[Wien] When to add a U.

[georg at chem.au.dk]

After posting the paper
> > http://xxx.lanl.gov/pdf/cond-mat/0412560
about calculating the U, a question was posted:
> Your paper almost implies (or does imply?) that one should always use a U
> for a transition metal (oxide?) -- or am I reading this wrong?

I'd like to answer it in this public forum, because I'd like to start a
discussion. My understanding of the subject isn't perfect and I'd be happy for
any comments

My opinion is yes and no.

YES because,
The LDA and GGA are only exact for the free electron gas and for all other
systems the spurious self interaction is a source off error. Off course both
the effect and the size off the U is the largest for the "strongly correlated
systems". However I recently read a nice paper where they calculated NMR
shielding parameters, which depend on the unoccupied bands:
J. Am. Chem. Soc.; 2004; 126(39); 12628-12635
The conclusion here is that one need a U for the unoccupied d-states of Ca.
This
would off course not influence any of the ground state properties, but it
surprised me because I would guess the shape off the d-state to be highly
diffuse.


NO because:
LDA and GGA are functionals with well defined potentials and energyfunctional.
The LDA+U is a basis-set dependent method with a poorly defined
energy-functional. One should concentrate on doing the LDA and GGA well (not
introducing unphysical atomic sphere approximations andthe like) and understand
when and why it might fail. David Singh stated this oppion. In a recent example
one would have overlooked a structural distortion, if the a disagreement with
experiment had just been blamed on some magical U.
P. Blaha, D.J. Singh, K. Schwarz, Physical Review Letters 93, 216403 (2004) 
Another example might be that you force a good agreement with experiment when
you need to describe many-body effects that are also not described with LDA+U
Phys Rev B , 67, 153106 (2003) 

These are my two Eurocents contribution. 

> 
> On Tue, 11 Jan 2005 georg at chem.au.dk wrote:
> 
> > Hi all
> >
> > there have been some request about calculating U in APW. I have uploaded a
> paper
> > where we do this for magnetite. Furthermore it is done for NiO and and FeO
> and
> > Fe2O3 as tests:
> > it should appear in EPL soon.
> >
> > The method should be described in there. I'll try and send a worked out
> example
> > for NiO when I get time.
> >
> >  Best wishes
> >    Georg