[Pw_forum] LDA+U character

[Matteo Cococcioni]

dear Ali,

I will try to answer your questions



ali kazempour wrote:
> Dear All
> I have some questions about LDA+U nature. Does U treate like a  
> perturbation( I know that GW( many body peturbation method) is 
> modified version of LDA+U? if yes why we are allowed to take 
> U=0,1,2,........ up to large values? and why we solve system 
> self-consistent?
>

no, U is not treated as a perturbation. it is more a correction to the 
"standard" DFT energy functional. you can check the relationship between 
+U and GW in the following
reference (probably there are many more):

Anisimov et al, Journal of Physics: Condensed Matter 9, 767 (1997)


> Does U comute with KS-hamiltonian in every U values? I mean  does the 
> order of states remains intact with respect to LDA or they can change?
> and final question:
>

For sure the +U correction to the potential commutes with the 
translation and other symmetries of the crystal.
I think it doesn't commute with the rest of the Hamiltonian (the 
unperturbed DFT one). So if you think to switch on the U from a
U=0 ground state, unless the KS states are already bloch sums of atomic 
orbitals (that would be a very unlikely accident) the +U correction
introduces interactions between them if allowed by symmetry and you are 
going to get a non trivial mixing of them besides a shift in the
eigenvalue. Probably the most significant modifications are going to 
take place for states around the Fermi level that may get more localized.
The ones that are deeper in energy are probably closer to be atomic-like 
already and they will, at most, get a shift in the corresponding 
eigenvalues.

> What is the effect of U on
> 1-empty states in conduction band  (with d-character)
>

pushed up

> 2-half filled states in conduction band(with d-character)
>

depends: see above

> 3-filled- states in conduction band (with d-character)
>

pushed down

> Thanks a lot
>
>
> Ali Kazempour
>
>


hope this helps.

Matteo


>
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>
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Matteo Cococcioni
Department of Chemical Engineering and Materials Science,
University of Minnesota
421 Washington Av. SE
Minneapolis, MN 55455
Tel. +1 612 624 9056    Fax +1 612 626 7246
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