Rotational diffusion of spherical top molecules in liquids. III. Semiclassical rotational diffusion model and the infrared band shapes of CH4 in gaseous and liquid mixtures

Abstract

Semiclassical analogs of the extended rotational diffusion models presented in previous papers in this series are investigated. Application of these semiclassical rotational diffusion models to calculation of the v₃ band contour of CH₄ indicates that these models account satisfactorily for the bandwidths and asymmetries observed in gaseous mixtures of CH₄ with helium or nitrogen in the density range 100–1000 amagat, in liquid methane and in liquid solutions of noble gases. The angular momentum correlation times obtained from the application of the semiclassical models are not greatly different from those obtained by application of the classical extended diffusion theory. This observation implies that the asymmetry of the spectral band is quantum mechanical in origin, but a classical analysis of the symmetric part of the band shape leads to essentially the same description of the molecular rotations in fluids as the quantum mechanical models do. The use of Fourier cosine transforms of band shapes to study the reorientation of molecules in liquids is, therefore, justified.