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Is it possible to find the Fermi energy with highest occupied and lowest unoccupied level from a single nscf caculation using quantum espresso?

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I don't think it is possible as it is required to use a smearing method in order to obtain the fermi energy. By doing so, you can not get the values of HOMO and LUMO levels. so obtaining both of them from a single calculation may not be feasible.

I would advise you to take the Fermi energy from a well-converged scf calculation because the Fermi energy value tends to slightly change from one type of calculation to another. To obtain the HOMO and LUMO levels, you will have to run another scf calculation without smearing and by using the nbnd command (number of Kohn-Sham states) with a value basically the same as the number of electrons in the system.

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