Ab initio calculations of the energy dependence of Si-O-Si angles in silica and Ge-O-Ge angles in germania crystalline systems

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.