Molecular motions in crystalline anthracene and naphthalene from multitemperature diffraction data

Atomic Displacement Parameters (ADPs) of anthracene (94-295 K), (D-30)anthr acene (16, 295 K), naphthalene (92 - 239 K). and (D-8)naphthalene (12, 295 K) have been analyzed with the help of an Einstein-type model of local, mol ecular normal modes. The low-frequency motions are expressed in terms of mo lecular translations, librations, and deformations, and account for the tem perature dependence of the experimental ADPs. Their frequencies decrease wi th increasing temperature due to crystal expansion. For anthracene, enough data of sufficient quality are available to determine two low-frequency out -of-plane deformation modes. The corresponding frequencies of naphthalene a re much higher and cannot be extracted from the available data, which are m ore limited qualitatively and quantitatively. The mean-square amplitudes du e to the high-frequency normal modes are also extracted from the diffractio n data. They agree satisfactorily with those obtained for molecules in the gas phase from density-functional theory. Contributions to the ADPs that ca nnot be interpreted in terms of motion are small hut significant. The case study presented here shows that dynamic aspects of molecular structure can he obtained from single-crystal diffraction studies. For optimal results, e xperiments must be performed over as large a temperature and resolution ran ge as possible, and factors affecting ADP's but not representing motion hav e to be kept to a minimum, e.g., by avoiding disorder. parametrizing X-ray data with multipole models, and minimizing absorption and extinction.