Stereoisomers number

Figure 2-74. Basic stages for describing a stereoisomer by a permutation descriptor. At the stereocenter, the molecule is separated into the skeleton and its ligands. Both are then numbered independently, with the indices of the skeleton in italics, the indices of the ligands in bold.

Isomeric alkenes may be either constitutional isomers or stereoisomers There is a sizable barrier to rotation about a carbon-carbon double bond which corresponds to the energy required to break the rr component of the double bond Stereoisomeric alkenes are configurationally stable under normal conditions The configurations of stereoisomeric alkenes are described according to two notational systems One system adds the prefix CIS to the name of the alkene when similar substituents are on the same side of the double bond and the prefix trans when they are on opposite sides The other ranks substituents according to a system of rules based on atomic number The prefix Z is used for alkenes that have higher ranked substituents on the same side of the double bond the prefix E is used when higher ranked substituents are on opposite sides... 

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... 

Eleven chirality centers may seem like a lot but it is nowhere close to a world record It is a modest number when compared with the more than 100 chirality centers typ ical for most small proteins and the thousands of chirality centers present m nucleic acids A molecule that contains both chirality centers and double bonds has additional opportunities for stereoisomerism For example the configuration of the chirality center m 3 penten 2 ol may be either R or S and the double bond may be either E or Z There fore 3 penten 2 ol has four stereoisomers even though it has only one chirality center... 

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... 

Chemical degradation of chlorophyll gives a number of substances including phytol The constitution of phytol is given by the name 3 7 11 15 tetramethyl 2 hexadecen 1 ol How many stereoisomers have this constitution" ... 

Relative to each other both hydroxyl groups are on the same side m Fischer pro jections of the erythrose enantiomers The remaining two stereoisomers have hydroxyl groups on opposite sides m their Fischer projections They are diastereomers of d and L erythrose and are called d and l threose The d and l prefixes again specify the con figuration of the highest numbered chirality center d Threose and l threose are enan tiomers of each other... 

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. 

When additional substituents ate bonded to other ahcycHc carbons, geometric isomers result. Table 2 fists primary (1°), secondary (2°), and tertiary (3°) amine derivatives of cyclohexane and includes CAS Registry Numbers for cis and trans isomers of the 2-, 3-, and 4-methylcyclohexylamines in addition to identification of the isomer mixtures usually sold commercially. For the 1,2- and 1,3-isomers, the racemic mixture of optical isomers is specified ultimate identification by CAS Registry Number is fisted for the (+) and (—) enantiomers of /n t-2-methylcyclohexylamine. The 1,4-isomer has a plane of symmetry and hence no chiral centers and no stereoisomers. The methylcyclohexylamine geometric isomers have different physical properties and are interconvertible by dehydrogenation—hydrogenation through the imine. 

The widespread use of cinnamic derivatives has led to the pursuit of reUable methods for thek dkect synthesis. Commercial processes have focused on condensation reactions between ben2aldehyde and a number of active methylene compounds for assembly of the requisite carbon skeleton. The presence of a disubstituted carbon—carbon double bond in the sidechain of these chemicals also gives rise to the existence of two distinct stereoisomers, the cis or (Z)- and trans or (E)- isomers ... 

Many classes of natural product possess heterocyclic components (e.g. alkaloids, carbohydrates). However, their structures are often complex, and although structure-based names derived by using the principles outlined in the foregoing sections can be devised, such names tend to be impossibly cumbersome. Furthermore, the properties of complex natural product structures are often closely bound up with their stereochemistry, and for a molecule containing a number of asymmetric elements the specification of a particular stereoisomer by using the fundamental descriptors (R/S, EjZ) is a job few chemists relish. 

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. 

The stereoisomers of olefin saturation are often those derived by cis addition of hydrogen to the least hindered side of the molecule (99). But there are many exceptions and complications (97), among which is the difficulty of determining which side of the molecule is the least hindered. Double-bond isomerization frequently occurs, and the hydrogenation product is the resultant of a number of competing reactions. Experimentally, stereochemistry has been found to vary, sometimes to a marked degree, with olefin purity, reaction parameters, solvent, and catalyst 30,100). Generalizing, it is expedient, when unwanted products arise as a result of prior isomerization, to avoid those catalysts and conditions that are known to favor isomerization. 

Spatial congruence of C-H graphs is applied essentially only in chemical formulas which represent a compound of carbon atoms and atoms of valence 1 (or radicals of valence 1). In this case condition (IV), besides (I), (II), (III), adds another restriction not only the relationships are important but also the spatial arrangement of the bonds. The spatial interpretation of the congruence of C-H graphs coincides with the interpretation of the chemical formula as stereoformula. I use stereoisomers in this sense. For example, the number of different stereoisomers is equal to the number of spati-... 

The number of asymmetric carbon atoms in this formula is a 3 the number of distinct stereoisomers is 4, not 8 the difference 8-4 appears in (3.1) as the first coefficient.]... 

Rather similar was the paper [PolG36a] which also derives asymptotic formulae for the number of several kinds of chemical compounds, for example the alcohols and benzene and naphthalene derivatives. Unlike the paper previously mentioned, this one gives proofs of the recursion formulae from which the asymptotic results are derived. A third paper on this topic [PolG36] covers the same sort of ground but ranges more broadly over the chemical compounds. Derivatives of anthracene, pyrene, phenanthrene, and thiophene are considered as well as primary, secondary, and tertiary alcohols, esters, and ketones. In this paper Polya addresses the question of enumerating stereoisomers -- a topic to which we shall return later. 

In the realm of chemical enumeration we note Polya s equation (4.4) which gives the generating function for stereoisomers of the alkyl radicals, or equivalently, alcohols — that is, equation (5.2) of this article. His equation (4.3) gives the corresponding result for the structural isomers of these compounds. His equations (4.2) and (4.5) correspond, respectively, to the cases of alcohols without any asymmetric carbon atoms and the number of embeddings in the plane of structural formulae for alcohols in general. The latter problem is not chemically very significant. 

Polya s Theorem clearly showed the way to the general enumeration of all acyclic hydrocarbons, irrespective of how many double or triple bonds they might have but it was to be 35 years before this enumeration was carried out. In two papers [ReaR72,76] I obtained the solution to this general problem in both the structural isomer and stereoisomer cases, as generating functions in three variables. Of these variables, x marks the number of carbon atoms, y the number of double bonds, and z the number of triple bonds. The de- rivation of these generating functions was Polya theory all the way — a succession of applications of Polya s Theorem with occasional use of Otter s result. The derivation was really rather tedious, but the generating functions, once obtained, can be used to compute the... 

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 ... 

Diels-Alder reaction and. 494-495 El reaction and, 392 E2 reaction and, 387-388 R.S configuration and, 297-300 S 1 reaction and, 374-375 S -2 reactions and, 363-364 Stereogenic center, 292 Stereoisomers, 111 kinds of, 310-311 number of, 302 properties of, 306 Stereospecilic, 228, 494 Stereospecific numbering, sn-glycerol 3-phosphate and, 1132 Steric hindrance, Sjvj2 reaction and, 365-366 Steric strain, 96... 

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