Question

How do the CO stretching frequencies of a bridging carbonly ligand depend on the number of metal centers bridged by the CO ligand?

Answer 1

CO is a L-type ligand. It bonds to the metal center via two ways.

First, it donates the electron pair on C to the metal (sigma bonding)

Second, now since the metal has become electron rich it tries to balance its d-orbital by donating electeon density to the $\pi$ ^{* orbital of C. This is known as back-bonding.}

The CO can bridge 2,3 or 4 metal atoms at a time. Thus, the more the metal centers the more will be the back bonding. Due to this the bond order of C-O will decrease resulting in a decrease in stretching frequency!