An introduction to the theory of local mode vibrations

A description is given of highly excited rotational and/or vibrational states of molecules in terms of localized vibrations or local modes. It is a didactic paper, making an attempt to unify the ideas and notations of the key publications on the subject in a manner that treats the vibrational and rotational motions equally and that demonstrates the importance of molecular symmetry. Emphasis is put on explaining the intimate relationship between local mode vibrations and the formation of both vibrational and rovibrational energy level clusters. In rovibrational cluster states, a molecule can sustain localized vibrations for very many vibrational periods, even with low vibrational excitation. Local mode behaviour is induced by both vibrational and rotational excitation. An important application of local mode theory is the derivation of relations between the effective rotation-vibration parameters for highly excited vibrational states of a molecule. It is shown here, using the (H2Se)-Se-80 molecule as example, that such relations are valid only for certain forms of the effective rotation-vibration Hamiltonian. Thus caution is required when the results of fittings to spectral data are compared with local mode theory.