Systematic errors in diffusion coefficients from long-time molecular dynamics simulations at constant pressure

Area of Science:

• Computational physics
• Physical chemistry

Background:

• Molecular dynamics (MD) simulations are crucial for understanding particle behavior.
• Periodic boundary conditions (PBC) are standard in MD, requiring particle positions to be wrapped within a reference box.
• Calculating diffusion coefficients using the Einstein relation necessitates unwrapping particle positions.

Purpose of the Study:

• To identify limitations of a common particle unwrapping heuristic in MD simulations.
• To propose and validate a novel, accurate unwrapping scheme for MD simulations.
• To provide a method for assessing the impact of previous unwrapping inaccuracies on simulation results.

Main Methods:

• The study analyzes a widely used heuristic particle unwrapping scheme.
• A new unwrapping scheme is proposed, adding minimal displacement vectors based on instantaneous box geometry at each time step.
• The new scheme was tested on extensive molecular dynamics and Brownian dynamics simulation data.

Main Results:

• The heuristic unwrapping scheme was found unsuitable for long simulations at constant pressure.
• Improper handling of box-volume fluctuations in the heuristic scheme leads to unphysical trajectories and inflated diffusion coefficients.
• The proposed alternative scheme effectively resolves these issues, yielding accurate simulation data.

Conclusions:

• The heuristic particle unwrapping method can introduce significant errors in diffusion coefficient calculations.
• The newly proposed unwrapping scheme provides accurate particle trajectories and diffusion coefficients, even in long simulations at constant pressure.
• A formula is provided to help researchers evaluate potential errors in prior simulation studies.