Isomerism refers to the existence of compounds that have the same formula but different structure. In simple terms, they have the same constituents but differ in structure and characteristics. These compounds also differ in their physical and chemical properties.
Isomers can be generally classified into two types-
(i) Constitutional Isomers- These isomers have the same parts but differ in connectivity. They can be further classified into chain, position and functional groups isomers.
(ii) Stereoisomers- On the contrary, the stereoisomer of a molecule will have the same connectivity but differ in orientation in space.
Isomers that comprise the same parts but differ in spatial orientation are termed as stereoisomers. These isomers can be classified into two types- enantiomers and diastereomers.
Before we find out how to calculate stereoisomers, it is important to learn the types of stereoisomers and the distinctions between them. Stereoisomers that form mirror images of each other are termed as enantiomers. These can be understood by one’s hands which are mirror images of each other. Diastereomers, on the other hand, are stereoisomers that do not form mirror images.
Difference Between Enantiomers and Diastereomers
When the mirror images of two isomers are not superimposable (i.e. the mirror images are distinguishable), they are termed chiral. Such molecules have one or more carbon atoms with four nonidentical substituents. These substituents are arranged in such a way that prevents superimposition of the mirror images, even though they have the same substituents attached. This carbon atom with four different groups attached to it is termed as the chiral centre or stereocenter of the molecule.
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Changing the positions of the substituent can result in two possible arrangements, denoted by R and S. Thus, every stereocenter can have two stereoisomers.
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Now, what happens as the molecules become more complex?
With an increase in the complexity of molecules, the number of stereocenters also increases. A molecule with one stereocenter can have two stereoisomers. Taking this into account, the answer to how to find number of stereoisomers can be found.
For a molecule with two stereocenters, both can be either R or S. This leads to four possible stereoisomers: RR, SS, RS and SR.
Similarly, in the case of three chiral atoms, there are eight possible combinations for stereoisomers: RRR, RRS, RSR, SRR, SSR, SRS, RSS, and SSS.
This can be generalized into the stereoisomers formula, which is:
Number of Stereoisomers= 2n, where n represents the number of stereogenic centres present in the molecule.
The 2n Rule
The number of stereoisomers increases exponentially with an increase in the number of stereocenters.
Therefore, the 2n rule states that a molecule with ‘n’ number of chiral atoms present may have 2n stereoisomers.
The 2n number of stereoisomers formula fails to provide the real number of stereoisomers in some cases. This happens in compounds with high symmetry.
For e.g., 2,3-dichlorobutane does not have SS and RR enantiomers but an identical pair of SR isomers. This happens due to the plane of symmetry that is present within the compound. This results in the formation of three isomers- two enantiomers and one achiral molecule.
This molecule can be termed as a meso compound that has a stereogenic atom, even though it is achiral. In other words, a meso compound is a stereoisomer of a chiral compound that has a superimposable mirror image.
This puts forth the question, how to find stereoisomers for a molecule. The most certain way of finding out enantiomers is to draw mirror images and check their superimposition.
Another point to note is that the presence of an atom with four different groups attached to it is not in itself sufficient for the molecule to be chiral. The chirality for complex molecules can only be determined absolutely by creating mirror images of the original molecule and checking their superimposition.
Some molecules do not have any atoms attached to four different groups but are still chiral as a result of the molecular architecture. An example of such a molecule is hexahelicene which has a spirally coiled structure that makes it chiral.