Electron-density distribution

The electron-density distribution is the three-dimensional realspace arrangement of the electrons in the material. Because electrons are quantum mechanically delocalized, each electron occupies a 'fuzzy' region of space (electron cloud). The total electron density--the summation of the electron distribution for every electron in every atom--is thus inherently spread spatially; e.g a map of electron distribution will have diffuse boundaries. Nevertheless, when the electron distribution is visualized, it is often shown as a surface, representing an isosurface of constant electron-density.

The exact electron-density distribution within a unit cell of a crystal can be reconstructed by carefully fitting the peak heights measured in an x-ray diffraction experiment (crystallographic 'structure solution').

The electron distribution at a larger scale can be similarly reconstructed by fitting small-angle scattering data (SAXS or GISAXS). In this case, one is probing the average electron-density distribution at the nanoscale, without resolving the exact arrangement of electron-distribution (atoms) within this nanostructure. The specific electron-distribution within a measurement volume (as opposed to the average structure defined by a unit-cell) can be reconstructed using coherent methods such as CDI or ptychography.

Mathematical form

The electron-density (number of electrons per unit volume) can be computed from the atomic scattering factor, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f_1} ; or from the refractive index:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{alignat}{2} \rho_e & = \frac{\rho N_a f_1}{M_a} \\ & = \frac{2 \pi}{\lambda^2 r_e} \delta \end{alignat} }

References

• Philip Coppens, Bo Iversen, Finn Krebs Larsen The use of synchrotron radiation in X-ray charge density analysis of coordination complexes Coordination Chemistry Reviews 2005, 249 (1-2), 179-195 doi: 10.1016/j.ccr.2004.02.019
• Mads R. V. Jørgensen, Venkatesha R. Hathwar, Niels Bindzus, Nanna Wahlberg, Yu-Sheng Chen, Jacob Overgaard and Bo B. Iversen Contemporary X-ray electron-density studies using synchrotron radiation IUCrJ 2014 1 (5), 267-280 doi: 10.1107/S2052252514018570