A COMPARISON OF EWALD SUMMATION TECHNIQUES FOR PLANAR SURFACES

Ewald-like summation methods to compute the electrostatic Coulomb pote ntial and the forces on charged particles in a two-dimensional periodi c system with nonperiodic extension to the third dimension are investi gated. The techniques by Hautman and Klein, Mel. Phys. 75 (1992) 379 ( HK), Heyes, Barber, and Clarke, J. Chem. Sec. Faraday Trans. II 73 (19 77) 1485 (HBC), and Nijboer and de Wette, Physica A 125 (1984) 275 (Nd W) are compared in respect to their numerical accuracy and efficiency. The convergence behaviour of the methods is analysed for different ma gnitudes of the nonperiodic z-separation between the charged particles up to twice the length of the square simulation cell. The HK method i s best suited for small z but becomes inefficient for large particle s eparations in the nonperiodic direction. HBC is not sensitive on the o ut-of-plane separation but is very slow. NdW is only suited for large out-of-plane distances because it fails completely if the z-separation of any two particles becomes zero. Ready-to-implement sets of equatio ns for the three algorithms are presented in the appendices. (C) 1997 Elsevier Science B.V.