Curvilinear Jacobi and Radau normal coordinates for linear triatomic molecules. Application to CO 2

Abstract

An investigation of different transformations of vibrational Jacobi and Radau coordinates for describing linear symmetric triatomic molecules is presented. The transformations used are an orthogonal rotation of radial coordinates and the change of them to plane polar variables giving a set of generalized hyperspherical coordinates. Both transformed coordinate systems can be chosen to be curvilinear normal coordinates by proper selection of the rotation angle and the parameters defining the polar transformation. All these curvilinear normal mode systems are used to compute vibrational energy levels for CO 2 concluding that the best one is the optimized hyperspherical system derived from Radau coordinates. A simple analytical expression is also obtained which predicts correctly the values of the optimization parameters for hyperspherical coordinates. We finally check the quality of the potential energy functions used for CO 2 by computing highly excited vibrational energy levels using the optimum coordinate system and comparing the results with the experimental values.