Magic Electron Counts for Networks of Condensed Octahedral Niobium Clusters in Oxoniobates

Chemical bonding in networks of octahedral oxoniobate clusters condensed through vertex-sharing is analyzed at the extended Hückel level of theory. Crystal or molecular orbitals of the condensed cluster networks are derived from the Nb-Nb bonding molecular orbitals of the monomeric Nb(6)O(18) cluster. Extended networks are treated by considering crystal orbitals at special points of the corresponding Brillouin zones. We find that cluster electron counts corresponding to optimal bonding in these networks decrease from 14 for the Nb(6)O(18) cluster to 12 per Nb octahedron for a dimer, 11 for a linear chain of clusters, 10-10(1)/(2) for a square network of clusters, and 7(3)/(4)-8(1)/(2) for cubic NbO in which all cluster vertices are shared. These results are in good agreement with both the counts derived from the experimentally observed structures and a previously devised counting scheme. The loss of Nb-Nb bonding at the shared cluster vertices and the Nb-O-Nb pi antibonding involving Nb atoms of neighboring octahedra are the reasons for the reduction of the magic cluster electron counts in the considered networks. It is proposed that similar counting schemes can be developed for other condensed cluster networks.