Theory and computer simulation of hard-sphere site models of ring molecules

Abstract

A previous theory for hard-sphere site models of non-spherical molecules, the bonded hard sphere (BHS) theory, is reviewed and a generalization is proposed to extend the theory to ring-like molecules. New simulation data are presented for rigid ring molecules formed from three, four and five tangent hard spheres of equal size, and the results are compared with the predictions of the generalization. In all, four models are studied consisting of hard spheres at the corners of an equilateral triangle, a square, a regular tetrahedron, and a regular pentagon, respectively. Good agreement between the exact Monte Carlo data and the approximate theory is found. The two approximations made in the BHS theory and in its generalization are discussed, as is the extent of their validity. Theories of this type, based on the bonding of spheres into the desired molecules, require distribution functions for three or more spheres; the problem of estimating these functions given only the pair radial distribution function is examined.