Quantification and optimization of dynamic kinetic resolution

A complete and exact kinetic analysis of the phenomenon of dynamic kinetic resolution is presented. This analysis is applicable to reactions of stable stereoisomeric substrates whose ratios can be controlled and is valid for any set of kinetic conditions within the constraint of first-order and pseudo-first-order processes. Two new linear relationships are found for the dependence of the initial product ratio on the initial substrate ratio and for the dependence of the final product excess on the initial substrate excess. These relationships yield the minimum number of rate constant ratios needed to characterize the energetics of a chemical system exhibiting dynamic kinetic resolution completely. A distinct experimental advantage of this method is that it is based entirely on product studies. A simple graphical representation of the second linear relationship depicts visually the limiting Curtin-Hammett and anti-Curtin-Hammett conditions. From these conditions, a new parameter is defined that characterizes the efficiency of dynamic kinetic resolution and Curtin-Hammett efficiency. Simulations based on enantiomeric substrates illustrate how reactions may be optimized using this graphical treatment. An extension of this analysis to related kinetic schemes of varying degrees of complexity shows that the above linear relationships are universal. Results from these treatments are compared with Noyori's quantitative work on the stereoselective hydrogenation of beta-ketoesters. Implications of this new analysis are also discussed in light of previous work done on the applicability of the Winstein-Holness and Curtin-Hammett approximations to reactions of substrates that are interconverting conformers. For these cases, an alternate definition of Curtin-Hammett efficiency is proposed that is based on the experimental determination of the initial and final product ratios and the equilibrium constant for substrate interconversion. This unified analysis can be readily applied to a wide variety of synthetic and mechanistic problems in organic chemistry where dynamic kinetic resolution is applicable.