(178z) Slab-Based (SB) Ewald: An Efficient Lattice Sum Method for Lennard-Jones Fluids with 1-D Density Variations

We present a modified Ewald sum for the Lennard-Jones (LJ) fluid called slab-based (SB) Ewald, which is more efficient than the full Ewald sum for systems in which the average density varies in only one direction, such as the planar liquid-vapor interface commonly used to measure surface tension. For homogeneous simulations (uniform average density) the LJ potential is usually truncated at some radial distance, and interactions beyond the cutoff are handled using standard tail corrections based on the average system density. However, for inhomogeneous (non-uniform) systems, these standard tail corrections may be inadequate and more sophisticated long-range corrections may need to be applied at every timestep. For instance, in the absence of proper long-range corrections, the surface tension and phase behavior, including the critical point, of an LJ fluid depend highly upon cutoff radius. For inhomogeneous LJ systems, one can use slab-based methods [1], which account for inhomogeneity in one direction but still assume that the radial distribution function is unity past the cutoff radius. However, traditional slab-based methods fail to properly account for periodic boundary conditions. The new SB Ewald sum presented here remedies this problem by essentially applying a lattice sum in one dimension and standard tail corrections (using the local density) in the other 2 dimensions.  The new method is much faster than the traditional (full) LJ Ewald sum for simulations of planar liquid-vapor interfaces and can also be used for the recently developed chemical potential perturbation (CPP) method of predicting chemical potential [2].  The SB Ewald method can also be extended to other intermolecular potentials of the form A*r^-n, where n>3.  The new SB Ewald sum method is tested by predicting the surface tension and chemical potential of an LJ fluid at several different temperatures, and results agree well with the full Ewald sum method as well as data reported previously in literature.

References:

[1] J. Janecek, J. Phys. Chem. B 110, 6264 (2006)

[2] S. G. Moore and D. R. Wheeler, J. Chem. Phys. 134, 114514 (2011)