Quantum and semiclassical vibrational transition frequencies for a Hamiltonian with stretch-bend potential energy coupling

Vibrational eigenvalues are calculated for a hydrocarbon fragment which consists of a coupled HC stretch and CCH bend. The particular coupling investigated is the attenuation of the CCH bending force as the HC bond is extended. Eigenvalues are calculated quantum mechanically and with the approximate Sorbie-Handy and DeLeon-Heller-Miller semiclassical methods. For many of the eigenstates large differences are found between the quantum mechanical and approximate semiclassical eigenvalues. Attenuating the CCH bending force is found to affect the HC stretch to CCH bend frequency ratio for a particular HC stretch excitation.