[QE-users] Tricky questions on the fake k-points method to get bandstructure with hybrids

[Lorenzo Sponza]

Hello everybody,

I know that the subject of calculating a bandstructure with hybrid 
potentials has been addressed already many times in the mailing list, 
but I couldn't found the answers to my questions. I'm using QE 7.0 and, 
among the existing methods mentioned elsewhere, I want to rely on the so 
called 'fake k-points' approach.

The procedure is globally clear to me: one first runs a SCF calculation 
on a regular grid, then runs a second SCF calculation with the hybrid 
potential of choice and an explicit list of k-points which includes the 
irreducible k-points with their associated weight plus those in the 
bandpath with a vanishing weight. The rest is basically just a matter of 
post-processing the output.

1/ What exactly is the first SCF calculation needed for? Is any of its 
output (density, wavefunctions, etc...) used by the subsequent hybrid 
calculation, or the only useful information is the list of irreducible 
k-points and their weights? In other words, if I get the correct list of 
k-points (grid, paths and weights) from an external source, can I just 
run directly the hybrid calculation with no preliminary step?

2/ I noticed that if I put the weight of the k-points in the bandpath 
exactly equal to 0, then their energies are not consistent with the rest 
of the calculation  and their occupation is vanishing for all bands (see 
below the example). I have the impression that this is also the case if 
one uses the 'ADDITIONAL_K_POINTS' card.  Instead, by putting a very low 
weight (0.0000001), I found no error. Why this? Is setting the weight = 
0.0 really the right way to proceed?

Let me give an example of this to be clearer. I calculate the 
bandstructure of Si along a path passing through Gamma. Also the regular 
k-point mesh contains Gamma though. So, the Gamma point appears twice in 
the list of k-points specified in the hybrid calculation: once with a 
finite weight in the regular grid, and once with weight = 0.0 along the 
bandpath. Here below is the output of the hybrid calculation associated 
to the two occurrences. Notice that the energies are different although 
it is the same k-point in the same calculation, and the occupation is 0 
in the second occurrence.

:: THE GRID OCCURRENCE WITH WEIGHT = 0.002 ::

k = 0.0000 0.0000 0.0000 (   749 PWs)   bands (ev):

     -7.0330   5.0739   5.0739   5.0739   9.7109   9.7109   9.7109  
10.6652    14.8522  14.8522

      occupation numbers

      1.0000   1.0000   1.0000   1.0000   0.0000   0.0000   0.0000   
0.0000     0.0000   0.0000

:: THE PATH OCCURRENCE WITH WEIGHT = 0.000 ::

k = 0.0000 0.0000 0.0000 (   749 PWs)   bands (ev):

     -4.6222   7.5761   7.5761   7.5761  10.5198  10.5198  10.5198  
11.6019    15.2911  15.6844

      occupation numbers

      0.0000   0.0000   0.0000   0.0000   0.0000   0.0000   0.0000   
0.0000     0.0000   0.0000

3/ In some hybrid calculations one has to set the variables nxq# > 1 to 
get accurate results. In this case, prescriptions are to add the 
k-points of the bandpath plus all the relevant k+q points. Where do I 
find them? How can I get them? How I can I get the very q-point grid 
used by the code?

Many thanks for your answers, help, tricks and suggestions.

Cheers

-- 
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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.quantum-espresso.org/pipermail/users/attachments/20220913/49c2d39d/attachment.html>