Quantum mechanics of rotating and translating molecules: part 2, far infrared spectrum of the harmonic oscillator/rigid rotor

Group theory is used in four dipolar point groups to determine the infrared selection rules and transition symmetries of a molecule whose dynamics are simultaneously those of the harmonic oscillator and rigid rotor. The motion is governed by the translational quantum number n of the harmonic oscillator and the quantum number J of the rigid rotor. The selection rules for the harmonic oscillator are modified from Δn = ± 1 to Δn = 0, ± 1. Those for the rigid rotor are changed from ΔJ = 0, ± 1 in the absence of translation to (1) ΔJ = 0, ± 1, ± 3; Δn = 0, n odd; (2) ΔJ = 0, ± 1; Δn = 0, n even; (3) ΔJ = 0, ± 2, Δn = ± 1; all n. The relative intensities of the rototranslational far infrared spectral lines are given for point groups C_3v, C_2v, C_1h, and C₁. The theory is in partial agreement with the experimental ΔJ = 1, 2, 3, 4 transitions observed in HD trapped in rare gas crystals at low temperature and with the selection rules for C_∞v symmetry obtained by Friedmann and Kimel.