A bit late but I didnt answer in time.
This is one of the cases where I still wheel out ALMN to do the self
rotation. It generates ALL symmetry peaks and allows you to select which
axis you want to take as the polar axis. (ncode = 1 c*, ncode = 2 a*,
ncode = 3 b* and so on)
And the program output also makes an attempt to explain what it is doing!
A script
#!/bin/csh -f
#
almn \
hklin /y/people/ccp4/projects/mao/maon5_all_scaleit1.mtz \
MAPOUT /y/work/ccp4//almn.map \
<<eof
SELF 3 25
RESO 10 3.5
TITL Jean
CRYS file 1 orth 1 flim 1 10000000000000
LABI FILE 1 F=F_natlo
LIMIT 0 180 5 1 ! Beta limit 90 because of symmetry
! If in doubt set Beta limit 180..
FIND 5 40
NOPR
MAP
END
eof
Dirk Kostrewa wrote:
> Dear CCP4ers,
>
> I've asked you about symmetry in stereographic projections of
> self-rotation functions, because I have in a monoclinic space group
> with beta=97 a peak for a NCS 7-fold axis at Phi=83, Psi=90,
> Kappa=51.4. In this self-rotation function, calculated with GLRF, the
> monoclinic b-axis is oriented from south-pole to north-pole. Thus,
> with Psi=90, the 7-fold lies in the a,c-plane, and I was wondering
> wether it points along the c-axis by some symmetry element, since
> 83=180-97. Pierre Rizkallah pointed to the fact that the self-rotation
> function is calculated in Patterson space which has an inversion
> centre, and Ian Tickle has pointed me to the POLARRFN documentation
> that discusses some of these symmetries. From this, I can, in my case,
> construct the following symmetry-equivalent positions:
>
> (1) Original Peak: Phi, Psi, Kappa --->
> 83, 90, 51.4
> (2) General equivalent position: 180+Phi, 180-Psi, -Kappa --->
> 263, 90, -51.4
> (3) Crystallographic Dyad || Poles: 180+Phi, Psi, Kappa --->
> 263, 90, 51.4
> (4) (3) combined with (2): Phi, 180-Psi, -Kappa --->
> 83, 90, -51.4
>
> Thus, none of these combinations gives a Phi-angle of 97 degrees.
> However, meanwhile Liang Tong, the author of GLRF, explained to me,
> that in his convention, a positive Phi angle goes from +X (=a) to -Z
> (=-c*), which means that Phi=83 points really along the (-)c-axis
> (thus confirming my initial hypothesis).
>
> 7-fold
> /
> /
> /
> b-------------- a
> /|
> / |
> / |
> / |
> c c*
>
> So, many thanks to all of you who replied and helped me to solve this
> puzzle!
> I would still be interested in a textbook or paper discussing symmetry
> in stereographic projections, though ...
>
> Best regards,
>
> Dirk.
>
> Am 22.11.2007 um 14:40 schrieb Dirk Kostrewa:
>
>> Dear CCP4ers,
>>
>> does any of you have a good reference describing the symmetry of
>> crystallographic stereographic projections? There is a lot of
>> literature describing rotational symmetry in Eulerian angular space,
>> but I'm not aware of any for polar angles. In particular, I've
>> calculated a self-rotation function for a crystal in space group C2
>> with a monoclinic beta-angle of 97 degrees in a convention where Phi
>> is the angle from the x-axis (=a-axis) and Psi is the angle from the
>> monoclinic b-axis. I get a beautiful peak for a seven-fold rotation
>> axis at Phi=83 degrees and Psi=90 degrees. I think that the
>> seven-fold NCS-axis should point along the crystallographic c-axis,
>> but then I would expect Phi=97 and Psi=90. Presumably, there must be
>> a symmetry with the term Phi' = 180-Phi, but I would like to _know_
>> it. I would be grateful for any pointer to a good reference
>> describing symmetry in crystallographic stereographic projections,
>> also for future cases.
>>
>> Best regards,
>>
>> Dirk.
>>
>> *******************************************************
>> Dirk Kostrewa
>> Gene Center, A 5.07
>> Ludwig-Maximilians-University
>> Feodor-Lynen-Str. 25
>> 81377 Munich
>> Germany
>> Phone: +49-89-2180-76845
>> Fax: +49-89-2180-76999
>> E-mail: [log in to unmask]
>> *******************************************************
>>
>>
>
>
> *******************************************************
> Dirk Kostrewa
> Gene Center, A 5.07
> Ludwig-Maximilians-University
> Feodor-Lynen-Str. 25
> 81377 Munich
> Germany
> Phone: +49-89-2180-76845
> Fax: +49-89-2180-76999
> E-mail: [log in to unmask]
> *******************************************************
>
>
>
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