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Q1. Is the $\sigma_\ce{C-H}$ bond a donor in this reaction? If not, then can we take the alternate combination (HOMO of alkene, LUMO of the $\ce{C-H}$ bond and, HOMO of the carbonyl)?

Q2. We can also draw the LUMO of the carbonyl group in the other possible manner(simply flip the shaded lobe on each atom, hence keeping the node). The reaction would then have to go through an antarafacial manner.

Why do we draw the LUMO in this manner?

Reaction leading to menthol

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  • $\begingroup$ Think about the role of ZnBr2: you know it is a Lewis acid. That should give you a hint as to whether the HOMO or the LUMO of the carbonyl component is more important. $\endgroup$ – orthocresol Jan 15 at 12:49
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    $\begingroup$ I'm not sure I fully buy that the "ene" portion here is part of the LUMO... Put it this way, if this were just a π system adding into a carbonyl leaving behind a carbocation, I think we would argue that the π system was part of the HOMO. $\endgroup$ – Zhe Jan 15 at 13:40
  • $\begingroup$ @Zhe, could you elaborate what you're saying? I can't understand it. $\endgroup$ – benzene11 Jan 15 at 13:56
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    $\begingroup$ If an alkene is reacting with a carbonyl, the most reasonable thing to suggest a priori is that the alkene is the nucleophile (HOMO) and the carbonyl is the electrophile (LUMO). $\endgroup$ – Zhe Jan 15 at 14:06
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First of all, a molecule only has one HOMO and LUMO. Don't confuse MOs with localized orbitals from VB theory.

You can basically approximate this mechanism with four MOs:

  • LUMO+1: Mainly $\pi^*_{C=C}$ with contributions from $\sigma^*_{C-H}$
  • LUMO: Mainly $\pi^*_{C=O}$
  • HOMO: Mainly $\pi_{C=C}$ with contributions from $\sigma_{C-H}$
  • HOMO-1: Mainly $p_O$ with contributions from $\sigma$-orbitals on the carbonyl carbon. We can regard this MO as one of the lone pairs of the oxygen.

The corresponding interactions will roughly look like this:

enter image description here

Hence, the HOMO - LUMO interaction explains the C-C bond formation, while the HOMO-1 - LUMO+1 interaction explains C-H bond breaking and O-H bond formation. Both HOMO and LUMO+1 also explain the shift of the double bond.

Now to your question:

  • Q1: Yes, $\sigma_{C-H}$ is part of HOMO, but has a lower contribution compared to $\pi_{C=C}$. So I would mainly call the C=C bond as donor. As you can see $\pi_{C=O}$ is not part of the FMOs, so your proposal makes little sense. It mainly contributes to more stable occupied MOs.
  • Q2: If I understand correctly, you propose an antarafacial [2+2], which is in principle symmetry allowed, but would lead to a very strained transition state with a high barrier. You are free to swap the sings on MOs, but as soon as interact with another MO, you take the one that leads to stabilization of course.

Edit: As reference, I got the FMOs from a HF/6-31G calculation on a slightly simplified system:

enter image description here

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  • $\begingroup$ a molecule only has one HOMO and LUMO That is strictly speaking incorrect. Please do not confuse localised orbitals with orbitals from VBT. Then you carry on arguing with somewhat localised orbitals; delimitations that do not exist in MOT, especially there are no lone pairs in MOT. If you want to put in this interpretation, localise your orbitals. If HOMO and LUMO of the molecule would interact, there would be different HOMO and LUMO. This answer doesn't make much sense. $\endgroup$ – Martin - マーチン Mar 3 at 22:11
  • $\begingroup$ 1) How would you obtain more HOMOs/LUMOs for this molecule? 2) Need to have another look on VBT. I'll get back on that. 3) Aren't the MOs in MOT always constructed from more localized orbitals? I don't see any issue in trying to weight their contributions to get some intuition. 4) Indeed, once you generate the combination of HOMO and LUMO, you get new orbitals of course, but don't you plot the original orbitals in FMO analysis? $\endgroup$ – Kexanone Mar 3 at 22:35

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