Centric and acentric reflections: Difference between revisions

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Properties: centric reflections have only two phase possibilities, e.g. 0° and 180° (but in any case 180° apart), and centric reflections do not have an anomalous signal (can these properties be easily derived here?).  
Properties: centric reflections have only two phase possibilities, e.g. 0° and 180° (but in any case 180° apart), and centric reflections do not have an anomalous signal (can these properties be easily derived here?).  


Furthermore, the "intensity statistics" [2] of acentric reflections  
Furthermore, with E being the structure factor, the statistical distribution [2] of acentric reflections is
(<math> P(|E|) = 2 |E| e^{-|E|^2} </math> )
<math> P(|E|) = 2 |E| e^{-|E|^2} </math>  


[[file:I_acentrics.png]]
[[file:I_acentrics.png]]


are different from those of centric reflections
which is different from those of centric reflections; these follow <math> P(|E|) = \sqrt{\frac{2}{\pi}} e^{-|E|^2/2} </math>
(<math> P(|E|) = \sqrt{\frac{2}{\pi}} e^{-|E|^2/2} </math> )


[[file:I_centrics.png]]
[[file:I_centrics.png]]
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Centric reflections have a special role in experimental [[phasing]].
Centric reflections have a special role in experimental [[phasing]].
The moments of intensities (centric <math><I^2>/<I>^2=3</math> ; acentric <math><I^2>/<I>^2=2</math>) can be calculated from the above formulas [3]; the first result can e.g. be obtained with [https://wolframalpha.com Wolframalpha] using  <code>(sqrt(2/Pi) * integral ( x^4 exp(-0.5x^2) from 0 to inf )) / (sqrt(2/Pi) * integral ( x^2 exp(-0.5x^2) from 0 to inf ))^2</code>, where the x stands for the E in the formula above.


== References ==
== References ==
1,330

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