Explain the bonding in metal carbonyls.

(N/A) The $M-C$ bond in metal carbonyls possesses both $\sigma$ and $\pi$ character.
$1$. The $M-C$ $\sigma$-bond is formed by the donation of a lone pair of electrons from the carbonyl carbon into a vacant orbital of the metal.
$2$. The $M-C$ $\pi$-bond is formed by the donation of a pair of electrons from a filled $d$-orbital of the metal into the vacant antibonding $\pi^*$ orbital of carbon monoxide. This is also known as back-bonding.