Flexibility of ideal zeolite frameworks

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.