 Electron density map

An electron density map is a spatial reconstruction of electron density, typically displayed as a grid or contours. In X-ray crystallography, a beam scattered by a crystal produces a diffraction pattern: measured intensities constrain structure factor magnitudes, while crystallographic phases are also required for reconstruction. Coordinates and experimental data are combined in common model-assessment maps.^[ref]

With fractional crystallographic coordinates $\mathbf{r}$, integer Miller index vector $\mathbf{h}$ and unit cell volume $V_c$, an ideal Fourier reconstruction has the formHere the structure factors are complex Fourier coefficients. Finite data and uncertain phases limit the reconstructed detail; this is part of the phase problem, not simply an issue of drawing contours more finely.

An original one-dimensional example makes the phase information visible:Both profiles have the same Fourier coefficient magnitudes, but their maxima occur half a period apart. Squared magnitudes alone cannot distinguish them.

An electron density map is also distinct from a macromolecular structural model fitted to it. A difference electron density map can highlight disagreement between observed and model-predicted scattering. Common map coefficients already incorporate information from the model, so the resulting map is not wholly independent confirmation of every modeling choice.^[ref]