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<p><font size="-1">Hi Vahid <br>
</font></p>
<p><font size="-1">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>
</font></p>
<p><font size="-1">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>
</font></p>
<p><font size="-1">regards Pietro<br>
</font></p>
<p><font size="-1"><br>
</font></p>
<div class="moz-cite-prefix">On 15/04/20 15:05, Vahid Askarpour
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:115BBDFE-391B-4511-B7D0-D9C40B0A7244@dal.ca">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
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><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>
<div class="" style="word-wrap:break-word;
line-break:after-white-space">
<div class=""><br class="">
<div class=""><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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