The interaction of rotation and local mode tunneling in the overtone spectra of symmetrical hydrides

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Abstract
In the ‘‘local mode limit’’ where the tunneling time for vibrational energy exchange is long compared to the classical rotational period, one expects that the effective rotational Hamiltonian will reflect the reduced symmetry of the local mode state. Hamiltonians in the local mode basis are given for interaction of rotation and local mode tunneling for molecules of the XH2, XH3, and XH4 type. Transformation of these Hamiltonians to a symmetrized basis (which diagonalizes the vibrational problem), produces rotational couplings between the vibrational states. Relations between the spectroscopic constants are derived that are less restrictive than those given earlier by Halonen and Robiette, but reduce to them when the assumptions of their model are met. The present algebraic procedure can be easily extended to include higher order terms. The effect of these couplings is to reduce the size of the pure vibrational splittings. This is due to the fact that in the rovibrational problem, in general, one must reorient the angular momentum vector in the body frame as well as transfer the vibrational action between bonds. This increases the length of the tunneling path and thus decreases the rate of vibrational energy transfer. Model calculations show that a simple semiclassical picture can rationalize the observed trends.