= Solution
Use neutral <electron counting> consistently: each terminal Cp supplies five <electrons>, while the eight pi <electrons> of neutral <pentalene> must be allocated across the shared fused framework rather than counted twice as two independent Cp <coordination ligands>. One set of \b[18-electron-consistent proposals] is:
* \b[Iron: syn $\mu$-$\eta^5:\eta^5$ <pentalene> with an Fe–Fe <single bond>.] The two iron–Cp fragments lie on the same face. Assigning four <pentalene> <electrons> to each iron gives $8+5+4=17$ before direct bonding; the Fe–Fe bond contributes one <electron> to each count, giving 18. Its direct bond naturally accounts for the especially short <metal>–<metal> separation. An anti arrangement cannot retain this short same-face bond.
* \b[Cobalt: $\mu$-$\eta^5:\eta^5$ <pentalene> without a Co–Co bond.] The count is $9+5+4=18$ at each <metal>. Syn and anti arrangements are possible at this formal level because there is no required direct bond. Removal of the bond relative to iron accounts for a larger separation.
* \b[Nickel: slipped $\mu$-$\eta^3:\eta^3$ coordination to the two outer allylic portions.] The fusion bond remains an uncoordinated <alkene> in this limiting bonding picture, while each outer three-carbon portion contributes three <electrons> in neutral counting: $10+5+3=18$. Equivalent ionic counting gives a nickel(II) $d^8$ centre, a six-electron Cp and a four-electron <allyl ligand>. Moving the <metal> binding sites toward the outer three-carbon portions increases the separation further. Syn and anti arrangements can again be drawn.
The original schematic shows the donor regions and the required iron–iron bond; dashed metal-to-region lines denote delocalized coordination rather than localized <carbon>–<metal> <single bonds>.
\Image[/past-exam-of-the-chemistry-b-course-of-the-university-of-cambridge/2021/paper-2-pentalene-models.png]
{title=Formal 18-electron models for the fused pentalene complexes}
These proposals explain the requested <electron> counts and distance ordering. \b[<electron counting> alone does not establish the unique ground-state structure]: orbital calculations on related <pentalene> complexes also identify stable formally electron-deficient arrangements. In particular, the formal requirement of a <metal>–<metal> bond in the proposed 18-electron iron model should not be converted into a claim that every known iron <pentalene> complex adopts that model.<The Versatility of Pentalene Coordination to Transition Metals: A Density Functional Theory Investigation by S. Bendjaballah and others>[Discussion of syn/anti coordination, hapticity and electron-count exceptions]{ref}
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