Heterochiral catalysts, asymmetric amplification

As described in the preceding sections, asymmetric amplification is generally a consequence of the formation of aggregates (i.e., dimers or oligomers that are homochiral or heterochiral) of a chiral catalyst. However, even a racemic catalyst can be used as a chiral catalyst with the aid of chiral additives (a simple model consisting of dimers is depicted in Scheme 9.17). If a chiral additive (R)-B is selectively associated with (S)-A in the racemic catalyst, the remaining (R)-A could operate as the chiral monomer catalyst (asymmetric deactivation). Conversely, the chiral additive (/ )-B can be selectively associated with (/ )-A in racemic catalyst to generate an active dimeric catalyst (asymmetric activation). 

In order to achieve an amplification of chirality, it requires that/> 1. If P = 0 (no meso catalyst) or g = 1 (same reactivity of meso and homochiral catalysts), then/= 1. The condition/> 1 is achieved for 1 + p > 1 + g ), or g < 1. Thus the necessary condition for asymmetric amplification in the above model is for the heterochiral or meso catalyst to be less reactive than the homochiral catalyst. If the meso catalyst is more reactive, then/< 1, and hence a negative nonlinear effect is observed. The size of the asymmetric amplification is regulated by the value off, which increases as K does. The more meso catalyst (of the lowest possible reactivity) there is, the higher will be eeproduct. This is well illustrated by computed curves in Scheme 11. The variation of eeproduct with eeaux is represented for various values of g (the relative reactivity of the meso complex) with K = 4 (corresponding to a statistical distribution of ligands Scheme 11, top). The variation in the relative amounts of the three complexes with eeaux is also represented for a statistical distribution of ligands (Scheme 11, bottom). 

It was soon recognized that in specific cases of asymmetric synthesis the relation between the ee of a chiral auxiliary and the ee of the product can deviate from linearity [17,18,72 - 74]. These so-called nonlinear effects (NLE) in asymmetric synthesis, in which the achievable eeprod becomes higher than the eeaux> represent chiral amplification while the opposite case represents chiral depletion. A variety of NLE have been found in asymmetric syntheses involving the interaction between organometallic compounds and chiral ligands to form enantioselective catalysts [74]. NLE reflect the complexity of the reaction mechanism involved and are usually caused by the association between chiral molecules during the course of the reaction. This leads to the formation of diastereoisomeric species (e.g., homochiral and heterochiral dimers) with possibly different relative quantities due to distinct kinetics of formation and thermodynamic stabilities, and also because of different catalytic activities. 

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