Additive energy functions have predictable landscape topologies

Brittany Story; Biswajit Sadhu; Henry Adams; Aurora E Clark

doi:10.1063/5.0140667

Additive energy functions have predictable landscape topologies

J Chem Phys. 2023 Apr 28;158(16):164104. doi: 10.1063/5.0140667.

Authors

Brittany Story^{1

2}, Biswajit Sadhu^{3

4}, Henry Adams^{1

5}, Aurora E Clark⁶

Affiliations

¹ Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523, USA.
² NIMBioS, University of Tennessee Knoxville, Knoxville, Tennessee 37996, USA.
³ Health Physics Division, Health Safety & Environment Group, Bhabha Atomic Research Centre, Mumbai, India.
⁴ Homi Bhabha National Institute, Mumbai, India.
⁵ Department of Mathematics, University of Florida, Gainesville, Florida 32611, USA.
⁶ Department of Chemistry, University of Utah, Salt Lake City, Utah 84112, USA.

PMID: 37096849
DOI: 10.1063/5.0140667

Abstract

Recent work [Mirth et al., J. Chem. Phys. 154, 114114 (2021)] has demonstrated that sublevelset persistent homology provides a compact representation of the complex features of an energy landscape in 3 N-dimensions. This includes information about all transition paths between local minima (connected by critical points of index ≥1) and allows for differentiation of energy landscapes that may appear similar when considering only the lowest energy pathways (as tracked by other representations, such as disconnectivity graphs, using index 1 critical points). Using the additive nature of the conformational potential energy landscape of n-alkanes, it became apparent that some topological features-such as the number of sublevelset persistence bars-could be proven. This work expands the notion of predictable energy landscape topology to any additive intramolecular energy function on a product space, including the number of sublevelset persistent bars as well as the birth and death times of these topological features. This amounts to a rigorous methodology to predict the relative energies of all topological features of the conformational energy landscape in 3N dimensions (without the need for dimensionality reduction). This approach is demonstrated for branched alkanes of varying complexity and connectivity patterns. More generally, this result explains how the sublevelset persistent homology of an additive energy landscape can be computed from the individual terms comprising that landscape.