Mathematical models of nonlinear effects in asymmetric catalysis: New insights based on the role of reaction rate

This work demonstrates how the mathematical models developed by Kagan and co-workers(1a,b) to describe nonlinear enantioselectivity behavior may also be used to predict reaction rate as a function of catalyst enantiomeric excess in asymmetric catalytic reactions. Comparison of these predictions with experimental reaction rate measurements may thus be used to provide an independent confirmation of the model. The predictions of reaction rate reveal striking consequences for nonlinear catalytic behavior. A strong amplification in product chirality may come at the cost of a severely suppressed rate of product formation; in comparison, a system exhibiting a negative nonlinear effect in product enantioselectivity can provide a significantly amplified rate of formation of the desired product. Consideration of the kinetic behavior of these systems can provide valuable mechanistic insights and may help in the development of efficient synthetic strategies using nonenantiopure catalyst mixtures.