[Pw_forum] The equal k-points cannot lead to the same energy band.

[Paolo Giannozzi]

The k-points (1/3,1/3,0) and (-1/3,2/3,0), in cartesian axis and in
units of 2\pi/a0, are not equivalent.

Paolo

On Sun, May 29, 2016 at 6:55 AM, lyzhao <lyzhao at zjnu.cn> wrote:
> Dear all,
> I ran a band structure calculation at some high symmetry k-points for a
> hexagonal structure (SiC 111).
> I try the following two sets of k-points:
> S1.
> K_POINTS
>  3
>  0.000 0.000  0.000 1.0
>  0.333 0.333  0.000 1.0
>  0.500 0.000  0.000 1.0
> S2.
> K_POINTS
>  3
>  0.0   0.0   0.0 1
> -0.333  0.667  0.000 1
>  0.000  0.500  0.000 1
>
> S1 leads to the following energy band:
>           k = 0.0000 0.0000 0.0000 (  1139 PWs)   bands (ev):
>    -17.6202  -7.0494  -4.2017  -4.2017  -0.4467   1.5150   1.6453   2.3677
>           k = 0.3330 0.3330 0.0000 (  1095 PWs)   bands (ev):
>    -15.2584 -10.1839  -6.6316  -4.3186   0.2328   1.6659   3.8224   4.8909
>           k = 0.5000 0.0000 0.0000 (  1096 PWs)   bands (ev):
>    -15.1008 -10.7511  -5.7976  -4.1069  -0.3499   0.3805   4.1445   5.3833
>      highest occupied, lowest unoccupied level (ev):    -4.1069   -0.4467
> however, S2 leads to:
>           k = 0.0000 0.0000 0.0000 (  1139 PWs)   bands (ev):
>    -17.7480  -7.1365  -4.3482  -4.3482  -0.5055   1.5128   1.6485   2.3416
>           k =-0.3330 0.6670 0.0000 (  1092 PWs)   bands (ev):
>    -15.8503  -9.8006  -5.8672  -4.9789   0.6816   0.8106   3.0639   4.2245
>           k = 0.0000 0.5000 0.0000 (  1102 PWs)   bands (ev):
>    -15.1554 -10.1200  -7.9378  -4.0954   0.0949   3.2276   4.3675   4.3703
>      highest occupied, lowest unoccupied level (ev):    -4.0954   -0.5055
>
> The differences between two results seem to be large.
> The differences between two jobs are only the setting of k-points.
> The input file is as follow:
> *********************************************
> &control
>  calculation='scf'
>  restart_mode='from_scratch',
>  prefix='SiC111'
> /
> &system
> ibrav=0,nat=2,ntyp=2
> ecutwfc = 15.0, occupations='fixed'
> nbnd=8
> /
> &electrons
>  diagonalization='david',
>  conv_thr =  1.0d-10,
>  mixing_beta = 0.5,
>  startingwfc='random',
> /
> ATOMIC_SPECIES
> Si  28.06 Si.pbe-mt_gipaw.UPF
> C   12.01 C.pbe-mt_gipaw.UPF
> K_POINTS
>  3
>  0.000 0.000  0.000 1.0
>  0.333 0.333  0.000 1.0
>  0.500 0.000  0.000 1.0
>
> CELL_PARAMETERS (angstrom)
>  2.6844596  -1.5498735   0.0000000
>  0.0000000   3.0997470   0.0000000
>  0.0000000   0.0000000  20.0077731
> ATOMIC_POSITIONS (crystal)
>  C     0.000000   0.000000   0.500000
>  Si    0.333333  -0.333333   0.500000
> *********************************************
>
>
> Any help will be appreciated.
>
> Youzhao Lan
> Zhejiang Normal University,
> China.
> --------------------------------------------------------
>
>
>
>
>
>
> ________________________________
> 2016-05-29  12:42:52
>
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-- 
Paolo Giannozzi, Dip. Scienze Matematiche Informatiche e Fisiche,
Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222