[Pw_forum] Electronic band structures for primitive and conventional unit cells

[Yun Wang]

Dear Pascal,

  What you found is related to the Brillouin zone folding. You can find
more details in Roarld Hoffmann's book: Solids and surfaces. The band
structure using the primitive cell is correct.

Cheers,
Yun

On Mon, Mar 18, 2013 at 9:05 PM, pascal boulet <pascal.boulet at univ-amu.fr>wrote:

> Dear all,
>
> We are facing a problem with differences in electronic band structures
> when we use primitive or conventional unit cells.
>
> The structure we are dealing with is Mg2Si for which the primitive UC is:
> ATOMIC_POSITIONS crystal
> Si       0.000000000   0.000000000   0.000000000
> Mg       0.250000000   0.250000000   0.250000000
> Mg       0.750000000   0.750000000   0.750000000
>
> The cubic space group is 225, a=12.0421785 bohr and Mg2Si is FCC.
>
> The rest of the input is (I make it short):
> K_POINTS crystal
> 120
>         0.5000000000    0.2500000000    0.7500000000    1.0
>         0.5000000000    0.2600000000    0.7400000000    1.0
>         0.5000000000    0.2700000000    0.7300000000    1.0
>  etc.
>  calculation   = 'bands',
>   celldm(1)   =12.0421785,
>   nat         = 3,
>   ibrav       = 2,
>
>
> If we use this UC we get a indirect band gap (G-X), which is correct. If
> we now use the conventional UC (12 atoms in the cube) we get a direct band
> gap at Gamma. In this case, we are using the following input file :
>   calculation   = 'bands',
>   celldm(1)   = 1,
>   nat         = 12,
>   ibrav       = 0,
>
> K_POINTS crystal
> 126
> .0   .0   .0   1.
> .020 .020 .020 1.
> .040 .040 .040 1.
> .060 .060 .060 1.
> .080 .080 .080 1.
> .100 .100 .100 1.
> .120 .120 .120 1.
> etc.
>
> CELL_PARAMETERS
> 12.03517200     0.0      0.0
> 0.0      12.03517200     0.0
> 0.0      0.0      12.03517200
> ATOMIC_POSITIONS crystal
> Si    0.00000    0.00000    0.00000
> Si    0.50000    0.50000    0.00000
> Si    0.00000    0.50000    0.50000
> Si    0.50000    0.00000    0.50000
> Mg    0.25       0.25       0.25
> Mg    0.75       0.75       0.75
> Mg    0.25       0.25       0.75
> Mg    0.25       0.75       0.25
> Mg    0.75       0.25       0.25
> Mg    0.25       0.75       0.75
> Mg    0.75       0.25       0.75
> Mg    0.75       0.75       0.25
>
> Could you please tell us what we are doing wrong in the second calculation?
>
> Thank you for your response.
>
> Best regards,
> Pascal
>
>
>
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-- 

Dr. Yun Wang
Research Fellow
Centre for Clean Environment and Energy
Griffith School of Environment
Gold Coast Campus, Griffith University
QLD 4222, Australia
Tel:(61-7) 5552 8456
Fax:(61-7) 5552 8067
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