We explore the flexibility windows of the 194 presently-known zeolite frameworks. The flexibility window represents a range of densities within which an ideal zeolite framework is stress-free. Here, we consider the ideal zeolite to be an assembly of rigid corner-sharing perfect tetrahedra. The corner linkages between tetrahedra are hard-sphere oxygen atoms, which are presumed to act as freely-rotating, force-free, spherical joints. All other inter-tetrahedral forces, such as coulomb interactions, are ignored. Thus, the flexibility window represents the null-space of the kinematic matrix that governs the allowable internal motions of the ideal zeolite framework. We show that almost all of the known aluminosilicate or aluminophosphate zeolites exhibit a flexibility window. Consequently, the presence of flexibility in a hypothetical framework topology promises to be a valuable indicator of synthetic feasibility. We describe computational methods for exploring the flexibility window, and discuss some of the exceptions to this flexibility rule.

The online database at contains over two million unique hypothetical zeolite structures. By a simple flexibility calculation, we have been able to identify a subset of 5824 flexible structures that exhibit characteristics for synthetic feasibility as zeolites. 78 out of 97 officially approved zeolite framework types that occur in the database are included in this flexible subset, including many that have been synthesized only in mixed and nonsilicate compositions. This suggests that framework flexibility (a geometric property) provides an effective filtering criterion for identifying realizable zeolite frameworks, independent of an accurately computed framework energy. We present statistics on internal surface area, occupiable volume, diameters of maximum included spheres, and maximum free spheres for the flexible subset and compare with the values for the approved framework types.

By treating idealized zeolite frameworks as periodic mechanical trusses, we show that the number of flexible folding mechanisms in zeolite frameworks is strongly peaked at the minimum density end of their flexibility window. 25 of the 197 known zeolite frameworks exhibit an extensive flexibility, where the number of unique mechanisms increases linearly with the volume when long wavelength mechanisms are included. Extensively flexible frameworks therefore have a maximum in configurational entropy, as large crystals, at their lowest density. Most real zeolites do not exhibit extensive flexibility, suggesting that surface and edge mechanisms are important, likely during the nucleation and growth stage. The prevalence of flexibility in real zeolites suggests that, in addition to low framework energy, it is an important criterion when searching large databases of hypothetical zeolites for potentially useful realizable structures.

Cristobalite is the only corner-sharing tetrahedral framework that can maintain perfectly regular SiO4 tetrahedra throughout the entire 180° range of Si–O–Si angles. It is, thus, the ideal system for a study of the energy dependence of the Si–O–Si angle in a crystalline framework. Using the VASP first principles density functional code, we have derived energy versus Si–O–Si angle curves for pure silica and versus Ge–O–Ge angles for pure germania models of cristobalite. In addition, the frameworks of quartz, tridymite, and the zeolites sodalite (SOD) and metavariscite (BCT) were studied. The range of angles with low energies is larger for silica, though the lowest-energy Ge–O–Ge angle is always lower than the corresponding lowest-energy Si–O–Si angle in the same framework type. We discuss which framework types are possible for pure-silica and pure-germania based on a rigid tetrahedron model.