Zeolites, a class of crystalline microporous silicate-based materials, have been widely used as adsorbents and catalysts due to their uniform pore sizes, catalytic activities, and hydrothermal stability. Crystal structures of zeolites are built from the TO4 tetrahedra (where T is Si, Al, B, Ga, etc.), resulting in more than 230 unique framework structures. The structure and the chemical composition of zeolites are two important factors for design of zeolite. Based on the empirical knowledge of zeolite synthesis, these two factors are known to be dependent on each other; however, their actual relationship has remained unclear due to the unclarified crystallization mechanism of zeolites. We recently rationalized this structure-composition relationship by performing in silico analysis of aluminosilicate zeolites with almost all known zeolite structures and different Si/Al molar ratios . The resulting energy-density landscape of modelled zeolites revealed that the relation between the relative framework energies versus the chemical compositions varies in accordance with the framework topologies. Extension of this approach to other trivalent atoms such as B and Ga is, however, not straightforward due to a lack of reasonable way to offset the energies of zeolites with different trivalent atoms.
Here, we analyze borosilicate, aluminosilicate and gallosilicate zeolites by utilizing a purely structural descriptor developed by Zimmerman et al., namely a tetrahedral ordering parameter, which can evaluate the distortion of TO4 tetrahedra effectively . Analysis of the ordering parameter of structurally optimized zeolites with uniform background charge reveals that B, Al, and Ga distort TO4 tetrahedra themselves as well as the neighboring SiO4 tetrahedra. Furthermore, this general behavior is inherent in the substituting trivalent atoms. The distortion caused by Al is relatively small because Al-O bond length (~1.72 Ang.) is relatively similar to Si-O (~1.61 Ang). Compared to Al, introduction of B in silicate zeolite framework causes larger overall structural distortion that seems to be mainly taken over by the distortion of surrounding SiO4 due to the lack of flexibility of BO4. Borosilicate zeolites with relatively low Si content (e.g., Si/B < 3) are structurally unfavorable judging from their very low ordering parameter, while aluminosilicates and gallosilicates give reasonably high values at the same composition. The structural distortion induced by Ga seems to be mainly undertaken by GaO4 itself, thereby minimizing the distortion of surrounding SiO4.
Such different characteristics observed in trivalent atoms seemingly control their structure-directing functions to crystallization of zeolites and explain the empirical knowledge of zeolite synthesis such as;
 K. Muraoka, W. Chaikittisilp, and T. Okubo, J. Am. Chem. Soc., 2016, 138 (19), 6184-6193.  N. E. R. Zimmermann, B. Vorselaars, D. Quigley, and B. Peters, J. Am. Chem. Soc., 2015, 137 (41), 13352-13361.