<div dir="ltr"><div dir="ltr"><div class="gmail_default" style="font-family:verdana,sans-serif;color:rgb(0,0,0)">Dear Xavier,</div><div class="gmail_default" style="font-family:verdana,sans-serif;color:rgb(0,0,0)"><br></div><div class="gmail_default" style="font-family:verdana,sans-serif;color:rgb(0,0,0)">"Fixed-Point" is the more mathematical term for "Self-Consistent". There is a lot of interesting math behind "Self-Consistent" that is not apparent. For instance, nasty oscillating problems may be related to what are called "Strange Attractors" (e.g. <a href="https://en.wikipedia.org/wiki/Attractor">https://en.wikipedia.org/wiki/Attractor</a>). While one hopes that scf problems converge nicely and cleanly, they don't have to! (I don't have the math to understand how to avoid some of the really nasty cases.)</div><div class="gmail_default" style="font-family:verdana,sans-serif;color:rgb(0,0,0)"><br></div><div class="gmail_default" style="font-family:verdana,sans-serif;color:rgb(0,0,0)">Interesting point about Fourier transform, not sure how one would do this transform. I will ponder.</div></div></div><br><div class="gmail_quote"><div dir="ltr">On Thu, Nov 1, 2018 at 12:39 PM Xavier Rocquefelte <<a href="mailto:xavier.rocquefelte@univ-rennes1.fr">xavier.rocquefelte@univ-rennes1.fr</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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<p>Thank you so much Laurence for this explanation which definitely enlight my understanding!
<br>
</p>
<p>Could you just give me more hints. What do you mean by "fixed point solution" when you are speaking about the spins?
<br>
</p>
<p>Brainstorming session:<br>
</p>
<p>I am a chemist but I can propose an idea without a clear understanding! The rotations are non-linear and we should find a way to express them in such a way to be linear.
<br>
</p>
<p>Is a Fourier transform (or fractional Fourier transform or something related) useful in such a case? </p>
<p>Cheers</p>
<p>Xavier<br>
</p>
<p><br>
</p>
<p><br>
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<br>
<div class="m_3252974082701169213moz-cite-prefix">Le 01/11/2018 à 17:19, Laurence Marks a écrit :<br>
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<div class="gmail_default" style="font-family:verdana,sans-serif;color:#000000">Quite a few things are going on "Under the hood" in these systems, so let me explain a little.</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;color:#000000"><br>
</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;color:#000000">For heavy atoms with large RMTs the initial pseudocharge (PW density inside the RMTs) from dstart is quite bad. In addition, unless you are careful to chose a "good" initial spin
state in case.inst, the spins can be quite far from the fixed point solution. While it might appear that the density and energy (:DIS and :ENE) are oscillating, in reality the pseudocharge and the spin/orbital moments are rotating slowly in a N-Dimensional
space. Rotations are non-linear, and the mixer (all versions in all DFT codes to my knowledge) use linear expansions. It can therefore take a long time for these rotations tocomplete. What you will often see if you look at the pseudocharge (grep :CPC in 18.1,
the pseudocharge was not monited in earlier versions as its role was not known) you will often see that it is slowly "walking" -- similarly the spin moments etc.</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;color:#000000"><br>
</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;color:#000000">When you add SOC and/or +U (or -eece) there will be large rotations of the spins and/or spin moments.</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;color:#000000"><br>
</div>
<div class="gmail_default" style="font-family:verdana,sans-serif;color:#000000">In an ideal world some transformation would be applied to the Wien2k variables to separate the pseudocharge and convert the rotations to linear variables. I do not know how to do
this, and simple ideas such as using the sum and difference of spins don't work. (As expected, since this is a linear transformation.) I am open to (mathematical) suggestions/inspirations. It has to be math not fudge -- the mixer only works when the math is
right!</div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr">On Thu, Nov 1, 2018 at 9:34 AM Xavier Rocquefelte <<a href="mailto:xavier.rocquefelte@univ-rennes1.fr" target="_blank">xavier.rocquefelte@univ-rennes1.fr</a>> wrote:<br>
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<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
I have exactly the same experience. It is really a matter of cooking to <br>
my point of view and strongly depends on the system and what is <br>
happening at the Fermi level.<br>
<br>
In my case I am using DFT+U+SOC for such systems. The hubbard term <br>
indeed allows to separate the 4f states. However, the SOC is also <br>
essential and leads to large effects in these systems.<br>
In the case of HoPtBi, all the elements requires SOC. In addition it is <br>
an intermetallic compound, meaning that you have both localized and <br>
delocalized electrons!<br>
<br>
Did you try the following procedure:<br>
- DFT+SOC in a self-consistent manner<br>
- DFT+SOC+U on top of the first calculation<br>
<br>
Sometimes the lift of degeneracy due to SOC is sufficient to converge <br>
more efficiently DFT+SOC and then after DFT+SOC+U. And sometimes it is <br>
the other way around;)<br>
<br>
Best wishes<br>
Xavier<br>
<br>
<br>
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<div dir="ltr"><span style="font-size:12.8px">Professor Laurence Marks</span><br>
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<div dir="ltr"><span style="font-size:12.8px">"Research is to see what everybody else has seen, and to think what nobody else has thought", </span><span style="font-size:12.8px">Albert Szent-Gyorgi</span><br>
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------------------------
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Univ Rennes - CNRS - UMR6226, France
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</blockquote></div><br clear="all"><div><br></div>-- <br><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><span style="font-size:12.8px">Professor Laurence Marks</span><br></div><div dir="ltr"><span style="font-size:12.8px">"Research is to see what everybody else has seen, and to think what nobody else has thought", </span><span style="font-size:12.8px">Albert Szent-Gyorgi</span><br><a href="http://www.numis.northwestern.edu" target="_blank">www.numis.northwestern.edu</a> ; <span style="font-size:12.8px">Corrosion in 4D: </span><a href="http://MURI4D.numis.northwestern.edu" style="font-size:12.8px" target="_blank">MURI4D.numis.northwestern.edu</a><div><span style="font-size:12.8px">Partner of the CFW 100% program for gender equity, </span><a href="http://www.cfw.org/100-percent" style="font-size:12.8px" target="_blank">www.cfw.org/100-percent</a></div><div>Co-Editor, Acta Cryst A</div></div></div></div></div></div></div></div></div></div></div>