Topological analysis of functions on arbitrary grids: Applications to quantum chemistry

17 June 2022, Version 2
This content is a preprint and has not undergone peer review at the time of posting.

Abstract

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 neighbourhood graph, allowing the topological analysis to be recast as a problem in 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 neighbourhood graph are found to correspond to chemically relevant topographical properties, such as Bader charges. These properties converge using an order of magnitude fewer grid points than uniform-grid approaches, whilst exhibiting an appealing O(N log(N)) 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.

Keywords

topology
quantum chemistry
density functional theory
algorithms
graph theory
bader analysis

Supplementary weblinks

Comments

Comments are not moderated before they are posted, but they can be removed by the site moderators if they are found to be in contravention of our Commenting Policy [opens in a new tab] - please read this policy before you post. Comments should be used for scholarly discussion of the content in question. You can find more information about how to use the commenting feature here [opens in a new tab] .
This site is protected by reCAPTCHA and the Google Privacy Policy [opens in a new tab] and Terms of Service [opens in a new tab] apply.