GENERALIZED HYPERSPHERICAL COORDINATES FOR MOLECULAR VIBRATIONS

A generalization of hyperspherical coordinates to describe molecular v ibrations is presented. The method consists of changing the origin wit h respect to which hyperspherical coordinates are defined. Thus the ge neralized coordinate system depends on two displacement parameters, sp ecifying its orientation and curvature, which can be properly optimize d. The usefulness of the generalized hyperspherical coordinates is ill ustrated for two nonbending models, corresponding to H2O and CO2. The optimum hyperspherical coordinates are shown to be local for H2O and n ormal for CO2. An analytical expression is obtained which predicts the optimum value of the displacement parameters for hyperspherical norma l coordinates.