X-ray diffraction data cannot provide anisotropic displacement parameters (ADPs) for H atoms, a major outstanding problem in charge-density analysis of molecular crystals. Although neutron diffraction experiments are the preferred source of this information, for a variety of reasons they are possible only for a minority of materials of interest. To date, approximate procedures combine rigid-body analysis of the molecular heavy-atom skeleton, based on ADPs derived from the X-ray data, with estimates of internal motion provided by spectroscopic data, analyses of neutron diffraction data on related compounds, or ab initio calculations on isolated molecules. Building on these efforts, an improved methodology is presented, incorporating information on internal vibrational motion from ab initio cluster calculations using the ONIOM approach implemented in GAUSSIAN03. The method is tested by comparing model H-atom ADPs with reference values, largely from neutron diffraction experiments, for a variety of molecular crystals: benzene, 1-methyluracil, α-glycine, xylitol and 2-methyl-4-nitroaniline. The results are impressive and, as the method is based on widely available software, and is in principle widely applicable, it offers considerable promise in future charge-density studies of molecular crystals.
Anisotropic displacement parameters for H atoms using an ONIOM approach