Brownian dynamics simulation of rotational correlation functions of simple rigid models

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Abstract
In this paper we investigate the ability of the Brownian dynamics simulation technique of Ermak and McCammon to evaluate rotational correlation functions of rigid hydrodynamic models. Concretely, we obtain from simulated trajectories the functions 〈Pi[cos θ(t)]〉, i=1,2 where Pi is the ith Legendre polynomial and θ(t) is the angle between two orientations, separated by time t, of a given vector. This function is closely related to the decay of fluorescence anisotropy and other time-dependent electro-optical properties. The simulation results are compared with exact results for these functions. We first consider dimers in a variety of conditions regarding the rigid constraint, the hydrodynamic interaction and the relative size of the two spheres. We next study bent trimers, for which the decays are typically multiexponential. In all cases we find that the simulated results of the correlation functions and the exact ones are in rather good agreement up to a time which is determined by the finite length of the simulated trajectory.