an interesting paradox: if one randomly selects a set of materials from Figure \[QadGroups\]a, one finds no experimental indication that an optimal heat of adsorption even exists. Yet, the approach of Bathia and Myers has indeed been shown to be useful in optimizing performance.

To shed some light on this paradox, we applied topological data analysis to the data in Figure \[QadGroups\]a. Analyzing the heat of adsorption for sets of geometrically similar structures, we obtain the desired ‘volcano plots’ shown in Figure \[QadGroups\]b, which allow us to systematically search for the optimal heat of adsorption within a class of geometrically similar structures, and hence the best-performing materials. Interestingly, this optimal heat of adsorption depends on the geometric type of a material[@bae101; @fro071] (see Figure \[QadGroups\]) and is not, as suggested by Bathia and Myers, a universal constant. In fact, Bathia and Myers assume implicitly that the entropy of adsorption is the same for all materials; for a set of similar materials as often chosen this assumption is more likely to hold.

The results above suggest that there is not a single class of optimal materials. For this particular example Simon [*et al*]{}.[@sim141] have used brute-force simulations to compute the performance 