[Wien] Hund's Exchange parameter (J)

[Wien2k User]

Thank you Dr. Gavin Abo

I agree that the occupation for spin-up (the addition of an electron) is 4
and 5
ε3d_up = (4*0.109629972+5*0.126221709)/9 = 0.11884760366667

 but when we remove an electron for spin-Dn we have to put 4 and 3 or 4
and5?

ε3d_dn = -(4*-0.292400769+(5or3)*-0.274004694)/ ...

2018-05-13 0:19 GMT+02:00 Gavin Abo <gsabo at crimson.ua.edu>:

> Yes, I believe that is correct that Constraint_U.pdf is performing the
> same calculation as Anisimov's paper.
>
> As illustrated nicely on slide 11 in
>
> http://www.fhi-berlin.mpg.de/~xinguo/talks/jiang_cdft-coffeetalk.pdf ,
> 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.
>
> 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 [
> https://doi.org/10.1103/PhysRevB.43.7570 ].  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:
>
> Ueff ≈ F^0_eff =  J + U
>
> In the NiO example, the U from the difference of the Fermi energies [
> https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg14460.html
> ]:
>
> U = -εF_up + εF_dn = -(0.4780996800)+0.5181842639 = 0.0400845839
>
> while the J from the difference of the "3d eigenvalues":
>
> ε3d_up = (4*0.109629972+5*0.126221709)/9 = 0.11884760366667
>
> ε3d_dn = -(4*-0.292400769+5*-0.274004694)/9 = -0.28218072733333
>
> J = ε3d_up - ε3d_dn = 0.11884760366667 - (-0.28218072733333) = 0.401028331
>
> Ueff ≈ F^0_eff = J + U = 0.0400845839 + 0.401028331 = .4411129148 Ry
>
>
> I agree with you regarding the calculation of Ueff using the method
> described in the following file
> http://susi.theochem.tuwien.ac.at/reg_user/textbooks/Constraint_U.pdf
>
> But according to Anisimov's paper , J=E3d'up'(n+0.5,n-0.5)- E3d'dn
> '(n+0.5,n-0.5)
> So we add an electron for the spin-up and we removed a electron for spin-dn
> and we calculate the difference Eup_3d-Edn3d for a one calculation
>
> that's what I did
>
> Is this correct?
>
>
>
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