Ab Initio Calculations of the Energy Dependence of Si–O–Si Angles in Silica and Ge–O–Ge Angles in Germania Crystalline Systems

Abstract

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.

Critical Role of Dynamic Flexibility in Ge‐Containing Zeolites: Impact on Diffusion

“…This is due to the smaller T‐O‐T angles in the presence of Ge, which allows absorbing the distortions “locally”, without large distortions beyond the GeO 4 tetrahedra, as shown in Figure . This is in line with the calculated energy dependences on T‐O‐T angles (T=Si or Ge) in cristobalite and zeolites, which show that angles having Ge atoms can be much lower than the analogous Si‐O‐Si at very low energetic cost …”

Preferential Location of Germanium in the UTL and IPC-2a Zeolites

“…The labeling of the unique T atom positions in Figure 1 is the same as that used by the International Zeolite Association (IZA). 35 36 have recently used periodic DFT calculations to study the dependence of the total energy on T− O−T angles for several silica and germania zeolites. They found that the broad minimum for Si−O−Si angles is centered around 146°while the minimum for germania zeolites is centered around 128°, results that are consistent with the data presented in Figure 4.…”

Synthesis and Post‐Synthesis Transformation of Germanosilicate Zeolites

“…[33] In ar ecent computational investigation, the stability ranges for Si-O-Si and Ge-O-Ge angles in pure silica and pure germania cristobalite were calculated based on aD FT analysis employing aperiodic model. [34] The stability range of Si-O-Si angel ranged from 1378 8 to 1808 8, while angles between 1208 8 and 1378 8 were preferred for Ge-O-Ge.Overall, this knowledge helps us to understand why some zeolite frameworks can be obtained in pure silica form, while pure silica forms have not been synthesized for other frameworks.…”