Is this molecule chiral? – Symmetry Elements, Symmetrical Conformations, Rotational Symmetry

A common exam question in sophomore organic involves determining whether a molecule is chiral or achiral. Just to be clear on the definitions:

Chiral: A chiral molecule has a non-super imposable mirror image. The mirror image of a chiral molecule is called its enantiomer. Enantiomers are both fundamentally the same, yet also different.

Achiral: An achiral molecule has a super imposable mirror image. An achiral molecule does not have an enantiomer because its mirror image is literally exactly the same thing.

Enantiomer: An enantiomer is a special kind of stereoisomer. An enantiomer is the mirror image of a chiral molecule. Enantiomers have the same relative energy, and in many environments they have the same physical and chemical properties.

Chirality is not really just a property of molecules. It is actually a property of all physical objects, be they big or small. Examples of chiral objects include screws, our hands and feet, most computer mice (or mouses??), scissors and countless others. Any object that has a plane of symmetry will be achiral. Thus achiral objects include most drinking glasses, many chairs, a piece of paper, spheres, cubes, rectangular prisms and many other 3 dimensional shapes. Humans are also roughly achiral. If we had perfect lines of symmetry, for example with shaved heads and no birth marks and perfectly symmetrical faces, then we would be achiral. Most animals are also roughly achiral.

It is often much more difficult to determine the chirality, or lack thereof, of organic molecules. Despite this challenge there is always a 100% reliable way to determine if a molecule is chiral:

Draw the molecule’s mirror image. If the mirror image is NOT super imposable, then the molecule is chiral and you have drawn two unique molecules called enantiomers. If the mirror image is super imposable, then the molecule is achiral and you have just drawn the same thing twice. This will ALWAYS be true.

Nonetheless there are a few very helpful rules to be aware of. Sometimes it is easier to follow these rules than to draw the mirror image and then do the mental gymnastics of reorienting the molecule to check for superimposability. I put asterisks next to tiny lies you can probably ignore and still get an A+.

1)      A molecule with a plane of symmetry, in any conformation, is always* achiral. Ignore the asterisk if you want to, and pretend they’re always achiral.

2)      A molecule with another symmetry element called an inversion center is also always* achiral

3)      A molecule lacking these symmetry elements is always** achiral.

4)      How does this relate to stereocenters? It’s helpful to know: a molecule with zero stereocenters is almost always achiral. A molecule with an odd number of stereocenters (1, 3, etc.) will always be chiral. A molecule with an even number of chiral centers may be chiral or achiral, considering the ubiquity of meso compounds. In these cases it becomes more necessary to look for planes of symmetry.

Planes of symmetry are usually easier to identify than inversion centers. Also most achiral organic molecules have planes of symmetry. Therefore I will focus mostly on planes of symmetry here.

Let’s look at a few achiral molecules and identify their planes of symmetry. Basically what we’re doing is cutting the molecule in half and ending up with the same thing on both sides. Molecules can be drawn so that they have a plane of symmetry that is either: a) perpendicular to the plane of a screen (or paper, or board), or b) in the plane of a screen. I will show a perpendicular plane of symmetry as a dotted line, and an “in plane” plane of symmetry as a box. I will also show inversion centers as dots in the center of the molecule, although one need not understand the inversion center to follow this tutorial. Remember: a molecule with a plane of symmetry, in any conformation, is usually achiral.

OCS-Symmetry-Elements

 Achiral molecules and their planes of symmetry. Top: Molecules drawn with perpendicular planes of symmetry. Bottom: Molecules drawn with planes of symmetry in the plane of the screen.

There’s one thing I’ve been doing so far to make your life easier that most professors won’t be so kind about. I’ve been intentionally drawing every achiral molecule in an achiral conformation. In reality many achiral molecules have chiral conformations! In most cases, however, any molecule with an achiral conformation is in fact achiral, even if it has other chiral conformations.

 In other words, many achiral molecules might appear chiral at first glance depending on how they are drawn. In many cases the achiral conformations we draw are either very high in energy, or do not really ever exist at all. For example eclipsed conformations of acyclic meso compounds or flat (and fully eclipsed) six membered rings.

Below are some examples of molecules with chiral conformations that are in fact achiral. Try to visualize how rotation around bonds can lead to a conformation with a plane of symmetry. It may be helpful to make models. Unfortunately some model kits are so rigid that you can’t jam a six membered ring into a flat conformation. This is the one downside of rigid model kits, which I think can actually be useful in other ways.

OCS-Symmetrical-Conformations

Various conformations of achiral molecules. Some have planes of symmetry and some do not. 

There is one more symmetry element that is helpful to recognize: an axis of rotational symmetry. Rotational symmetry will be especially useful later when you learn about spectroscopy, but for now it’s helpful to just recognize it. A rotationally symmetric object is an object that looks the same after a certain amount of rotation. Every molecule (and every object, really) therefore has a 360 degree rotational axis of symmetry. Many molecules have much more rotational symmetry. Here I will focus on the 180 degree rotational axis, sometimes called the 360/n axis, where n=2.

It is important to recognize that molecules with rotational symmetry often appear very “symmetrical” at first glance, but the presence of any kind of rotational symmetry has no effect a molecule’s chirality. Rotational symmetry elements may be present in both chiral and achiral molecules.

A 180 degree rotational axis is often present in chiral molecules. Below are some examples of chiral molecules with this type of symmetry element:

OCS-Rotational-Symmetry

 Conformations of chiral molecules with 180 degree rotational symmetry

It takes lot of practice to identify symmetry elements in molecules. Don’t expect to get it just after looking at the few examples I’ve shown here. This tutorial was simply meant to introduce most of the key pitfalls associated with determining whether a molecule is chiral or achiral. Any suggestions or questions are appreciated.

* Certain classes of molecules, such as sterically hindered biaryl compounds and crazy macrocycles, have planes of symmetry or inversion centers in some conformation but are unable to either: a) achieve a conformation with a plane of symmetry and/or b) equilibrate between two enantiomeric conformations to form an equilibrating racemic mixture. If neither of these things are possible than a molecule can be appear achiral when in fact it is actually chiral. This is very rare in Sophomore organic, so I will not discuss it further here except to say that conformational chirality is a fun topic in computational organic.

 **Planes of symmetry and inversion centers are actually not the only symmetry elements associated with achirality. There are other “higher order” symmetry elements that are also consistently associated with a lack of chirality. If you’re a chemistry major you’ll learn about these in inorganic chemistry. Most professional organic chemists don’t think about these compounds very much.