Knowledge Bank

We use the $C3$ and $C4$ symmetric-top representations $\mathrm{<mrow\; data-mjx-texclass="ORD">1,2</mrow>}$ for rapidly rotating spherical-top molecules to approximate the clustered values of $F3$ and diagonal $F4-$ coefficients with 3-J symbols. These coefficients then specify the intensities and wavenumbers, respectively, of absorption lines for the ``forbidden’’ pure rotational transitions in the vibrational ground state of tetrahedral $XY4$ molecules. We predict the absorption to be strongest for those states which correspond to rotation about the $C3$ axes, and which satisfy the selection rule $\Delta K=0,\pm 3$, Model spectra for $\Delta J=+1$ (far-infrared) and $\Delta J=0$ (microwave) transitions will be shown.