Spline Approximation of "Effective" Potentials under Periodic Boundary Conditions

Abstract

The use of spline functions to approximate the "effective" interparticle 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 Tm of a Yukawa system by means of molecular dynamics simulations, we observe values for Tm that are virtually independent of the particle number N if the pair potential includes the spline correction term and N ≥ 250, whereas using only the "minimum image" method gives Tm values that systematically decrease and attain the asymptotic value only for N ≥ 5000. © 1994 Academic Press. All rights reserved.