Kinetic plasticity and the determination of product ratios for kinetic schemes leading to multiple products without rate laws - New methods based on directed graphs
Kinetic plasticity and the determination of product ratios for kinetic schemes leading to multiple products without rate laws - New methods based on directed graphs
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DOI：
10.1139/v08-020
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发表时间：
2008-04-01
影响因子：
1.1
通讯作者：
Andraos, John
中科院分区：
文献类型：
--
作者：
Andraos, John
本文提出了两种新的快速方法来确定动力学方案的产物比率，从而产生多种产物，这是 Acree-Curtin-Hammett (ACH) 原理的基础。该方法涉及将给定的动力学方案重写为具有节点和连接节点的箭头的有向图，并利用动力学箭头的方向性和到各个目标产品节点的路径的枚举。第一个基于路径发散树，计算更简单，但在一组特定条件下工作，而第二个基于 Chou 图形方法的改编版本，适用于所有情况。通过图示的例子，这两种方法都被证明可以通过基于速率定律确定的传统的更繁琐的处理来完全验证。有向图概念也适用于涉及完全平衡物种的动力学方案。此外，本文将这些思想扩展到基本ACH方案的变体中，从而检验ACH原理的有效性并带来对其更深入的理解。结果的概括产生了一个新参数，称为动力学可塑性程度，它完整地描述了 ACH 行为（100% 动力学可塑性）和反 ACH 行为（100% 动力学刚性）的边界极限之间的动力学分辨率。结果表明，该参数是对这些限制之间（包括这些限制）的所有可能情况的良好描述，并且可以通过进行一种新型产品研究来通过实验确定，该研究跟踪最终产品过量行为作为初始底物过量的函数。生成的图始终呈正斜率线性。只需从单位中减去斜率即可得出动力学塑性程度。这些想法在复杂的动力学方案上进行了测试，通过有机催化展示了动态动力学分辨率（DKR）。
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.