Based on the detailed answers provided for the reasons for the underestimation of bandgaps in DFT calculations, can we deduce that it is based on an underestimation of the conduction band level but not the valence band level?
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No. Considering a DFT calculation of a molecule, the HOMO level could be in principle related to ionization energy, but is not equal to it. The problem goes beyond just a misplacement of the LUMO level.
You can do the analogy from a finite system, such as an atom or molecule, to a periodic system with electronic bands (HOMO -> valence band maximum and LUMO -> conduction band minimum).
