Abstract
The symmetry properties of the X${\mathrm{H}}_{3}$-type molecules are investigated. The possible wave functions of the molecule in the ground electronic state are calculated in the Born-Oppenheimer approximation and the question of the symmetry group of the molecular Hamiltonian (${\mathit{C}}_{3}$ or ${\mathit{C}}_{3\mathit{v}}$ or other) is considered. Further, the concept of quantum coherence is examined for the case of tunneling methyl groups. The results are extended to the high temperature region by introducing a suitable ``pointer basis'' which appears to be appropriate for the description of dynamics of the methyl groups interacting with lattice. Finally, the spin-lattice relaxation time is calculated within this model and is found to agree closely with the semiclassical result. \textcopyright{} 1996 The American Physical Society.
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