Story, Brittany M., authorAdams, Henry, advisorShipman, Patrick, committee memberAchter, Jeff, committee memberFremstad, Anders, committee member2022-05-302022-05-302022https://hdl.handle.net/10217/235320Energy 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.born digitaldoctoral dissertationsengCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.characterizationpersistence Kunneth formulabranched alkanessublevelset persistent homologyenergy landscapesText