= Solution
The <carbon> end of a <carbonyl ligand> has a filled $5\sigma$ <molecular orbital> with an outward-facing lobe. Its overlap with a vacant <metal> orbital of the same axial symmetry gives CO-to-<metal> <sigma donation>. Occupied <metal> $d_\pi$ orbitals can simultaneously overlap with the empty CO $2\pi^*$ <antibonding molecular orbitals>, giving <metal>-to-CO <pi backbonding>. Two perpendicular pi channels are possible; the schematic represents one. Orbital signs indicate phase, not <electric charge>.
\Image[/past-exam-of-the-chemistry-b-course-of-the-university-of-cambridge/2024/paper-2-bonding.png]
{title=Complementary donation and backbonding in carbonyl and alkene coordination}
The two interactions reinforce one another: <sigma donation> transfers density toward the <metal>, and <pi backbonding> distributes it into the ligand acceptor orbitals. \b[Both strengthen M–C attachment, while backbonding weakens C–O.] Occupation of CO $\pi^*$ decreases the internal C–O <bond order>, generally increasing its <bond length> and lowering its stretching <spectroscopic wavenumber>. This is why a strongly backbonded <carbonyl ligand> can have a strong <metal>–<carbon> bond and a weakened internal <carbon>–<oxygen> bond at the same time.
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