![]() Heuristic unwrapping overestimates the diffusion coefficient in long NpT MD simulations of small systems. The quality factor serves as a measure of how well the data concur with predictions from a minimal diffusive model. Even without a reference value to compare to, the issues of heuristic unwrapping became apparent in our analysis of the quality factor Q, which took values significantly below its expected value of Q ≈ 1/2 for heuristically unwrapped trajectories. 1 to results from a correct unwrapping scheme (see below). 2(a), where we compare the heuristically unwrapped NpT data of Fig. The associated diffusion coefficient was also grossly overestimated, as shown in Fig. Importantly, though, the MSD remained linear after ≈3 ps. For a few water molecules in the NpT simulation, the heuristic unwrapping scheme caused an unphysical speed-up, which resulted in an overall acceleration of the average MSD when compared to the NVT simulation. 1, where we compare MSD estimates from two 1 µs MD simulations of TIP4P-D water, which coincide in every aspect, except that one was performed in the NVT ensemble and the other in the NpT ensemble (further details of the simulation procedure can be found in the supplementary material). Repeated failures then result in unphysical amplifications of the corrective displacements, which eventually dominate over the actual particle motion.Ī consequence of these shortcomings is depicted in Fig. The heuristic unwrapping scheme fails at constant pressure because it uses the current box size to net-reverse all jumps through the periodic boundaries up to the most recent time step, instead of the respective box sizes for each time step where a jump occurred. The particles therefore experience two kinds of displacements: first, their ordinary motion due to collisions and interactions with neighboring particles and, second, a corrective displacement to maintain their relative position inside the box when its volume is varied by the barostat and particle positions are rescaled accordingly. In the NpT ensemble, barostats dynamically adjust the volume of the simulation box to maintain a constant pressure. In this Communication, we demonstrate that this widely used heuristic trajectory unwrapping scheme is not suitable for simulations at constant pressure p. 2 t i ( i = 0, 1, …) are the discrete time steps of the saved trajectory, with Δ t = t i+1 − t i being the time-step size if every structure is considered in the unwrapping procedure. MSDs are routinely used for diffusion coefficient estimation via ad hoc fitting to the Einstein relation, although recent developments show that more accurate results can be retrieved either from a rigorous analysis of the particle displacements 1 or by properly accounting for MSD correlations. Calculations of observables, such as the mean squared displacement (MSD), require that the saved, wrapped trajectories r → w ( t i ) are unwrapped back into full space, r → w ( t i ) ↦ r → u ( t i ), in a post-processing step. The particle positions in full space, r → u ∈ R 3, are then wrapped into a reference simulation box, e.g., centered at the origin with r → w ∈ − L / 2, L / 2 3 for a cubic box with edge length L. Molecular dynamics (MD) simulations are routinely performed under periodic boundary conditions (PBCs). We provide practitioners with a formula to assess if and by how much earlier results might have been affected by the widely used heuristic unwrapping scheme. Here and in another paper, we apply the new unwrapping scheme to extensive molecular dynamics and Brownian dynamics simulation data. At each time step, we add the minimal displacement vector according to periodic boundary conditions for the instantaneous box geometry. We propose an alternative unwrapping scheme that resolves this issue. Improper accounting for box-volume fluctuations creates, at long times, unphysical trajectories and, in turn, grossly exaggerated diffusion coefficients. Here, we show that a widely used heuristic unwrapping scheme is not suitable for long simulations at constant pressure. For diffusion coefficient calculations using the Einstein relation, the particle positions need to be unwrapped. In molecular dynamics simulations under periodic boundary conditions, particle positions are typically wrapped into a reference box. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |