# Old way of Space group determination

## Space group determination with pointless

The latest and currently easiest way of space group determination from a XDS formatted reflection file is via the pointless program:

echo SETTING SYMMETRY-BASED | pointless xdsin XDS_ASCII.HKL


From the latter pointless output, the correct space group should be deduced and CORRECT run with appropriate SPACE_GROUP_NUMBER and UNIT_CELL_PARAMETERS.

## Space group determination within XDS

the steps below are not needed anymore since version July-2008 so don't read on!

Space group determination can be done within XDS by following these steps:

• an initial data reduction in P1, using SPACE_GROUP_NUMBER=0 (or even omitting that line)
• after CORRECT has thus run in P1, one may try other spacegroups by inspecting the table DETERMINATION OF LATTICE CHARACTER AND BRAVAIS LATTICE in IDXREF.LP (see the example below). The sortlattices jiffy is useful here.
• for each possible lattice character, starting with the one corresponding to highest symmetry, do:
• look up space groups corresponding to lattice characters from the list BRAVAIS-TYPE / POSSIBLE SPACE-GROUPS FOR PROTEIN CRYSTALS in IDXREF.LP (repeated at bottom of this article).
• modify SPACE_GROUP_NUMBER=<number according to that list>
• modify or insert REIDX=<12 numbers corresponding to the lattice character, from the table>
• modify or insert UNIT_CELL_PARAMETERS= according to table, but make them obey space group requirements (e.g. orthorhombic: all angles 90°, tetragonal and trigonal: a=b, and so on).
• run XDS with JOB=CORRECT. Inspect CORRECT.LP and note R-factors, I/sigma and a and b modifiers of standard deviations
• for many Bravais types (defined at [1]), there are several possible point groups (tP and tI: 4, 422; hP: 3, 6, 312, 321, 622; hR: 3, 32; cP, cF and cI: 23 and 432) and thus several possible space groups. In these cases, each point group has to be tested: the SPACE_GROUP_NUMBER has to be changed to one of those consistent with the point group, and the CORRECT step re-run.
• repeat for each possible lattice character
• finally decide on the correct Bravais lattice and point group by comparing R-factors (in particular Rmeas), and, from there, come up with possible space groups by looking at the table of systematic absences along the h,0,0 0,k,0 and 0,0,l axes of the diffraction pattern.

Be aware of the possibility of twinning, and of the different, but equivalent ways to index a given diffraction pattern (reindexing)!

## Example

old versions of XDS produced a list sorted by Lattice Character number:

 LATTICE-  BRAVAIS-   QUALITY  UNIT CELL CONSTANTS (ANGSTROEM & DEGREES)  REINDEXING CARD (CORRECT)
CHARACTER  LATTICE     OF FIT      a      b      c   alpha  beta gamma

1        cF        999.0     329.1  328.9  329.5 120.2  83.7 127.4    1  1 -1  0  1 -1  1  0 -1 -1 -1  0
2        hR        919.0     219.6  285.4  329.4 114.5  85.4 109.9    1  1  0  0 -1  0 -1  0 -1  1  1  0
3        cP        919.7     145.8  164.1  245.4  90.1  90.0  90.1   -1  0  0  0  0  1  0  0  0  0 -1  0
5        cI        999.0     285.4  219.4  294.9  65.5  44.4  70.3   -1  0 -1  0 -1  1  0  0  0  1 -1  0
4        hR        917.8     219.6  285.4  328.9 114.5  85.5 109.8   -1 -1  0  0  1  0 -1  0  1 -1  1  0
6        tI        999.0     294.9  285.4  219.4  70.3  65.5  44.4    0  1 -1  0 -1  0 -1  0 -1  1  0  0
7        tI        999.0     285.4  219.4  294.9  65.5  44.4  70.3   -1  0 -1  0 -1  1  0  0  0  1 -1  0
8        oI        999.0     219.4  285.4  294.9  44.4  65.5  70.3    1 -1  0  0  1  0  1  0  0 -1  1  0
9        hR        881.8     145.8  219.4  767.9  91.8 101.0 131.6    1  0  0  0 -1  1  0  0 -1 -1  3  0
10        mC        135.8     219.4  219.6  245.4  89.9  90.1  96.8    1 -1  0  0  1  1  0  0  0  0  1  0
11        tP        136.4     145.8  164.1  245.4  90.1  90.0  90.1   -1  0  0  0  0  1  0  0  0  0 -1  0
12        hP        385.3     145.8  164.1  245.4  90.1  90.0  90.1   -1  0  0  0  0  1  0  0  0  0 -1  0
13        oC        135.8     219.4  219.6  245.4  90.1  90.1  83.2   -1  1  0  0  1  1  0  0  0  0 -1  0
15        tI        632.0     145.8  164.1  537.2  72.3  74.3  90.1   -1  0  0  0  0  1  0  0 -1  1 -2  0
16        oF        999.0     219.4  219.6  537.2  92.7 114.0  83.2    1 -1  0  0 -1 -1  0  0 -1  1 -2  0
14        mC        135.2     219.4  219.6  245.4  90.1  90.1  83.2   -1  1  0  0  1  1  0  0  0  0 -1  0
17        mC        999.0     219.6  219.4  285.4  70.3 109.9  83.2   -1 -1  0  0  1 -1  0  0  1  0  1  0
18        tI        999.0     294.9  329.4  145.8  63.7  90.0 110.0    0 -1  1  0  1 -1 -1  0  1  0  0  0
19        oI        999.0     145.8  294.9  329.4  70.0  63.7  90.0   -1  0  0  0  0 -1  1  0 -1  1  1  0
20        mC        783.5     295.5  294.9  145.8  90.0  90.0 112.4    0  1  1  0  0  1 -1  0 -1  0  0  0
21        tP        785.1     164.1  245.4  145.8  90.0  90.1  90.1    0  1  0  0  0  0 -1  0 -1  0  0  0
22        hP        999.0     164.1  245.4  145.8  90.0  90.1  90.1    0  1  0  0  0  0 -1  0 -1  0  0  0
23        oC        783.2     294.9  295.5  145.8  90.0  90.0  67.6    0  1 -1  0  0 -1 -1  0 -1  0  0  0
24        hR        999.0     434.5  295.5  145.8  90.0  70.5  87.2   -1  2 -1  0  0 -1 -1  0 -1  0  0  0
25        mC        782.6     294.9  295.5  145.8  90.0  90.0  67.6    0  1 -1  0  0 -1 -1  0 -1  0  0  0
26        oF        623.1     145.8  359.0  512.0  83.3 106.6 113.9    1  0  0  0 -1  2  0  0 -1  0  2  0
27        mC        500.0     359.0  145.8  294.9  90.0 120.5  66.1   -1  2  0  0 -1  0  0  0  0 -1  1  0
28        mC        252.2     145.8  512.0  164.1  89.9  90.1  73.4   -1  0  0  0 -1  0  2  0  0  1  0  0
29        mC        251.8     145.8  359.0  245.4  89.9  90.0  66.1    1  0  0  0  1 -2  0  0  0  0 -1  0
30        mC        315.8     164.1  517.1  145.8  90.0  90.1  71.6    0  1  0  0  0  1 -2  0 -1  0  0  0
31        aP          0.3     145.8  164.1  245.4  89.9  90.0  89.9    1  0  0  0  0  1  0  0  0  0  1  0
32        oP          2.8     145.8  164.1  245.4  90.1  90.0  90.1   -1  0  0  0  0  1  0  0  0  0 -1  0
40        oC        315.8     164.1  517.1  145.8  90.0  90.1 108.4    0 -1  0  0  0  1 -2  0  1  0  0  0
35        mP          0.9     164.1  145.8  245.4  90.0  90.1  90.1    0 -1  0  0  1  0  0  0  0  0  1  0
36        oC        252.2     145.8  511.9  164.1  89.9  90.1 106.5   -1  0  0  0  1  0  2  0  0  1  0  0
33        mP          2.5     145.8  164.1  245.4  90.1  90.0  90.1   -1  0  0  0  0  1  0  0  0  0 -1  0
38        oC        251.6     145.8  359.0  245.4  89.9  90.0 113.9    1  0  0  0 -1  2  0  0  0  0  1  0
34        mP          2.2     145.8  245.4  164.1  90.1  90.1  90.0    1  0  0  0  0  0  1  0  0 -1  0  0
42        oI        565.2     145.8  164.1  537.2 107.7 105.7  90.1    1  0  0  0  0 -1  0  0 -1  1 -2  0
41        mC        315.5     517.1  164.1  145.8  90.1  90.0  71.6    0 -1  2  0  0 -1  0  0  1  0  0  0
37        mC        250.3     511.9  145.8  164.1  90.1  90.1  73.5   -1  0 -2  0 -1  0  0  0  0  1  0  0
39        mC        249.7     359.0  145.8  245.4  90.0  90.1  66.1    1 -2  0  0  1  0  0  0  0  0  1  0
43        mI        999.0     219.4  537.2  164.1 107.7 138.4  66.0   -1  1  0  0 -1  1 -2  0  0 -1  0  0
44        aP          0.0     145.8  164.1  245.4  90.1  90.0  90.1   -1  0  0  0  0  1  0  0  0  0 -1  0


The top 12 sorted by "Quality of Fit (QoF)" are:

   44        aP          0.0     145.8  164.1  245.4  90.1  90.0  90.1   -1  0  0  0  0  1  0  0  0  0 -1  0
31        aP          0.3     145.8  164.1  245.4  89.9  90.0  89.9    1  0  0  0  0  1  0  0  0  0  1  0
35        mP          0.9     164.1  145.8  245.4  90.0  90.1  90.1    0 -1  0  0  1  0  0  0  0  0  1  0
34        mP          2.2     145.8  245.4  164.1  90.1  90.1  90.0    1  0  0  0  0  0  1  0  0 -1  0  0
33        mP          2.5     145.8  164.1  245.4  90.1  90.0  90.1   -1  0  0  0  0  1  0  0  0  0 -1  0
32        oP          2.8     145.8  164.1  245.4  90.1  90.0  90.1   -1  0  0  0  0  1  0  0  0  0 -1  0
14        mC        135.2     219.4  219.6  245.4  90.1  90.1  83.2   -1  1  0  0  1  1  0  0  0  0 -1  0
10        mC        135.8     219.4  219.6  245.4  89.9  90.1  96.8    1 -1  0  0  1  1  0  0  0  0  1  0
13        oC        135.8     219.4  219.6  245.4  90.1  90.1  83.2   -1  1  0  0  1  1  0  0  0  0 -1  0
11        tP        136.4     145.8  164.1  245.4  90.1  90.0  90.1   -1  0  0  0  0  1  0  0  0  0 -1  0
39        mC        249.7     359.0  145.8  245.4  90.0  90.1  66.1    1 -2  0  0  1  0  0  0  0  0  1  0
37        mC        250.3     511.9  145.8  164.1  90.1  90.1  73.5   -1  0 -2  0 -1  0  0  0  0  1  0  0


Obviously there's a sharp increase from Lattice character 32 (QoF=2.8) to 14 (QoF=135.2) indicating that the highest symmetry spacegroups consistent with the observed pattern of Bragg reflections are oP (orthorhombic primitive).

One would thus look up, in the list at the bottom, the different space groups for oP (of which P212121 is most likely), and then re-run CORRECT with

SPACE_GROUP_NUMBER= 19
UNIT_CELL_PARAMETERS= 145.8  164.1  245.4 90 90 90 ! note that all angles must be exactly 90°
REIDX= -1  0  0  0  0  1  0  0  0  0 -1  0


If the R-factors are good, one should then inspect the table REFLECTIONS OF TYPE H,0,0 0,K,0 0,0,L OR EXPECTED TO BE ABSENT (*) in CORRECT.LP to find out if the expected screw axes are indeed there.

## List of Bravais-lattices and their corresponding space group possibilities

BRAVAIS-            POSSIBLE SPACE-GROUPS FOR PROTEIN CRYSTALS
TYPE                     [SPACE GROUP NUMBER,SYMBOL]
aP      [1,P1]
mP      [3,P2] [4,P2(1)]
mC,mI    [5,C2]
oP      [16,P222] [17,P222(1)] [18,P2(1)2(1)2] [19,P2(1)2(1)2(1)]
oC      [21,C222] [20,C222(1)]
oF      [22,F222]
oI      [23,I222] [24,I2(1)2(1)2(1)]
tP      [75,P4] [76,P4(1)] [77,P4(2)] [78,P4(3)] [89,P422] [90,P42(1)2]
[91,P4(1)22] [92,P4(1)2(1)2] [93,P4(2)22] [94,P4(2)2(1)2]
[95,P4(3)22] [96,P4(3)2(1)2]
tI      [79,I4] [80,I4(1)] [97,I422] [98,I4(1)22]
hP      [143,P3] [144,P3(1)] [145,P3(2)] [149,P312] [150,P321] [151,P3(1)12]
[152,P3(1)21] [153,P3(2)12] [154,P3(2)21] [168,P6] [169,P6(1)]
[170,P6(5)] [171,P6(2)] [172,P6(4)] [173,P6(3)] [177,P622]
[178,P6(1)22] [179,P6(5)22] [180,P6(2)22] [181,P6(4)22] [182,P6(3)22]
hR      [146,R3] [155,R32]
cP      [195,P23] [198,P2(1)3] [207,P432] [208,P4(2)32] [212,P4(3)32]
[213,P4(1)32]
cF      [196,F23] [209,F432] [210,F4(1)32]
cI      [197,I23] [199,I2(1)3] [211,I432] [214,I4(1)32]