Kinetic Rationalization of Nonlinear Effects in Asymmetric Catalytic Cascade Reactions under Curtin-Hammett Conditions.

Observations of nonlinear effects of catalyst enantiopurity on product enantiomeric excess in asymmetric catalysis are often used to infer that more than one catalyst species is involved in one or more reaction steps. We demonstrate here, however, that in the case of asymmetric catalytic cascade reactions, a nonlinear effect may be observed in the absence of any higher order catalyst species or any reaction step involving two catalyst species. We illustrate this concept with an example from a recent report of an organocatalytic enantioselective [10 + 2] stepwise cyclization reaction. The disruption of pre-equilibria (Curtin-Hammett equilibrium) in reversible steps occurring prior to the final irreversible product formation step can result in an alteration of the final product from what would be expected based on a linear relationship with the enantiopure catalyst. The treatment accounts for either positive or negative nonlinear effects in systems over a wide range of conditions including "major-minor" kinetics or the more conventional "lock-and-key" kinetics. The mechanistic scenario proposed here may apply generally to other cascade reaction systems exhibiting similar kinetic features and should be considered as a viable alternative model whenever a nonlinear effect is observed in a cascade sequence of reactions.