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Topological Analysis of Functions on Arbitrary Grids: Applications to Quantum Chemistry
Michael J Hutcheon1, Andrew M Teale1
1School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, U.K.
Journal of Chemical Theory and Computation
|September 7, 2022
Summary
New graph theory algorithms enable topological analysis of functions on any grid. This method efficiently processes data, revealing chemical properties like Bader charges with fewer points and improved computational scaling.
Area of Science:
- Computational Chemistry
- Graph Theory
- Data Analysis
Background:
- Topological analysis of functions on grids is crucial in computational chemistry.
- Existing methods often require extensive computations and can be sensitive to grid density.
Purpose of the Study:
- To develop novel algorithms for topological analysis of arbitrary functions on arbitrary grids.
- To demonstrate the application of these algorithms in analyzing molecular properties.
- To address limitations of traditional grid-based approaches.
Main Methods:
- Post-processing of grid data using neighborhood graph construction.
- Recasting topological analysis as a graph theory problem.
- Utilizing Python for algorithm implementation.
Main Results:
- Algorithms successfully perform topological analysis without additional function evaluations.
- Demonstrated correspondence between graph features and chemically relevant properties (e.g., Bader charges).
- Achieved convergence with significantly fewer grid points compared to uniform-grid methods.
- Exhibited O[N log(N)] computational cost scaling.
Conclusions:
- The graph-based approach offers an efficient and flexible method for topological analysis.
- The algorithms mitigate issues related to grid bias.
- This technique provides a robust alternative for analyzing molecular charge and current densities.
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