Flack parameter
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In X-ray crystallography, the Flack parameter is a factor used to estimate the absolute configuration of a structural model determined by the single-crystal structure analysis.
It is preferable to determine the absolute structures of acentric crystals. The processes used to decide the absolute structure use the anomalous dispersion effect. If atomic scattering factors did not have imaginary parts, the Friedel pairs would have exactly the same amplitude (i.e., the scattering intensity | F(hkl) | 2 from crystal plane (h k l) is equal to | F( − h − k − l) | 2). However, atomic scattering factors have imaginary parts due to the anomalous dispersion effect, and Friedel's law is broken by this effect.
There are several ways to determine the absolute structure by X-ray crystallography. For example, a comparison of the intensity of the Bijvoet pair or the R factor given by the inverted structure can suggest the absolute configuration. Among these methods, one of the major approaches is using the Flack parameter, because this parameter indicates the absolute configuration clearly.
The Flack parameter is calculated during the structural refinement using the equation given below:
where x is the Flack parameter and I is the intensity.
By refining this x for all data, this parameter is usually determined from 0 to 1. If the value is near 0, the absolute structure given by the structural refinement seems to be correct, and if the value is near 1, then the inverted structure may be correct. If the value is near 0.5, the crystal may be racemic or twin. This technique is useful only when the crystal contains heavy atoms, because light atoms usually show a small anomalous dispersion effect.
