Vibration-rotation coordinates and kinetic energy operators for polyatomic molecules

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Abstract
In molecular vibration-rotation calculations it is frequently desirable to work in a nuclear coordinate system tailored to the nuclear potential energy surface. It is now possible to derive the kinetic energy operator for virtually any coordinate system by using computer algebra programs. We discuss how to choose coordinates for use in practical calculations, in particular variational energy level calculations, with special consideration of the vibration-rotation separation. As an example we present a kinetic energy operator suitable for calculating the rovibrational spectrum of sequentially bonded four-atomic molecules, using valence coordinates. We carry out a rigorous symmetry classification using the MS group, and also consider how the problem of singularities affects the choice of basis set.