Molecular Symmetry and Chirality
How to Spot a Chiral Compound
Note: viewing the structures on these pages requires use of the MDL Chime Plug-In.

In very nearly all cases, lack of both a mirror plane and an inversion centre means a compound is chiral. But not always. In other words, lack of both σ and i is necessary for chirality, and very nearly sufficient, but not quite.

The most precise and succinct requirement for chirality is the lack of any S_n rotation axis. Lack of S_n is both a necessary and sufficient condition for chirality. However, all odd-value S_n axes require the presence of a σ, and an S₂ axis is equivalent to i, so the lack of both an inversion centre and a mirror plane almost always amounts to a lack of S_n. Strictly speaking, it is possible for a molecule to lack both i and σ and still remain achiral: it must belong to an even-value S_n point group with n > 2. This is exceptionally unusual, and I dare you to draw something with S₄ symmetry.

Oh, all right. I'll do it.

The molecule below is 1,3,5,7-tetrafluorocyclooctatetraene. It has deceptively few symmetry elements: only one C₂ rotation axis, no perpendicular C₂' axes, no centre of inversion, and no mirror planes. With the absence of both i and σ you would initially expect the complex to be chiral. However, the compound possesses an S₄ improper rotation axis, and so belongs to the S₄ point group. Thus, the molecule is not chiral! The mirror images below are the same molecule, not enantiomers.

Push the button! Push it, I say!

So, how do you tell if a molecule is chiral? There are two guaranteed methods, and a series of quick-and-dirty rules, increasing in their sophistication, precision, and difficulty of application.

• Method One: draw the mirror image. A chiral compound, by definition, is non-superimposable on its mirror, so that the mirror images are enantiomers. Draw or build the mirror image, and compare -- it must be either the same achiral structure or a new enantiomer.
• Method Two: find the point group. Only molecules belonging to C_n (which includes E) and D_n point groups are chiral, because only these groups lack the S_n element.

The first method is tedious and often difficult. The second is usually pretty straightforward, and it's what I do if the first two tricks below don't immediately hand me the answer.

• Rule One (limited): A compound is chiral if it has four different bonds to carbon.
• Rule Two (good): A compound is chiral if it lacks a mirror plane.
• Rule Three (better): A compound is chiral if it lacks both σ and i.
• Rule Four (infallible): A compound is chiral if it lacks an S_n axis.

The first rule is very fast, but only applies to organic compounds with a single stereocentre. The second rule is also very fast, and applies to almost anything. The C_i and even-value S_n point groups break this rule, but those are exceedingly rare. The third rule is harder to sort out, and while the fourth is the only one that always works, it's scary -- most people can't find improper rotation axes when they are present, let alone conclusively demonstrate their absence. If I'm not certain Rule Two is working, then I find it much easier and more reliable simply to assign the point group, which guarantees the correct answer.