A pr 1 99 9 Fermi resonance - algebraic model for molecular vibrational spectra ∗

A Fermi resonance-algebraic model is proposed for molecular vibrations, where a U(2) algebra is used for describing the vibrations of each bond, and Fermi resonances between stretching and bending modes are taken into account. The model for a bent molecule XY2 and a molecule XY3 is successfully applied to fit the recently observed vibrational spectrum of the water molecule and arsine (AsH3), respectively, and results are compared with those of other models. Calculations show that algebraic approaches can be used as an effective method for describing molecular vibrations with small standard deviations.