= Solution
A <carbonyl ligand> binds through <carbon>, whose occupied $5\sigma$ <molecular orbital> has a substantial outward-facing <carbon> lobe. Overlap with an empty metal orbital along the M–C axis gives ligand-to-metal <sigma donation>. Conversely, an occupied metal $d_\pi$ orbital overlaps sideways with an empty CO $2\pi^*$ <antibonding molecular orbital>, giving metal-to-ligand <pi backbonding>. There are two mutually perpendicular pi channels. The original orbital schematic below shows one of them; $+$ and $-$ denote orbital phase, not <electric charge>.
\Image[/past-exam-of-the-chemistry-b-course-of-the-university-of-cambridge/2025/paper-2-orbitals.png]
{title=Carbonyl sigma donation and one pi-backbonding channel}
The interactions are synergic: donation makes <electron> density available at the metal, and backbonding helps accommodate it while strengthening the metal–<carbon> interaction. Occupying CO $\pi^*$ reduces the C–O <bond order>, lengthens that bond and lowers its <bond force constant>. Therefore stronger <pi backbonding> generally lowers the carbonyl stretching <spectroscopic wavenumber> even while strengthening the M–C attachment.
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