Creation of a Stereogenic Unit

The partial or total transformation of a racemic mixture by a chiral reagent that introduces one stereogenic unit has been discussed [18, 83, 84). Several examples are discussed in Chapter 6, and here our treatment is mainly theoretical. A mixture of diastereomeric products is formed in addition, there will be some residual starting material if the conversion is incomplete. Some relationships exist between 

If the conversion is total Xj = 0 (C = 1), then Equation 2.18 indicates that the ratio of the enantiomeric excesses of the diastereomeric product is equal to the inverse ratio of their relative amounts, as established by Guette and Horeau [86]. 

When there is a KR of the racemic mixture, it can be evaluated by measuring ee jjj = eej (ee j = enantiomeric excess of the recovered starting material) and by calculating the conversion C as a function of the enantiomeric excess and diastereomeric excess of the products. Then, from C and ee, one can get the 

The action of a chiral Homer-Wittig type reagent on a racemic aldehyde has been mentioned in Section 2.3.7. In the E/Z mixture of products arising from olefination of 109, the -stereoisomer is mainly formed from one enantiomer of the aldehyde 109 while the Z-isomer is derived from the other enantiomer. Here, each enantiomer gives a defined stereochemistry for the double bond that is created (69). A new stereogenic unit is formed, which is conceptually similar to the formation of a new asymmetric centre in a racemic substrate. 

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