An OrthoBoXY-Method for Various Alternative Box Geometries

TL;DR

This paper generalizes the OrthoBoXY method for orthorhombic MD simulations, optimizing box geometries to improve the accuracy and efficiency of calculating self-diffusion coefficients and shear viscosity.

Contribution

It introduces a generalized approach applicable to any orthorhombic box and identifies new optimal box ratios for system size independence of diffusion coefficients.

Findings

New 'magical' box ratios where $D_x$ becomes system size independent.

Optimized box geometries reduce statistical uncertainties in diffusion and viscosity calculations.

The approach enhances the efficiency of molecular dynamics simulations for isotropic fluids.

Abstract

We have shown in a recent contribution [J. Phys. Chem.B 127, 7983-7987 (2023)] that for molecular dynamics (MD) simulations of isotropic fluids based on orthorhombic periodic boundary conditions with "magic" box length ratios 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. They thus represent the true self-diffusion coefficient $D_0\!=\!(D_x+D_y)/2$, while the shear viscosity can be determined from diffusion coefficients in $x$-, $y$-, and $z$-direction, using the expression $\eta\!=\!k_\mathrm{B}T\cdot 8.1711245653/[3\pi L_z(D_{x}+D_{y}-2D_z)]$. Here we present a more generalized version of this "OrthoBoXY"-approach, which can be applied to any orthorhombic MD box. We would like to test, whether it is possible to improve the efficiency of the approach by using a shape more akin to the cubic form, albeit with different box-length ratios $L_x/L_z\!\neq\! L_y/L_z$ and $L_x\!<\!L_y\!<\!L_z$. We use simulations of systems of 1536 TIP4P/2005 water molecules as a benchmark and explore different box-geometries to determine the influence of the box shape on the computed statistical uncertainties for $D_0$ and $\eta$. Moreover, another "magical" set of box-length ratios is discovered with $L_y/L_z\!=\!0.57804765578$ and $L_x/L_z\!=\!0.33413909235$, where the self-diffusion coefficient in $x$-direction becomes system size independent, such that $D_0\!=\!D_x$.