Non-linear effects

In enantioselective synthesis, a non-linear effect refers to a process in which the enantiopurity of the catalyst or chiral auxiliary does not correspond with the enantiopurity of the product produced. For example: a racemic catalyst would be expected to convert a prochiral substrate into a racemic product (a linear effect), but this is not always the case and a chirally enriched product can be produced instead (a non-linear effect). In enantioselective synthesis, a non-linear effect refers to a process in which the enantiopurity of the catalyst or chiral auxiliary does not correspond with the enantiopurity of the product produced. For example: a racemic catalyst would be expected to convert a prochiral substrate into a racemic product (a linear effect), but this is not always the case and a chirally enriched product can be produced instead (a non-linear effect). This can be expressed mathematically, as shown in Equation 1. Stereoselection that is higher or lower than the enantiomeric excess of the catalyst is considered non-ideal behavior. In non-ideal behavior, this deviation from linearity is described as the non-linear effect, NLE. For an ideal asymmetric reaction, the eeproduct may be described as the product of eemax multiplied by the eecatalyst. This is not the case for reactions exhibiting NLE's. Non-linear effects often arise in reactions with a scalemic catalyst composition. As first observed by Wynberg and Feringa in 1976, different enantiomers of the chiral catalysts form heterochiral complexes, more specifically high order aggregates or dimeric forms of the catalyst. These heterochiral complexes influence the effective stereoinduction of a scalemic catalyst. Additional sources of non-linear effects include autocatalysis, the process in which the reaction catalyzes itself. General definitions and mathematical models are key to understanding non-linear effects and their application to specific chemical reactions. In the past two decades, the study of non-linear effects has shown to elucidate reaction mechanism and guide in synthetic applications. A positive non-linear effect, (+)-NLE, is present in an asymmetric reaction which demonstrates a higher product ee (eeproduct ) than predicted by an ideal linear situation (Figure 1). It is often referred to as asymmetric amplification, a term coined by Oguni and co-workers. An example of a positive non-linear effect is observed in the case of Sharpless epoxidation with the substrate geraniol. In all cases of chemical reactivity exhibiting (+)-NLE, there is an innate tradeoff between overall reaction rate and enantioselectivity. The overall rate is slower and the enantioselectivity is higher relative to a linear behaving reaction. Referred to as asymmetric depletion, a negative non-linear effect is present when the eeproduct is lower than predicted by an ideal linear situation. In contrast to a (+)-NLE, a (−)-NLE results in a faster overall reaction rate and a decrease in enantioselectivity. Synthetically, a (−)-NLE effect could be beneficial with a reasonable assay for separating product enantiomers and a high output is necessary . An interesting example of a (−)-NLE effect has been reported in asymmetric sulfide oxidations. 1n 1986, Kagan and coworkers observed a series of known reactions that followed a non-ideal behavior. A correction factor, f, was adapted to Equation 1 to fit the kinetic behavior of reactions with NLEs (Equation 2). Equation 2: A general mathematical equation that describes non-linear behavior Unfortunately, Equation 2 is too general to apply to specific chemical reactions. Due to this, Kagan and coworkers also developed simplified mathematical models to describe the behavior of catalysts which lead to non-linear effects. These models involve generic MLn species, based on a metal (M) bound to n number of enantiomeric ligands (L). The type of MLn model varies among asymmetric reactions, based on the goodness of fit with reaction data. With accurate modeling, NLE may elucidate mechanistic details of an enantioselective, catalytic reaction.