I recently stumbled upon a question asking how iron destabilizes the bonds in a nitrogen molecule. I have searched the web and my textbook for quite a while now and I cannot find a satisfactory answer. The only explanation I could muster was that the d-orbitals of the Iron atom interact with the HOMO and LUMO of the nitrogen molecule, due to the overlap of the molecular orbitals with d-orbitals. I am not sure if this makes sense. I'd really appreciate any answer or advice!
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You are on the right track with your answer.
Notice that the LUMO is a $\pi^*$ orbital, meaning that filling it with electrons would weaken the bonding. When nitrogen and iron interact, electrons from the d-orbitals on iron are well aligned, in terms of symmetry and energy, to fill into $\ce{N_2}$'s $\pi^*$ orbital. This forms a bond between $\ce{Fe}$ and $\ce{N_2}$, but at the cost of weakening the bond between the nitrogens. This is a very important concept in inorganic chemistry referred to as Pi Backbonding.
The classic example given of a ligand that exhibits $\pi$ backbonding in metal complexes is $\ce{CO}$, which is isoelectronic to $\ce{N_2}$ and has the same molecular orbital diagram (though the orbitals themselves look different due to the asymmetry of $\ce{CO}$).
