[QE-users] Born charges of PbS

Wed Apr 15 08:23:36 CEST 2020

Hello

from the pdos  2 electrons have /moved /from Pb 6p to fill the S 3p 
band, as expected.

The 3p band is hybridized with 6s and 6p orbitals of Pb and vice versa. 
So the S 3p is still made by orbitals centered on S ions but is spread 
to neighboring Pb ions. If a S ion is displaced it goes closer to some 
Pb ion and far from others, same thing happens dispacing a Pb.  As 
Stefano wrote the 3p orbitals would still be centered close to the S 
ion, Bader charge thus would  not change,  but the orbital will now   
lean towards the closer Pb and away from those that are now a little bit 
farther,   this enhances the dynamical charge with respect to the 
oxidation number.

Pietro

On 14/04/20 00:54, Vahid Askarpour wrote:
> 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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