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Space group determination

1,970 bytes added, 11:10, 3 November 2015
Notes
* [[pointless]] helps with identification of screw axes, and its identification of Laue group is more sensitive than that implemented in CORRECT. However it is not fail-safe, and cannot tell the correct enantiomorph.
* only when the structure is satisfactorily refined can the chosen space group be considered established and correct. Until then, it is just a hypothesis and its alternatives (see the table) should be kept in mind.
 
== An example ==
 
The following example shows the difficulty in deciding between higher and lower symmetry.
 
IDXREF reports:
<pre>
LATTICE- BRAVAIS- QUALITY UNIT CELL CONSTANTS (ANGSTROEM & DEGREES)
CHARACTER LATTICE OF FIT a b c alpha beta gamma
 
* 44 aP 0.0 74.0 78.6 124.0 108.2 105.1 90.4
* 31 aP 3.5 74.0 78.6 124.0 71.8 74.9 90.4
* 41 mC 7.4 235.7 78.6 74.0 90.4 106.1 89.7
* 37 mC 34.8 239.6 74.0 78.6 90.4 109.0 87.8
* 42 oI 38.7 74.0 78.6 226.6 90.2 92.2 90.4
14 mC 122.5 107.6 108.3 124.0 92.8 114.1 86.6
...
</pre>
so oI (space groups 23=I222 or 24=I2<sub>1</sub>2<sub>1</sub>2<sub>1</sub>) or the two mC (space group 5=C2) are possibilities for indexing, and of course P1. Integration in P1 (because of SPACE_GROUP_NUMBER=0 in XDS.INP) results in the following table for space group determination in CORRECT:
<pre>
SPACE-GROUP UNIT CELL CONSTANTS UNIQUE Rmeas COMPARED LATTICE-
NUMBER a b c alpha beta gamma CHARACTER
 
1 74.1 78.6 124.0 71.8 74.8 90.4 6959 22.5 5309 31 aP
* 23 74.1 78.6 226.6 90.0 90.0 90.0 2735 39.5 9533 42 oI
5 235.7 78.6 74.1 90.0 106.1 90.0 3922 31.0 8346 41 mC
5 239.6 74.1 78.6 90.0 109.0 90.0 5111 30.7 7157 37 mC
1 74.1 78.6 124.0 108.2 105.2 90.4 6959 22.5 5309 44 aP
</pre>
The automatic choice gave 23 as a result. This is because the associated R<sub>meas</sub> (39.5) is lower than MAX_FAC_RMEAS * (lowest R<sub>meas</sub>) = 2 * 22.5 = 45.0.
However, the C2 values of 30.7 and 31.0 are significantly lower still, and the question needs further investigation. <code>[[pointless]] XDS_ASCII.HKL</code> gives:
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