Knowledge Bank

It is now well established that the overtone spectra of most hydrides is dominated by transitions to states that are best described by the `local mode’ model where the vibrational energy is localized on a single X-H bond. For the case of exactly equivalent X-H bonds, this vibrational excitation tunnels between these bonds, leading to a lifting of the exact degeneracy of the different linear combinations corresponding to the irreducible representations (which are the eigenstates of the vibrational Hamiltonian). A model Hamiltonian that describes the effects of rotation of the local mode states will be discussed. In the limit where the tunneling frequency is much less than the rotational frequencies, the eigenstates of this Hamiltonian display the rotational structure consistent with the dynamically reduced symmetry of the molecule. For example a $XH4$ molecule give a symmetric top spectrum. Further, tunneling must now reorient the rotational angular momentum (in the body fixed frame) as well as transfer the vibrational action. As a result, the rotation about the proper axes can dramatically slow the rate of tunneling.""