Padé approximants to correlation functions for restricted rotational diffusion

Simple closed-form approximate expressions are presented for time-correlation functions of spherical harmonics, with l = 2, m = 0, ±1, and ±2, within the framework of the diffusion in the cone model. In this model, a unit vector, with orientation specified by the polar angles ϑ and φ, is restricted to diffuse in a cone of semiangle ϑ0. By comparing with exact numerical results, it is shown that our expressions are highly accurate when m = 0, ±2 for 0°⩽ϑ0⩽90° and when m = ±1 for 0°⩽ϑ0⩽75°. The utility of our results is demonstrated in the context of modeling the effect of hindered motion of probes in membranes on the fluorescence emission anisotropy and the effect of internal motions on the nuclear magnetic resonance relaxation times of protons in nucleic acids.