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 anharmonical
ly coupled local-mode model. As an example, the model for a molecule XY4 is
applied to recently observed spectra of methane in both gas and liquid pha
ses, and the results obtained are in good agreement with the experiments. (
C) 1999 Academic Press.