Find the weakest $\ce{C=O}$ bond among $\ce{[Mn(CO)6]+},$ $\ce{Fe[(CO)5]},$ $\ce{[Cr(CO)6]}$ and $\ce{[V(CO)6]-}.$
I thought the $\ce{C=O}$ bond strength would be lowest in $\ce{[V(CO)6]-}$ since the negative charge meant that vanadium had an excess of electrons, hence the metal-carbon back-bonding would be the strongest. As the result, the $\ce{C=O}$ bond order would be the least.
However, the answer given states that iron in $\ce{Fe[(CO)5]}$ has a $\mathrm{3d^8}$ configuration, which means four electron pairs for back-bonding as compared to $\mathrm{3d^6}$ in $\ce{V-},$ hence it would have a greater degree of back-bonding and thus its carbonyl bonding would be the weakest.
Is this correct or does $\ce{[V(CO)6]-}$ have the strongest metal-carbon synergistic bond? If the former is correct, then does a synergistic bond depend on the number of lone pairs first and a negative charge is only considered if the number of lone pairs is the same?