Local diffusion analysis using square displacement averaged in subspace.

Area of Science:

• Computational Chemistry
• Physical Chemistry
• Statistical Mechanics

Background:

• Mean square displacement (MSD) typically shows a linear relationship with time, yielding global diffusion coefficients.
• Local MSD, averaged over system subspaces, exhibits nonlinear time dependence, reflecting local diffusion.
• Extracting local diffusion coefficients requires analyzing this nonlinear MSD-time relationship.

Purpose of the Study:

• To derive an analytical expression for local MSD's nonlinear behavior.
• To enable accurate estimation of local diffusion coefficients.
• To validate the method for molecules in bulk water and near hydrophobic interfaces.

Main Methods:

• Derived an analytical expression for local MSD using Edgeworth expansion up to fourth order.
• Employed regression analysis to estimate local diffusion coefficients.
• Applied the method to hydrogen in water and methane near a hydrophobic interface.

Main Results:

• Accurate estimation of local diffusion coefficients for hydrogen in bulk water with <20% deviation.
• Successful analysis of methane diffusion near a hydrophobic interface.
• Identified limitations in regions influenced by higher-order Edgeworth expansion terms.

Conclusions:

• The developed method provides a reliable way to determine local diffusion coefficients.
• The approach is applicable to both homogeneous and heterogeneous systems.
• Further research is needed to address limitations in complex interfacial regions.