Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA.
J Chem Phys. 2017 Feb 7;146(5):054104. doi: 10.1063/1.4974508.
The quantification of nonexponential (dispersed) kinetics has relied on empirical functions, which yield parameters that are neither unique nor easily related to the underlying mechanism. Multidimensional kinetics provide more information on dispersed processes, but a good approach to their analysis is even less clear than for standard, one-dimensional kinetics. This paper is the first in a series that analyzes kinetic data in one or many dimensions with a scheme that is nonparametric: it quantifies nonexponential decays without relying on a specific functional form. The quantities obtained are directly related to properties of the mechanism causing the rate dispersion. Log-moments of decays, which parallel the standard moments of distributions (mean, standard deviation, etc.), are introduced for both one- and multi-dimensional decays. Kinetic spectra are defined to visualize the data. The utility of this approach is demonstrated on a simple, but general, model of dispersed kinetics-a nonexponential homogeneous decay combined with slowly exchanging rate heterogeneity. The first log-moments give a geometric-mean relaxation time. Second log-moments quantify the magnitude of rate dispersion, the fraction of the dispersion due to heterogeneity, and the dynamics of exchange between different rate subensembles. A suitable combination of these moments isolates exchange dynamics from three-dimensional kinetics without contamination by the rate-filtering effects that were identified in a recent paper [M. A. Berg and J. R. Darvin, J. Chem. Phys. 145, 054119 (2016)].
非指数（弥散）动力学的量化一直依赖于经验函数，这些函数产生的参数既不唯一，也不容易与潜在的机制相关联。多维动力学提供了更多关于弥散过程的信息，但对其分析的好方法甚至比标准的一维动力学更不清楚。本文是一系列分析一维或多维动力学数据的论文中的第一篇，该方案是非参数化的：它量化非指数衰减，而不依赖于特定的函数形式。所得到的量直接与导致速率弥散的机制的特性有关。对数矩衰减与分布的标准矩（均值、标准差等）平行，用于一维和多维衰减。定义了动力学谱来可视化数据。这种方法的实用性在一个简单但通用的弥散动力学模型上得到了验证，即非指数均匀衰减与缓慢交换的速率异质性相结合。第一对数矩给出了几何平均弛豫时间。第二对数矩量化了速率弥散的幅度、异质性引起的弥散分数，以及不同速率子集合之间的交换动力学。这些矩的适当组合可以在不受到最近一篇论文中识别的速率滤波效应污染的情况下，将交换动力学与三维动力学分离[M.A.伯格和 J.R.达尔文，J.化学物理 145,054119(2016)]。
