Comparison of the symmetrized Cartesian and angular momentum basis sets to describe vibrationally excited states in spherical top molecules

Recent analyses of the 3ν3 vibrational band in two spherical tops, SF6 and SiF4, have shown the Cartesian basis to be an appropriate description for this band in the octahedral case, while the tetrahedral case is adequately represented by the angular momentum basis. Using spectroscopic constants derived from force field analyses, the F1u/F2 subblocks of the vibrational Hamiltonian matrices of the bands of four vibrational quanta and one band of five quanta 2ν23ν3 are diagonalized in each bases set for SF6, CF4, and CH4 to extend the comparison to more general vibrational levels. Both bases fail to adequately describe CF4 and CH4. The validity of the various angular momentum designations as quantum numbers is strongly dependent on the particular set of spectroscopic parameters. SF6 is poorly described by the angular momentum basis. Within a vibrational band of SF6, only a component whose vibrational motion lies along a single Cartesian axis is well described by the Cartesian basis. It is the lowest energy component, well separated in energy from the remaining components because of the single bond anharmonicity.