Algebraic calculation of vibrational energy levels for polyatomic molecules XH3 and XH4: application to ammonia and silane

The vibrational energy levels of coupled stretching and bending overtone transitions in polyatomic molecules XH3 and XH4 are calculated using an algebraic method, in which couplings between stretching and bending are described by Fermi resonance terms. The algebraic Hamiltonian, established in terms of local creation (annihilation) operators, is shown to give results in good agreement with the experimental data available for ammonia and silane.