Diffusive and jump description of hindered motions

Site jump models are often used to interpret spectroscopic effects of molecular motions occurring in the presence of potential wells. Continuous diffusion equations, albeit complex to handle, are expected to give a more detailed picture of the dynamics and to provide molecular interpretation of the kinetic parameters. In the paper we show how the results of random walk models can be recovered from the correct solutions of the diffusion equations. To this purpose, two routes are followed. First, a procedure is developed for the exact calculation of the time integral of pertinent correlation functions, to be compared with the time constant for the kinetic process of interest. Secondly, the asymptotic solutions of the diffusion equations, valid in the limit of high potential gradients, are used to derive ‘localized functions’, which lead quite naturally to master equations for jumps among discrete sites. Rotational diffusion in uniaxial liquid crystals, translational motions across smectic layers, hindered internal motions and conformational changes are considered as physical examples of relevant experimental interest.