March's Advanced Organic Chemistry: Reactions, Mechanisms, and Structure, 7th Edition (2013)

Chapter 4. Stereochemistry and Conformation

4.F. Molecules with more than One Stereogenic Center

When a molecule has two stereogenic centers, each has its own configuration and can be classified (R) or (S) by the CIP method. There are a total of four isomers, since the first center may be (R) or (S) and so may the second. Each is drawn as both the Fischer projection and in the extended conformation. Since a molecule can have only one mirror image, only one of the other three can be the enantiomer of A. This enantiomer is B [the mirror image of an (R) center is always an (S) center]. Both C and D are a second pair of enantiomers and the relationship of C and D to A and B is designated by the term diastereomer. Diastereomers may be defined as stereoisomers that are not enantiomers (they are stereoisomers that are not mirror images, and not superimposable). Since C and D are enantiomers, they must have identical properties, except as noted in Section 4.A, and the same is true for A and B. However, the properties of A and B are not identical with those of C and D. They are different compounds, which means that they have different melting points, boiling points, solubilities, reactivity, and all other physical, chemical, and spectral properties. The properties are usually similar, but not identical. In particular, diastereomers have different specific rotations; indeed one diastereomer may be chiral and rotate the plane of polarized light while another may be achiral and not rotate at all (an example is presented below).

It is now possible to see why, as mentioned in Section 4.A, enantiomers react at different rates with other chiral molecules, but at the same rate with achiral molecules. In the latter case, the activated complex formed from the (R) enantiomer and the other molecule is the mirror image of the activated complex formed from the (S) enantiomer and the other molecule. Since the two activated complexes are enantiomeric, their energies are the same and the rates of the reactions in which they are formed must be the same (see Chapter 6). However, when an (R) enantiomer reacts with a chiral molecule that has, say, the (R) configuration, the activated complex has two chiral centers with configurations (R) and (R), while the activated complex formed from the (S) enantiomer has the configurations (S) and (R). The two activated complexes are diastereomeric, do not have the same energies, and consequently are formed at different rates.

Although four is the maximum possible number of isomers when the compound has two stereogenic centers (chiral compounds without a stereogenic carbon, or with one stereogenic carbon and another type of stereogenic center, also follow the rules described here), some compounds have fewer. When the three groups on one stereogenic atom are the same as those on the other, one of the isomers (called a meso form) has a plane of symmetry, and hence is optically inactive, even though it has two stereogenic carbons. Tartaric acid is a typical case. As shown, there are only three isomers of tartaric acid: a pair of enantiomers and an inactive meso form. For compounds that have two stereogenic atoms, meso forms are found only where the four groups on one of the chiral atoms are the same as those on the other chiral atom.

In compounds with two or more stereogenic centers, the maximum number of isomers can be calculated from the formula 2ⁿ, where n is the number of stereogenic centers. The actual number may be less than this, owing to meso forms,¹³¹ but never more. 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-carbons are both (R) [or both (S)]; labeled the dl pair. The compound when one of them is (R) and the other (S) is asymmetric (labeled meso). The middle carbon in such compounds is called a pseudoasymmetric carbon. In such cases, there are four isomers: two meso forms and one dl pair. Remember that the meso forms are superimposable on their mirror images, and that there are no other stereoisomers. Two diastereomers that have a different configuration at only one chiral center are called epimers.

The small letters used for the psuedoasymmetric center are assigned using established rules. An atom that is tetrahedrally substituted and bonded to four different entities, two and only two of which have opposite configurations, is stereogenic. The descriptors “r” and “s” are used to denote such centers; they are assigned in accordance with Sequence Rule 5, taking into consideration that “(R)” has precedence over “(S)” in the order of priority.¹³² Step 1: configuration “(R)” or “(S)” is assigned to stereogenic centers C-2 and C-4; Using 1,2,3-trichloropentane as an example, Step 2: Configuration at C-3 is assigned by applying sequence rule, “(R)” precedes “(S)”, and if (R) precedes (S), then Cl is the highest priority, followed by (R) and then (S): C-3 is r. The exchange of the Cl and H atoms at C-3 of the compound on the left generates the compound on the right, and “3r” becomes “3s”

In compounds with two or more steroegenic centers, the absolute configuration must be separately determined for each center. The usual procedure is to determine the configuration at one center by the methods discussed in Section 4.E.ii, and then to relate the configuration at that center to the others in the molecule. One method is X-ray crystallography, which, as previously noted, cannot be used to determine the absolute configuration at any stereogenic center. This method does give relative configurations of all the stereogenic centers in a molecule, and if the absolute configuration of one stereogenic center is independently determined, the absolute configurations of all are then known. Other physical and chemical methods have also been used for this purpose.

How to name the different stereoisomers of a compound when there are more than two is potentially a problem.² Enantiomers have the same IUPAC name, being distinguished by (R) and (S) or d and l or (+) or (−). In the early days of organic chemistry, it was customary to give each pair of enantiomers a different name or at least a different prefix (e.g., epi-, peri-, etc.). Thus the aldohexoses are called glucose, mannose, idose, and so on, although they are all 2,3,4,5,6-pentahydroxyhexanal (in their open-chain forms). This practice was partially due to lack of knowledge about which isomers had which configurations.¹³³ Today it is customary to describe each chiral position separately as either (R) or (S) or, in special fields, to use other symbols. Thus, in the case of steroids, groups above the “plane” of the ring system are designated β, and those below it α. Solid lines are typically used to depict β groups and dashed lines for α groups. An example is 1α-chloro-5-cholesten-3β-ol, showing the OH group on the top side of the molecule (up) and the chlorine atom on the bottom side (down).

For many open-chain compounds, prefixes are used that are derived from the names of the corresponding sugars and that describe the whole system rather than each chiral center separately. Two such common prefixes are erythro-and threo-, which are applied to systems containing two stereogenic carbons when two of the

groups are the same and the third is different.¹³⁴ The erythro pair has the identical groups on the same side when drawn in the Fischer convention, and if Y were changed to Z, it would be meso. The threo pair has them on opposite sides, and if Y were changed to Z, it would still be a dl pair. Another system¹³⁵ for designating stereoisomers¹³⁶ uses the terms syn and anti. The “main chain” of the molecule is drawn in the common zigzag manner. Then if two non-hydrogen substituents are on the same side of the plane defined by the main chain, the designation is syn; otherwise it is anti.