Quantum-Mechanical Theory of Orientational Ordering in Solid Methanes

Abstract

The quantum-mechanical theory of the low temperature phase transitions of the solid methanes is discussed. It is shown how the standard techniques for treating the molecular field approximation can be applied to these problems. It is shown how internal and external symmetries should be combined so as to utilize the full symmetry of the problem. This analysis is quite general and applicable to all problems of orientational ordering. Results of detailed calculations for the James–Keenan model of CH4 and CD4 are presented and compared with experimental results. The calculations assume octupole interactions, include no crystal fields, and include all states up to J = 6. It is suggested that the inclusion of crystal field and possibly states of higher J is essential for describing the low temperature behavior.