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Hi Pietro,
<div class=""><br class="">
</div>
<div class="">Thank you for taking the time to respond. This has been a very enlightening discussion for me. I will try the Wannier code and see what I get.</div>
<div class=""><br class="">
</div>
<div class="">Best wishes,</div>
<div class="">Vahid<br class="">
<div><br class="">
<blockquote type="cite" class="">
<div class="">On Apr 16, 2020, at 3:52 AM, Pietro Delugas <<a href="mailto:pdelugas@sissa.it" class="">pdelugas@sissa.it</a>> wrote:</div>
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<p class=""><font size="-1" class="">Hi Vahid <br class="">
</font></p>
<p class=""><font size="-1" class="">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.
<br class="">
</font></p>
<p class=""><font size="-1" class="">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.
<br class="">
</font></p>
<p class=""><font size="-1" class="">regards Pietro<br class="">
</font></p>
<p class=""><font size="-1" class=""><br class="">
</font></p>
<div class="moz-cite-prefix">On 15/04/20 15:05, Vahid Askarpour wrote:<br class="">
</div>
<blockquote type="cite" cite="mid:115BBDFE-391B-4511-B7D0-D9C40B0A7244@dal.ca" class="">
Hi Pietro,
<div class=""><br class="">
</div>
<div class="">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.</div>
<div class=""><br class="">
</div>
<div class="">Thanks,</div>
<div class="">Vahid<br class="">
<div class=""><br class="">
<blockquote type="cite" class="">
<div class="">On Apr 15, 2020, at 3:23 AM, Pietro Delugas <<a href="mailto:pdelugas@sissa.it" class="" moz-do-not-send="true">pdelugas@sissa.it</a>> wrote:</div>
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<div class="">
<p class=""><font class="" size="-1">Hello <br class="">
</font></p>
<p class=""><font class="" size="-1">from the pdos 2 electrons have <i class="">
moved </i>from Pb 6p to fill the S 3p band, as expected. <br class="">
</font></p>
<p class=""><font class="" size="-1">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.</font></p>
<p class=""><font class="" size="-1">Pietro<br class="">
</font></p>
<p class=""><font class="" size="-1"><br class="">
</font></p>
<div class="moz-cite-prefix">On 14/04/20 00:54, Vahid Askarpour wrote:<br class="">
</div>
<blockquote type="cite" cite="mid:EFAC0BCD-DF7D-4A3F-A765-36B3FB09EAA8@dal.ca" class="">
<div class="" style="word-wrap:break-word;
line-break:after-white-space">
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.
<div class=""><br class="">
</div>
<div class="">Cheers,</div>
<div class="">Vahid</div>
<div class=""><br class="">
</div>
</div>
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<div class="">On Apr 13, 2020, at 12:53 PM, Vahid Askarpour <<a href="mailto:vh261281@dal.ca" class="" moz-do-not-send="true">vh261281@dal.ca</a>> wrote:</div>
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<div class="">
<div class="">Dear Stefano,<br class="">
<br class="">
Thank you for this quick response. I was following Xavier Gonze’s argument in PRB58, 6224 (1998) Eq. 20 where
<br class="">
<br class="">
Z*(u)=dp/du, where p is the dipole moment and u is the displacement. Since p=u.Z(u), we get<br class="">
<br class="">
Z*(u)=Z(u)+udZ(u)/du, where Z(u) is the static charge.<br class="">
<br class="">
So here the Born charge is given in terms of change in charge.<br class="">
<br class="">
I will try the projected DOS to see if the charge transfer is actually that large.<br class="">
<br class="">
Best,<br class="">
Vahid<br class="">
<br class="">
<blockquote type="cite" class="">On Apr 13, 2020, at 12:35 PM, Stefano de Gironcoli <<a href="mailto:degironc@sissa.it" class="" moz-do-not-send="true">degironc@sissa.it</a>> wrote:<br class="">
<br class="">
CAUTION: The Sender of this email is not from within Dalhousie.<br class="">
<br class="">
I didnt follow completely your argument about the Bader charge but what<br class="">
one should keep in mind is that the effective charge is the change in<br class="">
polarization due to displacement not the change in charge...<br class="">
<br class="">
think of a core electron shell (as the d orbitals of Pb can<br class="">
approximately be considered) ... as you move the atom they follow<br class="">
rigidly (that would make a contribution of 10 not far from your estimate).<br class="">
<br class="">
from the PHONON result it looks like Pb gave away 4 all its valence<br class="">
electrons to S. or rather they are so weakly bound to Pb that they don't<br class="">
follow it, even if they can still belong its Bader volume.<br class="">
<br class="">
it looks a bit extreme but this appears to be the result. You could<br class="">
compute the atomic projected density of states and see if this seems the<br class="">
case.<br class="">
<br class="">
stefano<br class="">
<br class="">
On 13/04/20 17:11, Vahid Askarpour wrote:<br class="">
<blockquote type="cite" class="">Dear QE Community,<br class="">
<br class="">
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.<br class="">
<br class="">
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.<br class="">
<br class="">
do ipol = 1, 3<br class="">
do na = 1, nat<br class="">
zstareu (ipol, ipol, na) = zstareu (ipol, ipol, na) + zv (ityp ( na) )<br class="">
enddo<br class="">
enddo<br class="">
<br class="">
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.<br class="">
<br class="">
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%.<br class="">
<br class="">
For unstrained PbS, the Bader charges are 12.998 and 7.001.<br class="">
For the strained PbS, they are 13.004 and 6.995.<br class="">
<br class="">
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.<br class="">
<br class="">
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.<br class="">
<br class="">
Thank you,<br class="">
Vahid<br class="">
<br class="">
<br class="">
Vahid Askarpour<br class="">
Department of physics and atmospheric science<br class="">
Dalhousie University<br class="">
Halifax, NS<br class="">
Canada<br class="">
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