TABLE IV.
Errors of reciprocal potentials and derivatives generated by the charge of the water-1 H1 atom on the water-1 O atom at different PME setups. The analytical values [Eqs. (25)–(28)] were calculated using MATLAB. The interpolation order refers to the rank of the B-spline interpolation method used in PME (see Ref. 48 for details).
| Interpolation order | 5 | 6 | 7 | 8 | 9 | |
|---|---|---|---|---|---|---|
| Ewald coefficient β0 = 0.3 Å−1 | Potential | 1.4 × 10−6 | 3.7 × 10−8 | 6.5 × 10−8 | 1.4 × 10−8 | 5.3 × 10−9 |
| First derivative | 1.8 × 10−4 | 3.8 × 10−5 | 5.5 × 10−6 | 1.1 × 10−6 | 3.4 × 10−7 | |
| Second derivative | 7.7 × 10−4 | 2.1 × 10−4 | 3.0 × 10−5 | 7.8 × 10−6 | 1.8 × 10−6 | |
| Ewald coefficient β0 = 0.4 Å−1 | Potential | 1.4 × 10−5 | 3.7 × 10−6 | 1.6 × 10−6 | 6.8 × 10−7 | 3.2 × 10−7 |
| First derivative | 7.4 × 10−4 | 1.1 × 10−4 | 6.1 × 10−5 | 2.1 × 10−5 | 1.0 × 10−5 | |
| Second derivative | 2.5 × 10−3 | 7.7 × 10−4 | 2.1 × 10−4 | 7.5 × 10−5 | 3.0 × 10−5 | |
| Ewald coefficient β0 = 0.5 Å−1 | Potential | 8.1 × 10−5 | 3.9 × 10−5 | 1.9 × 10−5 | 1.2 × 10−5 | 7.0 × 10−6 |
| First derivative | 2.5 × 10−3 | 7.8 × 10−4 | 4.5 × 10−4 | 2.6 × 10−4 | 1.5 × 10−4 | |
| Second derivative | 6.7 × 10−3 | 2.6 × 10−3 | 1.1 × 10−3 | 6.3 × 10−4 | 3.4 × 10−4 | |