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

Abstract

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 C3v, C2v, C1h, 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.