Chiral molecules.

A chiral molecule (from the Greek word Chiros - 'hand') is a molecule that is distinguishable from, and not superposable onto, its mirror image in the same way that left and right hands are distinguishable. Chiral molecules are optically active and rotate plane-polarized light. A chiral molecule and its mirror image partner are called enantiomers (from the Greek word for 'both').
The group-theoretical criterion of whether or not a molecule is superimposable on its mirror image is that it should not have an improper-rotation axis Sn. However, we must be alert for improper-rotation axes that are present in disguise. From our definitions, we know that the S1 axis is identical to a mirror plane and that the inversion operation i is equivalent to S2. The consequence is that any molecule containing either of these operations in its multiplication table must be achiral.

Molecules without a center of inversion and a mirror plane are usually chiral, but it is important to verify that no improper rotation axis of higher-order exists.

For instance, the quaternary ammonium ion (shown to the left) has neither a mirror plane (S1) nor an inversion center (S2), but it does have an S4 axis and so it is not chiral.

When you are happy with these concepts, go through the example and the exercise on the next page.