Electrostatics in periodic slab geometries. I

We propose a new method to sum up electrostatic interactions in two-dimensional (2D) slab geometries. It consists of a combination of two recently proposed methods: the 3D Ewald variant of Yeh and Berkowitz [J. Chem. Phys. 111, 3155 (1999)] and the purely 2D method MMM2D by Arnold and Holm [Chem. Phys. Lett. 354, 324 (2002). The basic idea involves two steps: First we use a three-dimensional summation method whose summation order is changed to sum up the interactions in a slab-wise fashion. Second we subtract the unwanted interactions with the replicated layers analytically. The resulting method has full control over the introduced errors. The time to evaluate the layer correction term scales linearly with the number of charges, so that the full method scales like an ordinary 3D Ewald method, with an almost linear scaling in a mesh based implementation. In this paper we will introduce the basic ideas, derive the layer correction term, and numerically verify our analytical results. (C) 2002 American Institute of Physics