Symmetry Operations and Point Groups

Modern methods in order to illustrate the nature of point groups and symmetry operations are available [16]. Molecules are abstracted as a set of points in space. We can associate with these points coordinates. 

A symmetry element is a geometrical entity, i.e., a line, plane, or point, with respect to which some symmetry operations may be carried out. A symmetry operation is a prescription, in which way the coordinates of a molecule have to be changed. 

After performing a change of the coordinates of a molecule often, the result is another molecule that can be distinguished from the original in position of the constituting atoms. We address a symmetry operation as such a change in coordinates where the resultant molecule is the same. 

Symmetry operations are summarized in Table 15.4. A point group is a collection or group of symmetry operations, which leave at least one point where it was before the symmetry operation was done. We exemplify now the types of symmetry operations. We denote the symmetry operation like a function that acts on the coordinates of the points under consideration. 

Plane Center of inversion Proper axis Improper axis Reflection through plane Inversion of aU atoms through the center One or more rotations about the axis Rotation followed by a reflection in a plane to the rotation axis 

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