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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