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

Hutcheon, Michael J.; Teale, Andrew M.

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Michael J. Hutcheon

Professor of Computational and Theoretical Chemistry


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.

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 (ACS)
Peer Reviewed Peer Reviewed
Volume 18
Issue 10
Pages 6077-6091
Keywords Physical and Theoretical Chemistry; Computer Science Applications
Public URL
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