[QE-users] Born charges of PbS

Pietro Delugas pdelugas at sissa.it
Thu Apr 16 08:52:34 CEST 2020 

Hi Vahid

In principle all occupied bands could contribute to the big difference  
between  the dynamical charges and the oxydation numbers. How much they 
contribute  depends on their polarizability. And I agree with you that 
following what I said about the behavior of the S-3p  band, the Pb-6s 
should contribute in the opposite direction, but first they are only 2 
electrons/cell against 8 and also, I may be wrong, but I would expect 
the S 3p to be more polarizable.

If you are  curious about the detailed contributions to the dynamical 
charge anomaly from each  band you could try to compute them with 
wannier90 for example.

regards Pietro


On 15/04/20 15:05, Vahid Askarpour wrote:
> Hi Pietro,
>
> If I understand your argument correctly, then the same can be said of 
> the 2 electrons of s-Pb localized just above 0eV. These 2 electrons 
> are mainly centered on Pb, hybridized with other orbitals and move 
> with Pb (in addition to 10 d-electrons). So the dynamical charge for 
> Pb is ~ -12. Adding zv gives a Born charge of ~2. The PHONON code 
> gives a value of 4.122. So somehow, the 2 electrons from s-Pb should 
> move with sulphur and be loosely attached to Pb as noted by Stefano. 
> The DOS does not seem to support this idea.
>
> Thanks,
> Vahid
>
>> On Apr 15, 2020, at 3:23 AM, Pietro Delugas <pdelugas at sissa.it 
>> <mailto:pdelugas at sissa.it>> wrote:
>>
>> CAUTION: The Sender of this email is not from within Dalhousie.
>>
>> 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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