Molecular Motions in Crystalline Anthracene and Naphthalene from Multitemperature Diffraction Data

Abstract

Atomic Displacement Parameters (ADPs) of anthracene (94 – 295 K), (D10)anthracene (16, 295 K), naphthalene (92 – 239 K), and (D8)naphthalene (12, 295 K) have been analyzed with the help of an Einstein-type model of local, molecular normal modes. The low-frequency motions are expressed in terms of molecular translations, librations, and deformations, and account for the temperature dependence of the experimental ADPs. Their frequencies decrease with 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 are much higher and cannot be extracted from the available data, which are more limited qualitatively and quantitatively. The mean-square amplitudes due to the high-frequency normal modes are also extracted from the diffraction data. They agree satisfactorily with those obtained for molecules in the gas phase from density-functional theory. Contributions to the ADPs that cannot be interpreted in terms of motion are small but significant. The case study presented here shows that dynamic aspects of molecular structure can be obtained from single-crystal diffraction studies. For optimal results, experiments must be performed over as large a temperature and resolution range as possible, and factors affecting ADP's but not representing motion have to be kept to a minimum, e.g., by avoiding disorder, parametrizing X-ray data with multipole models, and minimizing absorption and extinction.