SPLINE APPROXIMATION OF EFFECTIVE POTENTIALS UNDER PERIODIC BOUNDARY-CONDITIONS

The use of spline functions to approximate the ''effective'' inter-particle potentials that result from taking into account all image particles in periodic-boundary-condition Monte Carlo or molecular dynamics simulations is described. Such approximations are intrinsically very ''smooth,'' easy to construct, relatively inexpensive to evaluate, and can provide a high degree of accuracy. The asymptotic properties of systems governed by long-range interactions may thus be determined using relatively small particle numbers. A number of implementation issues are discussed in detail, including the choice of end conditions, economical storage of the spline coefficients, conversion to B-spline form, and efficient evaluation procedures. Applied to the problem of locating the melting temperature T-m of a Yukawa system by means of molecular dynamics simulations, we observe values for T-m that are virtually independent of the particle number N if the pair potential includes the spline correction term and N greater than or similar to 250, whereas using only the ''minimum image'' method gives T-m values that systematically decrease and attain the asymptotic value only for N greater than or similar to 5000. (C) 1994 Academic Press, Inc.