Schonflies symmetry notation

Symmetry operations Order Schonflies notation International notation Symmetry notation Isomorphisms... 

Magnetic ordering, 746 Magnetic point groups, 738, 739 international notation, 739 properties of, 740 Schonflies notation, 739 Shubnikov notation, 739 Magnetic point symmetry, determination of, 744... 

Schonflies notation is widely used to describe molecules or assemblages of atoms (polyhedron) such as the local environment of an atom. Thus, it is widely used to describe the symmetry of structural sites. It is a more compact notation but less complete than the Hermann-Mauguin notation. It consists generally of one capital letter, followed by one subscript number and one final letter. 

List a sufficient number of symmetry elements in the molecules sketched in Figure 2.21 to enable you to identify the point group to which each belongs. Give the point group symbol in both Schonflies and International notation. 

The Hermann-Mauguin notation for the description of point group symmetry (in contrast to the Schonflies system used in Chapter 6) is widely adopted in crystallography. An n-fold rotation axis is simply designated as n. An object is said to possess an n-fold inversion axis h if it can be brought into an equivalent configuration by a rotation of 360°/n in combination with inversion through a... 

Fig. 23. Structures of the tetrasubstituted TEEs. Below the molecules the symmetry is given in international and Schonflies notation. In the upper right corner the different conjugation paths and the coordinate system are depicted as used in the derivation of the symmetry relations...

These simple examples serve to show that instinctive ideas about symmetry are not going to get us very far. We must put symmetry classification on a much firmer footing if it is to be useful. In order to do this we need to define only five types of elements of symmetry - and one of these is almost trivial. In discussing these we refer only to the free molecule, realized in the gas phase at low pressure, and not, for example, to crystals which have additional elements of symmetry relating the positions of different molecules within the unit cell. We shall use, therefore, the Schonflies notation rather than the Hermann Mauguin notation favoured in crystallography. 

A word about notation. For the points groups we shall generally use the Schonflies notation. In this notation basically the same symbols are used for the point groups as for the symmetry operations. Whenever there is any doubt as to the meaning we shall use a caret (example Cn) to indicate a symmetry operation. 

The inversion notation has become standard for a number of good reasons. In the Hermann-Mauguin terminology, the center of symmetry is dropped and the inversion axes maintained. In the Schonflies terminology, the center of symmetry is a key element and all the mirror reflections and simple or inversion rotation axes are dropped and replaced by other symbols these are described in Section V, as they are important in relation to site symmetry, group theory, and Raman scattering. 

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