TUD Organische Chemie  Immel  Tutorials  Symmetry  Examples: Molecules  View or Print (this frame only) 
On this page numerous examples of molecules belonging to different point groups are provided. For a detailed descriptions on the symmetry and properties of point groups (including the corresponding stereographic projections, shapes of objects, list of essential symmetry elements, and a detailed description on how to determine the point group of a given molecule) see the 'Symmetry and Point Groups' section of this web site.



Molecules in this group have a single nfold rotation axis C_{n} as their symmetry element. These compounds must be chiral, and
many of the most important ligands used in stereoselective synthesis of organic chemistry belong to the C_{2} point group.


Molecules having a nfold rotation axis C_{n} and n vertical mirror planes σ_{v} belong to
the C_{nv} point group. Linear molecules which do not possess an inversion center or a horizontal mirror plane σ_{h}
belong to the C_{∞v} point group, because all rotations about their axis are symmetry operations (conical molecules).


If, in addition to a nfold principal axis and n twofold axes perpendicular to it, a horizontal mirror plane σ_{h}
is present in a molecular structure, the point group is described as D_{nh}. The D_{∞h} point group includes all linear molecules
with an center of inversion, which also implies a horizontal mirror plane σ_{h} (cylindrical molecules).


The tetrahedral point groups are characterized by the presence of four C_{3} principal axes (and three C_{2} axes).
The T_{d} group is the point group of a regular tetrahedron. If, in addition, a center of inversion is present, the point group is T_{h} (molecules
of this group do not look like tetrahedrons, but retain the rotational symmetry of a tetrahedron). All objects possessing the rotational symmetry of a tetrahedron, but no
plane of reflection or center of inversion are based on the simpler point group T. Molecules of this group must be chiral, and examples are very rare.


The octahedral point groups O and O_{h} feature three C_{4} principal axes (and four C_{3} axes as well as multiple C_{2} axes).
A regular octahedron and a cube both belong to the O_{h} point group. In analogy to the tetrahedral point group T, the octahedral group O retains the
rotational symmetry of an regular octahedron, but none of its planes of reflection or the center of inversion. Examples of molecules belonging to the
O point group are extremely rare (these molecules must be chiral!).


The icosahedral point groups I and I_{h} posses six C_{5} principal axes (amongst 10 C_{3} and 15 C_{2} axes).
In analogy to the octahedral point groups O and O_{h} the I group does contain all rotational symmetry elements, but no
mirror planes or center of inversion. Molecules belonging to this chiral point groups are extremely rare. Shapes belonging to the more
symmetrical I_{h} point groups are the dodecahedron and the icosahedron.


The K_{h} point group resembles the symmetry of perfect spheres. Obviously, only atoms but no molecules belong to this point group.
