[QE-users] Effective Mass Tensor unit-cell dependency
Paolo Giannozzi
p.giannozzi at gmail.com
Tue Sep 21 09:49:18 CEST 2021
Funny: I have always called "primitive" the 2-atom cell. "conventional" the
8-atom one. Anyway, the 2-atom diamond structure (fcc lattice) is simply
ibrav=2, a=lattice parameter (A)
or
ibrav=2, celldm(1)=lattice parameter (a.u.)
(lattice parameter=side of the cube) plus
ATOMIC_POSITIONS (alat)
Si 0.00 0.00 0.00
Si 0.25 0.25 0.25
or
ATOMIC_POSITIONS (crystal)
Si 0.00 0.00 0.00
Si 0.25 0.25 0.25
or any of the various possible ways of specifying atomic positions. If you
do things properly you will find that the 2-atom and 8-atom cells give
exactly the same results.
Paolo
On Mon, Sep 20, 2021 at 1:28 PM Schön, Carl-Friedrich <
schoen at physik.rwth-aachen.de> wrote:
> Dear QE users,
>
> I have a question regarding the effective mass tensor, that I cannot seem
> to find the solution for. One could also rephrase this as a general
> question regarding the energy eigenvalues of k-points within different
> representations of unit-cells.
> I have used QE to calculate the bands/eigenvalues of Silicon. I have done
> this ones with the conventional unit cell (from materials project):
>
> *Si2*
> *1.0*
> *3.8681383004362986 0.0 0.0*
> *1.9340686210409386 3.349905532609194 0.0*
> *1.9340686210409386 1.1166353539288019 3.1583211568194507*
> *Si*
> *2*
> *Direct*
> *0.250000000 0.250000000 0.250000000*
> *0.000000000 0.000000000 0.000000000*
>
>
> As well as the primitive unitcell:
> *Si8*
> *1.0*
> *5.4687280655 0.0000000000 0.0000000000*
> *0.0000000000 5.4687280655 0.0000000000*
> *0.0000000000 0.0000000000 5.4687280655*
> *Si*
> *8*
> *Direct*
> *0.250000000 0.750000044 0.250000000*
> *-0.000000000 -0.000000000 0.500000000*
> *0.250000000 0.250000000 0.750000044*
> *-0.000000000 0.500000000 0.000000000*
> *0.750000044 0.750000044 0.750000044*
> *0.500000000 0.000000000 0.000000000*
> *0.750000044 0.250000000 0.250000000*
> *0.500000000 0.500000000 0.500000000*
>
>
> Let's look at the gamma point only at this point: I then constructed
> (using the emc.py script) a cartesian k-point grid around the Gamma point
> in order to get the effective mass tensor for the gamma point for each
> definition of the unit cell (Conduction Band). For the primitive, 8 atom
> unit cell, I get something like:
>
> -20.46496343 0.00000000 0.00000000
> 0.00000000 -20.46496343 0.00000000
> 0.00000000 0.00000000 -20.46496343
>
> with all Eigenvalues being -20.465 (the tensors are given in units of
> 1/m*). As far as I am aware, this is what it should look like in terms of
> symmetry/degeneracy (the absolute values are not of interest at this point).
>
> If I look at the conventional, 2 atom unit cell, I get something like:
> 0.88345374 -0.00018375 -0.00018375
> -0.00018375 0.11245293 -1.46684926
> -0.00018375 -1.46684926 2.17115005
> with non-degenerate eigenvalues of -0.65, 0.88, 2.93.
> I do not understand how this can be. I would understand that the tensors
> might look different due to different (absolute) orientation in k-space,
> but the eigenvalues should remain identical, should they not? Otherwise the
> physics would have changed. Especially in the example of the Gamma point
> above, I would have assumed to get the exact same tensor, as the effective
> masses are equal in all directions. Again, the dense grid around the Gamma
> point is constructed as cartesian cube in both cases.
>
> I therefore looked at the eigenvalues (energies in the conduction band) of
> the nscf calculation of said dense grid:
> Points that should be equivalent (and are indeed identical in the
> primitive 8 atom case) are not in the 2 atom case, e.g.
> E(0.01,0,0)!=E(0,0.01,0). I varied the spacing of the grid, but to no
> effect. The differences are also too big to be numeric errors:
>
> Position:
> 5.8000000E-03 0.0000000E+00 0.0000000E+00
> Eigenenergies:
> 1 -5.811100
> 2 5.989300
> 3 5.997400
> 4 6.001900
> 5 8.550800 à Conductino Band
> 6 8.552000
> 7 8.556000
> 8 9.102700
> 9 13.711000
> 10 13.716400
> 11 13.883000
> 12 17.181200
>
> Position:
> 0.0000000E+00 -5.8500000E-03 -0.0000000E+00
> Eigenenergies
> 1 -5.811100
> 2 5.988800
> 3 5.998800
> 4 6.000700
> 5 8.549800 àConduction Band
> 6 8.554400
> 7 8.554800
> 8 9.102800
> 9 13.710800
> 10 13.716400
> 11 13.883100
> 12 17.179600
>
> Here the input I used for the scf calculation:
>
> &control
> calculation = 'scf'
> prefix='Si_mp-149_computed_Relax_6'
> tstress = .true.
> tprnfor = .true.
> pseudo_dir='/rwthfs/rz/cluster/home/NC'
> outdir='tmp'
> disk_io='low'
> wf_collect=.true.
> verbosity= 'high'
> /
> &system
> ibrav =0,
> nat=2
> ntyp=1
> ecutwfc = 100
> ecutrho = 400
> occupations = 'fixed'
> /
> &electrons
> mixing_beta = 0.2
> conv_thr = 1.0d-10
> /
> ATOMIC_SPECIES
> Si 28.086 Si.upf
> ATOMIC_POSITIONS {crystal}
> Si 0.25 0.25 0.25
> Si 0.0 0.0 0.0
> CELL_PARAMETERS
> 7.309722 0.0 0.0
> 3.65486 6.330404 0.0
> 3.65486 2.110135 5.968362
> K_POINTS {automatic}
> 24 24 24 0 0 0
>
> I am not sure what I am missing… In my understanding the results should be
> (generelly) independent of the definitino of the used unit-cell…
>
> Thank you and all the best,
>
> Carl-Friedrich Schön, PhD Student, RWTH Aachen University
> _______________________________________________
> Quantum ESPRESSO is supported by MaX (www.max-centre.eu)
> users mailing list users at lists.quantum-espresso.org
> https://lists.quantum-espresso.org/mailman/listinfo/users
--
Paolo Giannozzi, Dip. Scienze Matematiche Informatiche e Fisiche,
Univ. Udine, via delle Scienze 206, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.quantum-espresso.org/pipermail/users/attachments/20210921/08071bbe/attachment.html>
More information about the users
mailing list