= Solution
The <Dewar-Chatt-Duncanson model> has two complementary interactions. \b[The filled <alkene> $\pi$ orbital donates to an empty <metal> orbital, and an occupied <metal> $d_\pi$ orbital back-donates into the empty <alkene> $\pi^*$ orbital.] The <metal> acceptor has the symmetry of the sum of the two ligand lobes facing it; the back-donor has opposite phases at the two <carbon> positions and matches the antisymmetric $\pi^*$ combination.
$$
\pi(\mathrm{C=C})\longrightarrow\mathrm M,\qquad
\mathrm M(d_\pi)\longrightarrow\pi^*(\mathrm{C=C}).
$$
Both channels strengthen <metal>–<alkene> attachment. Donation removes some <electron density> from the internal bonding orbital, while back-donation populates its antibonding partner, so coordination generally reduces C–C bond order. The schematic shows orbital phase signs, not positive and negative electric charges.
\Image[/past-exam-of-the-chemistry-b-course-of-the-university-of-cambridge/2023/paper-2-orbitals.png]
{title=Symmetry-matched alkene donation and backbonding, and the in-plane bonding channel of a coordinated aryne}
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