Table 3. Parameters used in long-timescale simulations of SPC-Fw water, and the accuracy of forces resulting from each approximation.
The four simulations utilize either SPME or MLE calculations for long-ranged electrostatic interactions. While all simulations make use of the same direct space cutoffs, the “conservative” simulations use roughly 60% more data in Q for their SPME or MLE calculations. The “conservative” MLE scheme approximates the SPME results much more accurately than the equivalent SPME calculation obtains the true electrostatic force on each particle, as judged by a high-quality SPME calculation using g = (96×96×96) and I(pm) = 8. In contrast, the “aggressive” SPME scheme is somewhat less accurate and the “aggressive” MLE scheme introduces roughly the same amount of error as the equivalent SPME scheme. Results from the simulations are presented in Figures 10 and 11 and Table 6.
| Parameter | Conservative | Aggressive | ||
|---|---|---|---|---|
| SPME | MLE | SPME | MLE | |
|
| ||||
| Lcut (LJ, Å)a | 10.0 | 10.0 | 10.0 | 10.0 |
| Lcut (Elec, Å)b | 9.0 | 9.0 | 8.0 | 8.0 |
| σ, Å | 1.58 | 1.58 | 1.43 | 1.43 |
| g | (24×36×36) | (24×36×36) | (21×32×32) | (21×32×32) |
| I (pm) | (6×4×4) | (6×4×4) | (6×4×4) | (6×4×4) |
| I (mm) | 8 | 8 | ||
| Cyz,2, Cyz,3 | (2,4) | (2,4) | ||
| Tcut,1, Tcut,2 | (1,5) | (0,4) | ||
|
| ||||
| ⟨ΔF(dir)⟩ c | 4.9×10−3 | 4.9×10−3 | 7.7×10−3 | 7.7×10−3 |
| ⟨ΔF(rec)⟩ d | 2.3×10−3 | 2.5×10−3 | 8.9×10−3 | 1.3×10−2 |
Lennard-Jones potential truncation length
Electrostatic direct space trucation length
RMS error in direct space electrostatic forces with this approximation
RMS error in reciprocal space electrostatic forces with this approximation (including MLE approximation, if applicable)