Multi-theta distributions of local structures in condensed matter: a new route to triplet and higher-order molecular distributions from scattering data

Abstract

Triplet and higher-order molecular distributions in condensed media are obtained from pair distributions by extension of a method based on the notion of spatial Markoffian-like processes for local ordered structures. The extension is achieved by defining the spatial process in terms of multivariate theta distributions, in full analogy with multivariate distributions of a temporal Gaussian process. This result enables one to obtain effective pair potentials from empirical radial distributions by solving the BKY integral equation relating the pair potential to pair and triplet distributions. The relative merits of a microscopic description of the condensed system in terms of effective pair potentials or in terms of local structures are discussed.