0 D ec 1 99 6 A general algebraic model for vibrational molecular spectroscopy

1 Algebraic Model We present a symmetry-adapted version of the vibron model [1]. The model exploits the isomorphism of the U(2) Lie Algebra and the one dimensional Morse oscillator [4]. A U(2) algebra is assigned to each relevant interatomic interaction. The operators in the model are expressed in terms of the generators of the molecular dynamical group [3], which in the case of triatomic molecules is given by the product U 1 (2) ⊗ U 2 (2) ⊗ U 3 (2). (1) A simple realization for those generators is given in terms of angular momentumˆJ ν,i and numberˆN i operators Instead of working with the generators in Eq. (2) we introduce a new set of generators with well-defined tensorial properties under the point group [2]. The choice of carte-sian coordinate system, irreducible representations and Clebsch-Gordan coefficients is given in Ref. [3]. The use of the symmetry-adapted generators allows the connection between the algebraic and the configuration space calculations clarifying the geometrical content of the algebraic approach [2]. The relevant symmetry projected generators for D 3h triatomic molecules are ˆ T A 1