Experimentally, determining the absolute valence and conductance band positions can be difficult. While DFT often underestimates band gaps, experimentally the band gap is a far more accessible measurement that could be used to find the band position of the valence or conductance band if one is known.

The fundamental question here is, can either the absolute valence or conductance band of a semiconductor be determined accurately with respect to vacuum using DFT. If so, what kind of error can be expected in these systems.


Absolute energy values (or more specifically, the Kohn-Sham eigenvalues) that you obtain from KS-DFT calculations are meaningless. You are right in that one could do a vacuum calculation in DFT and align the band-structure with respect to vacuum. The electronic band-gap that you obtain however, is still underestimated, as you mentioned (in KS-DFT). If your question is with regard to how much error is usually incurred in calculation of bandgaps, it depends on your system but it is definitely significant and there are many sources in literature that you could refer to.

On the other hand, if your question is with regard to how much error is incurred in calculation of the HOMO or LUMO, the error is not as significant typically. Let's assume you want to calculate the ionization energy ( as Evacuum - EHOMO ). I can't seem to find a comprehensive study of the efficacy of Ionization energy calculations in KS-DFT but this is a good starting point on the nuances involved in such a calculation - delving into the validity of Koopman's theorem etc. From what I have personally encountered, errors in ionization energy of up to 0.5 eV are not uncommon. A GW quasiparticle calculation can give you a better, more reliable estimate in this case. But this is certainly on the lesser side of the scale if you compare electronic band-gaps.


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