Electron density map

Definition

A three-dimensional description of the electron density in a crystal structure, determined from X-ray diffraction experiments. X-rays scatter from the electron clouds of atoms in the crystal lattice; the diffracted waves from scattering planes [math]h, k, l[/math] are described by structure factors [math]\mathbf{F}_{hkl}.[/math] The electron density as a function of position [math]x,y,z[/math] is the Fourier transform of the structure factors:

[math]\rho(xyz) = {1\over V}\sum_{hkl} F(hkl)\exp[-2\pi i(hx + ky + lz)][/math].

The electron density map describes the contents of the unit cells averaged over the whole crystal and not the contents of a single unit cell (a distinction that is important where structural disorder is present).

Three-dimensional maps are often evaluated as parallel two-dimensional contoured sections at different heights in the unit cell.

Units

Electron density is measured in electrons per cubic ångström, e Å^-3.