Theory of Relative Reorientational Correlation Times for First and Second Rank Spherical Harmonics

A theory is developed which relates the ratio of first to second rank orientational correlation times, τ1/τ2, to a single dimensionless parameter characteristic of the system of interest. The theory is based upon the Zwanzig-Mori formalism for time correlation functions and the Gaussian memory function approximation of Harp and Berne. The theory yields the exact overdamped (rotational diffusion) rotor result, and comes very close to the exact free rotor result, in the appropriate limits. The expected temperature dependence of the ratio, τ1/τ2, is calculated. The range of validity of the theory is discussed.