Dynamics of molecules in crystals from multi-temperature anisotropic displacement parameters. II. Application to benzene (C₆D₆) and urea [OC(NH)₂]

The temperature evolution of atomic anisotropic displacement parameters (ADP's) of perdeuterobenzene and of urea in the temperature range between 12 and 123 K is investigated in terms of the model presented in paper I. For the benzene molecule, the temperature-dependent contributions to the ADP's are well described by three molecular librations and three molecular translations. For the urea molecule, the analysis revealed a low-frequency high-amplitude normal mode (~64 cm^-1), which combines out-of-plane deformations of the NH₂ groups with molecular libration. The pyramidalization motion allows the hydrogen-bonding pattern to be retained quite well, whereas this pattern is heavily distorted in the higher-frequency molecular librations. The results presented for urea go a step beyond those obtainable in a conventional rigid-body or segmented-rigid-body analysis because they show how correlations of atomic displacements in molecular crystals can be determined from the temperature evolution of ADP's. For both molecules, the analysis reveals temperature-independent contributions to the ADP's accounting for the high-frequency internal vibrations. It is the first time that such contributions have been extracted directly from single-crystal diffraction data for light atoms like hydrogen and deuterium as well as for heavier atoms like carbon, nitrogen and oxygen. These contributions agree well with those calculated from independent spectroscopic information.