Pair Distribution Function for Particles in a Box

Abstract

ONE method of studying the thermodynamic properties of simple liquids is to consider the packing statistics of finite model assemblages of rigid spheres¹. This finite model approach yields not the well known pair distribution function, which describes the average distribution of atoms about a typical atom in an infinite liquid, but rather a pair distribution histogram R(ρ). For an assemblage containing N spheres, NR(ρ)δρ gives the number of pairs of spheres the centres of which are separated by distances in the interval (ρ, ρ + δρ). Of course, in the limit of an infinitely large model (N→∞) and infinitesimally small histogram interval (δρ→0), R(ρ) becomes equivalent to the usual pair distribution function. One of the difficulties associated with a finite model is that edge effects seriously impair the usefulness of R(ρ) as an approximation to the radial distribution function. Clearly, any method of eliminating the edge effects from R(ρ) is of considerable interest.