N chiral

When two or more of a molecule s chirality centers are equivalently substituted meso forms are possible and the number of stereoisomers is then less than 2" Thus 2" represents the maximum number of stereoisomers for a molecule containing n chirality centers... 

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. 

Some molecules have more than one chirality center. Enantiomers have opposite configuration at all chirality centers, whereas diastereomers have the same configuration in at least one center but opposite configurations at the others. Epimers are diastereomers that differ in configuration at only one chirality center. A compound with n chirality centers can have a maximum of 2n stereoisomers. 

With more than two unspecified chiral centres, problems multiply rapidly - three chiral centres yield eight stereoisomers, and thus four possible sets of signals and so on. From this, it follows that n chiral centres give rise to 2" chiral entities of which 2"/2 will be distinguishable by NMR. 

A parallel library of optically active bicyclic tertiary amines 127 bearing N-chiral bridgehead nitrogen atoms was readily prepared by condensation of primary amines, cyclic amino acids 126, and aldehydes. This method gives access to a large variety of substituted hexahydro-l/7-pyrrolo[l,2-/ ]imidazol-l-ones of type 127 (Scheme 16). These... 

Configurational isomerism involving one chiral centre provides two different structures, the two enantiomers. If a structure has more than one chiral centre, then there exist two ways of arranging the groups around each chiral centre. Thus, with n chiral centres in a molecule, there will be a maximum number of 2" configurational isomers. Sometimes, as we shall see in Section 3.4.5, there are less. 

Now for a rather unexpected twist. We have seen that if there are n chiral centres there should be 2" configurational isomers, and we have considered each of these for n = 2 (e.g. ephedrine, pseudoephedrine). It transpires that if the groups around chiral centres are the same, then the number of stereoisomers is less than 2". Thus, when n = 2, there are only three stereoisomers, not four. As one of the simplest examples, let us consider in detail tartaric acid, a component of grape juice and many other fruits. This fits the requirement, since each of the two chiral centres has the same substituents. 

Where more than one chiral centre is present in a molecule there is the possibility of diastereoisomers, e.g. captopril. Another example of a synthetic drug with two chiral centres is labetalol. The number of diastereoisomers arising from n chiral centres is 2"i.e. 2 in the case of labetalol. In the structure shown in Figure 2.5 chiral centres 1 and 2 in structure A have the configurations R and S respectively the enantiomer of this structure (B) has the S and R configurations in centres 1 and 2. In addition there is a pair of enantiomers C and D that are diastereoisomers of the structures A and B, which have the configurations R2R and 16 25 . 

In general, a molecule with n chiral centers can have 2 stereoisomers. Glyceraldehyde has 21 = 2 the aldohexoses, with four chiral centers, have 24 = 16 stereoisomers. The stereoisomers of monosaccharides... 

Because each chiral center added to a chain doubles the number of possible configurations, we expect eight different stereoisomers with three chiral carbons, sixteen with four, and so on. The simple rule then is 2n possible different stereoisomers for n chiral centers. As we shall see later, this rule has to be modified in some special cases. 

The idea that for every n chiral centers there can be 2M different configurations will be true only if none of the configurations has sufficient symmetry to be identical with its mirror image. For every meso form there will be one less pair of enantiomers and one less total number of possible configurations than is theoretically possible according to the number of chiral centers. At most, one meso compound is possible for structures with two chiral centers, whereas two are possible for structures with four chiral centers. An example is offered by the meso forms of tetrahydroxyhexanedioic acid which, with four chiral atoms, have configurations 28 and 29 ... 

Glyceraldehyde has only one chiral carbon atom and can exist as two enantiomers, but other sugars have two, three, four, or even more chiral carbons. In general, a compound with n chiral carbon atoms has a maximum of 2n possible isomeric forms. Glucose, for example, has four chiral carbon atoms, so a total of 24 = 16 isomers are possible, differing in the spatial arrangements of the substituents around the chiral carbon atoms. 

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. 

Water MS, Sidler DR, Simon AJ, Middaugh CR, Thompson R, August LJ, Bicker G, Perpall HJ, Grinberg N, Chirality 11 224 (1999). 

Senanayake, C. H., Jacobsen, E. N. Chiral (Salen)Mn(III) Complexes in Asymmetric Epoxidations Practical Synthesis of Ci s - Am i n o i n d ano 1 and Its Application to Enantiopure Drug Synthesis, Process Chemistry in the Pharmaceutical Industry, Gadamasetti, K. G. Marcel Dekker New York, 1999, Chapter 18, 327. 

Carbon atoms bearing four different substituents are said to be chiral centers. If a molecule has n chiral centers it will, in most cases, have 2n stereoisomers. There will, for example, be 256 stereoisomers of a compound with eight chiral centers. Each will have exactly the same chemical formula and pattern of connectivity among its atoms (A is connected to B is connected to C and D, and so on). Only the arrangements of those atoms in space will differ, and there will be 256 variations. Life functions by using only a small subset of all possible stereoisomers. 

These counterintuitive properties of racemization paths of three-dimensional labeled and unlabeled chiral tetrahedra, noted by Mislow, are referred to as Mislow s label paradox. More recently, it has been shown that Mislow s label paradox is general for n-chiral simplices in all finite dimensions n, and sufficient and necessary partial vertex labeling conditions have been given for chirality-preserving interconversion paths of mirror images of chiral -dimensional simplexes. 

Two relevant theorems were proven in an earlier study on n-dimensional transformations preserving or abandoning n-chirality. Here only the main results (Theorems 3 and 10 of the study ) are presented, using the explicit labeling notation for the proofs, see the original reference. ... 

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