Asymptotic decay of the pair correlation function in molecular fluids: Application to hard rods

We investigate the asymptotic decay of the total correlation function h(1,2) in molecular fluids. To this end, we expand the angular dependence of h(1,2) and the direct correlation function c(1,2) in the Ornstein-Zernike equation in a complete set of rotational invariants. We show that all the harmonic expansion coefficients h(l1)l(2)l(r) are governed by a common exponential decay length and a common wavelength of oscillations in the isotropic phase. We determine the asymptotic decay of the total correlation functions by investigating the pole structure of the reciprocal (q-space) harmonic expansion coefficients h(l1)l(2)l(q). The expansion coefficients in laboratory frame of reference h(l1)l(2)l(r) are calculated in computer simulations for an isotropic fluid of hard spherocylinders. We find that the asymptotic decay of h(1,2) is exponentially damped oscillatory for hard spherocylinders with a length-to-diameter ratio L/D <= 10 for all statepoints in the isotropic fluid phase. We compare our results on the pole structure using different theoretical Ansatze for c(1,2) for hard ellipsoids. The theoretical results show that the asymptotic decay of h(1,2) is exponentially damped oscillatory for all elongations of the ellipsoids.