Theory of Microwave Transitions in the Vibronic Ground State of Tetrahedral Molecules

Vibration-rotation interactions in the motion of tetrahedral molecules, which are conventionally nonpolar in their ground vibrational and electronic states, permit pure rotational transitions. These transitions, which are electric dipole in nature, occur at microwave frequencies for the following changes in rotational quantum numbers: $\Delta J=0\mathrm{}$ and $\Delta K=\pm 2$. General expressions for spectral line positions and absolute intensities are calculated for $J=0-20\mathrm{}$. The effects of tetrahedral fine-structure splittings and nuclear-spin statistical weights have been included. Detailed results are established for methane, the prototype of molecules with tetrahedral symmetry. Possible competing transitions are discussed.