[QE-users] Born charges of PbS

Tue Apr 14 00:54:16 CEST 2020

The attached projected DOS for PbS suggests that the Pb s- and p- states have significant DOS and so perhaps the 4 electrons of Pb have not moved to sulphur unless I am reading the DOS incorrectly. The Pb d-states are lower in energy and not shown.

Cheers,
Vahid

On Apr 13, 2020, at 12:53 PM, Vahid Askarpour <vh261281 at dal.ca<mailto:vh261281 at dal.ca>> wrote:

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<mailto: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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