Perturbation theory for equilibrium properties of molecular fluids

Perturbation theory for the angular pair correlation function g(r₁₂ ω ₁ ω ₂), using a fluid with isotropic intermolecular forces as the reference system, is applied to the calculation of a variety of macroscopic properties. Comparisons with experiment are made for methane, oxygen and nitrogen (and carbon monoxide for infra-red and Raman band moments) in the dense fluid and liquid states. Theoretical expressions are given and calculations made for thermodynamic properties (isothermal compressibility, pressure, configurational energy, entropy and specific heat) both along and away from the vapour-liquid co-existence curve, for infra-red and Raman band moments, and for neutron scattering cross sections. Excellent agreement with experiment is obtained for all properties, except for the infra-red and Raman band moments; this latter comparison is inconclusive because of large experimental uncertainties. The anisotropic intermolecular forces are found to have very little effect on the liquid isothermal compressibility, in agreement with the first-order theory. Molecular anisotropy has a relatively small effect on the configurational energy and on the Helmholtz free energy, but the effect is large for pressure and specific heat. The pressure is more sensitive to short-range anisotropic forces than the other properties, whereas the specific heat is particularly sensitive to the long-range anisotropic forces. Mean squared torques (derived from infra-red and Raman band moments) are very sensitive to the strengths of the anisotropic forces, and are more sensitive to higher terms in the multipole series than are the other properties. The structure factors for oxygen and nitrogen are found to be little affected by the anisotropic forces.