Sohncke space group

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In crystallography, Sohncke space groups are those 65 space groups that only contain symmetry operations of the first type ( rotations and screwings ). They are named after the German crystallographer and physicist Leonhard Sohncke , who first described them in 1876. Enantiomerically pure chiral chemical compounds can only crystallize in the Sohncke space groups, but there are also achiral substances that have such a space group.

history

The spatial structure of crystals goes back to the concept of the Bravais lattice , which was introduced by Auguste Bravais in 1848 . Including the work of Camille Jordan , Sohncke expanded the concept in his publications of 1876 and 1879. He only considered symmetry operations of the first kind (rotations and screwings, ie movements of the determinant +1). In his first publications, Sohncke received 66 room groups. Later two of them turned out to be identical, so that 65 remained. By using symmetry operations of the second kind, Jewgraf Stepanowitsch Fjodorow and Arthur Moritz Schoenflies obtained all 230 space groups in 1891.

Chiral space groups

In common usage, the Sohncke space groups are also referred to as chiral space groups because chiral molecules can only crystallize in these 65 space groups. In fact, only those space groups are chiral that are converted into another space group in the event of an inversion or reflection. For example, the space group is not chiral because the space group is created again through inversion . In contrast, the space group is chiral because it is transformed into by inversion or reflection . There are therefore only 22 chiral space groups (11 pairs of enantiomorphic space groups).

Individual evidence

  1. László Fábián, Carolyn P. Brock: A list of organic kryptoracemates . In: Acta Crystallographica / B , Vol. 66 (2010), pp. 94-103, ( doi : 10.1107 / S0108768109053610 , ISSN  0108-7681 ).
  2. Elna Pidcock: Achiral molecules in non-centrosymmetric space groups . In: Chemical Communications , Vol. 41 (2005), pp. 3457-3459 ( doi : 10.1039 / B505236J ).
  3. Leonhard Sohncke: The unlimited regular point systems as the basis of a theory of the crystal structure . In: Negotiations of the Natural Science Association in Karlsruhe , 1876, issue 7.
  4. Leonhard Sohncke: Development of a theory of the crystal structure . Teubner Verlag, Leipzig 1879.
  5. ^ Johann J. Burckhardt: The symmetry of the crystals. From René Haüy to the crystallographic school in Zurich, chapter 7 . Birkhäuser Verlag, Basel 1988, ISBN 3-7643-1918-6 .
  6. Howard D. Flack: Chiral and Achiral Crystal Structures . In: Helvetica Chimica Acta , Jg. 86 (2003), pp. 905-921 ( doi : 10.1002 / hlca.200390109 , ISSN  0018-019X ).