  Several alternative methods for description of interaction between rotation
and vibration are compared and contrasted using hyper-spherical coordinates for
a triatomic molecule. These methods differ by the choice of z-axis and by the
assumption of a prolate or oblate rotor shape of the molecule. For each case,
block-structure of the rotational-vibrational Hamiltonian matrix is derived and
analyzed, and the advantages and disadvantages of each method are made
explicit. This theory is then employed to compute ro-vibrational spectra of
singly substituted ozone; roughly, 600 vibrational states of 16O18O16O and
16O16O18O isomers combined, with rotational excitations up to J=5 and both
inversion parities (21600 coupled ro-vibrational states total). Splittings
between the states of different parities, so called K-doublings, are calculated
and analyzed. The roles of the asymmetric-top rotor term and the Coriolis
coupling term are determined individually, and it is found that they both
affect these splittings, but in the opposite directions. Thus, the two effects
partially cancel out, and the residual splittings are relatively small.
Energies of the ro-vibrational states reported in this work for 16O18O16O and
16O16O18O are in excellent agreement with literature (available for low
vibrational excitation). New data obtained here for the highly excited
vibrational states enable the first systematic study of the Coriolis effect in
symmetric and asymmetric isotopomers of ozone.
