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Space group determination: Difference between revisions
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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 || | | 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 || | | 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 || | | -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 || - || | | -3 || hR || 146 || - ||k,h,-l, and obverse (-h+k+l=3n) / reverse (h-k+l=3n)|| | ||
|- | |- | ||
| -3/m || hP || 149 || 151, 153 || | | -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 || | | -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 || | | 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 || | | m-3 || cP || 195 || 198 ||k,h,-l|| screw axis extinctions let you decide | ||
|- | |- | ||
| m-3 || cF || 196 ||-|| | | m-3 || cF || 196 ||-||k,h,-l|| | ||
|- | |- | ||
| m-3 || cI || 197 || 199 || | | 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 (better readable at http://www.csb.yale.edu/userguides/datamanip/ccp4/ccp4i/help/modules/appendices/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 ! | ||
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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. | 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 twinning adds a symmetry type, and leads to an apparent space group which is the supergroup of the true space group. | 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=" | {| cellpadding="0" cellspacing="0" border="1" | ||
! spacegroup number | ! spacegroup number | ||
! maximum ''translationengleiche'' subgroup | ! maximum ''translationengleiche'' subgroup | ||
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|- | |- | ||
|} | |} | ||
[[File:Spacegroups tree2a.png|800px]] | |||
(compare International Tables for Crystallography Vol A (2006), figure 10.1.3.2) | |||
== 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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In case of a crystal with an unknown space group (SPACE_GROUP_NUMBER=0 in [[XDS.INP]]), XDS (since [http://xds.mpimf-heidelberg.mpg.de/html_doc/Release_Notes.html version June 2008]) helps the user in determination of the correct space group, by suggesting possible space groups compatible with the Laue symmetry and Bravais type of the data, and by calculating the R<sub>meas</sub> for these space groups. | In case of a crystal with an unknown space group (SPACE_GROUP_NUMBER=0 in [[XDS.INP]]), XDS (since [http://xds.mpimf-heidelberg.mpg.de/html_doc/Release_Notes.html version June 2008]) helps the user in determination of the correct space group, by suggesting possible space groups compatible with the Laue symmetry and Bravais type of the data, and by calculating the R<sub>meas</sub> for these space groups. | ||
XDS (or rather, the [[CORRECT.LP|CORRECT]] step) makes an attempt to pick the correct space group automatically: it chooses | XDS (or rather, the [[CORRECT.LP|CORRECT]] step) makes an attempt to pick the correct space group automatically: it chooses the space group (or rather: Laue point group) which has the highest symmetry (thus yielding the lowest number of unique reflections) and still a tolerable R<sub>meas</sub> compared to the R<sub>meas</sub> the data have in any space group (which is most likely a low-symmetry space group - often P1). | ||
In some cases the automatic choice is the correct one, and re-running the [[CORRECT.LP|CORRECT]] step is then not necessary. However, neither the correct enantiomorph nor [[Space_group_determination#Screw_axes|screw axes]] (see below) are determined automatically by XDS. | In some cases the automatic choice is the correct one, and re-running the [[CORRECT.LP|CORRECT]] step is then not necessary. However, neither the correct enantiomorph nor [[Space_group_determination#Screw_axes|screw axes]] (see below) are determined automatically by XDS. [[Pointless]] is a very good program (usually better than CORRECT) to suggest possible space group (and alternatives). See also [[Space_group_determination#Notes|Notes]], and [[Space_group_determination#checking_the_CORRECT_assignment_with_pointless|checking the CORRECT assignment with pointless]] (below). | ||
== Space group selected by user == | == Space group selected by user == | ||