Polyoxometalates: A Class of Compounds with Remarkable Topology

Abstract

Structures of polyoxometalates frequently are discovered to be based upon regular convex polyhedra, including the Platonic and Archimedean solids. A topological approach involving barycentric subdivision of the faces of such polyhedra, leads to their description as combinations of triangular building blocks assembled according to systematic rules. An analysis of the Keggin structure of [Mo₁₂O₃₆(PO₄)]^3-, is presented. As it turns out, it is the only spherical polyhedral structure of T symmetry built up from six 8-gons and eight 6-gons. Similarly, there is only one spherical polyhedral structure of T symmetry built up from eight 6-gons and twenty-four 4-gons satisfying also some obvious chemical combinatorial constraints. Such a structure is observed for [H₉V₁₈O₄₂(VO₄)]^6-. Analysis of possible structures of lower symmetry (D₃, D₄), e.g. as observed for [V₁₅O₃₆(Hal)]^6- and [H₄V₁₈O₄₂(Hal)]^9-, reveals the onset of combinatorial explosion. For example, there are 67 D₃-structures satisfying the chemical condition.

Why and how does Nature assemble simple units, MO_n(M = V, Mo, W; n = 4, 5, 6), into an extreme variety of structures, including those corresponding to the regular (Platonic) polyhedra?

To whom correspondence should be addressed.

Supported by the Deutsche Forschungsgemeinschaft and the Fonds der chemischen Industrie.