The vibrational dependence of quartic centrifugal distortion

The dependence of the quartic centrifugal distortion coefficients of a molecule on the vibrational quantum number vk is of type H˜24 in the expansion of the effective Hamiltonian. It gives information on the quartic potential constants of the type k′kklm and is therefore additional to that provided by the anharmonicity constants xkl, which depend only on the quartic potential constants of the type k′kkll. The present work describes the calculation of these H˜24 terms from a given potential by perturbation theory, using a computer program which calculates the coefficients in the successive contact transformations. Results are presented, in terms of directional centrifugal distortion constants, for the SO2, ClO2, O3, and H2O molecules. Good agreement with observed coefficients is obtained for SO2 and ClO2. For O3, the strong rotational resonance between the (100) and (001) states complicates the comparison, and the transformation to the effective Hamiltonian used empirically requires further study. For H2O, poor agreement is obtained for the (010) level because of quasilinear behaviour. The effects of the resonance between (100) and (001) are less severe than for O3, and the agreement with the observed is somewhat better.