A Generalized Approach to the Calculation of Ro-vibrational Spectra of Triatomic Molecules

A generalization of the well known atom-diatom scattering hamiltonian to a coordinate system of two lengths and an angle is derived, another special case of which is a previously known bond angle-bond length hamiltonian. Different axis embeddings are also considered. The formalism is applied to the ro-vibrational levels of D2 H+, CH~ and HDHe (A 1A') and the advantage of a judicious choice of coordinates demonstrated. The vibrational band origins for HDHe*, the first predictions for this system for which previous calculations had failed, are obtained using a new geometrically defined coordinate system. It is suggested that these coordinates might be used to represent isotopically substituted van der Waals complexes.