Error estimation on the box size correction formula of diffusion coefficient in molecular simulations.

Area of Science:

• Computational Physics
• Materials Science
• Chemical Engineering

Background:

• Correcting diffusion coefficients for simulation box size is crucial for accurate extrapolation in molecular simulations.
• The Yeh-Hummer formula, a common fluid dynamics-based correction, presents application challenges and uncertainties.
• Review of error issues in diffusion coefficient calculations highlights the need for improved correction methods.

Purpose of the Study:

• To address uncertainties in applying the Yeh-Hummer correction formula for diffusion coefficients.
• To propose a novel correction formula based on mathematical statistics for improved simulation accuracy.
• To evaluate the performance of the new formula against the Yeh-Hummer method using simulation data.

Main Methods:

• Molecular dynamics simulations were performed using the LAMMPS package in the NVT ensemble.
• The Lennard-Jones 12-6 potential model was employed with specific parameters for reduced units.
• Extensive simulation steps were conducted to ensure system equilibration and accurate trajectory data collection.

Main Results:

• The study investigated the dependence of the diffusion coefficient on particle number in Lennard-Jones fluids.
• A new correction formula was developed, converging faster with increasing particle numbers.
• The proposed formula demonstrated slightly better agreement with simulation results compared to the Yeh-Hummer formula.

Conclusions:

• The new correction formula offers a more reliable approach for adjusting diffusion coefficients based on simulation box size.
• This work provides a statistically grounded alternative to existing methods, enhancing the predictive power of molecular simulations.
• Further validation and application of the new formula are recommended for broader use in computational studies.