Frank model, asymmetric autocatalysis

Asymmetric autocatalysis has the following intrinsic merits (1) the efficiency is high because the process is automultiplication (2) in an ideal asymmetric autocatalysis, no decrease in the amount of catalyst and no deterioration of the catalytic activity should be observed because the amount of catalyst increases during the reaction and (3) there is no need to separate the catalyst from the product because their structures are identical. Frank proposed a kinetic model of asymmetric autocatalysis without mentioning a specific compound or reaction." ... 

As if this were not enough, Soai et al. [4] also used this system to demonstrate for the first time the asymmetric amplification during autocatalysis that is inherent in the Frank model. Thus 20 mol% of (S)-9b with an ee of only 2% gave, with autocatalysis, (S)-9b with an ee of 10%. In further reaction cycles the enantiomeric excess rose from 10 through 57 to 81 and finally to 88% (Fig. 1). There was a 942-fold increase in the amount of product after four cycles. The asymmetric amplification shown by this simple selfrepli-cating system behaved, in fact, as predicted by the simple, theoretical Frank model. [18]... 

In 1953, Frank developed a mathematical model showing that spontaneous asymmetric synthesis is theoretically possible (21). If the chiral product of a catalytic reaction would act as a catalyst for its own formation and at the same time suppress the formation of its enantiomer, a basically enantiopirre product could be formed from near-racemic starling materials. About forty years later, Soai and coworkers provided the first experimental proof for this concept of asymmetric autocatalysis with the alkylation of pyrimidyl aldehydes with diallgrlzinc reagents (Figure 1) (22). 

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