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<p><font size="-1">Hello <br>
</font></p>
<p><font size="-1">from the pdos 2 electrons have <i>moved </i>from
Pb 6p to fill the S 3p band, as expected. <br>
</font></p>
<p><font 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><font size="-1">Pietro<br>
</font></p>
<p><font size="-1"><br>
</font></p>
<div class="moz-cite-prefix">On 14/04/20 00:54, Vahid Askarpour
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:EFAC0BCD-DF7D-4A3F-A765-36B3FB09EAA8@dal.ca">
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<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>
<div class="" style="word-wrap:break-word;
line-break:after-white-space">
<div class=""><br class="">
<div><br class="">
<blockquote type="cite" class="">
<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>
<br class="x_Apple-interchange-newline">
<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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