A model of molecular fluids: A three-parameter direct correlation function

A previous two-parameter model of a molecular fluid is extended to three parameters and applied to a fluid of hard ellipsoids with restricted orientations. The direct correlation function of the fluid is written as a linear combination of three basic functions derived from the geometry of two molecules and the coefficients determined from algebraic equations also satisfied by the Percus-Yevick (PY) solution of the problem. The theory yields the PY solution and PY equation of state in the special case of hard spheres. For ellipsoids the equation of state agrees better with the results of computer simulation than the two-parameter version although the discrepancy increases with increasing anisotropy of the molecules. According to the model the fluid makes a transition to a nematic state although the predicted densities at which the transition takes place are too low.