A lattice-dynamical interpretation of molecular rigid-body vibration tensors

Abstract

The rigid-body motions of molecules in crystals are treated with the aid of lattice dynamics of molecular crystals. An equation is derived in which the rigid-body vibration tensors TLS are related to the dynamical matrices of the crystal. Then the components of TLS are explicitly given in lattice-dynamical terms. A procedure is developed with which the trace of S, which cannot be determined from diffraction data, can be approximately determined. The principal motions of the rigid-body vibrations of molecules are discussed. Which types of coordinate systems can be used to give a physically meaningful description of the rigid-body motions is examined from a dynamical point of view. A 'dynamical' interpretation of the tensors TLS is given which consists in relating TLS to the intermolecular forces of the crystal and then comparing the intermolecular forces with the packing of the molecules in the crystal. The interpretation is illustrated with the structures of maleic anhydride and 5-chloro-l,4-naphthoquinone.