The temperature dependence of rotational tunneling

In the last few years tunneling transitions have been observed for the highly symmetric groups CH₄, CD₄, NH ₄ ⁺ , and CH₃ rotating in various environments. Typically the tunneling lines shift to lower energies with increasing temperatures. In this paper the shift of the tunneling energy is calculated in a microscopic approach to the problem. The coupling of the rotating groups to the lattice modes is studied in two stages. First the rotating group is coupled to a single oscillator, then to the modes of a Debye crystal. The first calculation leads to a set of discrete tunneling lines with an energy that diminishes as the oscillator is excited into higher levels. The second approach yields a single tunneling line shifted down-wards with increasing phonon population. The shift is proportional toT ⁴. The calculation explains the energy shift of the tunneling lines with reasonable values for the coupling parameters. In some cases also a broadening has been observed which does not follow from our calculations.