Exact method for the simulation of Coulombic systems by spherically truncated, pairwise r(-1) summation

Based on a recent result showing that the net Coulomb potential in condense d ionic systems is rather short ranged, an exact and physically transparent method permitting the evaluation of the Coulomb potential by direct summat ion over the r(-1) Coulomb pair potential is presented. The key observation is that the problems encountered in determining the Coulomb energy by pair wise, spherically truncated r(-1) summation are a direct consequence of the fact that the system summed over is practically never neutral. A simple me thod is developed that achieves charge neutralization wherever the r(-1) pa ir potential is truncated. This enables the extraction of the Coulomb energ y, forces, and stresses from a spherically truncated, usually charged envir onment in a manner that is independent of the grouping of the pair terms. T he close connection of our approach with the Ewald method is demonstrated a nd exploited, providing an efficient method for the simulation of even high ly disordered ionic systems by direct, pairwise r(-1) summation with spheri cal truncation at rather short range, i.e., a method which fully exploits t he short-ranged nature of the interactions in ionic systems. The method is validated by simulations of crystals, liquids, and interfacial systems, suc h as free surfaces and grain boundaries. (C) 1999 American Institute of Phy sics. [S0021-9606(99)51517-1].