Hutcheon Michael J, Teale Andrew M
School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, U.K.
J Chem Theory Comput. 2022 Oct 11;18(10):6077-6091. doi: 10.1021/acs.jctc.2c00649. Epub 2022 Sep 7.
Algorithms are presented for performing a topological analysis of an arbitrary function, evaluated on an arbitrary grid of points. These algorithms work strictly by post-processing the data and require no additional function evaluations. This is achieved by connecting the grid points with a neighborhood graph, allowing the topological analysis to be recast as a problem in the graph theory. The flexibility of the approach is demonstrated for various applications involving analysis of the charge and magnetically induced current densities in molecules, where features of the neighborhood graph are found to correspond to chemically relevant topographical properties, such as Bader charges. These properties converge using orders of magnitude fewer grid points than uniform-grid approaches while exhibiting an appealing [N log()] scaling of the computational cost. The issue of grid bias is discussed in the context of graph-based algorithms and strategies for avoiding this bias are presented. Python implementations of the algorithms are provided.
本文提出了用于对在任意点网格上求值的任意函数进行拓扑分析的算法。这些算法严格通过对数据进行后处理来工作，无需额外的函数求值。这是通过用邻域图连接网格点来实现的，从而使拓扑分析可以转化为图论中的一个问题。该方法的灵活性在涉及分子中电荷和磁感应电流密度分析的各种应用中得到了证明，其中发现邻域图的特征对应于化学相关的地形性质，如巴德电荷。与均匀网格方法相比，这些性质在使用数量级更少的网格点时就收敛了，同时计算成本呈现出吸引人的[N log()]缩放比例。在基于图的算法的背景下讨论了网格偏差问题，并提出了避免这种偏差的策略。还提供了这些算法的Python实现。
