Organic Chemistry: Concepts and Applications - Headley Allan D. 2020

Stereochemistry
5.6 Compounds with More Than One Stereogenic Carbon

It is possible for an optically active molecule to have more than one stereogenic carbon. For each stereogenic carbon in such a molecule, it is possible to assign absolute configuration about that carbon. As a result, there are many different stereoisomers that are possible. The relationship between such stereoisomers may or may not be enantiomerism. For a stereoisomer that has more than one stereogenic carbon, the possible combinations of R and S stereoisomers for the stereogenic carbons are 2n, where n represents the number of stereogenic carbons. Thus, for a compound with two stereogenic carbons, there is a maximum of four different stereoisomers. Shown in Figure 5.10 are the four stereoisomers of 2-bromo-3-chlorobutane, which has two stereogenic carbons.

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Figure 5.10 Fischer projections of different stereoisomers of 2-bromo-3-chlorobutane.

The first and second molecules are enantiomers of each other, and the third and fourth molecules are enantiomers of each other. The first and third molecules and the first and fourth molecules are not enantiomers of each other, however. Since the only difference between these molecules is the difference in configuration about one carbon, these molecules are different molecules and the relationship is not enantiomerism, but different stereoisomers and this special relationship is called diastereomerism, and the molecules are called diastereomers. Thus, (2S,3S)-2-bromo-3-chlorobutane and (2S,3R)-2-bromo-3-chlorobutane are diastereomers. Likewise, (2S,3S)-2-bromo-3-chlorobutane and (2R,3S)-2-bromo-3-chlorobutane are diastereomers. The other diastereomers are (2R,3R)-2-bromo-3-chlorobutane and (2R,3S)-2-bromo-3-chlorobutane. Diastereomers are stereoisomers that are not mirror images of each other and are not enantiomers of each other. The physical properties of diastereomers, such as the melting points and boiling points, are different from each other.

Problem 5.6

For 2-bromo-3-fluorobutane, (a) give a Fischer projection of this molecule, (b) assign R and S absolute configuration about each stereogenic carbon, (c) give the Fischer projection of the diastereomers of the molecule given in part (a) of this question.

The same analysis of stereoisomers can be carried out also using the dashed-wedge representation instead of the Fischer projection. Figure 5.11 shows the dashed-wedge representation for the stereoisomers shown in Figure 5.10.

Note that the Fischer projections shown in Figure 5.10 are the least stable since they are all eclipsed conformational isomers. Figure 5.12 gives the most stable anti conformers, which is accomplished by rotation about the C2—C3 bond by 180°.

For some molecules with more than one stereogenic carbon, not all stereoisomers that result from different spatial arrangements of the atoms or groups about the stereogenic carbons result in different stereoisomers. Consider the stereoisomers of 2,3-dibromobutane, which are shown below.

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For these stereoisomers, the first and second molecules are enantiomers; however, the third and fourth molecules are not enantiomers, but identical molecules. Making this assignment is tricky since the third and fourth molecules are mirror images of each other. Close examination of these two molecules reveals that they are superimposable on each other, hence the same. Another method that can be used to demonstrate that they are the same is to determine if there is a plane of symmetry in the molecule. As demonstrated earlier in the chapter, if there is a plane of symmetry, the mirror image of that molecule is not an enantiomer, but the same. For the third and fourth molecules, there is a plane of symmetry, which is a horizontal plane between carbons 2 and 3, as demonstrated below.

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Figure 5.11 Dashed-wedge representations of the stereoisomers shown in Figure 5.10.

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Figure 5.12 Dashed-wedge representation of the stereoisomers shown in Figure 5.11, but a rotation about the central carbon—carbon bond by 180° gives the most stable conformers.

Stereoisomers that have stereogenic carbons, and also a plane of symmetry, are called meso compounds. Meso compounds are stereoisomers that contain stereogenic carbons, but their mirror images are superimposable on each other.

Problem 5.7

i. Give a Fischer projection of (2S,3R)-2,3-butanediol; is this compound a meso compound or optically active?

ii. Give a Fischer projection of (2S,3S)-2,3-butanediol; is this compound a meso compound or optically active?

5.6.1 Cyclic Compounds with More Than One Stereogenic Center

It is possible to have cyclic compounds that have stereogenic carbons, such as carvone and thalidomide, as discussed earlier in the chapter, and the R and S stereoisomers are shown below.

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Figure 5.13 Symmetrical analysis of isomers of 1,2-dimethylcyclopropane.

It is possible to have cyclic compounds with two chiral carbons and for such compounds to be symmetric or asymmetric as discussed in the previous section. Shown in Figure 5.13 are the structures of 1,2-dimethylcyclopropane. Note that in the structure to the left, where the two methyl groups are on the same side of the plane of the cyclopropane ring (the cis stereoisomer), there is a plane of symmetry going through carbons 1 and 2. Hence, its mirror image is superimposable on itself and symmetric making the molecule achiral. On the other hand, the stereoisomer to the right (the trans stereoisomer) does not have a plane of symmetry and hence this stereoisomer is asymmetric and its mirror image is not the same; hence, it is a chiral molecule.

Problem 5.8

i. Which of the following molecules have a plane of symmetry and hence are achiral?Image

ii. Give the dashed/wedge structures of (1S,2R)-1,2-dichlorocyclopropane and (1S,2S)-1,2-dichlorocyclopropane and determine if these compounds are meso compounds or not.