Number of stereoisomers

Many naturally occurring compounds contain several chirality centers By an analysis similar to that described for the case of two chirality centers it can be shown that the maximum number of stereoisomers for a particular constitution is 2" where n is equal to the number of chirality centers... 

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... 

Section 7 12 For a particular constitution the maximum number of stereoisomers is 2" where n is the number of structural units capable of stereochemical variation—usually this is the number of chirality centers but can include E and Z double bonds as well The number of stereoisomers is reduced to less than 2" when there are meso forms... 

Compare 2 3 pentanediol and 2 4 pentanediol with respect to the number of stereoisomers possible for each constitution Which stereoisomers are chiraL Which are achiraL... 

Multiple Chiral Centers. The number of stereoisomers increases rapidly with an increase in the number of chiral centers in a molecule. A molecule possessing two chiral atoms should have four optical isomers, that is, four structures consisting of two pairs of enantiomers. However, if a compound has two chiral centers but both centers have the same four substituents attached, the total number of isomers is three rather than four. One isomer of such a compound is not chiral because it is identical with its mirror image it has an internal mirror plane. This is an example of a diaster-eomer. The achiral structure is denoted as a meso compound. Diastereomers have different physical and chemical properties from the optically active enantiomers. Recognition of a plane of symmetry is usually the easiest way to detect a meso compound. The stereoisomers of tartaric acid are examples of compounds with multiple chiral centers (see Fig. 1.14), and one of its isomers is a meso compound. 

Since the stereochemistry of the triene system of LTB4 had not been determined prior to synthesis, a number of stereoisomers of LTB4 were prepared for purposes of definitive comparison of physical properties and bioactivity with biologically produced LTB4. The various stereoisomers of LTB4 were much less active biologically than LTB4 itself. 

Indicate by asterisks the chirality centers present in each of the terpenoids shown in Problem 27.24. What is the maximum possible number of stereoisomers for each ... 

It is possible for a componnd to be its own mirror image. In such a case, the compound will not have a twin. It will be all by itself, and the total number of stereoisomers will be an odd number, rather than an even number. That one lonely compound is called a meso componnd. If you try to draw the enantiomer (using either of the methods we have seen), yon will find fhat your drawing will be the same compound as what yon started with. 

Sugars have large numbers of stereoisomers because they contain several asymmetric carbon atoms. 

The monosaccharide glucose contains four asymmetric carbons carbons 2, 3, 4 and 5. A general formula for calculating the maximum number of stereoisomers is given by 2n, where n is the number of asymmetric carbons. For this compound, since n = 4, the maximum number of stereoisomers is 24 = 16. 

If there remains any doubt that it is the symmetry of the frame and not of the inscribed tetrahedron that determines the number of isomers, it can be dispelled by considering example 28. The four points to which the bivalent ligands a, b,. are attached form a tetrahedron with Om symmetry, slightly compressed from the regular one. This inscribed tetrahedron would allow only half the number of stereoisomers that are actually permitted by the frame which belongs to point group S, (5) if a = b = c = d H2. 

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. 

Stereoisomers with more than one chiral center and which are not mirror images of each other hence, stereoisomers that are not enantiomers of each other. For example, L-threonine and D-threonine are an enantiomeric pair whereas L-threonine and D-allothreonine are a diastereomeric pair (as is L-threonine and L-allothreo-nine). Diastereomers will have similar physical, chemical, and spectral properties but those properties will not be identical. If n is the number of chiral centers, then the maximum number of stereoisomers will be equal to 2. However, the actual number for a given set of isomers may be less than 2 due to the presence of meso forms. See Enantiomer Epimer Meso Form... 

The maximum number of stereoisomers is 2" where n is the number of nonidentical chiral centers. Figure 1-2 shows the four stereoisomers present in a molecule with two chiral centers. Non-superimposable mirror images are enantiomers, while the other species in the figure are diastereomers. Unlike enantiomers, diastereomers have different physical properties. 

The total number of stereoisomers due to tetrahedral stereocenters does not exceed 2" where n is the number of tetrahedral stereocenters. For a compound with two stereocenters n = 2 giving a total of 4 (maximum) stereoisomers. 

With n dissimilar chiral atoms the number of stereoisomers is 2" and the number of racemic forms is 2" as illustrated below for 2-chloro-3-bromobutan.e (n = 2). The R,S configuration is shown next to... 

Problem 5.34 For the following reactions give the number of stereoisomers that are isolated, their R.S configurations and their optical activities. Use Fischer projections. 

Stereoisomerism in compounds with two stereo centres diastereomers and meso structure In compounds whose stereoisomerism is due to tetrahedral stereocentres, the total number of stereoisomers will not exceed 2", where n is the number of tetrahedral stereocentres. For example, in 2,3,4-trihydroxybutanal, there are two chiral carbons. The chiral centres are at C-2 and C-3. Therefore, the maximum number of possible isomers will be 2 = 4. All four stereoisomers of 2,3,4-trihydroxybutanal (A-D) are optically active, and among them there are two enantiomeric pairs, A and B, and C and D, as shown in the structures below. 

Incidentally, we can now see, in one case, why the correct number of stereoisomers could be predicted by assuming planar rings, even though they are not planar (p. 130). In the... 

The above mechanisms permit the formation of a large number of stereoisomers, but in practice this number is limited by their different energies. The following important factors, based on experimental and theoretical grounds, characterize the most preferred structures ... 

If a molecule is optically active, R In n must be added to its entropy estimate, where n is the total number of stereoisomers of equal energy. 

The four different groups attached to a chiral carbon can be different elements, isotopes, or functional groups, and chiral centers can be present in bodi open-chain molecules or cyclic compounds. The recognition of chirality and chiral centers in molecules is an important step in determining the numbers of stereoisomers that are possible for a given compound. 

A-3. Predict the number of stereoisomers possible for each of the following constitutions. For which of these will meso forms be possible ... 

The greater the number of these tetrahedral centers with four different groups that there are in a molecule, the greater the number of stereoisomers. For the most part, this is a simple exercise in probability and statistics. With two such centers, there are four stereoisomers possible (2 geometries at the one center X 2 at the second = 4), and with three such centers there are eight stereoisomers (2 X 2 X 2 = 8). 

According to the formula for the calculation of the theoretical number of stereoisomers (configurational isomers), x = 2W, 24 = 16 (where n = 4 = the number of stereogenic units) stereoisomers are possible for alitretinoin. Although the molecule contains five double bonds only those in the side chain can be considered, since because of ring strain the double bond in the six-membered ring can only have the Z configuration. 

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