The transition from free quantum tunnelling to thermally driven motion of methyl groups

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Abstract
Methyl groups in solids are representative of systems which exhibit tunnelling at low temperatures and thermally activated hopping motion at high temperatures. They exhibit very clearly all the features of the transition between free and thermally driven quantum tunnelling, the latter being describable in terms of classical hopping concepts. A satisfactory theoretical description has been lacking because the usual approaches, which treat the dynamic part of the scalar hindering potential by time-dependent perturbation theory are, the author suggest, incomplete. It is shown that a better description is possible if a vector potential arising from the motion of the lattice is introduced in addition to the scalar potential. This leads to a new Hamiltonian and a representation in which the important terms, which lead to the experimentally observed spectroscopic changes with increasing temperature, are diagonal. In this new representation a simple model emerges which exhibits most, if not all, of the observed experimental features. It also resolves an old problem: how to reconcile the quantum mechanical requirement that the rotation angles phi =0 and phi =2 pi are identical, with the classical assumption that they are distinguishable, and thus provides a bridge between the quantum and classical descriptions of rotation.