Results for Configurational Sampling

We compute the relative error in several average quantities, for each experiment shown in Fig. 7.6. These computed errors are relative to a baseline solution, computed using the Stochastic Position Verlet scheme, at y = 1/ps and h = 0.5 fs. The timestep for the baseline scheme is small enough that discretization effects will be negligible. 

One salient feature of the results of Fig. 7.7, is that for the BAOAB] scheme there is consistently less than a 1 % error in the computed configurational temperature (for moderate friction) across all step sizes, even the largest stable timesteps tested. The relative errors obtained were so small that no discernable trend (with step size) can be shown (due to the sampling error), whereas the other schemes tested show an error consistent with second-order discretization. 

In order to provide a more realistic comparison to practical molecular dynamics simulation, we immerse the alanine dipeptide molecule in a sphere of flexible TIP3P water (10 A radius, total system contains 424 atoms, see Fig. 7.8) and equilibrate for 1 ns at 300K to generate an initial configuration. Simulations were completed with each scheme considered in the unsolvated case, using a lOA cutoff for the electrostatic and van der Waals potentials. 

Given the significant increase in dimensionality of the system, we consider only measuring the effect of varying the stepsize on the computed averages. We choose a moderate value for the friction (we fix it at 1/ps in all simulations) which gave 

The ABOBA] and SPY schemes perform very well, with only a noticeable difference from the exact distribution as the step size approaches its stability limit. Some schemes, such as BBK or OABAO perform very poorly, with even the smallest step sizes tested giving a visible difference between the distributions. This indicates that the system is able to access much higher energy states than it would do in exact sampling. At the highest step sizes the exact and observed distributions have very little overlap, suggesting a complete failure to sample the system. 

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