Molecular Motion and the Moment Analysis of Molecular Spectra. III. Infrared Spectra

Abstract

The shapes of infrared rotation—vibration bands are analyzed theoretically in terms of their moments. The third and fourth moments of a band are found to increase when the molecular rotation is hindered, whereas the second moment is almost unchanged by the intermolecular torques. Explicit expressions are given for the third and fourth moments of interacting almost classical rigid asymmetric rotors, in terms of functions of the intermolecular torques, the temperature, the principal moments of inertia and the polarization direction of the transition. For the special case of a diatomic molecule or a parallel transition in a linear molecule, the theory is refined to include the first‐order quantum corrections, the rotation—vibration interaction, and the effects of frequency shifts. The analysis is applied to available infrared spectra of carbon monoxide in gaseous, liquid, and solid pure phases and mixtures. Values of the mean‐squared torque on the CO molecule are derived from the experimental data. It is found that the rotational motion of CO is strongly hindered in the solid, liquid, and highly compressed gas. The mean‐squared torque in gaseous CO and CO–Ar mixtures increases linearly with the density until densities close to those of the liquid. Therefore the intermolecular torques between CO–CO and CO–Ar must be of very short range. Sufficient data are available so that some tests of the consistency of this interpretation may be made.