Simulations of non-neutral slab systems with long-range electrostatic interactions in two-dimensional periodic boundary conditions

We introduce a regularization procedure to define electrostatic energies and forces in a slab system of thickness h that is periodic in two dimensions and carries a net charge. The regularization corresponds to a neutralization of the system by two charged walls and can be viewed as the extension to the two-dimensional (2D)+h geometry of the neutralization by a homogeneous background in the standard three-dimensional Ewald method. The energies and forces can be computed efficiently by using advanced methods for systems with 2D periodicity, such as MMM2D or P3M/ELC, or by introducing a simple background-charge correction to the Yeh-Berkowitz approach of slab systems. The results are checked against direct lattice sum calculations on simple systems. We show, in particular, that the Madelung energy of a 2D square charge lattice in a uniform compensating background is correctly reproduced to high accuracy. A molecular dynamics simulation of a sodium ion close to an air/water interface is performed to demonstrate that the method does indeed provide consistent long-range electrostatics. The mean force on the ion reduces at large distances to the image-charge interaction predicted by macroscopic electrostatics. This result is used to determine precisely the position of the macroscopic dielectric interface with respect to the true molecular surface.