Calculation of Coulomb interactions in two-dimensionally periodic systems

A generalized implementation is presented of the Lekner method (Lekner, J., 1991, Physica A, 176, 485) of calculating Coulomb interactions in two-dimensionally periodic systems. The generalized scheme eliminates the restriction on the shape of the primary cell, so it is now applicable to systems with non-rectangular shape. The generalized scheme retains the simplicity of the original method so it is easy to incorporate it into molecular dynamics and Monte Carlo codes. Comparisons are made with two other methods for calculating long range interactions in two-dimensionally periodic systems which are based on a Ewald type approach (Heyes, D. M., Barber, M., and Clarke, J. H. R., 1977, J. chem. Sec. Faraday Trans ii, 73, 1485; Hautman, J., and Klein, M. L., 1992, Molec. Phys., 75, 379). The results show that the generalized Lekner method is superior in terms of accuracy, and that the speed of the new implementation is comparable with the method devised by Hautman and Klein.