<div dir="ltr"><div>Thank you Dr. Gavin Abo<br></div><br><span id="gmail-result_box" class="gmail-" lang="en"><span class="gmail-">I agree that the
occupation for spin-up (the addition of an electron) is 4 and 5</span></span><br>ε3d_up = (4*0.109629972+5*0.126221709)/<wbr>9 = 0.11884760366667<span id="gmail-result_box" class="gmail-" lang="en"><span class="gmail-"><br><br> but
when we remove an electron for spin-Dn we have to put 4 and 3 or 4 and5?</span></span><br>
<br>
ε3d_dn = -(4*-0.292400769+(5or3)*-0.<wbr>274004694)/ ...<br></div><div class="gmail_extra"><br><div class="gmail_quote">2018-05-13 0:19 GMT+02:00 Gavin Abo <span dir="ltr"><<a href="mailto:gsabo@crimson.ua.edu" target="_blank">gsabo@crimson.ua.edu</a>></span>:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div text="#000000" bgcolor="#FFFFFF">
<p>Yes, I believe that is correct that Constraint_U.pdf is
performing the same calculation as Anisimov's paper.</p>
<p>As illustrated nicely on slide 11 in</p>
<p><a class="m_2701624311443698752moz-txt-link-freetext" href="http://www.fhi-berlin.mpg.de/~xinguo/talks/jiang_cdft-coffeetalk.pdf" target="_blank">http://www.fhi-berlin.mpg.de/~<wbr>xinguo/talks/jiang_cdft-<wbr>coffeetalk.pdf</a>
,<br>
</p>
just as you say, an electron is added for spin-up and an electron is
removed for spin-dn. That is what the case.inc* files are used for
in section III part A. and B. in Constraint_U.pdf.<br>
<br>
As you can see in F^0_eff EPL vol. 69, 777 (2005), it look like
equation 4 comes from equation 9 Anisimov's Phys. Rev. B vol. 43,
7570 (1991) paper [ <a class="m_2701624311443698752moz-txt-link-freetext" href="https://doi.org/10.1103/PhysRevB.43.7570" target="_blank">https://doi.org/10.1103/<wbr>PhysRevB.43.7570</a> ].
Relating that to Anisimov's equation 10 and 11 in Phys. Rev. B vol.
44, 943 (1991), it looks like we could write the equation for Ueff
as:<br>
<br>
Ueff ≈ F^0_eff = J + U<br>
<br>
In the NiO example, the U from the difference of the Fermi energies
[
<a class="m_2701624311443698752moz-txt-link-freetext" href="https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg14460.html" target="_blank">https://www.mail-archive.com/<wbr>wien@zeus.theochem.tuwien.ac.<wbr>at/msg14460.html</a>
]:<br>
<br>
U = -εF_up + εF_dn = -(0.4780996800)+0.5181842639 = 0.0400845839<br>
<br>
while the J from the difference of the "3d eigenvalues":<br>
<br>
ε3d_up = (4*0.109629972+5*0.126221709)/<wbr>9 = 0.11884760366667<br>
<br>
ε3d_dn = -(4*-0.292400769+5*-0.<wbr>274004694)/9 = -0.28218072733333<br>
<br>
J = ε3d_up - ε3d_dn = 0.11884760366667 - (-0.28218072733333) =
0.401028331<br>
<br>
Ueff ≈ F^0_eff = J + U = 0.0400845839 + 0.401028331 = .4411129148 Ry<span class=""><br>
<br>
<br>
<blockquote type="cite">
<div dir="ltr">
<div><span id="m_2701624311443698752gmail-result_box" class="m_2701624311443698752gmail-" lang="en"><span>I
agree with you regarding the calculation of Ueff using the
method described in the following file</span></span></div>
<div><span class="m_2701624311443698752gmail-" lang="en"><a href="http://susi.theochem.tuwien.ac.at/reg_user/textbooks/Constraint_U.pdf" target="_blank">http://susi.theochem.tuwien.<wbr>ac.at/reg_user/textbooks/<wbr>Constraint_U.pdf</a><br>
<br>
<span class="m_2701624311443698752gmail-">But according to <span>Anisimov's
paper</span>
, <span>J=E3d'up'(n+0.5,n-0.5)-<span> </span></span><span>E3d'dn<wbr>'(n+0.5,n-0.5)</span><span> </span> </span></span></div>
<div><span class="m_2701624311443698752gmail-" lang="en"><span class="m_2701624311443698752gmail-">So we
add an electron for the spin-up and we removed a electron
for </span></span>spin-<span class="m_2701624311443698752gmail-" lang="en"><span class="m_2701624311443698752gmail-">dn and we calculate the difference
Eup_3d-Edn3d for a one calculation</span></span></div>
<div><span class="m_2701624311443698752gmail-" lang="en"><span class="m_2701624311443698752gmail-"><span class="m_2701624311443698752gmail-short_text" lang="en"><span class="m_2701624311443698752gmail-"><br>
</span></span></span></span></div>
<div><span class="m_2701624311443698752gmail-" lang="en"><span class="m_2701624311443698752gmail-">
<span id="m_2701624311443698752gmail-result_box" class="m_2701624311443698752gmail-short_text" lang="en"><span class="m_2701624311443698752gmail-">that's what I did</span></span>
<br>
</span></span></div>
<div><span class="m_2701624311443698752gmail-" lang="en"><span class="m_2701624311443698752gmail-"><br>
</span></span></div>
<div><span class="m_2701624311443698752gmail-" lang="en"><span class="m_2701624311443698752gmail-">Is this
correct?</span></span></div>
</div>
</blockquote>
<br>
</span></div>
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