Dynamics of a Pair of Interacting Rotors

As a preliminary investigation of coupled rotation relevant to plastic crystals, the dynamics of two rigid-molecule rotors with parallel fixed axes is studied for a cosine potential of interaction. The problem is separable in terms of the sum and difference of the molecular angular displacements, and is soluble exactly; both quantum-mechanical and classical solutions are obtained. Owing to the form of the potential, the sum of the angles executes free rotation. The relative motion given by the difference of the angles corresponds to harmonic libration of the molecules in opposite senses at the lowest energies, and to uniform rotation in opposite senses at the highest energies. The classical behaviour is examined in some detail at intermediate energies.