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I know that the HOMO, LUMO, and its gap are useful in understanding the physical properties and chemical reactions of molecules.

Here, are there any phenomena in physics or chemistry that other orbitals are very important than the HOMO and LUMO?

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    $\begingroup$ A trivial example: suppose the HOMO of a molecule is localized on a functional group that is sterically hindered, but the HOMO-1 is well-exposed to external reactants. Then the HOMO-1 will probably substitute the role of HOMO in determining the regioselectivity. $\endgroup$
    – wzkchem5
    Oct 22, 2022 at 15:01
  • $\begingroup$ Thank you for the quick comment! I see. Does such example occur frequently (e.g., in a chemical reaction)? Actually, I consider the machine learning problem setting that the HOMO and LUMO are the input descriptor and an activity (e.g., of catalysis) is the output prediction. In such case, I believe that the input descriptor need to be rich, that is, it is better to consider the orbitals other than the HOMO and LUMO? $\endgroup$
    – neco
    Oct 23, 2022 at 2:10
  • $\begingroup$ As far as I know, this does not happen frequently in textbooks, but is extremely common in real life (where molecules are larger and sterically hindered groups are much more common). There are even a lot of cases where the HOMO/LUMO do not correlate with the reaction site even though no steric effects are present, for example the basic hydrolysis of methyl p-nitrobenzoate, whose LUMO is localized near the nitro group but of course the reaction happens on the ester group instead. $\endgroup$
    – wzkchem5
    Oct 23, 2022 at 8:27
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    $\begingroup$ And yes, the combined importance of all orbitals below HOMO and all orbitals above LUMO may well be much greater than that of HOMO and LUMO alone. $\endgroup$
    – wzkchem5
    Oct 23, 2022 at 8:44
  • $\begingroup$ Thank you for the detailed example. I also found your answer to a similar question (mattermodeling.stackexchange.com/questions/7150/…) and this is very helpful. I try to read and understand it. $\endgroup$
    – neco
    Oct 23, 2022 at 11:27

1 Answer 1

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The lower occupied orbitals are immensely important for all of chemistry and physics - especially physical properties and chemical reactions - because of Pauli repulsion. If the orbitals were not occupied, chemistry and physics would look completely different. Repulsion at short ranges arises from the Pauli potential; you cannot fit two electrons onto the same orbital.

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