A geometric solution to the largest-free-sphere problem in zeolite frameworks

We have applied Delaunay triangulation to models of the known zeolite frameworks. We show that this well-established technique from computational geometry provides for each framework; (i) the location and shape of the open pores and channels, (ii) the diameter of the largest possible included sphere, and indirectly (iii) the diameter of the largest-free-sphere that can diffuse through the framework by at least one lattice translation. Since Delaunay triangulation naturally locates the empty spaces within a set of points, it provides a powerful computer-automated tool for determining the physical characteristics of pores and channels of zeolite frameworks. Such tools will further enhance the usefulness of large databases of hypothetical framework materials.Here, we tabulate results for the 165 zeolite frameworks that are presently listed in the Atlas of Zeolite Frameworks. Of the known zeolites, refined as pure silicates, the largest included sphere occurs in the TSC framework, with a diameter of 16.39 Å. The largest-free-sphere has a diameter of 11.33 Å, for diffusion along the [0 0 1] direction in the VFI framework.