A simple yet realistic model Hamiltonian which describes the essence of many aspects of the interaction of vibrational modes in polyatomics is discussed. The general form of the Hamiltonian is that of an intermediate case between the purely local mode and purely normal mode limits. Resonance interactions of the Fermi and Darling–Dennison types are shown to be special cases. The classical limit of the Hamiltonian is used to provide a geometrical content for the model and to illustrate the ‘‘phase-like’’ transition between local and collective (i.e., normal) mode behavior. Such transitions are evident as the coupling parameters in the Hamiltonian are changed and also for a given Hamiltonian as the energy is changed. Applications are provided to higher lying vibrational states of specific molecules (H2O, O3, SO2, C2H2, and C2D2).

The algebraic approach to molecular rotation-vibration spectra introduced in a previous article is extended from di-to tri-and polyatomic molecules. The spectrum generating algebra appropriate to triatomic molecules U(4) ® U(4) is explicitly constructed. Its dynamical symmetries and their relation to rigid, nonrigid, linear, and nonlinear structures are discussed. Applications to the spectra of HCN, CO 2 , and Hj are considered. In particular, it is shown that the algebraic description can account for the Fermi resonances occurring in CO 2 , Some remarks are made on the spectrum generating algebras appropriate to polyatomic molecules.

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