Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2021 / Paper 1 / 3

A triangular prism has exactly the required nine metal–metal edges: six edges around two triangular faces and three edges joining corresponding vertices of those faces. It naturally offers two symmetry-distinct edge families, of sizes six and three.

With twelve $\mathrm{C}{\mathrm{l}}^{-}$ ligands, neutral $\mathrm{R}{\mathrm{e}}_6\mathrm{C}{\mathrm{l}}_{12}$ has total rhenium oxidation number $+12$, hence six formally Re(II), $d^5$ centres. After treating the Re–Cl interactions as ligand bonds, the available metal $d$ electrons areTwo localized bond order assignments use those fifteen pairs:In scheme I the three inter-triangle edges should be shorter; in scheme II the six triangle edges should be shorter. Both give each Re five electrons' worth of metal–metal bond-order contributions: two singles plus a triple, or two doubles plus a single. The electron count permits both schemes; identifying which family is shorter distinguishes them at this level. Actual cluster molecular orbitals are delocalized, so these integer bond orders summarize bonding rather than asserting isolated textbook multiple bonds on every edge.