FLUIDS OF HARD CONVEX MOLECULES .2. 2-POINT MEASURES

For fluids of hard convex molecules, the ring integrals occurring in t he diagrammatic expressions for the virial coefficients can be evaluat ed by direct integration in terms of a set of 2-point measures of 1-bo dy molecular geometry. A detailed study is reported of the properties of the 2-point measures, presenting methods of calculation, and useful functional relations between different measures. In particular, the c alculation 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-dimension al in the absence of symmetry, and 2-dimensional for molecules with an axis of symmetry. Two sensitive tests of the accuracy of 2-point meas ures calculated numerically are derived. Integrals of 2-point measures , and the asymptotic forms of 2-point measures for small r are both ex pressible in terms of 1-point measures, which are available in closed form for such typical models as spheroids, spherocylinders, and torocy linders.