Experimental and Theoretical Charge Density Studies at Subatomic Resolution

Analysis of accurate experimental and theoretical structure factors of diamond and silicon reveals that the contraction of the core shell due to covalent bond formation causes significant perturbations of the total charge density that cannot be ignored in precise charge density studies. We outline that the nature and origin of core contraction/expansion and core polarization phenomena can be analyzed by experimental studies employing an extended Hansen-Coppens multipolar model. Omission or insufficient treatment of these subatomic charge density phenomena might yield erroneous thermal displacement parameters and high residual densities in multipolar refinements. Our detailed studies therefore suggest that the refinement of contraction/expansion and population parameters of <i>all</i> atomic shells is essential to the precise reconstruction of electron density distributions by a multipolar model. Furthermore, our results imply that also the polarization of the inner shells needs to be adopted, especially in cases where second row or even heavier elements are involved in covalent bonding. These theoretical studies are supported by direct multipolar refinements of X-ray powder diffraction data of diamond obtained from a third-generation synchrotron-radiation source (SPring-8, BL02B2)

Powder X‑ray Diffraction Electron Density of Cubic Boron Nitride

Conventionally, the core electron density (ED) of atoms in molecules is considered to be virtually unperturbed by chemical bonding effects. Here we report a combined experimental and theoretical investigation of the ED of cubic boron nitride including a detailed modeling of the core ED. By modeling structure factors obtained from very-high-resolution synchrotron powder X-ray diffraction data, it is possible to model not only the valence ED but also the response of the core ED to the effects of chemical bonding. The biggest challenge when studying the core ED is the deconvolution of the thermal motion from the experimental structure factors, since the thermal motion is strongly correlated to core ED deformation. However, atomic displacement parameters could be estimated from a full pattern Rietveld-multipolar refinement, and they are shown to be in good correspondence with ab initio lattice dynamics calculations. The corresponding extended multipole model including both core and valence ED refinement suggests that 2.0 electrons are transferred from the boron atomic basin to the nitrogen atomic basin. The core density was found to deplete upon bonding, which is in line with a significant charge transfer