An OrthoBoXY-Method for Various Alternative Box Geometries

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 $D_0\!=\!D_x$.