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So I already asked yesterday about canonical and localized orbitals together with Koopman's theorem where we came to the conclusion that for for example ionization potentials localized orbitals cannot be used. So I assume a ionization would be from the HOMO which leaves me with the question, whenever we say an electron is excited from the HOMO into the LUMO of a system, are we talking about the canonical forms then? Because before I knew about those two I always imagined that there is a local position somewhere in the molecule like a double bond where one electron is exited into an antibonding MO creating a single bond or 1.5 bond and that you can really tell from where to where the transition is. But canonical orbitals do not really look like we imagine orbitals they are distributed over the whole molecule.

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  • $\begingroup$ I am not allowed to correct this, because its less than 6 characters ... but the guys actual name is "Koopmans" with the "s" at the end. $\endgroup$ – Feodoran Jul 7 '17 at 10:09
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Short answer is yes, HOMO and LUMO refer to canonical orbitals, since only those have at least some physical meaning.

Two more remarks about that:

Koopmans' Theorem does only work if you add or remove one electron.

If you change two or more electrons of your system (e.g. exciting one electron is first removing one, then adding one in another orbital) you get additional terms in energy difference between both states. Those terms are coming from the electron-electron interaction of the two changed orbitals/electrons.

In case of changing only one orbital, those additional terms do not appear since there is no electron-electron self-interaction.

Furthermore, the approximation of Koopmans' Theorem, that orbitals do not change (do not relax, remain stationary) on removing/adding electrons, gets worse the more electrons change.

Orbitals itself are only an approximation. Factorizing the total electronic wave function into orbitals is mathematically only possible for non-interaction electrons, or like in Hartree-Fock if you assume some mean-field for the electron-electron interaction. The resulting canonical orbitals do not always match the simplified picture based on our chemical intuition.

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