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<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="moz-txt-link-freetext" href="http://www.fhi-berlin.mpg.de/~xinguo/talks/jiang_cdft-coffeetalk.pdf">http://www.fhi-berlin.mpg.de/~xinguo/talks/jiang_cdft-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="moz-txt-link-freetext" href="https://doi.org/10.1103/PhysRevB.43.7570">https://doi.org/10.1103/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="moz-txt-link-freetext" href="https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg14460.html">https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.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)/9 = 0.11884760366667<br>
<br>
ε3d_dn = -(4*-0.292400769+5*-0.274004694)/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<br>
<br>
<br>
<blockquote type="cite"
cite="mid:CAHYowjHWPbt708J5NwpMQ6vPzzzfCc34vUn-73vyQXwjmQ--Jw@mail.gmail.com">
<div dir="ltr">
<div><span id="gmail-result_box" class="gmail-" 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="gmail-" lang="en"><a
href="http://susi.theochem.tuwien.ac.at/reg_user/textbooks/Constraint_U.pdf"
moz-do-not-send="true">http://susi.theochem.tuwien.ac.at/reg_user/textbooks/Constraint_U.pdf</a><br>
<br>
<span class="gmail-">But according to <span
style="color:rgb(85,85,85);font-family:"times new
roman",serif;font-size:large;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">Anisimov's
paper</span>
, <span style="font-family:"times new
roman",serif;font-size:large;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration-style:initial;text-decoration-color:initial;color:rgb(34,34,34);background-color:rgb(255,255,255);float:none;display:inline">J=E3d'up'(n+0.5,n-0.5)-<span> </span></span><span
style="font-family:"times new
roman",serif;font-size:large;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration-style:initial;text-decoration-color:initial;color:rgb(34,34,34);background-color:rgb(255,255,255);float:none;display:inline">E3d'<wbr>dn'(n+0.5,n-0.5)</span><span
style="color:rgb(85,85,85);font-family:"times new
roman",serif;font-size:large;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline"> </span> </span></span></div>
<div><span class="gmail-" lang="en"><span class="gmail-">So we
add an electron for the spin-up and we removed a electron
for </span></span>spin-<span class="gmail-" lang="en"><span
class="gmail-">dn and we calculate the difference
Eup_3d-Edn3d for a one calculation</span></span></div>
<div><span class="gmail-" lang="en"><span class="gmail-"><span
class="gmail-short_text" lang="en"><span class="gmail-"><br>
</span></span></span></span></div>
<div><span class="gmail-" lang="en"><span class="gmail-">
<span id="gmail-result_box" class="gmail-short_text"
lang="en"><span class="gmail-">that's what I did</span></span>
<br>
</span></span></div>
<div><span class="gmail-" lang="en"><span class="gmail-"><br>
</span></span></div>
<div><span class="gmail-" lang="en"><span class="gmail-">Is this
correct?</span></span></div>
</div>
</blockquote>
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