Vibrations of Water
One of the more significant applications of symmetry is the analysis of molecular vibrations. Knowing nothing more than the point group of a molecule, you can predict the number and types of vibrational peaks that will show up in the infrared and Raman spectra. Shown below are two (of three) vibrations of the water molecule. Not surprisingly, they are called the symmetric and antisymmetric stretching modes.
A chiral molecule is a molecule that cannot be superimposed on its mirror image. If you've taken organic chemistry, you may have learned to look for four different groups on a carbon atom to determine if the molecule contains a chiral center. So how do point groups apply here? It turns out that the only chiral point groups are: C1, Cn, Dn, T, O, and I. The last three are very uncommon, so virtually all chiral molecules fall into the first three types of groups. Who knew it was so easy! If you want to see some examples of these chiral point groups, stop by the Symmetry Gallery (if you look carefully, all the Cn and Dn molecules have a certain twist in their structures).
A polar molecule contains a permanent dipole moment. The presence of certain symmetry elements will interchange bonds, thereby canceling out any net dipole of the molecule. In this case, only molecules of point groups C1, Cs, Cn, and Cnv can be polar. Some common examples of polar molecules include water (C2v) and ammonia (C3v).