pore regions. Technically, this makes the descriptor an overall descriptor of the geometry of the embedding of the pore-surface in the ambient space and not strictly describing the pore surface with respect to the pore space only. Fortunately, the technique does not tend to misidentify structures since the material part is typically much larger than the pore part. However, our maximal filtration parameter is not sufficiently large for all homology classes to die – these correspond to essential intervals in the barcodes – especially for zeolites having large pores. Therefore, to take account of these homology classes in computing distances between two barcodes, a maximal value for the death time has to be assigned, which is especially important in dimension 2 because of the small cardinality of barcodes. For 2-dimensional barcodes, we assign a death times to essential intervals based on the relation between the diameter $D_{i}$ of the largest included sphere and the death time for small and medium pores which is linearly fitted. An example for zeolites with methane is shown in Figure \[PH2\_CH4\]. The 1-dimensional barcodes contain sufficiently many intervals to distinguish different structures and we discard essential intervals.

-2cm ![\[PH2\_CH4\] Correlation of the death time of 