Line frequency expressions for triply degenerate fundamentals of spherical top molecules appropriate for large angular momentum

For states of high angular momentum we obtain expressions for the transition frequencies in the triply degenerate fundamental of a “heavy” spherical top, that are accurate to spectroscopic resolution, without tedious calculation of octahedral (or tetrahedral) vector coupling coefficients or diagonalization of matrices. Our calculations are based upon the physical assumption that as the molecule rotates with larger angular momentum it behaves like a symmetric top with the coupled pure rotational angular momentum quantized along either the four- or threefold body-fixed axes. We find that the approximate calculation which involves only 3-J symbols quite accurately reproduces the result of a complete diagonalization of the Hamiltonian, so that for all but the most accurate saturated absorption spectra theoretical analysis may be carried out without reference to the octahedral (or tetrahedral) subgroup of the rotation group.