[QE-users] K-points, smearing and hybrid functionals in metals.

[Lorenzo Sponza]

Hello everybody.

I'm having some troubles in calculating the band structure of bulk 
Iridium with HSE06. In order to do that, I'm using the 'fake k-points' 
method, so I extract the band structure from a SCF calculation using an 
home-made post-processing code which is attached to this email. I run 
each simulation in a different folder to be sure not to overwrite 
important files. I'm using the marzari-vanderbilt smearing method with 
degauss values ranging from 0.011 to 1.0 and regular k-point grids 
ranging from 2x2x2 to 12x12x12 while the fake k-points list counts 26 
k-points in all cases. You can find an example of input file attached to 
the email. In parallel I have done also some PBE calculations with the 
standard procedure SCF+BANDS.

In the case of the PBE calculation, I don't observe differences in the 
band dispersion depending on the degauss value, but the Fermi level 
moves up for higher values of degauss and the k-point convergence is 
faster.

What I observe in the case of HSE06 is that the dispersion itself does 
change depending on the degauss value. Please see the attached graphs. 
In particular, for quite "standard" values of the degauss (0.02), the 
band structure presents weird jumps crossing the Fermi level, whereas 
for high values ( degauss = 0.8 ) the dispersion is smoother across 
Fermi, converges very quickly with the regular k-point grid and looks 
somewhat similar to the PBE one. I understand it as a consequence of the 
fact that hybrids have a certain amount of EXX which act only on 
occupied states. Since the occupation is not abrupt in metals and is 
modified by the smearing, then the potential changes in a continuous way 
as a function of degauss.

Hence my questions:

- In PBE calculations, how can I know what is the right value of the 
degauss parameter? I saw answers in the forum as if it is a compromise 
between k-points and smearing amplitude and ideally an infinitely dense 
grid would give the exact result with no smearing. However this answer 
does not help me in understanding where is the right Fermi energy 
because a finer grid does not solve the issue.

- Are hybrid functionals a safe choice for the calculation of the 
electronic structure and band alignment in metals?

- Is there a rule (rigorous or rule of thumb) to set the degauss value 
in metals when using hybrid potentials?

- Am I completely wrong, and I'm just making some mistake at the level 
of scf or of the band extraction? (I have no experience on metals and 
little on hybrids)

Thanks a lot for your help !

-- 
Dr. Lorenzo Sponza
Chargé de Recherche au CNRS
Laboratoire d'étude de microstructures (LEM), CNRS-ONERA
29 Avenue de la division Leclerc, 92322 Châtillon
Tel: +33146734464
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