  We discuss a symmetry-adapted algebraic (or vibron) model for molecular
spectroscopy. The model is formulated in terms of tensor operators under the
molecular point group. In this way, we have identified interactions that are
absent in previous versions of the vibron model, in which the Hamiltonian is
expressed in terms of Casimir operators and their products. The inclusion of
these new interactions leads to reliable spectroscopic predictions. As an
example we study the vibrational excitations of the methane molecule, and
compare our results with those obtained in other algebraic models.
