GENERALIZED HYPERSPHERICAL COORDINATES FOR MOLECULAR VIBRATIONS

A generalization of hyperspherical coordinates to describe molecular vibrations is presented. The method consists of changing the origin with respect to which hyperspherical coordinates are defined. Thus the generalized coordinate system depends on two displacement parameters, specifying its orientation and curvature, which can be properly optimized. The usefulness of the generalized hyperspherical coordinates is illustrated for two nonbending models, corresponding to H2O and CO2. The optimum hyperspherical coordinates are shown to be local for H2O and normal for CO2. An analytical expression is obtained which predicts the optimum value of the displacement parameters for hyperspherical normal coordinates.