Electrostatic potentials for simulations of thin layers

We consider coulombic interactions between particles confined to a region between two half spaces of a dielectric constant different to that of the region in between and with periodic boundary conditions with square unit cells imposed along the surfaces of the plane slab shaped region. We find two representations for the resulting lattice sums and discuss the construction of an algorithm which can optimize numerical performance (in terms of computer time) by using the two representations in different circumstances. Analysis of the resulting algorithm for the coulombic interactions shows that the computation time for the optimized algorithm for an N particle system should grow as N 5/3.

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