Rotational Brownian motion of an asymmetric top

Abstract

We describe a method which enables us to calculate both the orientational and the angular-velocity autocorrelation functions of an asymmetric top driven by white noise. The results are valid for both short and long times, and provide inertial corrections to the classical result of Perrin. They are applied to the calculation of complex polarizabilities for asymmetric-top molecules and the correlation times associated with the dipolar broadening of nuclear magnetic resonance lines. We take the angular-velocity vector to be the stationary solution of the Euler-Langevin equation, and obtain it in the form of a perturbation series. The random angular velocity drives the random orientational motion, and we use methods of stochastic differential equations to obtain an equation of motion for the aftereffect function. This cannot be solved in general by direct integration, and we use the method of averaging to obtain the aftereffect function in a form which is asymptotically correct both for large and small times.