Title:  Molecular Configurations and Persistence: Branched alkanes and additive energies

Advisor:  Dr. Henry Adams

Committee:  Dr. Jeff Achter, Dr. Patrick Shipman, Dr. Anders Fremstad

Energy landscapes are high-dimensional functions that encapsulate how certain molecular properties affect the energy of a molecule. Chemists use disconnectivity graphs to find transition paths, the lowest amount of energy needed to transfer from one energy minimum to another. But disconnectivity graphs fail to show not only some lower-dimensional features, such as transition paths with an energy value only slightly higher than the minimum transition path, but also all higher-dimensional features. Sublevelset persistent homology is a tool that can be used to capture other relevant features, including all transition paths. In this paper, we will use sublevelset persistent homology to find the structure of the energy landscapes of branched alkanes: tree-like molecules consisting of only carbons and hydrogens. We derive complete characterizations of the sublevelset persistent homology of the OPLS-UA energy function on two different families of branched alkanes. More generally, we explain how the sublevelset persistent homology of any additive energy landscape can be computed from the individual terms comprising that landscape.

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