On the calculation of orientational correlation functions for simple models of molecular reorientation in the presence of dipole-dipole interaction

Budó's theory of orientational relaxation of an assembly of molecules containing rotating polar groups, which may interact through dipole-dipole coupling between nearest neighbours of the group, is re-examined. It is shown that many of his results, pertaining to dielectric relaxation, may be rederived in a far simpler way by making use of linear response theory and it is indicated how the treatment may be extended to obtain the relaxation times and correlation functions appropriate to Kerr effect relaxation etc. Further, in the particular case where the dipole-dipole coupling is represented by a harmonic torque, it is shown how both the auto- and cross-correlation functions of the dipoles may be obtained in closed form. Both the two- and the three-dimensional versions of the molecular model predict the occurrence of a distribution of relaxation times and this distribution will always be present, irrespective of the mathematical form of V, the interaction potential, the single exception being the case of free rotation where V = 0. Finally, when the effect of inertia is included the model predicts, in accordance with a suggestion of Scaife, the possibility of resonance absorption peaks with a distribution of resonant frequencies, occurring typically in the terahertz region.