New Framework for Computing a General Local Self-Diffusion Coefficient Using Statistical Mechanics.

Area of Science:

• Statistical Mechanics
• Physical Chemistry
• Computational Materials Science

Background:

• The local diffusion coefficient (D) is crucial for understanding molecular transport.
• Existing definitions of D often lack a rigorous statistical mechanical basis.
• Anisotropic diffusion and inhomogeneous systems present challenges for accurate D determination.

Purpose of the Study:

• To derive modified Green-Kubo expressions for the local diffusion coefficient (D).
• To establish these expressions as valid statistical mechanical results.
• To ensure broad applicability, especially in complex nanoscale and inhomogeneous systems.

Main Methods:

• Application of linear response theory.
• Development of modified Green-Kubo expressions.
• Validation using molecular simulations of systems with anisotropic diffusion and inhomogeneous density profiles.

Main Results:

• Obtained widely applicable, modified Green-Kubo expressions for D.
• Confirmed that these expressions are statistical mechanical results.
• Demonstrated agreement between different expressions in large systems.
• Validated applicability to arbitrarily small local regions.

Conclusions:

• The derived Green-Kubo expressions offer a robust statistical mechanical framework for calculating local diffusion coefficients.
• These expressions are suitable for analyzing nanoscale and inhomogeneous systems.
• The findings advance the understanding and simulation of diffusion in complex materials.