Rotational dynamics of axially symmetric solutes in isotropic solvents. II. The stochastic model

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Abstract
In paper I of this series, a molecular dynamics (MD) study of liquid chlorine was performed, and it includes the definition and observation of operational cage variables. These cage variables were used to describe the local environment of a rotating axially symmetric molecule, or probe. Probe and cage properties of interest, such as rotational correlation functions and momentum correlation functions, were computed, together with an effective distribution of librational cage frequencies. In the second part of this work, we develop a stochastic model which includes the relevant elementary relaxation processes previously identified by the MD study. This stochastic model is based upon a multi-dimensional Fokker–Planck equation for the coupled dynamics of the probe and cage orientations, the angular momentum of the probe, and the librational frequencies for the probe in the cage. Semi-analytical approximations, based upon a ‘‘Born–Oppenheimer’’-type separability of fast and slow variables, are used in order to calculate probe and cage correlation functions, and they are found to be in reasonable agreement with the MD results. In an appendix the Born–Oppenheimer approximation for stochastic operators is developed.