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In a paper by Zhang and Musgrave it is stated that

Unfortunately, although molecular orbital (MO) theory is of immense utility, commonly used DFT functionals that can economically calculate the electronic structure of molecules may not predict orbital energies accurately.

I was wondering while DFT is an ab initio method to calculate molecular properties, why it not performing well for computing frontier molecular orbital energies.

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Density functional theory really is a total energy method, and total energies as functionals of the electron densities are often relatively well predicted; even better is the prediction of total energy differences (i.e. reaction energies) due to somewhat fortuitous error cancellation.

Orbital or spectral properties are here based on interpreting the Kohn-Sham eigenvalues as quasiparticle (or "orbital") energies, while the Kohn-Sham equations are only an auxiliary construct to approximate the non-interacting (electronic) kinetic energy. In other words: Kohn-Sham orbital energies do not - strictly speaking - have any physical meaning in terms of observable spectral properties. However, the (not necessarily well understood) resemblance of the Kohn-Sham spectrum and actual single-/quasiparticle spectra, and the lower computational cost compared to other ab initio methods makes it tempting to interpret the Kohn-Sham spectrum as an actual electronic spectrum. Another well-known example of the failure of "over-interpreting" the Kohn-Sham spectrum this way is the significant underestimation of band gaps. To properly compute electronic spectra starting from DFT, one has to incorporate quasiparticle corrections, e.g. in the form of the so-called GW approach (which is computationally significantly more expensive than DFT).

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  • $\begingroup$ Thanks for the response. I don't fully understand what you mean, would you mind expanding it a little bit? $\endgroup$
    – Blade
    Commented Nov 11, 2019 at 0:52
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    $\begingroup$ Elaborated a little bit. The fact that orbital energies are not too well represented is also related to the DFT band gap problem discussed e.g. here: physics.stackexchange.com/questions/176419/… $\endgroup$
    – Gianluca
    Commented Nov 11, 2019 at 1:19
  • $\begingroup$ So we have ab initio DFT with more accuracy but computationally very expensive, on the other hand we have KS approximate DFT that is accurate for many properties and less expensive, but for HOMO-LUMO it does not give a good approximation. So researchers started to either use hybrid DFT methods or started to incorporate empirical results from -IP and EA to correct these values. Does this sound a reasonable interpretation? $\endgroup$
    – Blade
    Commented Nov 11, 2019 at 1:41
  • $\begingroup$ Both standard DFT and DFT+GW are ab initio methods in the sense that nothing is fitted against experiments: it is only the latter that provides reliable electronic spectra and not only total energies. While DFT tends to underestimate gaps, Hartree-Fock tends to overestimate them, and a mixture can more ore less get things right (how this mixture is chosen might not really be an ab initio procedure anymore). $\endgroup$
    – Gianluca
    Commented Nov 11, 2019 at 3:19
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    $\begingroup$ The band gap in a semiconductor is simply a particular kind of a HOMO-LUMO gap (the HOMO is the valence band maximum and the LUMO the conduction band minimum in this case). And yes, the discussion of DFT problems in describing band gaps applies to HOMO LUMO gaps in general as well. $\endgroup$
    – Gianluca
    Commented Nov 18, 2019 at 17:39

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