Algebraic approach to molecular rotation-vibration spectra. II. Triatomic molecules

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, CO₂, and H₃⁺ are considered. In particular, it is shown that the algebraic description can account for the Fermi resonances occurring in CO₂. Some remarks are made on the spectrum generating algebras appropriate to polyatomic molecules.