fermi energy in band structure calculation

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fermi energy in band structure calculation

#1 Post by decai » Mon Dec 31, 2007 2:07 am

I have a question on determining the fermi energy in band structure calculation.
First, I do a self-consistent run using Tetrahedron method (ISMEAR=-5).
Second, I calculate the band structure with CHGCAR AND WAVECAR from step one using ISMEAR=1 because ISMEAR=-5 is not accepted in this case.
My question is :
Can I use the fermi energy from step 1 as my band structure fermi energy?
Obviously in my calculations, the smearing methods are different for these two steps.

Thanks a lot and Happy new year!

Last edited by decai on Mon Dec 31, 2007 2:07 am, edited 1 time in total.

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fermi energy in band structure calculation

#2 Post by admin » Thu Jan 03, 2008 11:09 am

The Fermi level is determined via the Kohn-Sham eigenvalue of the highest occupied state. Therefore please check from your band structure run if the corresponding k-point (state) was included in the kmesh you used for the runs done with ISMEAR=-5 at all.
please also mind that the absolute values of the KS-eigenvalues (and hence the Fermi levels) are only given to within a constant offset in energy, because the E=0 is not defined when 3D periodic boundary conditions are used. This may cause subtle differences in the absolute values of the KS energies in 2 different runs as well (a rough estimate can be obtained by comparing alpha+bet as written in OUTCAR).
Last edited by admin on Thu Jan 03, 2008 11:09 am, edited 1 time in total.

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Re: fermi energy in band structure calculation

#3 Post by ralf_tonner1 » Fri Jul 16, 2021 3:39 pm

Dear admin,
Although this thread seems to be quite old but recently, I came across a similar problem again. As was mentioned in your comment that in different run absolute KS eigenvalues could be different due to difference in constant offset. However, I calculated bulk GaAs (3D periodic) band structure (along L-G-X-K U-G) with the same settings 20 times and every time I got the same absolute band energies at every k-points. The Fermi energies are exactly the same as well. So, I was wondering if I am misunderstanding something. If I am not wrong, we are basically solving this below Schrödinger equation. So, I was wondering in which part of the below equation the constant offset is contributing. If you don't mind I would like to ask for a little more clarification about the 'constant offset' part. Also, if possible providing some reference could be extremely helpful.
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Re: fermi energy in band structure calculation

#4 Post by henrique_miranda » Mon Jul 19, 2021 2:27 pm

This is indeed quite an old thread.
I don't know if I am still able to find the person that answered this question in the first place to explain what is meant. Unfortunately, different people could have answered under the admin alias.

I will try to explain it in my own words. Hopefully, this clarifies your doubts.

To the question of the user I would have simply have answered that yes, you can and should use the fermi energy from the first run because to determine the fermi-energy you need a regular grid.
Computing the fermi level from the band-structure run (i.e. only with k-points along a path in the BZ) while technically possible is meaningless. For hybrid functionals, the current recommendation is to use a regular grid + k-points along a path with zero weight:
wiki/index.php/Si_bandstructure#Procedu ... Hybrids.29

As for the discussion about the constant energy offset, I do not know what was meant originally.
The only thing that comes to mind is how the total energies in VASP are computed with respect to the isolated reference atoms that was used to generate the POTCAR:
wiki/index.php/Calculation_of_atoms#Det ... y_of_atoms
This would refer to the v_ext term in the equation you posted.

This being said, this is not something you need to worry about in this situation since you are not changing the POTCAR file between the SCF and band-structure calculation.

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