# How many optical isomers can exist for any given molecule?

Sep 3, 2016

In principle there are ${2}^{n}$ optical isomers for an organic molecule with $n$ chiral centres. Of course that's in principle.

#### Explanation:

For a molecule with 2 chiral centres we could have $R , R$; $S , S$; $R , S$; and $S , R$. This is ${2}^{n}$ where $n$ is the number of chiral centres (here $n = 2$). But of course, there is a catch.

Often with these sorts of systems, the pair $R , S$, and $S , R$ (which are diastereomeric with respect to $R , R$, and $S , S$) are symmetric, i.e. these are $\text{meso}$ comounds with an internal plane of symmetry: $R , S$ $\equiv$ $S , R$ upon reflection, and these are thus equivalent molecules. If you look at your text you will find a section in the chirality chapter that considers the stereoisomerism of $2 , 3 - \text{dimethylbutan-1,4-diol}$. This is a relatively simple formula that generates such diastereomers.

You will note that here, only carbon stereoisomerism is considered.