Reindexing

There are two uses of the REIDX= keyword.

The first of these is during space group determination.

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The other use is in a final step that might have to be done in order to make the reduced data consistent with another existing dataset, or an atomic model. For some background, see reindexing. The classic description of this is that these are crystals where the Laue symmetry is of a lower order than the apparent crystal lattice symmetry. Unfortunately, however, even P1 crystals can have cells which may be transformed such that the indexing is different. An example is a triclinic cell with parameters a=58.5 b=73.1 c=83.6 alpha=80 beta=70 gamma=89 which gives similar cell parameters under the transformation REIDX=1 0 0 0 0 -1 0 0 1 0 -1 0.

We should rather use the term "alternative indexing" for this mode of reindexing.

Possible alternative indexing operators available for this purpose, and consistent with the cell parameters, are listed at the bottom of IDXREF.LP:

!!! WARNING !!! SOLUTION MAY NOT BE UNIQUE.
OTHER POSSIBLE SOLUTIONS CAN BE TRIED IN THE "CORRECT" STEP
BY USING THE REINDEXING CARDS PRINTED BELOW.
          REINDEXING CARD           QUALITY
 1  1  0  0  0 -1  0  0  0  0 -1  0    0.00

if the IDXREF step is run in the correct spacegroup. These operators (usually there's only one) are then applied in the CORRECT step, using the REIDX= keyword and the 12 numbers given. For this to work correctly, INTEGRATE has to use the correct spacegroup, too.

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Attention: whenever there is a possibility of alternative indexing, there is also a chance that the crystal (and its data) may be twinned! In the example above, the twinning law is h, -k , h-l . A good tool to identify this situation is sfcheck. Whenever you see !!! WARNING !!! SOLUTION MAY NOT BE UNIQUE. in IDXREF.LP, you should be aware of this possible problem. FIXME: shortly discuss merohedral and non-merohedral twinning (example above) here.

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The two uses of REIDX= outlined above are mutually exclusive: only when the spacegroup is known, it makes sense to test alternative ways of indexing. That means: one cannot run IDXREF and INTEGRATE with SPACE_GROUP_NUMBER=0, and still try alternative indexing in CORRECT (unless one does the required matrix multiplication manually).

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To explain in a different way - there are two possible strategies for XDS data reduction:

1. to use SPACE_GROUP_NUMBER=0 up to and including INTEGRATE, and to use CORRECT to decide upon the spacegroup with the help of the REIDX= operators from the DETERMINATION OF LATTICE CHARACTER AND BRAVAIS LATTICE table in IDXREF.LP.
2. to use the known SPACE_GROUP_NUMBER for IDXREF, INTEGRATE and CORRECT. Only using this strategy may alternative indexing possibilities provided by the list OTHER POSSIBLE SOLUTIONS CAN BE TRIED ... be explored.

The connection between these two mutually exclusive strategies is by optimization: the first pass through the data (JOB=XYCORR INIT COLSPOT IDXREF DEFPIX INTEGRATE CORRECT) is done to determine the space group, using the first strategy.
Then the optimization is performed (JOB=INTEGRATE CORRECT) in the correct spacegroup.
After this, one obtains possible reindexing operators (JOB=IDXREF), which may then be tested (JOB=CORRECT).