Changes

where <math alt="theta(t)">\theta(t)</math> and <math alt="phi(t)">\phi(t)</math> are the time dependent spherical angles in the dimensionless radian units. The time t is normal time and hence has no hidden radian units. Spherical harmonics are the angular portion of the solution to Laplace's equationand, and I would assume that because it is angular, it is using the radian angular SI unit.  

My opinion here is that the The rotational correlation time is adescriptor of the change of angles - and these angles are in thehiddenidden, dimensionless radian units. Hence the correlation time ismeasured in s/rad or in the hidden supplementary unit notation simplys. But I prefer it is better to think of the concept as the diffusion rate, ameasure of the rate of rotational Brownian diffusion.