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Additive energy functions have predictable landscape topologies.

Brittany Story1,2, Biswajit Sadhu3,4, Henry Adams1,5

  • 1Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523, USA.

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|April 25, 2023
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Summary
This summary is machine-generated.

This study shows how to predict the topology of molecular energy landscapes using additive functions. This method accurately determines all topological features without dimensionality reduction.

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Area of Science:

  • Computational Chemistry
  • Topology
  • Data Analysis

Background:

  • Sublevelset persistent homology offers a compact representation of complex energy landscapes.
  • Previous methods like disconnectivity graphs may not fully differentiate similar landscapes.
  • Additive energy functions in n-alkanes hinted at predictable topological features.

Purpose of the Study:

  • To expand the prediction of energy landscape topology to any additive intramolecular energy function on a product space.
  • To develop a rigorous methodology for predicting the relative energies of all topological features in 3N dimensions.
  • To demonstrate a method for computing sublevelset persistent homology from individual energy function terms.

Main Methods:

  • Utilizing the additive nature of intramolecular energy functions on product spaces.
  • Applying sublevelset persistent homology to analyze energy landscapes.
  • Developing a predictive framework for topological features, including birth and death times.

Main Results:

  • Demonstrated that the number of sublevelset persistence bars and their birth/death times are predictable for additive energy landscapes.
  • Developed a rigorous methodology to predict the relative energies of all topological features in 3N dimensions without dimensionality reduction.
  • Successfully applied the approach to branched alkanes of varying complexity.

Conclusions:

  • The topology of additive energy landscapes can be rigorously predicted.
  • Sublevelset persistent homology provides a comprehensive tool for understanding complex molecular energy landscapes.
  • This work offers a general method for computing persistent homology from the components of an additive energy function.