A molecule is achiral if it is superimposable to its mirror image. Most achiral molecules have a symmetry plane or a symmetry center. Achiral molecules containing a stereocentre are called meso.
The molecules discussed in the previous section are achiral because they have either a symmetry plane or a symmetry center.
The left molecule has a symmetry plan through the central carbon. This is a mirrored plane; in other words, half of the molecule is a perfect reflection of the other half of the molecule. This molecule is achiral because of its mirror plane.
The right molecule has a symmetry center or an inversion center. An inversion center is a point in the molecule – not necessarily an atom – through which all other atoms can be reflected 180 degrees in another identical atom. (In terms closer to symmetry, a reversal through a center is equivalent to rotating groups by 180 degrees and then reflects the groups through a plane perpendicular to the axis of rotation.)
This type of symmetry is rare in organic molecules and is more frequently in inorganic molecules. The inversion center is represented by the blue circle in the example above. The same molecule is shown three-dimensionally below. The reversing center is at the center of the average carbon-carbon bond. This molecule is achiral because of its inversion center.