Point groups are used to describe molecular symmetries and are a condesed representation of the symmetrry elements a molecule may posses. This includes both bond and orbital symmetry. Knowing molecular symmetry allows for a greater understanding of molecular structure and can help to predict many molecular properties.
Point groups are a quick and easy way to gain knowledge of a molecule. They not only contain a molecule's symmetry elements, but also give rise to a charcter table, which is a the complete set of irreducible representations for a point group. A molecule's point group can be determined by either elucidating each symmetry element contained in a molecule or by proper use of the Schreiber chart (see below).
Point groups usually consist (but are not limited to) the following elements:
E - The identity operator. This operation leaves a molecule completely unchanged and exists for mathematical purposes.
See the section on symmetry elements for a more thorough explanation of each
Each point group is associated with a specific combination of symmetry elements
Each point group has it's own combination of symmetry elements. Listed below are some of the many point groups and their respective symmetry elements according to category followed by a representative example.
Non axial groups
C1: E C1: E, i
C2: E, C2 (notice the major axis of rotation is the point group) C3: E, C3, C32
D2: E C2(z), C2(y), C2(x) D3: E, 2C3, 3C2
C2v: E, C2, σv(xz), σv'(yz) C3v: E, 2C3, 3σv
C2h: E, C2, i, σh C3h: E, C3, C32, σh, S3, S33
How to determine a molecules point group
A molecule's point group can be determined by calculating all the symmetry elements of a molecule and matching them to it's respective point group. This process, however, is greatly simplified when the Schreiber chart is used:
1) Determine the point group of BH3 by calculating all it's symmetry elements then use the chart and determine which method is faster.
2) Determine the point groups of BH3 and NH3. Why is there a difference?
3) What is the point group of PPh3?
4) Determine the point groups of CO2 and H2O and then compare them.
5) Propose a molecule with no symmetry. What is it's point group?
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