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While learning about ferrocene I've come across this molecular orbital diagram. MO Diagram of Ferrocene What particularly confused me is the nature of the a'1g orbital. My professor taught that a'1g and e2g are considered HOMO bonding orbitals, but this MO diagram clearly shows the a'1g as an MO with antibonding character.

To make sure it wasn't just a bad MO diagram, I looked for other MO diagrams, but they consistently display a'1g as a higher energy orbital compared to Iron's $3dz^2$ orbital.[a][b] So, slight anti-bonding character, right?

The problem is, looking at bond-length comparison, the a'1g orbital is slightly bonding. The Fe-Cp distance for ferrocene is 1.66 Å; for ferrocenium, it's 1.68 Å.[c] Given that the removal of an electron from the HOMO a'1g orbital resulted in the lengthening of Fe-Cp distance, it should have bonding character.

So what is going on here? Why is there this discrepancy? How are these orbitals actually interacting with each other?

[a]http://alpha.chem.umb.edu/chemistry/ch612/documents/ConstructingpiMOdiagramssandwichcomplexes.pdf

[b]https://doi.org/10.1021/ja00744a011

[c]https://doi.org/10.1107/S0108270189005883

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    $\begingroup$ HOMO stands for highest occupied molecular orbital. Of the nine occupied MOs in that diagram, the one that is highest in energy is a'1g. Your assumption that the HOMO cannot be antibonding is not correct. $\endgroup$ – Zhe Jan 16 at 20:08
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    $\begingroup$ @Zhe I understand that. My question is about the seeming discrepancy between its position on the MO diagram (showing antibonding character) and physical analyses (Fe-Cp distance comparison showing bonding character). $\endgroup$ – Anson Jan 17 at 3:03
  • $\begingroup$ But ferrocenium is charged. What's more important in determining structure, changes in electronic structure or charge/charge repulsion? $\endgroup$ – Zhe Jan 17 at 16:54
  • $\begingroup$ @Zhe If anything, I would think ferrocenium should have greater coulombic attraction with the negatively-charged cyclopentadienyl ligands and result in shorter bond lengths. Is that wrong? $\endgroup$ – Anson Jan 17 at 18:42
  • $\begingroup$ My intuition says it's more complicated than that. You're assuming that even in the complex, the Cp's are strongly charged negative and the positive is more localized to the Fe center, and I'm not convinced that that's the case. $\endgroup$ – Zhe Jan 17 at 20:03
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I've recently done an NBO calculation on the staggered conformation of the ferrocene molecule, using the 3-21G basis set, using the embedded Gaussian engine on the free version of the WebMO application.

This calculation is easily reproducible, so I am not going to post the exact details here- the important conculsion from the calculation is that there are three nearly fully occupied "lone pair"s of bonding character (denoted as LP) and six partially occupied "lone pair"s of antibonding character (denoted as LP*) on the central iron atom. Three filled lone pairs correspond to six electrons, exactly what iron(II) should have.

Therefore, the a1g lone pair is likely not of antibonding character.

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    $\begingroup$ Is there a particular reason why you chose to make this post community wiki? Usually these are for large-scale community efforts such as compilations. Normal posts can already be edited by all, just like a community wiki, but will retain attribution to the original author i.e. you. Some figures would also be useful. $\endgroup$ – orthocresol Jun 7 at 11:56
  • $\begingroup$ I posted this on community wiki because, as a chemistry beginner, felt that intuitive, VB-based models of coordination complexes should be more known to chemistry beginners (for the sake of simplicity and interlectual digestibility)) before they venture into the more accurate MO-based models. $\endgroup$ – Just Some Nerdy Teen Jun 7 at 11:59
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    $\begingroup$ Community wiki isn't to do with the level of the post or the target audience; actually the content of the post has no bearing on whether it should be CW or not, they're orthogonal to each other. CW is a marker to indicate that an answer is meant to be a collaborative effort between multiple people. $\endgroup$ – orthocresol Jun 7 at 12:01
  • $\begingroup$ I'm going to convert all your answers back to regular answers as opposed to community wiki answers. There's no apparent reason why any of this needs to be CW; if you genuinely think it should be a collaborative effort, then make it clearer as to what aspects of it you want people to contribute to. $\endgroup$ – orthocresol Jun 7 at 13:40
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    $\begingroup$ Can you elaborate your answer please? You say the calculation is easily reporducible, but not everyone is a computational chemist (not to mention that not even all computational chemists deal with QM calculations) so it would be good if you could explain the energy levels and your data briefly here. $\endgroup$ – S R Maiti Jun 7 at 17:42

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