X-ray crystallography X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles ...

, a difference density map shows the spatial distribution of the difference between the measured

electron density In quantum chemistry, electron density or electronic density is the measure of the probability of an electron being present at an infinitesimal element of space surrounding any given point. It is a scalar quantity depending upon three spatial va ...

of the crystal and the electron density explained by the current model. These coefficients are derived from the gradient of the likelihood function of the observed structure factors on the basis of the current model.

Display

Conventionally, they are displayed as

isosurface An isosurface is a three-dimensional analog of an isoline. It is a surface that represents points of a constant value (e.g. pressure, temperature, velocity, density) within a volume of space; in other words, it is a level set of a continuous fu ...

s with positive density—electron density where there's nothing in the model, usually corresponding to some constituent of the crystal that hasn't been modelled, for example a

ligand In coordination chemistry, a ligand is an ion or molecule (functional group) that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's electr ...

or a

crystallisation adjutant A crystallization adjutant is a material used to promote crystallization, normally in a context where a material does not crystallize naturally from a pure solution. Additives in Macromolecular Crystallization In macromolecular crystallography, the ...

-- in green, and negative density—parts of the model not backed up by electron density, indicating either that an atom has been disordered by

radiation damage Radiation damage is the effect of ionizing radiation on physical objects including non-living structural materials. It can be either detrimental or beneficial for materials. Radiobiology is the study of the action of ionizing radiation on livin ...

or that it is modelled in the wrong place—in red.

Calculation

Difference density maps are usually calculated using Fourier coefficients which are the differences between the observed structure factor amplitudes from the X-ray diffraction experiment and the calculated structure factor amplitudes from the current model, using the phase from the model for both terms (since no phases are available for the observed data). The two sets of structure factors must be on the same scale. It is now normal to also include weighting terms which take into account the estimated errors in the current model: :

C_ = ( m , F_,  - D , F_,  ) exp( 2\pi i \phi_ )

where ''m'' is a

figure of merit A figure of merit is a quantity used to characterize the performance of a device, system or method, relative to its alternatives. Examples *Clock rate of a CPU * Calories per serving *Contrast ratio of an LCD *Frequency response of a speaker * ...

which is an estimate of the cosine of the error in the phase, and ''D'' is a scale factor.

References

{{DEFAULTSORT:Difference Density Map Crystallography