Space group determination: Difference between revisions

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Space group determination (view source)

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→‎Table of space groups by Laue class and Bravais type
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! Bravais type
! Bravais type
! spacegroup <br> number <br> suggested by <br> CORRECT
! spacegroup <br> number <br> suggested by <br> CORRECT
! other possibilities
! other possibilities (with screw axes)
! alternative indexing <br> possible?
! alternative indexing <br> possible?
! choosing among all spacegroup possibilities
! choosing among all spacegroup possibilities
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| mmm || oI || 23 || 24 |||| screw axis extinctions do '''not''' let you decide because the I centering results in h+k+l=2n and the screw axis extinction 00l=2n is just a special case of that. 23/24 do '''not''' form an enantiomorphic, but a ''special'' pair (ITC A §3.5, p. 46 in the 1995 edition).
| mmm || oI || 23 || 24 |||| screw axis extinctions do '''not''' let you decide because the I centering results in h+k+l=2n and the screw axis extinction 00l=2n is just a special case of that. 23/24 do '''not''' form an enantiomorphic, but a ''special'' pair (ITC A §3.5, p. 46 in the 1995 edition).
|-
|-
| 4/m || tP || 75 || 76, 77, 78 ||yes|| screw axis extinctions let you decide, except between 76/78 enantiomorphs
| 4/m || tP || 75 || 76, 77, 78 ||k,h,-l|| screw axis extinctions let you decide, except between 76/78 enantiomorphs
|-
|-
| 4/m || tI || 79 || 80 ||yes|| screw axis extinctions let you decide
| 4/m || tI || 79 || 80 ||k,h,-l|| screw axis extinctions let you decide
|-
|-
| 4/mmm || tP || 89 || 90, 91, 92, 93, 94, 95, 96 |||| screw axis extinctions let you decide, except between 91/95 and 92/96 enantiomorphs
| 4/mmm || tP || 89 || 90, 91, 92, 93, 94, 95, 96 |||| screw axis extinctions let you decide, except between 91/95 and 92/96 enantiomorphs
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| 4/mmm || tI || 97 || 98 |||| screw axis extinctions let you decide
| 4/mmm || tI || 97 || 98 |||| screw axis extinctions let you decide
|-
|-
| -3 || hP || 143 || 144, 145 ||4 possibilities|| screw axis extinctions let you decide, except between 144/145 enantiomorphs
| -3 || hP || 143 || 144, 145 ||-h,-k,l; k,h,-l; -k,-h,-l|| screw axis extinctions let you decide, except between 144/145 enantiomorphs
|-
|-
| -3 || hR || 146 || - ||yes, and obverse/reverse||  
| -3 || hR || 146 || - ||k,h,-l, and obverse (-h+k+l=3n) / reverse (h-k+l=3n)||  
|-
|-
| -3/m || hP || 149 || 151, 153 ||yes|| screw axis extinctions let you decide, except between 151/153 enantiomorphs. Note: the twofold goes along the diagonal between a and b.
| -3/m || hP || 149 || 151, 153 ||k,h,-l|| screw axis extinctions let you decide, except between 151/153 enantiomorphs. Note: the twofold goes along the diagonal between a and b.
|-
|-
| -3/m || hP || 150 || 152, 154 ||yes|| screw axis extinctions let you decide, except between 152/154 enantiomorphs. Note: compared to previous line, the twofold goes along a.
| -3/m || hP || 150 || 152, 154 ||-h,-k,l|| screw axis extinctions let you decide, except between 152/154 enantiomorphs. Note: compared to previous line, the twofold goes along a.
|-
|-
| -3/m || hR || 155 || - ||obverse/reverse||  
| -3/m || hR || 155 || - ||obverse/reverse||  
|-
|-
| 6/m || hP || 168 || 169, 170, 171, 172, 173 ||yes|| screw axis extinctions let you decide, except between 169/170 and 171/172 enantiomorphs
| 6/m || hP || 168 || 169, 170, 171, 172, 173 ||k,h,-l|| screw axis extinctions let you decide, except between 169/170 and 171/172 enantiomorphs
|-
|-
| 6/mmm || hP || 177 || 178, 179, 180, 181, 182 |||| screw axis extinctions let you decide, except between 178/179 and 180/181 enantiomorphs
| 6/mmm || hP || 177 || 178, 179, 180, 181, 182 |||| screw axis extinctions let you decide, except between 178/179 and 180/181 enantiomorphs
|-
|-
| m-3 || cP || 195 || 198 ||yes|| screw axis extinctions let you decide
| m-3 || cP || 195 || 198 ||k,h,-l|| screw axis extinctions let you decide
|-
|-
| m-3 || cF || 196 ||-||yes ||  
| m-3 || cF || 196 ||-||k,h,-l||  
|-
|-
| m-3 || cI || 197 || 199 ||yes|| screw axis extinctions do '''not''' let you decide because the I centering results in h+k+l=2n and the screw axis extinction 00l=2n is just a special case of that. 197/199 do '''not''' form an enantiomorphic, but a ''special'' pair (ITC A §3.5, p. 46 in the 1995 edition).
| m-3 || cI || 197 || 199 ||k,h,-l|| screw axis extinctions do '''not''' let you decide because the I centering results in h+k+l=2n and the screw axis extinction 00l=2n is just a special case of that. 197/199 do '''not''' form an enantiomorphic, but a ''special'' pair (ITC A §3.5, p. 46 in the 1995 edition).
|-
|-
| m-3m || cP || 207 || 208, 212, 213 |||| screw axis extinctions let you decide, except between 212/213 enantiomorphs
| m-3m || cP || 207 || 208, 212, 213 |||| screw axis extinctions let you decide, except between 212/213 enantiomorphs
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|}
|}


 
Alternative indexing possibilities taken from http://www.ccp4.ac.uk/html/reindexing.html (for R3 and R32, obverse/reverse are specified).
If you find an error in the table please send an email to kay dot diederichs at uni-konstanz dot de !
If you find an error in the table please send an email to kay dot diederichs at uni-konstanz dot de !


== The 65 space groups in which proteins composed of L-amino acids can crystallize ==
== The 65 Sohncke space groups in which proteins composed of L-amino acids can crystallize ==




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=== Subgroup and supergroup relations of these space groups ===
Compiled from [https://onlinelibrary.wiley.com/doi/book/10.1107/97809553602060000001 International Tables for Crystallography (2006) Vol. A1 (Wiley)]. Simply put, for each space group, a maximum ''translationengleiche'' subgroup has lost a single type of symmetry, and a minimum ''translationengleiche'' supergroup has gained a single symmetry type. Example: P222 is a supergroup of P2, and a subgroup of P422 (and P4222 and P23). Of course the sub-/supergroup relation is recursive, which is why P1 is also a (sub-)subgroup of P222 (but not a maximum ''translationengleiche'' subgroup). The table below does not show other types of relations, e.g. non-isomorphic ''klassengleiche'' supergroups which may result e.g. from centring translations, because I find them less relevant in space group determination.
The table is relevant because in particular (perfect) twinning adds a symmetry type, and leads to an apparent space group which is the supergroup of the true space group.
{| cellpadding="0" cellspacing="0" border="1"
! spacegroup number
! maximum ''translationengleiche'' subgroup
! minimum ''translationengleiche'' supergroup
! spacegroup name
|-
|  1 ||-|| 3, 4, 5, 143, 144, 145, 146 || P 1
|- 
|  3 || 1 || 16, 17, 18, 21, 75, 77, 168, 171, 172 || P 2
|- 
|  4 || 1 || 17, 18, 19, 20, 76, 78, 169, 170, 173 || P 21
|- 
|  5 || 1 || 20, 21, 22, 23, 24, 79, 80, 149, 150, 151, 152, 153, 154, 155 || C2
|- 
|  16 || 3 || 89, 93, 195 || P 2 2 2
|-
|  17 || 3, 4 || 91, 95 || P 2 2 21
|-
|  18 || 3, 4 || 90, 94 || P 21 21 2
|-
|  19 || 4 || 92, 96, 198 || P 21 21 21
|-
|  20 || 4, 5 || 91, 92, 95, 96, 178, 179, 182 || C 2 2 21
|-
|  21 || 3, 5 || 89, 90, 93, 94, 177, 180, 181 || C 2 2 2
|-
|  22 || 5 || 97, 98, 196 || F 2 2 2
|-
|  23 || 5 || 97, 197 || I 2 2 2
|-
|  24 || 5 || 98, 199 || I 21 21 21
|-
|  75 || 3 || 89, 90 || P 4
|-
|  76 || 4 || 91, 92 || P 41
|-
|  77 || 3 || 93, 94 || P 42
|-
|  78 || 4 || 95, 96 || P 43
|-
|  79 || 5 || 97 || I 4
|-
|  80 || 5 || 98 || I 41
|-
|  89 || 16, 21, 75 || 207 || P 4 2 2
|-
|  90 || 18, 21, 75 || - || P 4 21 2
|-
|  91 || 17, 20, 76 || - || P 41 2 2
|-
|  92 || 19, 20, 76 || 213 || P 41 21 2
|-
|  93 || 16, 21, 77 || 208 || P 42 2 2
|-
|  94 || 18, 21, 77 || 93, 97 || P 42 21 2
|-
|  95 || 17, 20, 78 || - || P 43 2 2
|-
|  96 || 19, 20, 78 || 212 || P 43 21 2
|-
|  97 || 22, 23, 79 || 209, 211 || I 4 2 2
|-
|  98 || 22, 24, 80 || 210, 214 || I 41 2 2
|-
| 143 || 1 || 149, 150, 168, 173 || P 3
|-
| 144 || 1 || 151, 152, 169, 172 || P 31
|-
| 145 || 1 || 153, 154, 170, 171 || P 32
|-
| 146 || 1 || 155, 195, 196, 197, 198, 199 || R 3
|-
| 149 || 5, 143 || 177, 182 || P 3 1 2
|-
| 150 || 5, 143 || 177, 182 || P 3 2 1
|-
| 151 || 5, 144 || 178, 181 || P 31 1 2
|-
| 152 || 5, 144 || 178, 181 || P 31 2 1
|-
| 153 || 5, 145 || 179, 180 || P 32 1 2
|-
| 154 || 5, 145 || 179, 180 || P 32 2 1
|-
| 155 || 5, 146 || 207, 208, 209, 210, 211, 212, 213, 214 || R 3 2
|-
| 168 || 3, 143 || 177 || P 6
|-
| 169 || 4, 144 || 178 || P 61
|-
| 170 || 4, 145 || 179 || P 65
|-
| 171 || 3, 145 || 180 || P 62
|-
| 172 || 3, 144 || 181 || P 64
|-
| 173 || 4, 143 || 182 || P 63
|-
| 177 || 21, 149, 150, 168 || - || P 6 2 2
|-
| 178 || 20, 151, 152, 169 || - || P 61 2 2
|-
| 179 || 20, 153, 154, 170 || - || P 65 2 2
|-
| 180 || 21, 153, 154, 171 || - || P 62 2 2
|-
| 181 || 21, 151, 152, 172 || - || P 64 2 2
|-
| 182 || 20, 149, 150, 173 || - || P 63 2 2
|-
| 195 || 16, 146 || 207, 208 || P 2 3
|-
| 196 || 22, 146 || 209, 210 || F 2 3
|-
| 197 || 23, 146 || 211 || I 2 3
|-
| 198 || 19, 146 || 212, 213 || P 21 3
|-
| 199 || 24, 146 || 214 || I 21 3
|-
| 207 || 89, 155, 195 || - || P 4 3 2
|-
| 208 || 93, 155, 195 || - || P 42 3 2
|-
| 209 || 97, 155, 196 || - || F 4 3 2
|-
| 210 || 98, 155, 196 || - || F 41 3 2
|-
| 211 || 97, 155, 197 || - || I 4 3 2
|-
| 212 || 96, 155, 198 || - || P 43 3 2
|-
| 213 || 92, 155, 198 || - || P 41 3 2
|-
| 214 || 98, 155, 199 || - || I 41 3 2
|-
|}


== Space group selected by XDS: ambiguous with respect to enantiomorph and screw axes ==
== Space group selected by XDS: ambiguous with respect to enantiomorph and screw axes ==
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<pre>
<pre>
SPACE_GROUP_NUMBER=5  
SPACE_GROUP_NUMBER=5  
UNIT_CELL_CONSTANTS= 233.70  78.42  73.22    90.31 105.34  89.77
UNIT_CELL_CONSTANTS= 233.70  78.42  73.22    90 105.34  90
</pre>
</pre>
because this enforces just the correct cell constraints.
because this enforces just the correct cell constraints.


== See also ==
== See also ==


[http://pd.chem.ucl.ac.uk/pdnn/symm3/allsgp.htm The 230  3-Dimensional Space Groups]
[http://pd.chem.ucl.ac.uk/pdnn/symm3/allsgp.htm The 230  3-Dimensional Space Groups]
Kay
Bureaucrats
2,651

edits

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