Brownian dynamics simulation of restricted rotational diffusion.

The restricted rotational diffusion of an axially symmetric particle is simulated by the Brownian dynamics technique. In addition to the wobbling-in-a-cone model, several continuous potentials are considered. The particle studied is particularly simple: a sphere anchored to a point fixed in space. However, presenting the results in a convenient, reduced form, they are valid for any axially symmetric particle. From simulated rotational trajectories, we calculate (P2(cos alpha] as a function of t, where alpha is the angle between two orientations separated by time t and P2 is the second Legendre polynomial. This correlation function is closely related to time-resolved electro-optic and spectroscopic properties. Simulated results for the cone model are in excellent agreement with the quasiexact results of Lipari and Szabo (1981, J. Chem. Phys., 75:2971-2976). Thus we confirm the good performance of the simulation technique and the validity of our working conditions. Novel results are presented for continuous restricting potentials, V(theta). The (P2) results for V = 1/2K theta 2 and V = Q(1 - cos theta) are practically the same if K and Q are chosen so tht the long-time (P2) values coincide. Thus, the quadratic potential seems to be a good representation of any monotonically increasing potential. However, for an uniaxial potential such as V = Csin2 theta, the decay is appreciably faster. The (P2) decays simulated for the continuous potentials are analyzed by the monoexponential version of the cone model. We found that such an analysis produces an overestimation of the true rotational diffusion coefficient of approximately 15% only, although for uniaxial potentials the error may be larger.