Discussion: For the same reasons as it is important to recognize and classify stereoisomers it is valuable to be able to draw enantiomers and diastereomers as well.
Drawing enantiomers: Recall that enantiomers are molecules which are nonsuperposable mirror images. Because these are mirror image molecules, and because stereoisomers can only have two absolute configurations, all the stereocenters of one enantiomer will be the mirror image of the other enantiomer. A mirror image stereocenter can be draw by switching the place of two groups attached to that stereocenter. We can also draw the mirror image of the enantiomer, using an imaginary mirror.
Example 1: Draw the enantiomer of (R)-2-chlorobutane shown below.
Solution 1: Let's switch the places of the methyl and ethyl groups. This gives us (S)-2-chlorobutane. (You should label the stereocenter as R or S to verify this.)
Example 2: Draw the enantiomer of (2R,3R)-tartaric acid, shown below.
Solution 2: Let's use the mirror image technique for this example. Once again, you may wish to verify the answer by labeling the stereocenters of the mirror image molecule as R or S.
Drawing diastereomers: Recall that stereoisomers differ in the
position of the atoms in space, and that diastereomers are stereoisomers
that are not enantiomers. Some thought on this will suggest that we can
draw the diastereomer of a given structure by inverting one or more, but
not all of the stereocenters.
Example 3: Draw all the diastereomers of (2R,3R)-tartaric acid (structure shown above).
Solution 3: How many diastereomers can there be? Recall that for a molecule with n stereocenters, the molecule can have 2n stereoisomers (section 4.4 of the text). Thus, (2R,3R)-tartaric acid, which has two stereocenters, can have at most 22 = 4 stereoisomers. The (2S,3S) stereoisomer cannot be a diastereomer of (2R,3R) because both stereocenters have been inverted. This leaves two possibilities, each of which has one stereocenter the same as the given molecule: (2R,3S) and (2S,3R). The structures can be drawn by inverting the stereocenter that is altered.
(In this particular case, the new diastereomers are meso
compounds, and are identical. This happens when the two stereocenters
have the same attachments.)
Exercises: Draw the enantiomer for each compound.
Draw a diastereomer for each structure.
