Dynamic density and structure factors for rigid molecules with large librations

Abstract

For rigid molecules which undergo large librations, the dynamic density and the dynamic molecular scattering factor are derived. The general case is treated where translations and librations of the molecule are coupled (no site symmetry). The dynamic molecular scattering factor is an integral which cannot generally be solved, and temperature factors generally do not appear. For the special case of statistically independent translations and librations, a temperature factor for the translations of the molecule is obtained. Moreover, temperature factors are obtained for density units which are spherically symmetric, since the motions of these density units can be described by translations only. The possible cases for which spherically symmetric density units can be assumed and, hence, temperature factors can be applied, are discussed.