Algebraic-matrix calculation of vibrational levels of triatomic molecules.

We introduce an accurate and efficient algebraic technique for the computation of the vibrational spectra of triatomic molecules, of both linear and bent equilibrium geometry. The full three-dimensional potential energy surface (PES), which can be based on entirely ab initio data, is parametrized as a product Morse-cosine expansion, expressed in bond angle internal coordinates, and includes explicit interactions among the local modes. We describe the stretching degrees of freedom in the framework of a Morse-type expansion on a suitable algebraic basis, which provides exact analytical expressions for the elements of a sparse Hamiltonian matrix.