# How many stereoisomers does this compound have? The 2^n rule and a new term: the stereounit

How do we figure out how many stereoisomers a compound has? We are commonly taught that organic molecules have (2n-the number of meso compounds it forms)possible stereoisomers, where n = the total number of stereocenters. In organic chemistry a stereocenter is a tetrahedral atom with four different groups.

This works great with some molecules. Below is a simple example of a molecule with two stereocenters. It has two total stereocenters and three stereoisomers, because one of its stereoisomers is meso. I.E. 2^2-1 = 3

The 3 stereoisomers of a molecule with 2 stereocenters

Now let’s look at a couple of relatively simple case where this formula seems to break down. A (1,4)-disubstituted cyclohexane has zero true stereocenters, yet it has two stereoisomers. Many alkenes also have zero stereocenters, yet they also have two possible stereoisomers.

Molecules with zero stereocenters that have multiple stereoisomers

How can we come up with a new formula, and a new way of thinking about stereoisomerism, that accounts for these types of ubiquitous examples? One way is through the use of an idea called the stereounit. A stereounit is an atom, or group of atoms that has two possible stereochemical ways of existing. Thus every stereocenter is a stereounit, but not every stereounit is a stereo center.

What are the stereo units in the graphics above? We don’t need to define them precisely in every case, as long as we understand what needs to be changed to give a different stereoisomer. In both of the cases in the graphics above, it is the cis/trans relationship that forms the stereounit.

Now we can modify our classic sophomore organic formula to better suit reality! We can still say that a molecule has a number of stereoisomers equal to (2n-the number of meso compounds it forms). But now we’ll define “n” as the number of stereounits, rather than the number of stereo centers. Even more precisely we need some additional language to express the fact that the stereo units we’re dealing with have two possible ways of existing, perhaps we could call them binary stereounits?

Here’s a tricky example of a chiral molecule. We can draw the enantiomer of this monstrosity in a variety of ways: for example by flipping the configuration of the pi bond, or switching wedge and dash on the tetrahedral carbon bearing a methyl group.

A chiral molecule with a single stereounit

The molecules above are the two possible stereoisomers of a compound with its connectivity. They are enantiomers. In this case the stereo unit must encompass both the alkene, as well as the tetrahedral carbon bearing a methyl group.

Now let’s consider an even bigger head ache. In the graphic below I’ve drawn all eight possible stereoisomers of a molecule with three stereounits. Two of the stereounits are also stereocenters. The cis/trans relationship around the alkene is strictly a stereounit. . This molecule fits our new formula perfectly: there are three stereounits and zero meso stereoisomers, thus there are 23=8 stereoisomers in total.

The eight stereoisomers a chiral alkene with three stereounits and zero possible meso compounds

Although it requires learning one more piece of vocabulary, the term “stereounit” greatly simplifies the discussion when describing a variety of common organic molecules.

The stereounit concept can also be applied to figure out how many possible conformations a molecule can have. In this case one would potentially have to accommodate both binary stereounits as well “higher order” stereounits. This analysis is useful in computational organic chemistry, where the complete conformational analysis of a multitude of conformationally flexible molecules is often required. Thanks to my graduate adviser, Professor Paul Cheong, for teaching me most of what I know about conformational analysis!