Are there optically active molecules in which all atoms lie in the same plane?

Question

I've learnt that when a molecule is non-superposable on its mirror image, it exists as a pair of enantiomers and is optically active. Absence of plane of symmetry is given to be one of the properties of chiral molecules.

Are there optically active molecules in which all atoms lie in the same plane?

I think, it is not possible for a molecule to be optically active when all atoms are coplanar (lie in the same plane) because such a planar molecule would always have a plane of symmetry coinciding with the plane of atoms. But it would be helpful if you could clarify this, since there are a lot of exceptions in chemistry.

Answer 1

This is not possible.

The definition of chirality ultimately relies on the superimposability of a structure on its mirror image. If they are non-superimposable, then the molecule is chiral. In terms of molecular symmetry, this is equivalent to saying:

If a molecule possesses an improper rotation axis $S_n$, then it is not chiral.

(An improper rotation is a combination of a normal rotation $C_n$ by $(360/n)^\circ$, followed by reflection in a plane perpendicular to that rotation axis.)

It turns out that the plane of symmetry and the inversion centre are the two most common forms of these (they are $S_1$ and $S_2$ respectively). Consequently, if a molecule has a plane of symmetry, it cannot be chiral. Likewise, if a molecule has an inversion centre, it cannot be chiral. There are also exotic molecules which possess neither a plane nor inversion centre, but possess a higher-order $S_n$ axis, and are therefore not chiral too.

However, the possession of a chiral centre has nothing to do with an $S_n$ axis. Consequently, there is no direct link between having a chiral centre and being chiral. Sure, there are trends that you can draw; for example, if there is only one chiral centre, then the molecule will not possess an $S_n$ axis, and thus it will be chiral. But the link is not quite as clear-cut as it is for the plane of symmetry, and consequently there are exceptions to the rule, and exceptions to the exceptions.