Electron density map: Difference between revisions
From Online Dictionary of Crystallography
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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 factor]]s <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: | 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 factor]]s <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>. | <center><math>\rho(xyz) = {1\over V}\sum_{hkl} F(hkl)\exp[-2\pi i(hx + ky + lz)]</math></center>. | ||
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). | 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). | ||
Latest revision as of 08:40, 25 October 2026
Carte de densité électronique (Fr). Elektronendichte-Karte (Ge). Mappa di densità elettronica (It). 電子密度図 (Ja). Mapa de densidad electrónica (Sp).
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]\textstyle{ h, k, l }[/math] are described by structure factors [math]\textstyle{ \mathbf{F}_{hkl}. }[/math] The electron density as a function of position [math]\textstyle{ x, y, z }[/math] is the Fourier transform of the structure factors:
.
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.