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Recently, an analytical expression for the system size dependence anddirection-dependence of self-diffusion coefficients for neat liquids due tohydrodynamic interactions has been derived for molecular dynamics (MD)simulations using orthorhombic unit cells. Based on this description, we showthat 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 andrepresent 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 areasonable degree of accuracy from the difference of components of thediffusion coefficients in $x$-,$y$- and $z$-direction using the simpleexpression $\eta\!=\!k_\mathrm{B}T\cdot 8.1711245653/[3\piL_z(D_{x}+D_{y}-2D_z)]$, where $k_\mathrm{B}$ denotes Boltzmann's constant, and$T$ represents the temperature. MD simulations of TIP4P/2005 water for varioussystem-sizes using both orthorhombic and cubic box geometries are used to testthe approach.

the journal of physical chemistry. b

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