These plots clearly justify well-known chemical intuition, which is that any geometry optimization or algorithm aimed at identifying degenerate global or local minima should start in the lowest energy configurations possible so as to avoid the higher-dimensional critical points. Of course, higherdimensional critical points are also relevant to understand the dynamic behavior of a physical system, including transitions between different configurations. In this case both the distribution of critical points and the heights of the barriers that must be overcome in order to effectively traverse the PEL are relevant. Here, we can turn again to the barcodes of the component functions that comprise the PEL, where in Appendix A we rigorously prove each bar length. In the case of 2,8-dimethyl,5-propylnonane only bar lengths (or barriers on the PEL) of 2.4, 2.74, and 3.2 kcal/mol are allowed.