离子聚集和氢键网络的持久同源性分析
Persistent homology analysis of ion aggregation and hydrogen-bonding network
摘要：
尽管实验工具和理论模型的巨大进步，离子聚集体及其相关的水氢键网络的微观结构的定量表征仍然是一个具有挑战性的问题。本文首次引入一种新的数学方法--持久同源法，定量地分析了离子聚集体系和氢键网络的内在拓扑性质。装配系统的持久同源性分析的两个最显著的特性如下。首先，它不需要预定义的键长来构建离子或氢网络。持久的同源性结果仅由数据的形态结构决定。其次，它可以直接测量离子聚集体和氢键网络中的圆或孔的大小。为了验证我们的模型，我们考虑了两个经过充分研究的系统，即，NaCl和KSCN溶液，由分子动力学模拟生成。它们被认为代表两种形态学类型的聚集，即，局域团簇和扩展离子网络。结果表明，这两种聚集类型具有明显的拓扑特征，可以用我们的拓扑模型很好地描述。对于氢键网络，KSCN系统表现出更显着的变化，在其本地的环结构的浓度增加。观察到大尺寸局部圆结构的一致增加，并且这些圆的尺寸变得越来越多样化。相比之下，NaCl体系没有显示出大尺寸圆的明显增加。相反，观察到圆形结构的平均尺寸的一致下降，并且随着浓度的增加，这些圆形的尺寸变得越来越均匀。
英文摘要：
Despite the great advancement of experimental tools and theoretical models, a quantitative characterization of the microscopic structures of ion aggregates and its associated water hydrogen-bonding networks still remains a challenging problem. In this paper, a newly-invented mathematical method called persistent homology is introduced, for the first time, to quantitatively analyze the intrinsic topological properties of ion aggregation systems and hydrogen-bonding networks. Two most distinguishable properties of persistent homology analysis of assembly systems are as follows. First, it does not require a predefined bond length to construct the ion or hydrogen network. Persistent homology results are determined by the morphological structure of the data only. Second, it can directly measure the size of circles or holes in ion aggregates and hydrogen-bonding networks. To validate our model, we consider two well-studied systems, i.e., NaCl and KSCN solutions, generated from molecular dynamics simulations. They are believed to represent two morphological types of aggregation, i.e., local clusters and extended ion network. It has been found that the two aggregation types have distinguishable topological features and can be characterized by our topological model very well. For hydrogen-bonding networks, KSCN systems demonstrate much more dramatic variations in their local circle structures with the concentration increase. A consistent increase of large-sized local circle structures is observed and the sizes of these circles become more and more diverse. In contrast, NaCl systems show no obvious increase of large-sized circles. Instead a consistent decline of the average size of circle structures is observed and the sizes of these circles become more and more uniformed with the concentration increase.
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