Experimental and Theoretical Charge Density Studies at Subatomic Resolution

Abstract

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 all 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).

Aspherical‐Atom Modeling of Coordination Compounds by Single‐Crystal X‐ray Diffraction Allows the Correct Metal Atom To Be Identified

“…Disorder also prohibits, at the current stage, Hirshfeld-atom refinement (HAR), [23,24] and subsequent X-ray wavefunction refinement. [25,26] Examples of modeling challenges encountered include the dominance of core over valence scattering [27][28][29] and inaccurate radial functions [30,31]5 of the Hansen/Coppens multipole model. A detailed discussion of these and other related issues was recently given by Schmøkel et al [32] However, omitting disordered and/or metal-containing structures from aspherical-atom modeling altogether would, from a scientific interest point of view, be clearly limiting and unsatisfactory.…”

Unconstrained and X-ray constrained extremely localized molecular orbitals: analysis of the reconstructed electron density

“…2 shows that the two most flexible multipolar models reproduce the low-angle diffracted intensities much better than the high-angle ones, whereas this is not true for the XC-ELMO technique that seems more 'tempered'. This might be interpreted as an over-fitting of the low-angle data by the multipolar models, which, in fact, converge to lower 2 , or otherwise as the evidence of a too restricted model that could be improved by a more flexible treatment of the core electrons, as suggested by Fischer et al (2011). A model with strictly hybridized atoms, MM1, is instead closer to 2 ¼ 1, and shows a more uniform agreement with the observed structure factors, like the XC-ELMO calculations (Fig.…”

“…Such a study would require even higher resolution and, at present, has been applied only on smaller and more symmetric crystals (Fischer et al, 2011).…”

“…This will enable us to compare all the densities, affected in the same way by the inherent limitations of the multipolar expansion (Fischer et al, 2011). Of course, all the atomic coordinates and ADPs (for XC-ELMO) were kept fixed to those from the MM2 refinement against experimental data.…”

Electron density building block approach for metal organic frameworks

“…The variables κ and κ' allow the radial flexibility, whereas the spherical harmonics functions guarantee the aspherical flexibility. A more detailed treatment of the core shells has been recently proposed [16]:…”