# Space group determination

In case of a crystal with an unknown space group (SPACE_GROUP_NUMBER=0 in XDS.INP), XDS (since version June 2008) helps the user in determination of the correct space group, by suggesting possible space groups compatible with the lattice symmetry of the data, and by calculating the R_{meas} for these space groups.

## Space group selected by XDS

XDS (or rather, the CORRECT step) makes an attempt to pick the correct space group automatically: it chooses that space group which has the highest symmetry (thus yielding the lowest number of unique reflections) and still a tolerable R_{meas} compared to the R_{meas} the data have in any space group (which is most likely a low-symmetry space group - often P1).

In many cases the automatic choice is the correct one, and re-running the CORRECT step is then not necessary. However, screw axes (see below) are not determined automatically in the XDS version of June 2008.

## Space group selected by user

Even in case the space group selected by XDS should be incorrect, the resulting list (in CORRECT.LP) should give the user enough information to pick the correct space group herself. The user may then put suitable lines with SPACE_GROUP_NUMBER=, UNIT_CELL_CONSTANTS= into XDS.INP and re-run the CORRECT step to obtain the desired result. (The REIDX= line is no longer required; XDS figures the matrix out.)

## Influencing the selection by XDS

### new parameters

The automatic choice is influenced by a number of decision constants that may be put into XDS.INP but which have defaults as indicated below:

- MAX_CELL_AXIS_ERROR= 0.03 ! relative deviation of unconstrained cell axes from those constrained by lattice symmetry
- MAX_CELL_ANGLE_ERROR= 3.0 ! degrees deviation of unconstrained cell angles from those constrained by lattice symmetry
- TEST_RESOLUTION_RANGE= 10.0 5.0 ! resolution range for calculation of R
_{meas} - MIN_RFL_Rmeas= 50 ! at least this number of reflections are required
- MAX_FAC_Rmeas= 2.0 ! factor to multiply the lowest R
_{meas}with to still be acceptable

The user may experiment with adjusting these values to make the automatic mode of space group determination more successful. However, it is much easier to just input the space group and cell parameters that the user thinks are correct.

### alternative indexing

As the old REIDX= input has lost its importance, it is useful to keep in mind that there are two ways to have XDS choose an indexing consistent with some other dataset:

- using REFERENCE_DATA_SET=
- using UNIT_CELL_A-AXIS=, UNIT_CELL_B-AXIS=, UNIT_CELL_C-AXIS= from a previous data collection run with the same crystal (see [1])

## Screw axes

The current version makes no attempt to find out about screw axes. It is assumed that the user checks the table in CORRECT.LP entitled "REFLECTIONS OF TYPE H,0,0 0,K,0 0,0,L OR EXPECTED TO BE ABSENT (*)", and identifies whether the intensities follow the rules

- a two-fold screw axis along an axis in reciprocal space (theoretically) results in zero intensity for the odd-numbered (e.g. 0,K,0 with K = 2*n + 1) reflections, leaving the reflections of type 2*n as candidates for medium to strong reflections (they don't
*have*to be strong, but they*may*be strong!). - similarly, a three-fold screw axis (theoretically) results in zero intensity for the reflections of type 3*n+1 and 3*n+2, and allows possibly strong 3*n reflections . 3
_{1}and 3_{2}cannot be distinguished. - analogously for four-fold and six-fold axes.

Once screw axes have been deduced from the patterns of intensities along H,0,0 0,K,0 0,0,L , the resulting space group should be identified in the lists of space group numbers printed in IDXREF.LP and CORRECT.LP, and the CORRECT step can be re-run. Those reflections that should theoretically have zero intensity are then marked with a "*" in the table. In practice, they should be (hopefully quite) weak, or even negative.

## Notes

- There is still the old Wiki page Old way of Space group determination
- To prevent XDS from trying to find a better space group than the one with the lowest R
_{meas}(often P1), you could just use MAX_FAC_Rmeas= 1.0 - Space group determination is not a trivial task. There is a number of difficulties that arise -
- ambiguity of hand of screw axis (e.g. 3
_{1}versus 3_{2}, or 6_{2}versus 6_{4}) - twinning may make a low-symmetry space group look like a high-symmetry one

- ambiguity of hand of screw axis (e.g. 3