# 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, ; or from the refractive index:

## 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