Rigid-body molecular motion in crystals. The centre of libration

It is shown that the concept of the molecular centre of libration in the description of the average rigid-body thermal behaviour of molecules is a useful approximation. A restriction is made on the full theory, making the centre of libration model a constrained version of the complete model. The relationship between the models is discussed. Some examples are chosen to demonstrate the closeness of the approximation. These results show that for data reaching a reliability factor of no better than 7% an analysis using the full theory might yield a meaningless result. Some data of much higher accuracy does, however, show the need for the full theory.