Neighborship partition of the radial distribution function for simple liquids

Publisher Website
Google Scholar
Abstract
In a disordered system of N particles, the probability of finding any neighbor at a given distance from a reference particle is described by the radial distribution function G(r). In many instances it would also be useful to know the distribution functions P(1,r),P(2,r),...,P(n,r) corresponding to each subset of ‘‘neighborship;’’ namely, the nearest, next nearest, ...nth nearest neighbor. While G(r) is a two-particle correlation function, each P(n,r) is formally dependent upon all levels of multiparticle correlations. By means of suitable approximations relating higher-order correlations to two-particle correlations, it becomes possible to calculate P(n,r) from G(r). This approach takes advantage of the fact that G(r) is often accurately known from either experiment or theory. For the case of hard spheres, the superposition approximation and a first-order correction to it are found to give P(1,r) in good agreement with simulations and earlier analytic results, even at high densities. P(n,r) for neighborships n≥1 are obtained for the first time. These reveal some interesting features of structure within and beyond the first shell.