[QE-users] Born charges of PbS

[Stefano de Gironcoli]

I didnt follow completely your argument about the Bader charge but what 
one should keep in mind is that the effective charge is the change in 
polarization due to displacement not the change in charge...

think of a core electron shell (as the d orbitals of Pb can 
approximately be considered) ... as you move the atom they follow 
rigidly (that would make a contribution of 10 not far from your estimate).

from the PHONON result it looks like Pb gave away 4 all its valence 
electrons to S. or rather they are so weakly bound to Pb that they don't 
follow it, even if they can still belong its Bader volume.

it looks a bit extreme but this appears to be the result. You could 
compute the atomic projected density of states and see if this seems the 
case.

stefano

On 13/04/20 17:11, Vahid Askarpour wrote:
> Dear QE Community,
>
> I have calculated the Born charges using the PHONON code for PbS. The only non-zero elements are the diagonal ones and are 4.122 and -4.168, respectively.
>
> In the zstar_eu.f90, Born charges consist of two terms as seen below: a part due to polarization calculation (dynamic) and the other is zv (static) which is the z_valence according to read_upf_v2.f90.
>
>   do ipol = 1, 3
>       do na = 1, nat
>          zstareu (ipol, ipol, na) = zstareu (ipol, ipol, na) + zv (ityp ( na) )
>       enddo
>    enddo
>
> The zv values for Pb and S are 14 and 6 given in the PSP. If we subtract zv from the Born charges, we get the term due to polarization: -9.878 and -10.168. These values seem too large because of the argument below.
>
> To estimate the polarization term, I reduce the alat by 1% and relax the atoms. This shifts the atoms from the unstrained position. I calculate the Bader charges for the unstrained and the strained cases. The change in the Bader charge is related to the atomic displacement. I have also tried keeping alat fixed and moving the atoms by 1%.
>
> For unstrained PbS, the Bader charges are 12.998 and 7.001.
> For the strained PbS, they are 13.004 and 6.995.
>
> So a ~1% change in atomic positions results in a +/-0.006 change in Bader charge. From this calculation, I expect the contribution from polarization to be u(dZ/du), where u is interatomic distance, which amount to +0.6 for Pb and -0.6 for S.
>
> The contribution from polarization I get (0.6 and -0.6) are quite different from the those of the PHONON code (-9.878 and -10.168). I am assuming that the code is correct and my logic is flawed. I would appreciate any thoughts you may have on this discrepancy.
>
> Thank you,
> Vahid
>
>
> Vahid Askarpour
> Department of physics and atmospheric science
> Dalhousie University
> Halifax, NS
> Canada
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