2 | –0.2 | 3.2 | –3.0 |
| S66 (pol)d |
C15e |
I9 |
large water |
|||||
|---|---|---|---|---|---|---|---|---|
| method | RMSD | MSD | RMSD | MSD | RMSD | MSD | RMSD | MSD |
| DFTB3b | 2.9 | 2.6 | 6.0 | 4.8 | 5.6 | 4.7 | 14.2 | 11.1 |
| DFTB3-D3b | 1.8 | 1.3 | 5.0 | 3.6 | 3.9 | 2.6 | 2.0 | –1.4 |
| DFTB3-D3H4b | 1.0 | –0.2 | 4.1 | 2.2 | 4.7 | 2.7 | 23.9 | –20.3 |
| DFTB3/CPE(q)-D3b | 0.6 | 0.1 | 1.5 | 0.6 | 1.7 | 0.5 | 3.0 | –1.9 |
| PM6b | 3.8 | 3.2 | 4.6 | 4.3 | 9.1 | 8.5 | 34.8 | 27.9 |
| PM6-D3H4b | 0.6 | 0.0 | 1.5 | 0.8 | 6.0 | 5.6 | 11.0 | 8.9 |
| OM2 | 3.0 | 2.9 | 3.2 | 2.9 | (5.7)f | (6.1)f | 26.0 | 20.4 |
| OM2-D3 | 1.9 | 1.7 | 2.3 | 1.9 | (4.1)f | (4.6)f | 14.0 | 10.9 |
| B3LYP/6-31G(d) | 1.4 | –1.2 | 3.5 | –3.2 | 10.0 | –8.7 | 53.0 | –44.8 |
| B3LYP-D3/6-31G(d) | 3.3 | –3.2 | 5.2 | –5.0 | 12.8 | –12.0 | 72.5 | –60.4 |
| B3LYP/def2-QZVP | 1.6 | 1.4 | 1.0 | 0.9 | 1.3 | 1.2 | 10.5 | 6.7 |
| B3LYP-D3/def2-QZVP | 0.7 | –0.6 | 1.0 | –0.9 | 2.3 | –2.1 | 9.7 | –8.9 |
a
The root-mean-squared deviation (RMSD) and the mean signed deviation (MSD) between the calculated and reference energies are given in units of kcal/mol. A positive MSD value implies a tendency to the underbinding of complexes.
b
DFTB and PM6 values from ref (117).
c
Only the “dispersion” subset of S66 is considered here.
d
Only the “polar” subset of S66 is considered here.
e
“C15” refers to the set of 15 charged hydrogen-bonding complexes from ref (121).
f
Due to lack of OM2 parameters for sulfur, three complexes are left out of the OM2 and OM2-D3 statistics for the I9 set.