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CCP4BB  October 2010

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Subject:

Summary : [ccp4bb] embarrassingly simple MAD phasing question

From:

William Scott <[log in to unmask]>

Reply-To:

William Scott <[log in to unmask]>

Date:

Wed, 13 Oct 2010 13:58:56 -0700

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Thanks for the overwhelming response.  I think I probably didn't phrase the question quite right, but I pieced together an answer to the question I wanted to ask, which hopefully is right.


On Oct 13, 2010, at 1:14 PM, SHEPARD William wrote:

> It is very simple, the structure factor for the anomalous scatterer is 
> 
> FA = FN + F'A + iF"A (vector addition)
> 
> The vector F"A is by definition always +i (90 degrees anti-clockwise) with respect to the vector FN (normal scattering), and it represents the phase lag in the scattered wave.



So I guess I should have started by saying I knew f'' was imaginary, the absorption term, and always needs to be 90 degrees in phase ahead of the f' (dispersive component).

So here is what I think the answer to my question is, if I understood everyone correctly:

Starting with what everyone I guess thought I was asking,

> FA = FN + F'A + iF"A (vector addition)

for an absorbing atom at the origin, FN (the standard atomic scattering factor component) is purely real, and the f' dispersive term is purely real, and the f" absorption term is purely imaginary (and 90 degrees ahead).

Displacement from the origin rotates the resultant vector FA in the complex plane.  That implies each component in the vector summation is rotated by that same phase angle, since their magnitudes aren't changed from displacement from the origin, and F" must still be perpendicular to F'.  Hence the absorption term F" is no longer pointed in the imaginary axis direction.

Put slightly differently, the fundamental requirement is that the positive 90 degree angle between f' and f" must always be maintained, but their absolute orientations are only enforced for atoms at the origin.

Please correct me if this is wrong.

Also, since F" then has a projection upon the real axis, it now has a real component (and I guess this is also an explanation for why you don't get this with centrosymmetric structures).

Thanks again for everyone's help.

-- Bill




William G. Scott
Professor
Department of Chemistry and Biochemistry
and The Center for the Molecular Biology of RNA
228 Sinsheimer Laboratories
University of California at Santa Cruz
Santa Cruz, California 95064
USA

phone:  +1-831-459-5367 (office)
             +1-831-459-5292 (lab)
fax:        +1-831-4593139  (fax) 

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