Fluids of hard convex molecules II. Two-point measures

Abstract

For fluids of hard convex molecules, the ring integrals occurring in the diagrammatic expressions for the virial coefficients can be evaluated by direct integration in terms of a set of 2-point measures of 1-body molecular geometry. A detailed study is reported of the properties ofthe 2-point measures, presenting methods of calculation, and useful functional relations between different measures. In particular, the calculation of measures with one or two volume points is reduced to the calculation of 2-point measures with two surface points. This reduces the calculation of 2-point measures to integrals that are 3- dimensional in the absence of symmetry, and 2-dimensional for molecules with an axis of symmetry. Two sensitive tests of the accuracy of 2-point measures calculated numerically are derived. Integrals of 2-point measures, and the asymptotic forms of 2-point measures for small r are both expressible in terms of 1-point measures, which are available in closed form for such typical models as spheroids, spherocylinders, and torocylinders.