Generalization to anomalous diffusion of Budó's treatment of polar molecules containing interacting rotating groups

A fractional Smoluchowski equation for the orientational distribution of dipoles incorporating interactions with continuous time random walk Ansatz for the collision term is obtained. This equation is written via the non-inertial Langevin equations for the evolution of the Eulerian angles and their associated Smoluchowski equation. These equations govern the normal rotational diffusion of an assembly of non-interacting dipolar molecules with similar internal interacting polar groups hindering their rotation owing to their mutual potential energy. The resulting fractional Smoluchowski equation is then solved in the frequency domain using scalar continued fractions yielding the linear dielectric response as a function of the fractional parameter for extensive ranges of the interaction parameter and friction ratios. The complex susceptibility comprises a multimode Cole-Cole-like low frequency band with width dependent on the fractional parameter and is analogous to the discrete set of Debye mechanisms of the normal diffusion. The results, in general, comprise an extension of Budó's treatment [A. Budó, J. Chem. Phys. 17, 686 (1949)] of the dynamics of complex molecules with internal hindered rotation to anomalous diffusion.