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[交流] 转贴：晶体解析中flack parameter的物理意义和取值范围已有3人参与

关于手性结构和非中心对称结构都需要精修flack parameter。许多人包括我，对flack parameter都非常困惑，不明白它所表达的物理含义，以及不太知道该怎样精修这个参数，还有怎样才能够使得flack parameter取值合理。
下面转贴一篇英国大学网站上关于flack parameter的解释，相信对我们更好理解这个物理概念有帮助:

Flack parameter
The Flack parameter describes how enantiopure a crystal structure is in a non-centrosymmetric space group - a space group without inversion or mirror planes.

In a centrosymmetric space group more reflections (both weak and strong) depend on one another, giving a broad distribution for the | E2 - 1 | parameter not near the mean ~ 0.74. For non-centrosymmetric space groups (where you need to refine a Flack parameter each time regardless of whether your structure if chiral or not) the value is ~ 0.94.

I (hkl) = ( 1 - x ) | F (hkl) |2 + x | F (-h-k-l) |2

When x = Flack parameter

The value of x ranges from 0 to 1; 0 means that the solution determined is only that enantiomer, 1 means that the incorrect enantiomer has been determined - and the structure should be inverted. A value around 0.5 is for racemically twinned structure - where both enantiomers are present.

The uncertainty associated with the Flack parameter is considered by many to be more important than the value itself. If the value is large then the Flack parameter deduces nothing.

To correctly refine the Flack parameter, you need to input near the top of the .res file the command TWIN, and BASF 0.5. This tells XSHELL to work out the Flack parameter.

You will also need to work out the amount of Friedel pairs from the unique data. This can be calculated by looking in the .lst file, The number of unique reflections (before merging Friedel pairs) will be near the top of the file, after the coordinates of the atoms and the total number of reflections. The number after merging can be found at the end of the .lst file. Minus the after from the before value, and you now your Friedel pairs number for the data (which you need to input in the .cif).

Friedel pairs are defined by:

h k l ≡ -h -k -l

Anomalous scattering / dispersion
The energy of incident X-ray photons is slightly larger than the absorption edge of certain atoms present in a structure. This causes ionisation and emission of Kα radiation, which increases the background radiation. These photons are not absorbed, but interact strongly, altering slightly in both magnitude and phase.

Absorption is proportional to anomalous scattering effects, so if the atom has a high scattering factor, it will also have a high atomic absorption coefficient.

With Mo radiation, the structure needs to contain atoms bigger than Na (ie. Mg and bigger)
With Cu radiation, the structure needs to contain atoms bigger than C (ie. N and bigger)
In non-centrosymmetric space groups this results in Bijvoet differences - when indices are inverted the anomalous contribution to the structure factor does not change, giving different amplitudes and phases. This creates intensity differences between Friedel reflections - ie. Bijvoet differences.

These intensity differences are discernible in the data, but at the end of the structure determination can be assessed - hence the Flack parameter is calculated at the end of the solving the structure.

If the anomalous scatterers are significant, Friedel laws are broken. This leads to a departure from Laue symmetry, and allows distinction between enantiomers.

网站连接是：http://xray.chm.bris.ac.uk/xrayu ... lography/flack.html

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