Statistical dynamics of a rotator in a potential of cubic symmetry

Abstract

The thermal angular motion of a classical linear rotator in an octahedral field with eight wells is studied both analytically and numerically. The strength of the coupling with the thermal bath is introduced. It is shown that in the deep-well case, for a coupling of intermediate strength, the ‘nex-twell-jump’ hypothesis is fulfilled and an absolute value can be calculated for the long-time exponential decay of the angular time correlation functions. The short-time behaviour of these functions reflects damped librations in the wells. The numerical simulation employs random torque impulses to represent the coupling with the thermal bath. For different values of the two parameters of the model (depth of the wells V and mean interval τ _i between torque impulses), the complete correlation functions and the corresponding spectra are computed. The results are compared with experimental data bearing on matrix-isolated molecules, ‘plastic crystals’ and liquids.