Stereoisomers in Molecules with Two Chiral Centers


- The number of possible stereoisomers of a molecule is related to the number of chiral centers present in a molecule.
The exact relationship is m = 2n

where m is the number of possible isomers and n is the number of chiral centers.
- Thus, for molecules with two chiral centers there are four possible stereoismers. (More complicated systems will not be considered here.)

- Consider the stereoisomers of 2-bromo-3-fluorobutane:

(2R,3R) (2S,3S)

(2R,3S) (2S,3R)

- The pairs of compounds which share a line are enantiomers.

In order to see this relationship, rotate each molecule so that the bromine (red atom) of is pointed up and the methyl group pointed towards the center of the page.

Notice that these pairs of molecules are not superimposable, but that they are mirror images.

Notice, also, the absolute configurations of each molecule:

The top pair of enantiomers are the (2R,3R) and the (2S,3S) compounds.

The bottom pair of enantiomers are the (2R,3S) and the (2S,3R) compounds.

In both cases , the pairs have the opposite configuration at both stereocenters. This is a general characteristic of enantiomers.

- What about the relationship between the rows of compounds? For example, the (2R,3R) compound and (2R,3S) compound OR between the (2S,3S) and the (2S,3R) compounds.

- These pairs of compounds are not superimposable (If they were they would be the same compound!) but they are also not mirror images.
In order to see this relationship, rotate the molecules so that the bromines of each pair are pointed towards each other, and the methyl groups pointed towards the middle of each page.

Two molecules that are non-superimposable, non-mirror images are called diastereomers.

Again, notice the absolute configurations of each pair of diastereomers:
The left pair are the (2R,3R) and the (2R,3S) compounds.

The right pair are the (2S,3S) and the (2S,3R) compounds.
In both cases, the absolute configuration at one chiral center is the same (C-2 in the left pair and C-3 in the right pair) and different at the other. Again, this is a general characteristic of diastereomers.
- What is the relationship between the "diagonal" pairs of compounds?

That is, (2R,3R) and the (2S,3R) compounds or the (2S,3S) ant the (2R,3S) compounds.

Notice that in each pair the absolute configuration at one chiral center is the same (C-3 for the first pair and C-2 for the second), while the configuration at the other chiral center is different.

These pairs of compounds are diastereomers (see the defination, above).


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