Theory of Pure Rotational Transitions in the Vibronic Ground State of Methane

It is shown that vibration-rotation interaction terms in the Hamiltonian of tetrahedral molecules like ${\mathrm{CH}}_4$ permit transitions, in the ground vibrational and electronic states, in which only the rotational quantum numbers change. Selection rules, spectral line positions, and absolute intensities are calculated. Effects of tetrahedral fine-structure splittings and nuclear-spin statistical weights are considered. Possible competing transitions are discussed.