[QE-users] Born charges of PbS

[Vahid Askarpour]

Dear Stefano,

Thank you for this quick response. I was following Xavier Gonze’s argument in PRB58, 6224 (1998) Eq. 20 where 

Z*(u)=dp/du, where p is the dipole moment and u is the displacement. Since p=u.Z(u), we get

Z*(u)=Z(u)+udZ(u)/du, where Z(u) is the static charge.

So here the Born charge is given in terms of change in charge.

I will try the projected DOS to see if the charge transfer is actually that large.

Best,
Vahid

> On Apr 13, 2020, at 12:35 PM, Stefano de Gironcoli <degironc at sissa.it> wrote:
> 
> CAUTION: The Sender of this email is not from within Dalhousie.
> 
> 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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