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

lyzhao lyzhao at zjnu.cn
Sun May 29 06:55:48 CEST 2016

```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
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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