Perturbation theory for molecular fluids: Third-order term in the Pople expansion

We derive the expression for the third-order perturbation term A3 in the Pople expansion of the Helmholtz free energy, for an arbitrary anisotropic intermolecular pair potential. The corresponding expression for the second-order perturbation term g2 in the expansion of the angular pair correlation function is also obtained. We then apply this expansion, and also a Padé approximation to the series, to the case in which the molecules interact with an anisotropic charge overlap model proposed by Pople. Comparison of the calculated internal energies with molecular dynamics results for this model show that the Padé gives good results in the range −0.2?δ?0.35, where δ is an anisotropic shape parameter (positive for prolate and negative for oblate spheroids). This range includes small polyatomic molecules (CO2, ethane, N2, etc.). We also apply the theory to binary mixtures in which one of the molecular species obeys a spherical Lennard-Jones potential while the other obeys spherical Lennard-Jones plus the Pople anisotropic overlap model. The anisotropic overlap forces have little effect on the phase diagram for such small polyatomics, in contrast to the large effect of electrostatic forces.