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

Bisma Akram1,2, Xiangfei Ji3, Yimeng Zhang1,2

  • 1School of Semiconductor and Physics, North University of China, Taiyuan, 030051, China.

Journal of Molecular Modeling
|May 18, 2026
PubMed
Summary

A new formula improves diffusion coefficient corrections in molecular simulations, offering better accuracy than the Yeh-Hummer method for extrapolating small simulation box sizes to real systems.

Keywords:
Box size correctionDiffusion coefficientError estimationMolecular dynamics

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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.