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Step: 106
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The knowledge of the symmetry has great importance for many subsections of chemistry. It is important aid to clarifying the geometrical structure of the molecules and crystals and the electronic structure of chemical compounds. We differentiate between symmetry elements and symmetry operations.
Symmetry elements are geometrical objects within a molecule: Even one, levels and points. At them symmetry operations can be executed.
Symmetry operations are movements, those concerning the straight lines, levels and points at the molecule to be executed can and the molecule into an equivalent or identical arrangement indistinguishable in relation to the output arrangement transfer.
On the close relationship between symmetry element and symmetry operation is particularly referred to. Both cause themselves mutually. A symmetry operation can be defined and executed only regarding a symmetry element, while the presence of a symmetry element can be only shown, if in addition appropriate symmetry operations exist.
Symmetry elements and symmetry operations are named by the same symbols.
Symmetry operations, which to the identical (output -) arrangement lead, are called identity operations E.
In the following outline the symmetry elements and the symmetry operations produced by them are summarized:
| Symmetry elements | Symbol | Symmetry operation | Symbols |
| Axis of proper rotation of n-th steps | Cn | One or more turns around the angle 2p /n around this axis | Cn, Cn2, Cn3,.., Cnn = E |
| Symmetry plane | s | n-multiple reflections at the symmetry plane | sn = s (n oddly) sn = E (n even |
| Symmetry center | i | Inversion of all atoms at the symmetry center | in = i (n oddly) in = E (n even |
| axis of improper rotation of n-th steps | Sn | improper rotation, i.e. turn around the angle 2p / n and reflection on one level perpendicularly to the axis of proper rotation | n even: Sn, Cn/2, Sn3... snn/z = i... snn = E n oddly: Sn, Cn2..., Snn = s Snzn = E |
The product of symmetry operations is the stepwise made of these symmetry operations. C3 i means that first the inversion is executed, then the turning operation.
The product of two symmetry operations corresponds again to a symmetry operation.
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