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I just had a question about molecular orbitals. I was just wondering if the energies of the LUMO (virtual orbitals) derived from CCSD(T)/cc-pTVZ calculations could be trusted. I remember reading some time ago that these orbital energies could not be trusted since they contained no electrons. If they cannot be trusted, could you suggest any calculations I could perform to obtain the LUMO molecular orbital energies (perhaps TD-DFT or some other method)?

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    $\begingroup$ Related: chemistry.stackexchange.com/q/86469 $\endgroup$ – Tyberius Oct 31 at 23:27
  • $\begingroup$ I think a key question is what you mean by "trusted." Do you mean "does the LUMO eigenvalue correspond to the electron affinity" or "does the LUMO eigenvalue tell you about the first excited state" (among two somewhat similar properties). It might also help to know what kind of molecules you're considering (since some species have unbound LUMOs) $\endgroup$ – Geoff Hutchison Nov 1 at 5:45
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When thinking about orbital energy levels, it is not a good idea to think of them as fixed energy 'levels' that can be filled with electrons. This kind of picture is often found in introductory textbooks, but it is wrong. For example, it is known that even for the Hartree-Fock theory, the energy of a molecule is not a sum of the orbital energies. In this sense, you can never really consider orbital energies as the energies of the given electrons - which is really a meaningless quantity, if you think about it. Basically the only interesting quantity that you can get from an orbital energy is the first ionization energy based on Koopmans' theorem, which also is just approximately true.

So can you trust orbital energies? It really depends what you want to calculate. One thing that people often want is to calculate the UV-VIS spectrum of a molecule, which is, of course, the energy required to move an electron form an occupied orbital to a virtual orbital. But this energy should not be calculated as the difference of the energies of the two orbitals. The reason for this is not that virtual orbital energies can not be trusted, but the fact that when you move an electron, you now have a different electron configuration, that is, a different wavefunction. And with a different wavefunction, of course, you would get different energy levels. You should not use the energy levels of the original wavefunction to describe the energy levels of an excited state.

So in order to calculate UV-VIS spectra, you should rather use a multi-reference method with a large enough active space that includes both the ground and the excited states and also some 'buffering states' to expand the difference in the electron correlation. If you can afford a CCSD(T) calculation, then you might also be able to afford a CAS-SCF calculation with a formidable active space, maybe even add a bit of NEVPT2 to it. I also have some good experience with the SORCI method of Orca, if you want to check that out. And if you can not afford to do such large calculations, you might also fall back to TD-DFT - some good double hybrid methods have been made available this year.

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