On the Second Virial Coefficients for Assemblies of Nonspherical Molecules

A method of calculating the second virial coefficients for nonspherical molecules is presented which differs from the usual procedure in the following ways: (a) The long-range directional forces between molecules are generally represented by a multipole expansion of the Coulomb interaction; this expansion is not valid for small intermolecular distances. However, these forces are usually extended into the region of small separations between molecular centers in the calculation of the second virial coefficients. The magnitude of the error introduced by this extension is investigated and found to be appreciable. The customary method is modified in such a way that the long-range orientational forces are cut off inside the molecular diameter r0. (b) Effects resulting from anisotropy in the London forces are taken into account. It is shown that this component of the directional field is usually predominant, even for molecules with large quadrupole moments. (c) Induction forces are considered, especially those resulting from permanent quadrupole moments. It is found that the effect of these forces is, in general, not negligible. The results are applied to an evaluation of the second virial coefficients for carbon dioxide, nitrous oxide, nitrogen, carbon monoxide, ethane, and ethylene. A comparison is made between the effects of the long-range directional forces on the physical properties of nitrogen, carbon monoxide, and carbon dioxide in the gaseous state and in the crystal.