Fermi Resonances and Vibrational Spectrum of a Polyatomic Molecule XY4: an Algebraic Approach

A U(2) algebraic model is introduced for the spectrum of a molecule XY₄, where the interactions between the stretch and bend modes aredescribed by T_d symmetric Fermi resonance terms. The presented algebraic model in a limit corresponds to another model in recent literature. The vibrational spectrum of methane(CH₄) measured recently with modern spectroscopy techniquesis employed to test those models. The obtained standarddeviation between the observed and the calculated vibrational energylevels in the algebraic model is smaller than thatin the corresponding model.