Separation of fast and slow processes from a stochastic cage model of molecular dynamics

The linear solute cage model (LSCM) has been proposed in the past [Moro, G. J., Polimeno, A. J. Chem. Phys. 1997, 107, 7884] to account for the action of the confining potential generated by neighboring solvent molecules on a linear solute, in the presence of fluctuations of the resulting cage structure. Rotational correlation functions, directly related to spectroscopic observables such as dielectric permittivity and far-infrared spectra in molecular liquids, can be calculated from the numerical solution of the model. However, to understand the influence of different relaxation processes on the solute dynamics, it is useful to explore semianalytical approximations, able to connect directly predictions with physical ingredients of the model. In this work, we present a detailed analysis of LSCM based on the application of a Born-Oppenheimer time-scale separation procedure, which allows a complete description of the probe fast libration motions and the cage slow rotation and restructuring modes.