Applications of group theory to the vibrations of methane molecules in the gaseous and solid phases

Abstract

<p> We present a discussion of the application of group theory to the particular case of solid methane, in all its crystalline phases. </p> <p> We also employ the quantum mechanical mean approximation to derive the mean square angle of deviation of the methane free molecule. By means of group theory we derive the normal modes, the symmetry coordinates and the nuclear spin functions of methane, which may be found useful for many other purposes in the study of methane. Finally, using these results, we give a discussion of the infrared and Raman spectra based on group theory again, to explain the observed transitions of the methane molecule in its condensed phases. We conclude that the λ type transitional are caused by changes in molecular orientation. Phase I is probably disordered,while phase II has structure of symmetry D2d. Phase III (of CD4) is ordered but of lower symmetry and unclear structure. </p> <p> A possible explanation probably requires an arrangement having more molecules per unit cell than in phases I and II. </p>