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Why can carbon monoxide act as both a Lewis base and a Lewis acid in metal carbonyls?

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periodic table with group numbers and the s, p, d, and f blocks — organometallic compound The periodic table of the elements, displaying the group numbers and the s, p, d, and f blocks. Elements in the shaded area are the metals of organometallic chemistry.

In metal carbonyls, the carbon monoxide (CO) ligand acts as both a Lewis base and a Lewis acid due to its unique electronic structure, which facilitates a process known as synergic bonding.12

Lewis Base Behavior: The highest occupied molecular orbital (HOMO) of the CO molecule is largely localized on the carbon atom and contains a lone pair of electrons with $σ$ symmetry. CO acts as a Lewis base by donating this lone pair into an empty orbital on the metal atom, forming a $σ$ bond.12
Lewis Acid Behavior: The lowest unfilled molecular orbital (LUMO) of the CO molecule has $π$ symmetry. This orbital can accept electron density from filled metal $d$ orbitals, a process known as $π$ backbonding. By accepting these electrons, the CO ligand functions as a Lewis acid.12

This two-way exchange of electrons stabilizes the metal-carbon bond and is fundamental to the structure and stability of these organometallic compounds.12