[Wien] Hund's Exchange parameter (J)

[Gavin Abo]

That calculation I did quite some time ago.  So, I cannot remember my 
reasoning behind it.  Since I didn't see an explanation for it in 
Constraint_U.pdf and didn't know how Madsen and Pavel got the weights, I 
likely just assumed the ε3d_dn would be the same as the ε3d_up.

I could be wrong, but I think the value for ":3dd001" and ":3d 001" are 
from the "x lcore -up" [ 
https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg17160.html 
].

So it might be that the weights (occupation numbers) come from 
NiO.incup_+.50 and NiO.incup_+.5-1.

*In Constraint_U.pdf*

NiO.incup_+.50 contains:

N,KAPPA,OCCUP
3, 2,4 3D* or :3dd001
3,-3,5 3D or :3d 001

NiO.incup_+.5-1 contains:

3, 2,4
3,-3,5

> 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)/ ...

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