OrthoBoXY: A Simple Way to Compute True Self-Diffusion Coefficients from MD Simulations with Periodic Boundary Conditions Without Prior Knowledge of the Viscosity

TL;DR

OrthoBoXY introduces a straightforward method to accurately compute true self-diffusion coefficients and viscosity from MD simulations with specific orthorhombic box geometries, eliminating the need for prior viscosity knowledge.

Contribution

The paper presents a novel analytical approach using a specific box ratio to determine true self-diffusion coefficients and viscosity directly from MD simulations without prior viscosity data.

Findings

Self-diffusion coefficients become system-size independent at a specific box ratio.

Viscosity can be estimated accurately from diffusion coefficient differences.

Validated approach with TIP4P/2005 water simulations.

Abstract

Recently, an analytical expression for the system size dependence and direction-dependence of self-diffusion coefficients for neat liquids due to hydrodynamic interactions has been derived for molecular dynamics (MD) simulations using orthorhombic unit cells. Based on this description, we show that for systems with a "magic" box length ratio of $L_z/L_x\!=\!L_z/L_y\!=\!2.7933596497$ the computed self-diffusion coefficients $D_x$ and $D_y$ in $x$- and $y$-direction become system-size independent and represent the true self-diffusion coefficient $D_0\!=\!(D_x+D_y)/2$. Moreover, by using this particular box geometry, the viscosity can be determined with a reasonable degree of accuracy from the difference of components of the diffusion coefficients in $x$-,$y$- and $z$-direction using the simple expression $\eta\!=\!k_\mathrm{B}T\cdot 8.1711245653/[3\pi L_z(D_{x}+D_{y}-2D_z)]$, where $k_\mathrm{B}$ denotes Boltzmann's constant, and $T$ represents the temperature. MD simulations of TIP4P/2005 water for various system-sizes using both orthorhombic and cubic box geometries are used to test the approach.