Mathematical Description of Kinetic Resolution with an Enantiomerically Impure Catalyst and Nonracemic Substrate

Abstract

Kinetic resolution is an important method in organic chemistry; catalytic kinetic resolution is especially attractive because a smaller amount of the optically active material is required. In principle, a naturally occurring catalyst (enzyme) or a synthetic catalyst can be employed. Possible disadvantages of an enzymatic catalyst include limited scope of reactions and substrates; therefore, there is an increasing effort targeted at the design of chemical catalysts for kinetic resolution. The most useful parameter in comparing different catalysts is the selectivity factor S, which is the ratio of the rate constants for the reaction of the catalyst with the two enantiomers of the substrate (S = (k_1/k_2), see below). Mathematical treatment of kinetic resolution should provide a way to calculate S from experimental observables, and for enantiomerically pure catalysts the equations are well-known from the work of Kagan and others.