Modeling of self-organization processes in crystal-forming systems: Symmetry and topology code for cluster self-assembly of crystal structures for molecular and framework compounds

This is a review over the state of art in self-organization in crystal-forming systems, where a longrange order appears spontaneously in the arrangement of nanoscale building units of any nature (atomic clusters and molecules), which initially existed in a dynamic state as a chaotic mixture. The focus is on bimolecular compounds where building units are M-octahedra M(O, OH, H2O) and T-tetrahedra T(O, OH)4 bonded by OH–O hydrogen bonds and/or bridging oxygen atoms O. The combinatorial–topological modeling of 1D and 2D packings of suprapolyhedral clusters (MT)n has been carried out. These packings are symmetrically and topologically conceivable types of molecular MT clusters S03, from which chains S13 and 2D microlayers S23 are formed. The theoretically derived model MT-clusters (MT)n are compared with known types of precursor clusters in the molecular and framework MT-structures of polyvalent metal sulfates and their analogues. Combinatorial–topological analysis algorithms are provided to restore, from structure data, the convergent matrix crystal structure self-assembly code in the form of the sequence of significant elementary events. Crystal structure modeling involves combinatorial–topological analysis methods, whose underlying idea is the recogniition of packing-forming precursor nanoclusters and the construction of the relevant basal 2D and 3D networks in the form of graphs where nodes correspond to the positions of their centroids. The model is universal and has first been used to model the cluster self-assembly of molecular MT structures for V(2+)(H2O)4(SO4) (V-Rozenite), V(4+)O(H2O)5(SO4)(H2O) (SYN1), V(4+)O(H2O)5(SO4) (Orthominasragrite, Minasragrite, Anorthominasragrite), V(4+)O(H2O)3(SO4) (Bobjonesite); framework MT structures V(4+)O(SO4)(H2(SO4) (SYN2), V(4+)O(SO4) (Pauflerite and SYN3), V(4+)2O3(SO4)2 (SYN4), V(4+)2O3(SeO4)2 (SYN5), Fe(3+)2(SO4)3 (LIPHOS), and Fe(3+)2(SO4)3 (NASICON); and for templated framework MT structures (NH4)2[Ga2(PO4)2F2] (KTP), (NH4)2[Ga2(PO4)2(HF)F2] (p-KTP), TlMo2(PO4)3 (SYN06), and K2Mg2(SO4)3 (Langbeinite). Frequency analysis of topological and symmetry pathways in the formation and evolution of clusters (from primary chain S13 through microlayer S23 to microframework S33) elucidates new crystal-formation trends in diverse chemical systems at the microscopic level.