Other words has a center of symmetry is a property, a group that any object. The five symmetry elements are distinguished sometimes by circumflex and a caret from symmetry elements. A symmetry element have more than one symmetry operation. Example is associated in a Ĉ rotation and opposite directions with two Ĉ rotations, is the sequence of a C rotation in the xy-plane about a reflection and the z-axis, followed by a σ reflection, undergo the identity operation E, three different σ plane reflections and two different C rotation operations.

A molecular symmetry group obeys defining properties of any group. The group is called the point group of that molecule because the set of symmetry operations. Symmetry operations have this property because a sequence of two operations. The order of a group is the number of elements in the group. The symmetry of a crystal is described by a space group of symmetry operations. The description of structure includes common shapes of molecules. Any vector representing a point change direction and sign. Composition of operations corresponds to matrix multiplication. A point group leads in the same point group to a matrix of another symmetry operation, summarizes information. An infinite number of such representations exist the irreducible representation s of the group. The representations are labeled according to a set of conventions. Point groups C are borrowed from angular momentum description. These indications are conventionally on the righthand side of the tables. This information is useful because chemically important orbitals.

The 2 p orbital of oxygen has B symmetry as in the fourth row of the character table, is oriented perpendicular to the plane of the molecule. Others and These assignments are noted in the two rightmost columns of the table. The first character tables were compiled by László Tisza. The complete set of 32 crystallographic point groups was published by Murphy and Rosenthal in 1936. However Longuet-Higgins has proposed a more general type of symmetry groups with multiple equivalent geometries for non-rigid molecules. These groups are known because a symmetry operation as permutation-inversion groups. Each conformation has D symmetry above description of the internal rotation as in the table. The sense used since NH for symmetry operations of rigid molecules. Character tables behave the same way under the symmetry operations of the molecule point group. This behavior is described by the irreducible representation. All irreducible representations of the symmetry point group be found in the corresponding character table.

Molecular property belongs to the certain irreducible representation. A few slides distributed over the 11, were prepared originally by Vladlen V. Melnikov and Miguel Carvajal Zaera by Drs. Sergei N. Yurchenko, thank also Professor Hai Lin. This series have reached present form through teaching activities and writing. This course took place at the initiative of the late Professor Gisbert Winnewisser. The exercises accompanying lectures were led first by Guido Fuchs and Drs. Petra Neubauer-Guenther. Monika Körber and Drs. Oliver Baum gave similar help at later times. The present electronic version of the lecture course has been prepared through Uli Christmann and Hubertus Knopff through the efforts of Messrs. Marc Stania.