Rovibrational Hamiltonian of a triatomic molecule in local and collective internal coordinates

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Abstract
Generalised spherical polar coordinates for a description of the internal motions of a triatomic molecule are presented. These coordinates depend on two external parameters. They can be varied in order to adopt the internal coordinates of a given type of local mode motions of a molecule. The rovibrational (RV) Hamiltonian expressed in these coordinates is derived. It takes a simple form in orthogonal internal coordinates which can be obtained by appropriately choosing the external parameters. The collective hyperspherical coordinates are proposed for the description of symmetric and antisymmetric stretching vibrations of a triatomic molecule. The RV Hamiltonian in these coordinates is approximately separable for a wide class of vibrational potentials.