In X-ray crystallography, the Flack parameter is a factor used to estimate the absolute configuration of a structural model determined by single-crystal structure analysis. In this approach, one determines the absolute structure of a noncentrosymmetric crystal. The processes used to decide the absolute structure use the

anomalous dispersion effect Anomaly may refer to: Science Natural *Anomaly (natural sciences) **Atmospheric anomaly **Geophysical anomaly Medical *Congenital anomaly (birth defect), a disorder present at birth ** Physical anomaly, a deformation of an anatomical structure ...

. If atomic

scattering Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including ...

factors did not have imaginary parts, the

Friedel pair Friedel's law, named after Georges Friedel, is a property of Fourier transforms of real functions. Given a real function f(x), its Fourier transform :F(k)=\int^_f(x)e^dx has the following properties. *F(k)=F^*(-k) \, where F^* is the complex co ...

s would have exactly the same amplitudes (i.e., the scattering intensity

, F(h k l), ^

from crystal plane (h k l) is equal to

, F(-h -k -l), ^

). However, atomic scattering factors have imaginary parts due to the

, 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 intensities of

Bijvoet pairs Johannes Martin Bijvoet (23 January 1892, Amsterdam – 4 March 1980, Winterswijk) was a Dutch chemist and crystallographer at the van 't Hoff Laboratory at Utrecht University. He is famous for devising a method of establishing the absolute con ...

or of the R-factors for the two possible structures can suggest the correct absolute structure. One of the more powerful and simple approaches is using the Flack parameter, because this single parameter clearly indicates the absolute structure. The Flack parameter is calculated during the structural refinement using the equation given below: :

\ I(hkl) = (1-x), F(h k l), ^ + x, F(-h -k -l), ^

where ''x'' is the Flack parameter, ''I'' is the square of the scaled observed structure factor and ''F'' is the calculated structure factor. By determining ''x'' for all data, ''x'' is usually found to be between 0 and 1. If the value is near 0, with a small standard uncertainty, the absolute structure given by the structure refinement is likely correct, and if the value is near 1, then the inverted structure is likely correct. If the value is near 0.5, the crystal may be racemic or twinned. The technique is most effective when the crystal contains both lighter and heavier atoms. Light atoms usually show only a small anomalous dispersion effect. In this case, the Flack parameter can refine to a physically unrealistic value (less than 0 or greater than 1) and has no meaning. This parameter, introduced by H. D. Flack became one of a standard set of values being checked for structures with noncentrosymmetric space groups.

References

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