Molecular Motions in Crystalline Anthracene and Naphthalene from Multitemperature Diffraction Data

Abstract

Dedicated to Edgar Heilbronner, in adminationAtomic Displacement Parameters (ADPs) of anthracene (94 ± 295 K), (D 10 )anthracene (16, 295 K), naphthalene (92 ± 239 K), and (D 8 )naphthalene (12, 295 K) have been analyzed with the help of an Einsteintype 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 ADPs 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.

Large uniaxial negative thermal expansion in pentacene due to steric hindrance

“…This analysis is carried out in the molecular inertial system and assumes rigid molecules. Bürgi et al showed the amplitudes of the intramolecular modes to be small compared with the rigid body motion 21 . Additionally, molecular dynamics studies indicate that in the energy range of interest the excited modes are to a high degree of intermolecular type 22 .…”

Anisotropic displacement parameters for H atoms using an ONIOM approach

“…Bü rgi and co-workers have recently described an elegant method for studying the dynamics of molecules in crystals through the analysis of multi-temperature neutron diffraction data (Bü rgi & Fö rtsch, 1999;Bü rgi & Capelli, 1999Bü rgi et al, 2001;Capelli et al, 2000). The normal modes derived from this approach incorporate both internal and external degrees of freedom, and can also be used to estimate the ADPs for any atom at any intermediate temperature (Bü rgi et al, 2002).…”

A positive to negative uniaxial thermal expansion crossover in an organic benzothienobenzothiophene structure

“…Thermal expansion is closely connected to the correlated movements of these rigid bodies. It can be shown that the amplitudes of the intramolecular modes are much smaller than those of the rigid bodies (Bü rgi et al, 2001). The rigid body position itself is described by three eulerian angles and a position vector and its motion by a translation T tensor, a librational L tensor, and a coupling tensor S within the molecular inertial system I.…”