Additive energy functions have predictable landscape topologies.

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.