Knowledge Bank

The treatment of a vibrating, rapidly rotating spherical-top molecule with $Td$ or $Oh$, symmetry) as a nearly rigid symmetric top, whose axis of symmetry coincides with a four-fold or three-fold body axis, greatly simplifies the calculation of the positions of perturbed clustered lines in fundamental band spectra. This treatment permits interactions between clustered states $(R,KR)$ and with $\Delta KR=0,\pm 4$ in the fourfold symmetric case and with $\Delta KR=0,\pm 3$ in the three-fold case. Matrix elements are proportional to Clebsch-Gordon coefficients Instead of off-diagonal $F(4)$-coefficients. To high accuracy, first-order perturbation theory in a smaller ""cluster"" basis replaces numerical diagonalization in the complete set of $JJ+1,JJ$ and $JJ-1$ states belonging to the same octahedral (or tetrahedral) symmetry species. Numerical details will be presented for the: $\nu 3$ band of $SF6$.