Measurements of electron densities in solids: a real-space view of electronic structure and bonding in inorganic crystals

Abstract

This review summarizes the recent progress in experimental determination of electron densities in inorganic crystals and its contribution to our understanding of bonding and density functional approximations. The experimental techniques for electron density mapping are presented, including the accurate measurement of experimental structure factors by electron diffraction and multipole electron density modelling. Interpretation of electron density maps by combining first-principles calculations and spectroscopic measurements will be illustrated through the example of bonding in copper and cuprite. The significance of experimental electron density is demonstrated by selected examples of materials representative of ionic, metallic and covalent bonding and testing of theory.

Bond analysis of phosphorus skutterudites: Elongated lanthanum electron buildup in LaFe4P12

“…A more direct approach is to perform diffraction experiments and refine the structure factors by starting from overlapping atomic orbitals [38,44,45]. This reference is in principle equivalent to the previously discussed procrystal.…”

Probing core-electron orbitals by scanning transmission electron microscopy and measuring the delocalization of core-level excitations

“…However, acquiring experimental low-noise, atomic-resolution maps for such analyses has been challenging, and the outcomes have been suitable only for basic qualitative interpretation. In this report, using high-quality low-noise STEM-EDX maps of single-crystal SrTiO 3 (STO), we demonstrate that STEM-EDX mapping can go beyond elemental profiling of whole atoms to quantitatively probe core-level electron orbitals. Details of experiments, analysis, and results are discussed below, including limitations of the method.…”

“…Nevertheless, the mapping of electron densities in near-defect-free crystals has been demonstrated by structure factor determination using X-ray diffraction [1] and transmission electron microscopy (TEM) convergent beam electron diffraction [2][3][4]. Real-space characterization of the bonding electron orbitals of individual molecules and surface atoms has also been shown using atomic force microscopy [5,6] and scanning tunneling microscopy [7,8].…”

Validation of density functionals for transition metals and intermetallics using data from quantitative electron diffraction

“…14,15 Quantitative convergent beam electron diffraction methods (QCBED) of transmission electron microscopy (TEM) can provide very precise and accurate low-order F g , as nano-scale defect-free sample volumes can be readily used for measurements with electron beam probes as small as 0.5nm in diameter. 15 Crystalline defects that would significantly and detrimentally contribute to scattering, e. g. grain boundaries, dislocations and planar faults, can readily be identified using diffraction-contrast imaging techniques of TEM and hence can be avoided. 16 Electron structure factors can be converted into X-ray structure factors through the Mott formula.…”