Understanding the energy distribution of the local minima (0-dimensional bars) is a key step toward improving approaches designed for energy landscape exploration. Many algorithms rely upon the ability to overcome the index 1 critical points that connect local minima, and to avoid or escape out of "false minima" that are higher-index critical points. To illustrate how the sublevelset persistent barcodes are relevant in this context, we plot the distribution of the critical points as a function of energy in Figure . For each index, the number of critical points were binned into 1 kcal/mol increments and fit to a Gaussian distribution (black curve). The maximum of the observed density in index 1 critical points occurs at 7.6 kcal/mol with a height of 12,600 critical points and a full-width at half maximum (FWHM) of 3.7 kcal/mol. Importantly, there is significant overlap in the index 1 and index 2 critical point Gaussian distributions; in the 10 kcal/mol energy region, there is even overlap with the index 1, index 2, and index 3 critical points. The overlap in the index k and index k + 1 critical point Gaussian distributions is highest at the two extremes of the energy range of the PEL, indicating that it is challenge to avoid k + 1 critical points if you were traversing the energy landscape within these energy windows. All other index k critical point distributions except for index 1 and index 7 have overlap with both the k + 1 and k -1 critical point distributions, and knowledge of the location of the k -1 critical points may provide avenues for systematically following those critical points to the global minimum on the PEL.