Chiral Molecules with Two Stereogenic Centers

When a molecule contains two stereogenic centers, as does 2,3-dihydroxybutanoic acid, how many stereoisomers are possible  

We can use straightforward reasoning to come up with the answer. The absolute configuration at C-2 may be 7 or 5. Likewise, C-3 may have either the R or the S configuration. The four possible combinations of these two stereogenic centers are 

Stereoisomer I is not a mirror image of in or IV, so is not an enantiomer of either one. Stereoisomers that are not related as an object and its mirror image are called diastereomers diastereomers are stereoisomers that are not enantiomers. Thus, stereoisomer I is a diastereomer of III and a diastereomer of IV. Similarly, n is a diaste-reomer of III and IV. 

To convert a molecule with two stereogenic centers to its enantiomer, the configuration at both centers must be changed. Reversing the configuration at only one stereogenic center converts it to a diastereomeric structure. 

Organic chemists nse an informal nomenclatnre system based on Fischer projections to distinguish between diastereomers. When the carbon chain is vertical and like substituents are on the same side of the Fischer projection, the molecnle is described as the erythro diastereomer. When like substitnents are on opposite sides of the Fischer projection, the molecule is described as the threo diastereomer. Thus, as seen in the Fischer projections of the stereoisomeric 2,3-dihydroxybntanoic acids, compounds I and II are erythro stereoisomers and III and IV are threo. 

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We have now seen many examples of compounds containing one tetrahedral stereogenic center. The situation is more complex for compounds with two stereogenic centers, because more stereoisomers are possible. Moreover, a molecule with two stereogenic centers may or may not be chiral. 

The basic principles of the mechanism of this Lewis-base-catalyzed aldol reaction have already been described in Section 6.2.1.1. With regard to the course of the enantio- and diastereoselective formation of aldol adducts with two stereogenic centers, it is proposed that synthesis of anti-products proceeds via a chair-like transition structure. A distinctive feature of the cationic transition state complex is a hexacoordinated silicon atom bearing two chiral phosphoramide molecules as ligands (Scheme 6.30). 

When there is more titan one chiral center in a molecule, the number of possible stereoisomers increases. Since each chiral center can have either the R or S configuration, for a molecule of n chiral centers, there will be 2" possible stereoisomers. Thus 3-pheny 1-2-butanol has two stereogenic centers and four possible stereoisomers. These are shown below with the configuration of each chiral center designated. 

All of the optically active terpenes mentioned in this chapter are commercially available in bulk (> kg) quantities and are fairly inexpensive. Although many of them are isolated from natural sources, they can also be produced economically by synthetic methods. In fact, two thirds of these monoterpenes sold in the market today are manufactured by synthetic or semisynthetic routes. These optically active molecules usually possess simple carbocyclic rings with one or two stereogenic centers and have modest functionality for convenient structural manipulations. These unique features render them attractive as chiral pool materials for... 

The reactions of 24 with ammonia or hydrazine are most unusual. Although the correspondingly substituted disilene does not react, the diene participates in spontaneous 1,2-additions even at room temperature to furnish the 1,4-diamino- (34) or 1,4-dihydrazinotetrasilane (35) in almost quantitative yields. On account of the presence of two stereogenic centers in these molecules the existence of a diastereomeric meso form in addition to the enantiomeric R,R and S,S form is possible. The X-ray crystallographic analyses of both compounds revealed the existence of conglomerates of enantiomerically pure substances [18, 19], Although the individual molecules of the tetrachlorotetrasilane 36 are also chiral, this compound crystallizes as a racemate [18]. 

Going from one to two stereogenic centers in a molecule led to greater complexity with respect to the number of stereoisomers. Molecules with three or more chiral centers are even more complex, in accord with the 2" rule, where three stereogenic centers lead to a maximum of eight stereoisomers. 

Compounds in which one or more carbon atoms have four nonidentical substituents are the largest class of chiral molecules. Carbon atoms with four nonidentical ligands are referred to as asymmetric carbon atoms because the molecular environment at such a carbon atom possesses no element of symmetry. Asymmetric carbons are a specific example of a stereogenic center. A stereogenic center is any structural feature that gives rise to chirality in a molecule. 2-Butanol is an example of a chiral molecule and exists as two nonsuperimposable mirror images. Carbon-2 is a stereogenic center. 

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