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

摘要

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-HaEuro broken vertical bar 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 a (TM) 1H(2)O (Kieserite), and CuSO4 a (TM) 3H2O (Bonattite) having 3D MT strucutres; MgSO4 a (TM) 2H(2)O (Sanderite), MgSO4 center dot 2.5H(2)O, MnSO4 center dot 3H(2)O, and MnSO4(OH) center dot 2H(2)O having 2D MT structures; MgSO4 center dot 4H(2)O (Cranswickite) and MgSO4 center dot 5H(2)O (Pentahydrite) having 1D MT structures; and MgSO4 center dot 4H(2)O (Starkeyite) having a 0D MT structure, for the following phosphates: (VO)(HPO4) (P-1), MgSO4 center dot H2O (Kieserite), and CuSO4 center dot 3H(2)O (Bonattite) having 3D MT structures; (VO)(HPO4)(H2O)(0.5) (P121/c1 and Pmmn), (VO)(HPO4)(H2O)(2) (P4mm and P121/c1), V(3+)(PO4)(H2O)(2) (P1211), 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) (P4(1)) 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 S (3) (0) -> primary chain S (3) (1) -> microlayer S (3) (2) -> microframework S (3) (3) . At the stage of primary chain S (3) (1) 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 S (3) (1) through microlayer S (3) (2) to microframework S (3) (3) ) elucidates new crystal-formation trends in diverse chemical systems at the microscopic level.