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I have run the Self-Consistent Field calculations and found the highest unoccupied and lowest unoccupied energy level for Bismuth (hR2) crystal structure. Now, bismuth is a semi metal with Fermi level around 0eV. But after taking the mean/average of the highest occupied and unoccupied energy level, my Fermi energy is coming out to be around 9eV. Even in the SCF.out file, the Fermi energy is around 9eV.

I don't understand how to determine the correct Fermi energy, and why is this value coming around 9 when it should be around 0. The aim of my work is to determine the direct band gap at some specific k point (L and T). But without knowing the fermi energy, I can't find the valence and conduction band and hence I can't find the direct band gap at these k points. I have also run the band structure calculation to obtain the band structure for the higher symmetry points. For this, I used seek k-path to find the correct k-path for band structure calculation. But it's useless unless I know how to find the band gap. I don't even have the correct fermi energy I think. Please help me understand where am I going wrong.

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    $\begingroup$ Never see a Fermi level of 0eV. In general, when you see Fermi=0eV is because it was shifted. 0eV is not the real value of it. $\endgroup$
    – Camps ♦
    Commented Dec 9 at 12:14
  • $\begingroup$ @Camps Can you please share some resource that explains the calculation of direct band gap at some specific k point from band structure data? $\endgroup$
    – Samyak Marathe
    Commented Dec 9 at 13:04
  • $\begingroup$ Visually, you can plot the band around the Fermi level and look for the Valence Band Maximum and Conduction Band Minimum, then go to the data for a precise calculation. Or use a script like this (be aware it is a shell script and I didn't test it as I don't play with QuantumEspresso). $\endgroup$
    – Camps ♦
    Commented Dec 9 at 18:01
  • $\begingroup$ The absolute energies that come out from DFT are fictitious Kohn-Sham energies that have no physical meaning. Thus, you can shift the energy spectrum by any arbitrary value without changing any physics. $\endgroup$
    – franz
    Commented 2 days ago
  • $\begingroup$ ohh okay. Thanks $\endgroup$
    – Samyak Marathe
    Commented yesterday

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