5.2. Point Groups

Point groups are mathematical entities defined by group theory that describe the complete symmetry of an object or moelcule (i.e. all its symmetry elements). It is necessary to determine the point group of a molecule in order to be able to use its symmetry to determine, for instance, the symmetries of the molecular vibrations or molecular orbitals. It is not, however, necessary to recognise all the symmetry elements of a molecule in order to be able to determine its point group. Figure 5.11 gives a simple scheme that allows the point group to be determined by recognising only key symmetry elements.

Figure 5.11 A simple scheme for determining the point group of a molecule.

The most common point groups are C₁ (no symmetry at all) and C_s (just one mirror plane). The C_n, C_nv and C_nh point groups have just one proper rotation axis of order n and are distinguished from each other by their mirror planes. The D_n, D_nh and D_nd point groups are those with additional C₂-axes perpendicaular to the principal axis. The point groups of the molecule shown in the molecular orbital plots are given in the long list of molecules in Sect. 6, so that you can try to use Figure 5.11 to reproduce these point group assignments in order to familiarise yourself with the concept.

Symmetry Elements
Point Groups
Next:
Irreducible Representations and Character Tables
Degenerate Orbitals