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How CrystFEL handles symmetry
-----------------------------
Currently, only process_hkl and render_hkl understand symmetry (and render_hkl
only understands it when plotting a zone axis pattern). get_hkl does NOT
currently understand symmetry, which means you'll have to expand any molecular
model (the PDB) out to P1 to get the correct results. You can achieve that, for
example, by loading it into Mercury, turning on "Packing", and re-saving.
Alternatively, using CCP4:
$ echo symgen P63 | pdbset xyzin model.pdb xyzout model-P1.pdb
[ While on this subject, you'll probably also want to include hydrogens in the
model using something like:
$ echo HYDROGENS APPEND | hgen xyzin model.pdb xyzout model-with-H.pdb ]
Symmetry definitions are included in src/symmetry.c. Point group definitions
are required for merging and the display of merged results (since merging does
not care about systematic absences (i.e. the space group) - as far as merging is
concerned, systematic absences are just measurements which happen to have values
of zero. Each space group belongs to exactly one point group, which you can
look up in the International Tables for X-Ray Crystallography.
Space groups would be needed to make get_hkl handle symmetry properly, but that
hasn't been done yet, so symmetry.c just handles point groups for now. The
method used in symmetry.c is general to both point groups and space groups, even
though the code currently is not.
Point groups are being added here as they are required, so it's likely that the
exact one you want hasn't been added yet. Here's how to add a new one:
First, expand the check_cond() function to include a description of the
asymmetric reciprocal unit cell for the point group. Every reflection in the
whole of reciprocal space must map onto exactly one reflection in the asymmetric
unit cell so defined. The asymmetric cell is usually defined with positive h, k
and l, but it doesn't really matter. Working out the required condition means
visualising the cell and taking care to properly handle situations such as the
(000) reflection.
Now, expand the num_equivs() function. Given a point group and a set of Miller
indices, this function must return the number of equivalent reflections,
including the given reflection, taking into account the multiplicity of the
reflection. For example, high-symmetry reflections (usually ones with zeroes
in their indices) have fewer equivalents. Label the different classes of
reflection according to their Wyckoff letters. This information can be found in
the International Tables.
Finally, add the new point group to the get_equiv() function. This function
takes a set of Miller indices, a point group and an index, "n", and returns (by
reference) the indices of the "n"th equivalent reflection. Again, you have to
distinguish between the different Wyckoff positions. Lists of equivalent
reflection, grouped according to Wyckoff symbol, can also be found in the
International Tables. get_equiv() should return the original indices as the
first set of equivalent indices, i.e. when idx=0.
It's not normally necessary to write an individual table of equivalents for each
Wyckoff position, because many positions are just "truncated" sub-classes of
other positions. For example, in 6/mmm, the equivalent reflections for "b" and
"c" can be generated simply by working through the list for "g" (the general
position) with indices set to zero or equal as appropriate, and by stopping
after the first six equivalents. Therefore, the num_equivs() function combined
with a single table for positions b-g in get_equivs() is sufficient to deal with
all cases. Check carefully whether this really works for your chosen point
group first.
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