Rotational Relaxation of Molecules in Fluids for Reorientations of Arbitrary Angle

A theory of rotational motion of molecules in liquids is presented. The traditional Debye diffusion model is generalized so as to include arbitrary reorientation angles by means of a nonlocal master equation. Random walk models are a special case of this generalization. We have obtained the conditional probabilities for the orientation of a body and of a vector fixed in the body for arbitrary body geometry. These results are then specialized to specific symmetries. From these conditional probabilities we calculate correlation functions which describe a large number of spectroscopic experiments such as NMR, ESR, NQR, dielectric relaxation, and infrared and Raman spectroscopy. We find that the form of these results for the correlation functions depend only on medium isotropy and body geometry. The same number of decaying exponentials are found as in the diffusion model regardless of the details of the reorientation mechanism. Only the amplitudes and relaxation times depend on these details.