Kinetic plasticity and the determination of product ratios for kinetic schemes leading to multiple products without rate laws — New methods based on directed graphs

Abstract

This paper presents two new and fast methods of determining product ratios for kinetic schemes leading to more than one product on which the Acree–Curtin–Hammett (ACH) principle is based. The methods involve rewriting a given kinetic scheme as a directed graph with nodes and arrows connecting the nodes and takes advantage of the directionality of the kinetic arrows and the enumeration of paths to the various target product nodes. The first, based on path divergent trees, is computationally simpler but works under a specific set of conditions, whereas the second, based on an adapted version of Chou’s graphical method, works for all cases. By means of illustrated examples, both methods are shown to be completely verifiable with conventional more tedious treatments based on rate law determinations. The directed graph concept also works for kinetic schemes that involve entirely equilibrated species. In addition, the paper extends these ideas to variants of the basic ACH scheme, thereby testing the validity of the ACH principle and bringing about a deeper understanding of it. Generalization of the results yields a new parameter, called degree of kinetic plasticity, which completely describes the dynamics of kinetic resolution between the boundary limits of ACH behaviour (100% kinetic plasticity) and anti-ACH behaviour (100% kinetic rigidity). It is shown that this parameter is a good descriptor of all possible scenarios between and including these limits and can be determined experimentally by conducting a new kind of product study that tracks the behaviour of final product excesses as a function of initial substrate excesses. The resulting plot is always linear with a positive slope. The degree of kinetic plasticity is found by simply subtracting the slope from unity. These ideas are tested on complex kinetic schemes exhibiting dynamic kinetic resolution (DKR) by means of organocatalysis.Key words: physical organic chemistry, kinetics, mechanism, directed graph, Chou digraph, Chou graphical rule, Acree-Curtin-Hammett principle, product ratio, dynamic kinetic resolution, organocatalysis.