Modeling of the self-organization processes in crystal-forming systems: Symmetry and topological code of cluster self-assembly of molecular (island) and framework MT structures of vanadyl sulfates

Abstract

The supramolecular chemistry of vanadyl sulfates, consisting of polyhedral clusters V(O, OH, H2O)6 with octahedral O coordination (M polyhedra) and SO4 tetrahedra (T polyhedra) and forming molecular (island) and framework 3D MT structures, is considered. Algorithms of combinatorial and topological analysis are developed that make it possible to reconstruct (based on known structural data) the symmetry and topological code of the matrix convergent self-assembly of crystal structure. Cluster modeling of the selfassembly of molecular (island) MT structures of the V2O2(H2O)6(SO4)2 · 4H2O (anorthominasragrite (ANM)) and V2O2(H2O)6(SO4)2 (bobjonesite (BBN)) compositions and topologically different framework 3D MT structures with covalent bonds, V2O2(SO4)2 (pauflerite (PAF) and synthetic phase (SYN)), is performed. A 3D reconstruction of the self-assembly mechanism in the form nanocluster precursor S 0 3 → primary chain → S 1 3 microlayer S 2 3 → microframework S 3 3 has revealed an invariant type of cyclic cluster precursor M2T2 (with a symmetry \(g = \overline 1 \)) for all compounds; differences in the self-assembly mechanisms are found for ANM and BBN in the stage of formation of primary chain S 1 3 and for PAF and SYN in the stage of formation of microlayer S 2 3. Basic 2D and 3D nets are presented in the form of graphs, the sites of which correspond to the positions of centroids of cluster precursors M2T2. The same topological type of basic 2D nets (4.4.4.4) is ascertained for all compounds. A basic 3D net corresponding to a simple cubic structure of Po (coordination number (CN) = 6) is established for ANM, SYN, and PAF; the basic 3D net for BBN corresponds to the cubic F structure of Cu (CN = 12).