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.<br /

New refinement strategies for pseudoatom databank - towards wider range of application

Pseudoatom databanks, collecting parameters of multipole model of electron densities for various atom types, are used to replace Independent Atom Model by the more accurate Transferable Aspherical Atom Model (TAAM) in crystal structure refinement. They may also be used to reconstruct electron density of a molecule, crystal or biomacromolecular complex in fast yet quite accurate way and compute from it various properties, like energy of electrostatic interactions, for example. Even faster, but similarly accurate in electrostatic energy estimations model exists, the aug-PROmol. Model analogous to aug-PROmol cannot be built from the current pseudoatom databanks, as they perform badly when truncated to the monopole level. Here we searched for new strategies of multipole model refinements, leading to better parametrization already at the monopole level. This would allow to create in a single route of model parametrization a pseudoatom databank, which would be suitable for both crystal structure refinement and rapid electrostatic energy calculations. Such a route does not exist yet, because as we show here, the aug-PROmol model, alternative to the current pseudoatom databanks, is not suitable for crystal X-ray structure refinement. Here we show that cumulative approach to multipole model refinements, as oppose to simultaneous or iterative refinements of all multipole model parameters (Pv, κ, Plm, κ\u27) leads to substantially different models of electron density. Cumulative refinement of Plm first and then κ\u27 parameters is much worse than simultaneous. It results in electron density model giving wrong estimates of electrostatic interaction energies and atomic displacement parameters. Cumulative refinement of two blocks of parameters, Pv and κ first and then Plm and κ\u27, on the other hand, leads to the Pv|Plm’ model having promising properties. It is similarly good as University at Buffalo DataBank (UBDB) of pseudoatoms in X-ray structure TAAM refinement and electrostatic energy estimations, especially for less polar molecules. When truncated to monopole level, the Pv model has a chance to replace the aug-PROmol in fast yet accurate electrostatics energy calculations, although some improvements in κ parametrization for polar functional groups are still needed. The Pv|Plm’ model is also a source of point charges which behave similarly to the RESP charges in electrostatic interaction energy estimations