= Solution
Write $L=[\mathrm{C_2B_9H_{11}}]^{2-}$ for the open-face <dicarbollide ligand>. The structure consistent with the stated attachment is \b[$[L\mathrm{Mo(CO)_3\rightarrow Mo(CO)_5}]^{2-}$], with a direct Mo–Mo connection, three carbonyls on the cage-capping Mo and five on the outside Mo. The first Mo has an $\eta^5$ interaction with the five-vertex face and completes a 12-vertex <metallacarborane> cage; the second is exo to that cage. The two <tetramethylammonium> ions are counterions.
The unsaturated $\mathrm{Mo(CO)_5}$ fragment is a 16-electron Lewis acceptor; $[L\mathrm{Mo(CO)_3}]^{2-}$ is an 18-electron metal-base fragment in ionic counting, $d^6+6e(L)+6e(3CO)$. Donation from a filled Mo-based orbital supplies the external fragment with a pair. This donor–acceptor representation avoids the mistaken claim that both initially saturated 18-electron fragments simply add a new conventional bond without changing anything.
An alternative formal oxidation-state allocation for a single covalent Mo–Mo bond is cage Mo(I) and external Mo(−I): the local counts are $d^5+6+6+1=18$ and $d^7+10+1=18$. These are electron-bookkeeping alternatives to the metal-base/metal-acid picture, not a measurement of integral site charges. With terminal carbonyls, the external $\mathrm{Mo(CO)_5}$ group can be approximately octahedral when the Mo–Mo direction occupies its sixth coordination direction. The cage-containing unit must accommodate an exo metal interaction in addition to its facial cage/CO environment; its geometry need not be a perfectly undistorted isolated half-sandwich.
\Image[/past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1-carbonyl-dimers.png]
{title=Original donor–acceptor models for the exo Mo and Fe carbonyl fragments attached to cage-bound metal donors}
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