Knowledge Bank

Analysis of the $3\nu 3$ band in two spherical tops, $SF6\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}$ and $SiF4\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$, has shown that the cartesian basis is 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, $2\nu 23\nu 3$, are diagonalized in each basis set for both $SF6$ and $CF4$ to extend the comparison to more general vibrational levels. Both bases fail to adequately describe $CF4$. Examination of the relative quality of the various angular momentum and cartesian quantum numbers suggests a hybrid basis as a better representation of the tetrahedral case. $SF6$ 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. Overtone spectroscopy was performed with an optical parametric oscillator in the region $2800-4200cm-1$. Only components well described by the cartesian basis have measureable oscillator strength. $\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}$C. W. Patterson, B. J. Krohn and A. S. Pine, J. Mol. Spectrose. 88(1) 133-166 (1981). $\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$C. W. Patterson and A. S. Pine, J. Mol. Spectrose. 96(2) 404-421 (1982).