= Solution
\b[<chromium> is the characteristic assignment, giving Cr(I)–Cr(I) with a formal <quintuple bond>.] Each formamidinate is monoanionic, so $2x-3=-1$ gives $x=+1$. <chromium>(I) is $d^5$ and the pair supplies ten d electrons. Relative to a metal–metal $z$ axis, the idealized bonding combinations are $d_{z^2}$ sigma, $d_{xz},d_{yz}$ pi and $d_{xy},d_{x^2-y^2}$ delta:
$$
\boxed{\sigma^2\pi^4\delta^4,\qquad\mathrm{BO}=\frac{10-0}{2}=5.}
$$
End-on sigma overlap gives the largest splitting, pi overlap a smaller splitting, and delta overlap the weakest. A useful qualitative ordering places bonding sigma lowest, then the two pi combinations, then the two delta combinations; all are occupied. Their antibonding partners are empty, with the weakly split delta-star levels nearest their bonding counterparts. The actual three-bridge ligand field can mix and split symmetry-compatible levels, so the diagram is a bond-axis model rather than five perfectly degenerate metal d levels in the molecular complex.
The identified lantern-type anion has an experimentally determined Cr–Cr distance near $1.740$ Å; reduction of its nine-bonding-electron precursor supplies the tenth <electron>. This corroborates the model more specifically than citing “short bonds” in an unrelated framework.<Remarkably Short Metal-Metal Bonds: A Lantern-Type Quintuply Bonded Dichromium(I) Complex by Yi-Chou Tsai and others>[2008, abstract and structural/orbital discussion: reduced anion and 1.7397(9) Å contact]{ref}
\Image[/past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1-quintuple-orbitals.png]
{title=Original idealized d-orbital combinations and ten-electron occupancy for a sigma-two-pi-two-delta quintuple bond}
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