What are the elements of symmetry

Symmetry elements and operations

As Symmetry operations these are operations that bring an object to coincide with itself. With respect to a molecule, such operations are symmetry operations if and only if the appearance of the molecule is exactly the same before and after the operation is carried out.
If a point remains fixed in space when performing the symmetry operation, one speaks of point symmetry; if a translation is included in the symmetry operation, the spatial symmetry is considered. Molecules are always point-symmetric; the translation is only possible with three-dimensional infinite particle arrangements, i.e. crystals.

Symmetry symbols are used to denote symmetry in a taut form. In particular, two types of symbols are used: the Schoenflies symbols and the Hermann Mauguin symbols, also International symbols called. The Schoenflies symbols are historically older; today they are mainly used to describe the symmetry of molecules and in spectroscopy; they are rarely used in crystallography. Additionally there is Picture iconsthat are used in illustrations.

All molecules can pass through a maximum of five Symmetry operations to be discribed. Here, a symmetry element is a point, a straight line or a plane with respect to which the symmetry operation is carried out. Each symmetry element is linked to one or more symmetry operations, which means the movement of a molecule in such a way that, relative to the symmetry element, all points of the molecule coincide with equivalent (or identical) points of the starting position after this operation has been carried out.

  1. A symmetry operation with no resulting effect, such as a rotation through 360 °, is known as Identity operation and symbolizes them with E..

  2. It may seem that such an operation is pointless because it does nothing. However, it is included for the sake of completeness. In addition, some molecules (e.g. CHBrClF) only have this element of symmetry and the formalism of group theory also requires this element (it is the neutral element that must be present in every group).
  3. A n-numerous rotation (the symmetry operation) is a rotation of 360 ° / n around one n-numerous axis of rotationC.n (the associated symmetry element).
  4. At a inversion (Point mirroring: the operation) on one Inversion centeri (the symmetry element), all points are mirrored to the other side along a straight line through the center of inversion.
  5. A reflection (the operation) is done on one Plane of symmetry or Mirror planes (the element).
  6. A Rotating mirroring (the operation) by one Rotating mirror axisS.n (the element) consists of one n-numerous rotation, followed by a reflection on a horizontal mirror plane.


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