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<p>Hi,</p>
<p>You are absolutely right, the way we treat core-states in
spin-polarized calculations is "wrong", as we do two separate
calculations in the spin-up and dn potential, respectively. This
leads to 4 eigenvalues of p,d or f states, all of them get "half
occupation", which is not correct.<br>
</p>
<p>However, a couple of comments below:</p>
<p>i) Long time ago this was cross-checked for Fe using a
fully-relativistic KKR code.<br>
</p>
<p> </p>
<span lang="de-AT"><span style="mso-tab-count:1"> ( </span>Solid
State Commun. <b style="mso-bidi-font-weight:normal">79</b>, 121
(1991) ) <br>
</span>
<p class="Normal"
style="margin-left:35.4pt;text-indent:-35.4pt;tab-stops:-36.0pt
0cm 35.4pt"><span lang="de-AT">If I remember correctly, the
differences were negligible, at least for the quantities of
interest there.<br>
</span></p>
<p class="Normal"
style="margin-left:35.4pt;text-indent:-35.4pt;tab-stops:-36.0pt
0cm 35.4pt"><span lang="de-AT">ii) Spin-orbit + spin-polarization
has always a problem in DFT, as one uses commonly a
"spin-averaged" potential to evaluate the Spin-Orbit term, which
is certainly also an approximation. If you want, we average in a
different way.<br>
</span></p>
<p class="Normal"
style="margin-left:35.4pt;text-indent:-35.4pt;tab-stops:-36.0pt
0cm 35.4pt"><span lang="de-AT">iii) Yes, for open-core with
different occupations this is an additional approximation.
However, note that open-core calculations always have a fairly
large core-leakage. Distributing a couple of percent of 4f
charge as constant in the interstitial (or renormalizing this
inside the sphere) is a MUCH larger approximation anyway and in
addition dependent on RMT.</span></p>
<p class="Normal"
style="margin-left:35.4pt;text-indent:-35.4pt;tab-stops:-36.0pt
0cm 35.4pt"><span lang="de-AT">I would not trust total energy
differences of different open-core calculations too much, but
mainly because of different amounts of charge leakage. The
problem is anyway, that one cannot compare total energies with
different number of core electrons (this is true even for
semicore s-electrons which do not have SO effects, but the total
energy is not the same if treated as core or valence.<br>
</span></p>
<p class="Normal"
style="margin-left:35.4pt;text-indent:-35.4pt;tab-stops:-36.0pt
0cm 35.4pt"><span lang="de-AT">I've used open-core for
bandstructures only (and with fixed 4f number).</span> </p>
<p class="Normal"
style="margin-left:35.4pt;text-indent:-35.4pt;tab-stops:-36.0pt
0cm 35.4pt"><span lang="de-AT"></span></p>
<p class="Normal"
style="margin-left:35.4pt;text-indent:-35.4pt;tab-stops:-36.0pt
0cm 35.4pt"><span lang="de-AT"> </span></p>
<p class="Normal"
style="margin-left:35.4pt;text-indent:-35.4pt;tab-stops:-36.0pt
0cm 35.4pt"><span lang="de-AT">iii) Of course, open-core is
"computational convenient" since the input is "trivial" and the
calculations converge easily. But you can also use the FSM
method + GGA+U to select a certain magnetic moment (and thus
roughly the number of 4f states). And yes, surprisingly the U
value for 4f should not be one too large. For such heavy systems
it is also often not justified to use an "effective" U, but
should use U and J individually. In addition, note that with ONE
U, but different starting situations, one may run into different
metastable solutions, so one may need to search for the lowest
energy state.<br>
</span></p>
<p class="Normal"
style="margin-left:35.4pt;text-indent:-35.4pt;tab-stops:-36.0pt
0cm 35.4pt"><span lang="de-AT">Best regards</span></p>
<p class="Normal"
style="margin-left:35.4pt;text-indent:-35.4pt;tab-stops:-36.0pt
0cm 35.4pt"><span lang="de-AT">Peter Blaha</span></p>
<p class="Normal"
style="margin-left:35.4pt;text-indent:-35.4pt;tab-stops:-36.0pt
0cm 35.4pt"><span lang="de-AT"><br>
</span></p>
<p></p>
<div class="moz-cite-prefix">Am 17.07.2023 um 13:51 schrieb Jindrich
Kolorenc:<br>
</div>
<blockquote type="cite"
cite="mid:20230717135111.46d2a730@pc190b.fzu.cz">
<pre class="moz-quote-pre" wrap="">Dear Wien2k developers and users,
I would be grateful for your opinion, clarification or pointers to
literature about core states in Wien2k or LAPW in general. My
message is a bit long, I am sorry for that.
It seems to me that there is some inconsistency in the way Wien2k
treats the core states in spin-polarized calculations. As far as I
understand it, LCORE is run twice, once for spin-up potential and
once for spin-down potential. In each of these runs, the core states
are full (up and dn occupied). Then, I suppose, the up charge density
is set to 1/2 of the LCORE charge run for the up potential and dn
charge density is set to 1/2 of the LCORE charge run for the dn
potential. That is different than running a core solver once, each spin
channel feeling its own potential, which would seem to me as a more
"rigorous" strategy (but one could not use the same quantum numbers
for the core states as LCORE does).
I suppose that different approaches to the core states have some effect
also on the total-energy expression, since it contains sum of
eigenvalues (I suppose since mixer reads them from case.scf). In
Wien2k, there are two eigenvalues for each core state for
spin-polarized calculations. I checked Elk, and if I understand its
output correctly, it lists only one eigenvalue for each core state for
spin-polarized calculations. That probably means, that Elk runs one
core calculation for an averaged potential (though I did not
investigate Elk in detail to know for sure).
Do you know about any book or paper where different strategies would
be discussed and/or tested/compared? My LAPW reference, the David
Singh's book, does not appear to touch this.
It may well be that for full core states all this is usually
negligible, but I am more concerned about consequences for the
open-core approximation for 4f states (which is where I actually
noticed this "issue")
<a class="moz-txt-link-freetext" href="http://www.wien2k.at/reg_user/faq/open_core.html">http://www.wien2k.at/reg_user/faq/open_core.html</a>
The FAQ entry does not mention spin-polarized calculations, but runsp
does look for case.inc[up,dn] and it will use them if they exist. Then,
fully spin-polarized polarized f^7 state is calculated as 1/2 (I
suppose) of f^14 state, for instance. That is likely a good
approximation for Eu^2+ charge density (full shell vs full subshell),
but the eigenvalues/total energy are less obvious. And accuracy of
approximating fully spin-polarized f^6 with 1/2 of spin-restricted f^12
is even less obvious even for the charge density.
I see that the FAQ entry says that one should use LDA+U instead of open
core, but it has its own set of problems when applied to localized 4f
too. And open core has one attractive feature for me - it gives an
easy way to do calculations with constrained number of 4f electrons. Do
you think it is meaningful to compare total energies for such
calculations with different number of 4f electrons (charge-neutral
cells, electrons shuffled between 4f and valence s,p,d).
Any comments welcome.
Best regards,
Jindrich
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</pre>
</blockquote>
<pre class="moz-signature" cols="72">--
-----------------------------------------------------------------------
Peter Blaha, Inst. f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-158801165300
Email: <a class="moz-txt-link-abbreviated" href="mailto:peter.blaha@tuwien.ac.at">peter.blaha@tuwien.ac.at</a>
WWW: <a class="moz-txt-link-freetext" href="http://www.imc.tuwien.ac.at">http://www.imc.tuwien.ac.at</a> WIEN2k: <a class="moz-txt-link-freetext" href="http://www.wien2k.at">http://www.wien2k.at</a>
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