Topological Analysis of Functions on Arbitrary Grids: Applications to Quantum Chemistry

Hutcheon, Michael J.; Teale, Andrew M.

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 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 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.

Citation

Hutcheon, M. J., & Teale, A. M. (2022). Topological Analysis of Functions on Arbitrary Grids: Applications to Quantum Chemistry. Journal of Chemical Theory and Computation, 18(10), 6077-6091. https://doi.org/10.1021/acs.jctc.2c00649

• Journal Article Type: Article
• Acceptance Date: Aug 25, 2022
• Online Publication Date: Sep 7, 2022
• Publication Date: Oct 11, 2022
• Deposit Date: Sep 26, 2022
• Publicly Available Date: Sep 27, 2022
• Journal: Journal of Chemical Theory and Computation
• Print ISSN: 1549-9618
• Electronic ISSN: 1549-9626
• Publisher: American Chemical Society
• Peer Reviewed: Peer Reviewed
• Volume: 18
• Issue: 10
• Pages: 6077-6091
• DOI: https://doi.org/10.1021/acs.jctc.2c00649
• Keywords: Physical and Theoretical Chemistry; Computer Science Applications
• Public URL: https://nottingham-repository.worktribe.com/output/10920048
• Publisher URL: https://pubs.acs.org/doi/10.1021/acs.jctc.2c00649