Theoretical studies on doubly and triply linked polymers of Ge9 clusters

Experimental isolation of singly-bonded polymers of Ge₉, Sn₉ clusters and oligomers of doubly linked Ge₉ clusters encouraged us to explore other possibilities of polymerizing Ge₉ units. The electron counts in the reported oligomers are not consistent with simple ideas of localized intercluster bonding; demanding a detailed theoretical analysis. Band structure calculations suggest delocalized bonding with a charge requirement of 2− per Ge₉ unit for all polymeric doubly linked chains. DFT-based geometry optimization of model doubly linked polymers shows that one of the two possible forms is stable and has a band gap of ≈1.0 eV. A detailed bonding analysis of a theoretical model, Rb₄Ge₁₈, shows that the increased inter-polyhedral bond weakens the intra-polyhedral bonding. Ternary fusions are found to be generally unstable - for triple linkages the intrapolyhedral bonding is still further reduced; the polymers appear to be unstable towards dissociation into individual Ge₉ units.