The current work proposes that for any energy landscape that is comprised of additive energy terms for intramolecular interactions, there is a mathematical means to prove the pattern of the sublevelset persistent homology. We provide a recipe for determining the birth and death values of each bar. The generality of this approach is established for complex branched alkanes, where we derive conformational potential energy landscape topologies (in a persistent homology barcode representation) as the dimensionality is increased by both carbon number and diversification of branching patterns.