[Wien] Hund's Exchange parameter (J)

[Gavin Abo]

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?

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://zeus.theochem.tuwien.ac.at/pipermail/wien/attachments/20180512/70a269cc/attachment.html>