Electrostatics in Periodic Slab Geometries II
  In a previous paper a method was developed to subtract the interactions due to periodically replicated charges (or other long-range entities) in one spatial dimension. The method constitutes a generalized "electrostatic layer correction" (ELC) which adapts any standard 3D summation method to slab-like conditions. Here the implementation of the layer correction is considered in detail for the standard Ewald (EW3DLC) and the PPPM mesh Ewald (PPPMLC) methods. In particular this method offers a strong control on the accuracy and an improved computational complexity of O(N log N) for mesh-based implementations. We derive anisotropic Ewald error formulas and give some fundamental guidelines for optimization. A demonstration of the accuracy, error formulas and computation times for typical systems is also presented. 
Jason de Joannis, Axel Arnold, Christian Holm