Modeling of self-organization processes in crystal-forming systems: Symmetry and topology code for cluster self-assembly of crystal structures in MT-structures of polyvalent sulfates and phosphates

Abstract

We consider the supramolecular chemistry of polyvalent metal sulfates and phosphates built of M(n+)(O, OH, H2O)6 polyhedral clusters with octahedral O-coordination (M-polyhedra) and SO4 and PO4 polyhedral clusters with tetrahedral O-coordination (T-polyhedra). These compounds form molecular (insular), chain, layered, or framework 3D MT structures by means of directed (bridging) hydrogen bonds O–H…O and/or bridging covalent O-bonds. Combinatorial–topological analysis algorithms are provided to restore, from structure data, the convergent matrix crystal structure self-assembly code. Cluster self-assembly modeling has been performed for the following sulfates: MgSO4 (Pnma and Cmcm), MgSO4 ∙ 1H2O (Kieserite), and CuSO4 ∙ 3H2O (Bonattite) having 3D MT strucutres; MgSO4 ∙ 2H2O (Sanderite), MgSO4 · 2.5H2O, MnSO4 · 3H2O, and MnSO4(OH) · 2H2O having 2D MT structures; MgSO4 · 4H2O (Cranswickite) and MgSO4 · 5H2O (Pentahydrite) having 1D MT structures; and MgSO4 · 4H2O (Starkeyite) having a 0D MT structure, for the following phosphates: (VO)(HPO4) (P-1), MgSO4 · H2O (Kieserite), and CuSO4 · 3H2O (Bonattite) having 3D MT structures; (VO)(HPO4)(H2O)0.5 (P121/c1 and Pmmn), (VO)(HPO4)(H2O)2 (P4/nmm and P121/c1), V(3+)(PO4)(H2O)2 (P121/n1), V(3+)(PO4)(H2O)4 (C12/c1), and Mg(HPO4)(H2O)3 (Newberyite, Pbca) having 2D MT structures; phosphite (VO(H2O)2)(HPO3)(H2O)3 (P41) and phosphate (VO)(HPO4)(H2O)4 (P-1) having 1D MT structures. For all compounds, the symmetry and combinatorial codes of cluster self-assembly code in the form of the following sequence: precursor nanocluster S30 → primary chain S31→ microlayer S32→ microframework S33. At the stage of primary chain S31 formation, in all of MT crystal structures considered, precursor clusters are four-polyhedral MTMT chains, transor cis, and their derivatives with additional O-bonds between polyhedra and ring cluster M2T2 (the result of coiling a cis-chain into a ring). Frequency analysis of topological and symmetry pathways in the formation and evolution of MT-clusters (from primary chain S31 through microlayer S32 to microframework S33) elucidates new crystal-formation trends in diverse chemical systems at the microscopic level.