An OrthoBoXY-method for various alternative box geometries

Abstract

We have shown in a recent contribution [Busch and Paschek, J. Phys. Chem. B, 2023 127, 7983–7987] that for molecular dynamics (MD) simulations of isotropic fluids based on orthorhombic periodic boundary conditions with “magical” 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 D₀ = (D_x + D_y)/2, while the shear viscosity can be determined from diffusion coefficients in x-, y-, and z-direction, using the expression η = k_BT·8.1711245653/[3πL_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 of any shape. In particular, we would like to test, how the efficiency is affected by using a shape more akin to the cubic form, albeit with different box length ratios L_x/L_z ≠ L_y/L_z and L_x < L_y < L_z. We use NVT and NpT 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 D₀ and η. 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 D₀ = D_x.