On the Zero Point Entropy of Methane Crystal

Possible crystalline structure are suggested for the low temperature modifications of CH4, CD4, and CH3D crystals from the consideration of interatomic distances, assuming that the molecules are vibrating rather than rotating in the crystals. The degrees of degeneracy of several lowest eigenstates of the molecular motion are investigated by group theoretical considerations on the simplifying assumption that each molecule is subjected to a field of a certain symmetry, namely, of octahedral, tetrahedral, trigonal, or of no symmetry. It results that the lowest rotational state of the para-CH4 molecule, j = 2, splits into several components in the octahedral and tetrahedral field, of which the lowest state has a degree of spatial degeneracy 4 and 2, respectively. An explanation of Clusius's measurement of the zero-point entropy of the CH4 crystal can be given by assuming a tetrahedral field and assuming that the conversion between different symmetry types of the molecule does not occur. The alternative and more probable explanation can be given by the assumption that 12 lowest levels resulting from the symmetry operations of the molecule are quasi-degenerate and the symmetry of the field is tetrahedral or lower. The occurrence of the conversion does not matter in the latter case. The zero-point entropy of CH3D can also be accounted for by the second type of assumption.