Molecules with More Than Two Chirality Centers

S Molecules with More Than Two Chirality Centers... 

In most cases with more than two chiral centers, the number of isomers can be calculated from the formula 2", where n is the number of chiral centers, although in some cases the actual number is less than this, owing to meso forms.An interesting case is that of 2,3,4-pentanetriol (or any similar molecule). The middle carbon is not asymmetric when the 2- and 4-carbon atoms are both (/ ) [or both (5)] but is asymmetric when one of them is (/ ) and the other (5). Such a carbon is called a pseudoasymmetric carbon. In these cases, there are four isomers two meso forms and one dl pair. The student should satisfy himself or herself, remembering the rules... 

A similar analysis holds for molecules that have more than two chirality centers Each chirality center may have either the R or the 5 configuration. The number of possible stereoisomers can be calculated by using simple probability theory. A molecule with a number of chirality centers equal to n has a maximum of 2" stereoisomers ... 

Diastereomers with two or More Stereogenic Centers Isomers of chiral molecules that possess two or more stereogenic centers may be either enantiomers or diastereomers. Diastereomers are not mirror images of each other. For molecules with more than one stereogenic center, the enantiomeric pair must have the opposite configuration at each center. 

Molecules like lactic acid, alanine, and glyceraldehyde are relatively simple because each has only one chirality center and only two stereoisomers. The situation becomes more complex, however, with molecules that have more than one chirality center. As a general rule, a molecule with n chirality centers can have up to 2n stereoisomers (although it may have fewer, as we ll see shortly). Take the amino acid threonine (2-amino-3-hydroxybutanoic acid), for example. Since threonine has two chirality centers (C2 and C3), there are four possible stereoisomers, as shown in Figure 9.10. Check for yourself that the R,S configurations are correct. 

We have seen examples of molecules with one chiral center that exist in two mirror-image configurations, which we call enantiomers. What happens when there is more than one chiral center How many stereoisomers should we expect Consider the stereoisomers of the important amino acid, threonine, (2-amino-3-hydroxybutanoic acid). For this substance, if we write all of the possible configurations of its two chiral carbons, we have four different projection formulas, 19-22, corresponding to four different stereoisomers ... 

Molecules like lactic acid, alanine, and glyceraldehyde are relatively simple because each has only one chirality center and only two stereoisomers. The situation becomes more complex, however, with molecules that have] more than one chirality center. 

So far we have mainly considered chiral molecules that contain only one chirality center. Many organic molecules, especially those important in biology, contain more than one chirality center. Cholesterol (Section 23.4B), for example, contains eight chirality centers. (Can you locate them ) We can begin, however, with simpler molecules. Let us consider 2,3-dibromopentane, shown here in a two-dimensional bond-line formula. 2,3-Dibromopentane has two chirality centers ... 

The successful achievement of the (/ )-LSB catalyst in asymmetric Michael addition suggested that the metal centers other than rare earths might lead to a novel heterobime-talhc asymmetric catalyst with unique properties. With this foundation, the same group further developed a new heterobimetallic chiral catalyst (/ )-ALB consisting of aluminum, lithium, and (/ )-BINOL in 1996 (Table 9.3). They reported that this type of catalyst could be more efficiently prepared from LiAlH with two equivalents of (/ )-BINOL. When this AlLibis(binaphthoxide) complex (/ )-ALB was employed as catalyst, up to 99% ee and 88% yield of products could be obtained in the reaction of dibenzyl malonate to 2-cyclohexen-l-one. Notably, both dimethyl and diethyl malonates furnished the 1,4-adducts with more than 90% of enantioselectivities. In particular, the catalytic asymmetric tandem Michael-aldol reactions were also achieved in the presence of (/ )-ALB. This protocol provides a usefid method for the catalytic asymmetric synthesis of complex molecules. 

Either by hand or by computer, it s reasonably easy to draw and manipulate real stereochemical representations of molecules with two chiral centers, sometimes even with three. However, many biological molecules have many more chiral centers than this, and Fischer devised a way of representing these in a flat form, in which it is easy to see stereochemical relationships and, particularly, to identify meso-compounds. Fischer projections consist of a cross motif, 7.89, and in this, groups b and d are pointing toward us, out of the paper, while groups a and c point away from us, behind the paper. 

The 1,3-dipolar cycloadditions of 1,3-dipoles with chiral alkenes has been extensively reviewed and thus only selected examples will be highlighted here. We have chosen to divide this section on the basis of the different types of alkenes rather than on the basis of the type of 1,3-dipole. For 1,3-dipolar cycloadditions, as well as for other reactions, it is important that the chiral center intended to control the stereoselectivity of the reaction is located as close as possible to the functional group of the molecule at which the reaction takes place. Hence, alkenes bearing the chiral center vicinal to the double bond are most frequently apphed in asymmetric 1,3-dipolar cycloadditions. Examples of the application of alkenes with the chiral center localized two or more bonds apart from the alkene will also be mentioned. Application of chiral auxiliaries for alkenes is very common and will be described separately in Section 12.3. 

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