of all materials. This allows us to use the TDA approach to analyze the geometric diversity of the top-performing structures, and to visualize the topography of the zeolite library by generating the mapper plot[@car091; @lum131] shown in Figure \[mapper\], encoding the topological structure of the set of the best 1% performing zeolites with respect to methane storage.

The shape of the diagram shows seven topologically different classes of top-performing materials. For example, group C consists of materials that have one-dimensional small cylinders, while group E has two-dimensional channels (see Table \[Groups\] for all different groups). The color coding of the mapper plot nicely illustrates that materials in classes of different pore shapes have very different optimal heats of adsorption.

In this article we have developed a topology-based methodology to quantify similarity of the chemical environment of adsorbed molecules, focusing on applications in which the pores play a passive role in providing adsorption sites. For applications in which the pores play a more active role, such as catalysis, a logical step would be to extend the methodology to include chemical specificity and charge distribution. From a topology viewpoint this application is of particular significance because it is one of the first 