that best resemble the experimentally known structures ZESFUY and OGURAK.](hMOFexMOFU)

Global structural properties {#screening}
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In the main text we explained that the different dimensions of the persistent homology of the structures that we consider admit geometric interpretation. It is therefore interesting to see whether we can detect this geometric content when we use our method to test the capability of PerH to screen zeolites for the following conventional structural properties: $D_i$, $D_f$, $\rho$, $ASA$, $AV$, the Henry coefficient ($K_H$), and the heat of adsorption ($Q_{ad}$). We use methane as a probe molecule.

Starting with a highly diverse training set of 600 structures chosen by the min-max algorithm ([*10*]{}) , we perform high-throughput screening for the entire set of zeolites, using five different PerH’s: $PD_{0}$ (=$L_{0}$ as defined in \[methods\]), $PD_1$, and $PD_2$, which use only 0-, 1-, or 2-dimensional persistent homology information respectively, as well as $PD_{12}$ and $PD_{012}$ which combine information from 1- and 2- or 0-, 1-, and 2-dimensional persistent homology. For $PD_{12}$ equal weights were used and for $PD_{012}$ the same weights described previously. For each screening, we compare the conventional properties of each zeolite with those of the most similar one in the training set. 