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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would be affected (i) if electrons were donated into the LUMO (e.g., from a metal centre); (ii) if electrons were withdrawn from the HOMO (e.g., by a metal centre).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 :)

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    $\begingroup$ I love symmetry and I can probably help you. Just to check how much you understood though, can you show a molecular orbital diagram of how you derived the HOMO and LUMO of CO? If you don't know how to do that, I will have to make my answer a lot longer... $\endgroup$
    – selkie222
    Apr 5 '16 at 15:27

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