Nonlinear effect asymmetric amplification

It has recently been found that Et2Zn promotes the 1,3-dipolar cycloaddition of nitrile oxides to allyl alcohol in the presence of catalytic amounts of diisopropyl tartrate (DIPT). By this method, 2-isoxazlines are obtained in good yields and up to 96% ee (Eq. 8.73).124a A positive nonlinear effect (amplification of ee of the product) has been observed in this reaction. There is an excellent review on positive and negative nonlinear effects in asymmetric induction.124b... 

Blackmond pointed out that asymmetric amplification always has, as a consequence, a decrease in reactivity when compared to the enantiopure catalyst. This can be calculated on the various models proposed for the interpretation of nonlinear effects. It is qualitatively visible in the reservoir model above as well as in the ML2 model, where the asymmetric amplification given by g < 1 (low reactivity of the meso catalyst) has as consequence the overall slowdown in reaction rate. The generalized model ML has been discussed (for n = 2,3,4) when the various species are in equilibrium. The complexity of the curve can increase sharply as soon as n > 2. 

The expression positive nonlinear effect reflects the fact that the observed ee (eCprod) is higher then the expected ee (eeiinear) calculated on the basis of Eq. (7.1). For example, let us consider an enantiopure catalyst that generates a product of 60% ee (eemax)- If the ligand is of 50% ee (eeaux), one now calculates eeprod = 30%. If instead the reaction provides a product of 58% ee, this can be considered as an excellent case of asymmetric amplification. 

Recently, examples of catalytic asymmetric synthesis have been reported in which the enantiomeric purity of the product is much higher than that of the chiral catalyst. A positive nonlinear effect, that is, asymmetric amplification, is synthetically useful because a chiral catalyst of high enantiopurity is not needed to prepare a chiral product with high enantiomeric excess (% ee) (Scheme 9.1). 

Due to the intensive studies by many groups, the number of examples of asymmetric amplification has been substantially increasing. Aggregation state of the enantiomers of a chiral catalyst can be estimated based on the observation of a nonlinear effect between the enantiopurity of the chiral catalyst and that of the product. 

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. 

The value y2 is much higher than the normal value obtained in the linear correlation, hence the term (+)-NLE. Oguni et al. introduced in 1988 the expression asymmetric amplification as being synonymous with (+)-NLE in order to describe these effects. Although this expression is now widely used in the context of nonlinear effects, its validity is questionable (vide supra). 

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). 

The presence of a nonlinear effect, either negative or positive, is a useful piece of information for the mechanistic study of a reaction. It implies that diastereomeric species are formed from the chiral auxiliary. If an asymmetric amplification is observed, it can be indicative of the formation of meso dimers (or tetramers etc.) of low reactivity. When the kinetic study of an asymmetric catalysis shows a rate second order with respect to catalyst concentration, it may be useful to investigate the possibility of nonlinear effects in the system. Jacobsen et al., for example, studied the... 

In the case of proline-catalyzed a-amination of aldehydes, the generally accepted catalytic cycle presented in Scheme 2.25 does not seem detailed enough to explain some of the results obtained for this particular transformation by Black-mond and co-workers [9]. In fact, their studies revealed product acceleration, a positive nonlinear effect, and asymmetric amplification. These properties of the... 

Carbonyl-Ene Reaction. BINOL-TiX2 reagent exhibits a remarkable level of asymmetric catalysis in the carbonyl-ene reaction of prochiral glyoxylates, thereby providing practical access to a-hydroxy esters. These reactions exhibit a remarkable positive nonlinear effect (asymmetric amplification) that is of practical and mechanistic importance (eq 19). The desymmetrization of prochiral ene substrates with planar symmetry by the enantiofacial selective carbonyl-ene reaction provides an efficient solution to remote internal asymmetric induction (eq 20). The kinetic resolution of a racemic allylic ether by the glyoxylate-ene reaction also provides efficient access to remote but relative asymmetric induction (eq 21). Both the dibromide and dichloride catalysts provide the (2R,5S)-syn product with 97% diastereoselectivity and >95% ee. 

The use of enantiomerically impure chiral ligands can sometimes lead to products with significantly higher or lower enantiomeric excesses [42]. When there is increased enantioselection, such nonlinear effects have been termed asymmetric amplification. Asymmetric amplification has been noted for the hydroborating... 

It was established for several examples that it was possible to observe some departure from the expected proportionality between the enantiomeric excess of the catalyst and the enantiomeric excess of the product. Nonlinear effects (NLE) are categorized as a positive nonlinear effect ((-i-)-NLE) if the curve ee(product) = f(ee(catalyst)) is above the straight line characterizing the expected proportionality between ee(product) and ee(catalyst). The (-i-)-NLE has also been named asymmetric amplification [92]. A negative nonlinear effect ((-)-NLE) means that the experimental curve ee(product) =f( ee(catalyst)) lies below the straight line of the linear correlation. The departure from linearity reflects the formation of diastereomeric species (catalytically active or not) which perturb the predictions based only on mixture of enantiomeric catalysts and the... 

Nonlinear effects is becoming very common (see Ref. [115] for a review) and is often a mechanistic tool. Asymmetric amplification has been discovered in many different kinds of catalytic reactions (for a recent review, see Ref. [ 116]). It has also been very useful in the devising of efficient asymmetric autocatalytic systems [117]. 

Mikami and coworkers conducted the Diels-Alder reaction with a catalyst prepared by mixing enantiomerically pure R)-56 and racemic 56 and observed a positive nonlinear effect however, they found no asymmetric amplification when they prepared the catalyst by mixing enantiomerically pure R)-56 and enantiomerically pure (S)-56 (i.e., linear correlation between catalyst and product ee). Introduction of molecular sieves restores the asymmetric amplification in the latter case, apparently by equilibration of R) R) and (S)(S) dimers into catalytically less active R) S) dimers. As expected, the reaction rate was faster for R)-56 than for ( )-56 derived from racemic binaphthol hgand ca. 5-fold faster). 

Recently, the concept of kinetic resolution has been extended to the case where enantioimpure catalysts are used. Kagan discovered the first examples of nonlinear effects in asymmetric catalysis, where there was no proportionality between the ee of the auxiliary and the ee of product (Figure 5.27) and gave some mathematical models to discuss these effects. The nonlinear effect (NLE) originates from the formation of diastereomeric species when the chiral auxiliary is not enantiomerically pure, either inside or outside the catalytic cycle. The observed effects were classified as (+)-NLE and (-)-NLE where "asymmetric amplification" and "asymmetric depletion" respectively occured. 

During their studies on the Biginelli reactions of para-nitrobenzaldehyde, thiourea, and ethyl acetoacetate with the promotion of 10mol% of the nonenantiopure 3,3 -ditriphenylsilyl binol-derived phosphoric acid 5c in toluene, a strong positive nonlinear effect was observed. The asymmetric amplification was also found to occur in several other phosphoric acid-catalyzed reactions [14]. 

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