Stereoisomerism resulting from several centers of chirality in acyclic molecules

In a molecule containing n centers of chirality, the number of possible stereoisomers varies depending whether the molecule is constitutionally unsymmetrical (nonidentical centers of chirality) or constitutionally symmetrical. 

An acyclic, constitutionally unsymmetrical molecule can exist as 2 stereoisomers which are enantiomeric in pairs. In other words, such a molecule can exist as 2( -1) diastereoisomeric pairs of enantiomers. Any stereoisomer will thus have one enantiomer (that stereoisomer of opposed configuration on every chiral center) and 2 — 2 diastereoisomers. The latter may have as little as 1 and as much as n — 1 centers of opposed configuration. Those diastereoisomers which differ in the configuration of a single chiral center (i.e., which have identical configuration on n — 1 centers) are called epimers. Any stereoisomer in such a series has n epimers. 

As a simple example with n = 2, let us consider norephedrine (XLIX). Two 

Molecules with n centers of chirality are called constitutionally symmetrical when those centers equidistant from the geometrical center of the molecule are identically substituted. For such molecules, 2(n l) stereoisomers exist when n is odd, and 2 -1 + 2(n 2 /2 when n is even. 

Tartaric acid (L) is a classical example for n even. One pair of enantiomers is 

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