The potential energy of a molecule is often written in an additive manner based upon contributions from different degrees of freedom. Here, we prove that the topology of those additive contributions can be used to determine the energies of all critical points on the total potential energy landscape and their associated molecular conformations. The sublevelset persistent homology barcode representation of the potential energy landscape is used, which provides a compact and quantitative description of the energy landscape in all 3N dimensions. We show that whenever an energy function V can be written additively as a sum of building block functions g i , the Künneth formula may be used to determine the sublevelset persistence of V in terms of the barcode information of g i . This includes the number of bars and the birth and death times of the sublevelset persistent bars across 3N dimensions. The approach is demonstrated for branched alkanes of varying complexity using dihedral angle building block potential energy functions; however any function that contributes to the internal degrees of freedom could be employed. This work is transferable to a number of applications within chemical physics, notably classical force field coarse-graining, PEL exploration and sampling algorithms, as well as understanding the multiple timescale dynamics of chemical systems. By characterizing the topological features of the full 3N dimensional energy land-scape all information about the chemical system is retained and the information lost during applications that require dimensionality reduction can be quantified. contains results that apply to any additive function over a product space.