[Pw_forum] LDA+U character

[ali kazempour]

Dear Matteo
Thanks many for your reply. But my special case is for the defect states (has d-character  )in TiO2 that is in resonance with conduction band and is filled with 2 electrons. When I increased the U from 1 to 4 I saw that the defect state bieng pushed up instead lowering of this state as we expected from theory of LDA+U. Is it true? Moreover for another defect state that is empty and is above conduction band I saw it  being peshed down in contrast with LDA+U expection. But when I perform GW@ GGA+U I see that the behavior is reversed in which empty states being pushed up while filled state is pushing down. what does it mean? is it rational?
thanks a lot

Ali Kazempour



Fritz-Haber-Institut fax : ++49-30-8413 4701
der Max-Planck-Gesellschaft
Faradayweg 4-6 e-mail: kazempou at fhi-berlin.mpg.de
D-14 195 Berlin-Dahlem / German

--- On Sun, 7/4/10, Matteo Cococcioni <matteo at umn.edu> wrote:


From: Matteo Cococcioni <matteo at umn.edu>
Subject: Re: [Pw_forum] LDA+U character
To: "PWSCF Forum" <pw_forum at pwscf.org>
Date: Sunday, July 4, 2010, 8:29 PM



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


>
> Fritz-Haber-Institut fax : ++49-30-8413 4701
> der Max-Planck-Gesellschaft
> Faradayweg 4-6 e-mail: kazempou at fhi-berlin.mpg.de
> D-14 195 Berlin-Dahlem / German
>
>
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Matteo Cococcioni
Department of Chemical Engineering and Materials Science,
University of Minnesota
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