The temperature dependence of rotational tunnelling frequencies in molecular solids

In molecular solids, symmetrical groups like CH 3 and NH 4 undergoing torsional oscillation and tunnelling rotation in a hindering potential, also experience temperature-dependent inertial forces due to the lattice vibrations. The main effect can be described in terms of a fluctuating displacement of the hindering potential. The stationary states in this fluctuating potential are temperature-dependent mixtures of the torsional oscillator states of the static potential. As a result, the frequency of tunnelling rotation of the lowest stationary state is a thermal average of the tunnelling frequencies of the torsional oscillator states of the static potential. This tunnelling frequency falls with increasing temperature, while remaining well defined, in agreement with experimental observations.