Refinement of Organic Crystal Structure with Multipolar Electron Scattering Factors

A revolution in resolution is occurring now in electron microscopy arising from the development of methods for imaging single particles at cryogenic temperatures and obtaining electron diffraction data from nanocrystals of small organic molecules or macromolecules. Near- atomic or even atomic resolution of molecular structures can be achieved. The basis of these methods is the scattering of an electron beam due to the electrostatic potential of the sample. To analyze this high-quality experimental data, it is necessary to use appropriate atomic scattering factors. The independent atomic model (IAM) is commonly used although various more advanced models, already known from X-ray diffraction, can also be applied to enhance the analysis.
In this study we present a comparison of IAM and TAAM (Transferable Aspherical Atom Model), the latter with the parameters of the Hansen-Coppens multipole model transferred from the University at Buffalo Databank (UBDB). By this method, TAAM takes into account the fact that atoms in molecules are partially charged and are not spherical. We performed structure refinements on a carbamazepine crystal using electron structure factor amplitudes determined experimentally (Jones et al., 2018) or modeled with theoretical quantum-mechanical methods. The results show the possibilities and limitations of the TAAM method when applied to electron diffraction. Among others, the method clearly improves model fitting statistics, when compared to IAM, and allows for reliable refinement of atomic thermal parameters. The improvements are more pronounced with poorer resolution of diffraction data.