Algebraic description of anharmonic stretching vibrations

A U(2) algebraic model is presented to describe stretching vibrations of XY$_n$ (n=2, 3, and 4) systems, where anharmonic interactions between the bond modes are considered. This model in a limit corresponds to an anharmonically coupled local mode model. As an example, the model for a molecule XY$_4$ is applied to recently observed spectra of methane in both gas and liquid phases, and the results obtained are in good agreement with the experiments.