CURVILINEAR JACOBI AND RADAU NORMAL COORDINATES FOR LINEAR TRIATOMIC-MOLECULES - APPLICATION TO CO2

An investigation of different transformations of vibrational Jacobi an d Radau coordinates for describing linear symmetric triatomic molecule s is presented. The transformations used are an orthogonal rotation of radial coordinates and the change of them to plane polar variables gi ving 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 a re used to compute vibrational energy levels for CO2 concluding that t he best one is the optimized hyperspherical system derived from Radau coordinates. A simple analytical expression is also obtained which pre dicts correctly the values of the optimization parameters for hypersph erical coordinates. We finally check the quality of the potential ener gy functions used for CO2 by computing highly excited vibrational ener gy levels using the optimum coordinate system and comparing the result s with the experimental values.