Analysis of metal carbonyl bonding in Fe(CO)5 using molecular orbitals

I am really struggling with this question we have been set in class:


Metal-carbonyl bonding: Conceptionally, one can build up $\ce{[Fe(CO)5]}$ from the $\ce{Fe(CO)4}$ fragment plus free $\ce{CO}$ in order to analyse the bonding between the two moieties. Consider first the HOMO and LUMO of free $\ce{CO}$: Describe both MOs with respect to their $\ce{C-O}$ bonding character (bonding/anti-bonding). Note the type of bond that would be formed if $\ce{CO}$ bonded to another moiety through the HOMO and LUMO respectively.


Predict how the $\ce{C-O}$ bond itself would be affected
(i) if electrons were donated into the LUMO (e.g., from a metal centre);
(ii) if electrons were withdrawn from the HOMO (e.g., by a metal centre).


Next consider the $\ce{Fe(CO)4}$ complex fragment: Does its LUMO possess significant amplitude at the location where the additional $\ce{CO}$ will bind? Does the LUMO’S shape and symmetry (by visual inspection) match the symmetry of the HOMO of $\ce{CO}$? Conversely, does the HOMO of the complex fragment match the LUMO of $\ce{CO}$?


Based on these considerations, describe the bonding and orbital interactions between the $\ce{Fe(CO)4}$ fragment and $\ce{CO}$. Predict how binding to the metal centre would affect the structure and vibrational frequency of $\ce{CO}$.


Compare your prediction with the structural and vibrational data obtained for $\ce{CO}$. $\ce{[Fe(CO)5]}$ and $\ce{[Fe(CO)4]^{2-}}$and rationalise the observed trends.


I know that the HOMO of $\ce{CO}$ is 3σ which is primarily carbon in character and the LUMO is $2π^\*$ which is also more carbon in character.


Symmetry is one of my worst topics so if someone could give me a hand on this and could even suggest some further reading material it would be awesome :)


