Non-linear effects

Stereoselection (i.e. the eeproduct) that is higher or lower than the enantiomeric excess of the catalyst (eecatalyst, relative to the equation) is considered non-routine behavior.

[5] In 1981, Kagan and collaborators described the first non-linear effects in asymmetric catalysis and gave rational explanations for these phenomena.

[6] General definitions and mathematical models are essential for understanding nonlinear effects and their application to specific chemical reactions.

In recent decades, the study of nonlinear effects has helped elucidate reaction mechanism and guide 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).

Referred to as asymmetric depletion, a negative non-linear effect is present when the eeproduct is lower than predicted by an ideal linear situation.

Synthetically, a (−)-NLE effect could be beneficial with a reasonable assay for separating product enantiomers and a high output is necessary .

Due to this, Kagan and coworkers also developed simplified mathematical models to describe the behavior of catalysts which lead to non-linear effects.

[3] These models involve generic MLn species, based on a metal (M) bound to n number of enantiomeric ligands (L).

In addition to the catalyzed reaction of interest, the model accounts for a steady state equilibrium between the unbound and bound catalyst complexes.

[4] Obeying the same kinetic rate law, each of the three catalytic complexes catalyze the desired reaction to form product.

[7] As enantiomers of each other, the homochiral complexes catalyze the reaction at the same rate, although opposite absolute configuration of the product is induced (i.e. rRR=rSS).

With these relative reaction rates, Blackmond showed how the ML2 model could be used to formulate kinetic predictions which could then be compared to experimental data.

However, the same steady state assumption applies to the equilibrium between unbound and bound catalytic complexes as in the more simple ML2 model.

However, since the heterochiral complexes lead to enantiomerically enriched product, the overall equation for calculating the eeproduct becomes more difficult.

[4] In general, interpreting the correction parameter values of g to predict positive and negative non-linear effects is considerably more difficult.

One of these could potentially be an aggregation effect amongst the heterochiral catalytic complexes that takes place prior to the steady state equilibrium.

Under Sharpless oxidizing conditions with Ti(O-i-Pr)4/(+)-DET/t-BuOOH, Kagan and coworkers were able to demonstrate that there was a non-linear correlation between the eeproduct and the ee of the chiral catalyst, diethyl tartrate (DET).

[1] In pre-biotic chemistry, autocatalytic systems play a significant rule in understanding the origin of chirality in life.

The relationship between the ee product and the ee catalyst in the (+)-NLE, linear, and (−)-NLE scenarios. [ 3 ]
Figure 9: When the heterochiral complexes are more selective and reactive than the homochiral complexes. [ 4 ]
Figure 10: When the homochiral complexes are more selective and reactive than the heterochiral complexes. [ 4 ]
Figure 11: The general reaction scheme studied by Kagan and coworkers for the Sharpless epoxidation of geraniol. [ 9 ]
Figure 12: A clear indication of a negative non-linear effect in the asymmetric sulfide oxidation reaction. [ 1 ]