The Debye model of rotational Brownian motion and the rotational random jump model have been extended to allow for time fluctuations of the rotational diffusion constant and the jump rate constant, respectively. The treatment is applicable to experimental situations which are conventionally described in terms of a distribution of correlation times and to systems where molecular reorientation is complicated, e.g., by rapid chemical exchange processes. Correlation functions for spin relaxation are discussed in some detail and are compared with the corresponding correlation functions for dielectric relaxation. In particular, the ESR (or NMR) line shape is given for a simple example of very slow reorientation where the rotational correlation time is comparable with the spin relaxation time. In this case, the Debye model and the jump model yield different line shapes, and further changes occur if environmental fluctuations are considered. Details are given for fluctuations described by an Uhlenbeck–Ornstein process.
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