Dispersion Corrections to the Surface Tension at Planar Surfaces

Molecular dynamics simulations are usually performed using cutoffs (r(c)) for the short-ranged dispersion interactions (r(-6)). For isotropic systems, long-range interactions are often added in a continuum approximation. This usually leads to excellent results that are independent of the cutoff length down to about 1 nm. For systems with interfaces or other anisotropic systems the situation is more complicated. We study here planar interfaces, focusing on the surface tension, which is sensitive to cutoffs. Previous analytic results giving the long-range correction to the surface tension of a liquid-vapor interface as a two- or three-dimensional integral are revisited. They are generalized by introducing a dispersion density profile which makes it possible to handle multicomponent systems. For the simple but common hyperbolic tangent profile the integral may be Taylor-expanded in the dimensionless parameter obtained by dividing the profile width with the cutoff length. This parameter is usually small, and excellent agreement with numerical calculations of the integral is obtained by keeping two terms in the expansion. The results are compared to simulations with different lengths of the cutoff for some simple systems. The surface tension in the simulations varies linearly in r(c)(-2), although a small r(c)(-4)-term may be added to improve the agreement. The slope of the r(c)(-2)-line could in several cases be predicted from the change in dispersion density at the interface. The disagreements observed in some cases when comparing to theory occur when the finite cutoff used in the simulations causes structural differences compared to long-range cutoffs or Ewald summation for the r(-6)-interactions.