Algebraic approach to vibrational spectra of tetrahedral molecules: a case study of silicon tetrafluoride

Both the stretch and bend vibrational spectrum and the intensity of infrared transitions in a tetrahedral molecule are studied in a U(2) algebraic model, where the spurious states in the model Hamiltonian and the wavefunctions are exactly removed. As an example, we apply the model to silicon tetrafluoride SiF$_4$.