# 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 Rmeas for these space groups.

## Space group selected by XDS: ambiguous with respect to enantiomorph and screw axes

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 Rmeas compared to the Rmeas 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, neither the correct enantiomorph nor screw axes (see below) are determined automatically by XDS.

## Table of space groups to consider based on CORRECT suggestion

If CORRECT suggests it could just as well be Comment
1 -
3 4 screw axis listing lets you decide
5 -
16 17, 18, 19 screw axis listing lets you decide
21 20 screw axis listing does not let you decide
22 -
23 24 screw axis listing does not let you decide
75 76, 77, 78 screw axis listing lets you decide, except between 76/78 enantiomorphs
89 90, 91, 92, 93, 94, 95, 96 screw axis listing lets you decide, except between 91/95 and 92/96 enantiomorphs
79 80 screw axis listing lets you decide
97 98 screw axis listing lets you decide
143 144, 145 screw axis listing lets you decide, except between 144/145 enantiomorphs
146 -
149 151, 153 screw axis listing lets you decide, except between 151/153 enantiomorphs
150 152, 154 screw axis listing lets you decide, except between 152/154 enantiomorphs
155 -
168 169, 170, 171, 172, 173 screw axis listing lets you decide, except between 169/170 and 171/172 enantiomorphs
177 178, 179, 180, 181, 182 screw axis listing lets you decide, except between 178/179 and 180/181 enantiomorphs
195 198 screw axis listing lets you decide
196 -
197 199 screw axis listing does not let you decide
207 208, 212, 213 screw axis listing lets you decide, except between 212/213 enantiomorphs
209 210 screw axis listing lets you decide
211 214 screw axis listing lets you decide

Attention: this table was set up on February 15, 2015 and has been not verified by anyone.

## 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

### keywords and 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 Rmeas
• MIN_RFL_Rmeas= 50 ! at least this number of reflections are required
• MAX_FAC_Rmeas= 2.0 ! factor to multiply the lowest Rmeas with to still be acceptable

The user may experiment with adjusting these values to make the automatic mode of space group determination more successful. For example, if the crystal diffracts weakly, all Rmeas values will be high and no valid decision can be made. In this case, I suggest to use e.g.

TEST_RESOLUTION_RANGE= 50.0 10.0


### 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 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

1. 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!).
2. 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 . 31 and 32 cannot be distinguished.
3. 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 Rmeas (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. 31 versus 32, or 62 versus 64)
• twinning may make a low-symmetry space group look like a high-symmetry one