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

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 Lz/Lx = Lz/Ly = 2.7933596497 the computed self-diffusion coefficients Dx and Dy in the x- and y-direction become system-size independent and represent the true self-diffusion coefficient D0 = (Dx + Dy)/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-directions using the simple expression η = kBT × 8.1711245653/[3πLz(Dx + Dy - 2Dz)], where kB 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.