Computing Accurate True Self-Diffusion Coefficients and Shear Viscosities Using the OrthoBoXY-Approach

In a recent paper [J. Phys. Chem.B 127, 7983-7987 (2023)] , we have shown that for molecular dynamics (MD) simulations using orthorhombic periodic boundary conditions with "magic" box length ratios of $L_z/L_x=L_z/L_y=2.7933596497$, the self-diffusion coefficients $D_x$ and $D_y$ in $x$- and $y$-direction are independent from the system size. They both represent the true self-diffusion coefficient $D_0=(D_x+D_y)/2$, while the shear viscosity can be calculated from diffusion coefficients in $x$-,$y$- and $z$-direction, using $\eta=k_\mathrm{B}T\cdot 8.1711245653/[3\pi L_z(D_{x}+D_{y}-2D_z)]$. In this contribution, we test this "OrthoBoXY"-approach by its application to a variety of different systems: liquid water, dimethyl ether, methanol, triglyme, water/methanol mixtures, water/triglyme mixtures, and imidazolium based ionic liquids. The chosen systems range from small-sized molecular liquids to complex mixtures and ionic liquids, while spanning a viscosity range of almost three orders of magnitude. We assess the efficiency of the method for computing true self-diffusion and viscosity data and provide simple formulae for estimating the required MD simulation lengths and sizes for delivering reliable data with targeted uncertainty levels. Our analysis of the system-size dependence of statistical uncertainties for both the viscosity and the self-diffusion coefficient leads us to the conclusion that it is preferable to extend the simulation length instead of increasing the system size. MD simulations consisting of 768 molecules or ion pairs seem to be perfectly adequate.