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It is said that $\ce{(\eta^4-C4H4)Fe(CO)3}$ can undergo electrophilic substitution reactions. Therefore, it displays aromaticity.
For the iron atom, it has $8$ electrons in its outer shell initially and it receives $6$ electrons from three carbonyls. It achieves the stable state of $18e$ after bonding with cyclobutadiene. Therefore, the oxidation state of iron should be zero, and the $\pi$ electrons of cyclobutadiene in the complex is still $4$.
But this result contradicts with Huckel's rule, which states that the $\pi$ electrons should be $4n+2$. Where did I go wrong?

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    $\begingroup$ You imply that during bonding the C4H4 gives its 4 electrons to iron for nothing in return. Now there is a catch: bonding is a game for two. $\endgroup$ – Ivan Neretin Oct 1 at 5:00
  • $\begingroup$ @IvanNeretin One of my professors once said ‘you notice that that, what doesn’t work with humans, namely socialism, works beautifully with electrons.’ $\endgroup$ – Jan Oct 1 at 14:24
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    $\begingroup$ @Jan True, or so it seems. Then again, I never had a chance to discuss that with an electron. $\endgroup$ – Ivan Neretin Oct 1 at 14:29
  • $\begingroup$ @IvanNeretin Exactly, this was what I thought. I have never thought about the delta bond. Now I understand, with the help of the paper, the beautiful game for these two fragments and the exactly same symmetry of MOs. $\endgroup$ – Kemono Chen Oct 2 at 3:07
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In the paper "(Cyclobutadiene)iron Tricarbonyls - A Case of Theory before Experiment", Organometallics 2003, 22, 2-20 https://pubs.acs.org/doi/pdf/10.1021/om020946c, at the page 12 nice explanation of bonding in this compound is provided:

The electronic structure of (cyclobutadiene)iron tricarbonyl has been the subject of many papers. He I and He II low-energy photoelectron spectra provided useful information.77,78 The eight observed bands in the lowenergy PE spectrum of (cyclobutadiene)iron tricarbonyl in the range 7.65-20.31 eV all were assigned.78 The calculations (ab initio SCF MO) showed that there is a net negative charge on the cyclobutadiene ligand that results from π back-bonding from the iron atom into an antibonding MO of the ligand (δ bond). Better agreement between the experimental assignments and theoretical calculations was obtained by Chinn and Hall using generalized MO calculations with configuration interaction.79 A simple textbook approach to the bonding is shown in Figure 8.80 It is assumed that it is triplet state cyclobutadiene that is involved with unpaired electrons in the two degenerate ψ2 and ψ3 molecular orbitals. These interact with two singly occupied iron orbitals, generating two covalent bonds.

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