[Wien] When to add a U.

[Pavel Novak]

Let me join the club:

contrary to Georg I am more optimistic and no longer think that 'LDA+U is
a basis set dependent method with poorly defined energy functional'.
Providing the radial part of basis functions is not varied, the LDA+U
potential is obtained by variation of LDA+U functional (A.S. Shick et al.
PRB60, 10763, 1999). It is true that the method is partly empirical as no
truly 'ab initio' and 'always correct' U, J exist. The fact not often
appreciated is that LDA+U might have several selfconsistent solutions,
depending on how at the start the correlated electrons are distributed
between the |l,m> states (i.e. on starting density matrix). Now, as a
rule, correlated electrons are localized and the selfinteraction may be
big. Selfinteraction is not removed in LDA+U (notation LDA+U(SIC) in WIEN
is misleading - my fault, it should be called Fully Localized Limit) and
the lowest total energy might not correspond to the true ground state (see
J. Kunes et al. PRB 68, 115101 for an example and brief analysis).

To return to the original question: add U whenever LSDA and GGA give wrong
ground state and also when there is a disagreement with experiment and
strongly correlated electrons are present. Be careful, however, because of
possible multiplicity of the solutions and ambiguity as to which version
of LDA+U to choose.

Regards
Pavel

_________________________________________________
Dr. Pavel Novak
Department of Magnetism and Superconductivity
Institute of Physics AS CR
Cukrovarnicka 10, 162 53 Praha 6, Czech Republic
tel: +420 2 20 318 532
e-mail: novakp at fzu.cz

On Sun, 23 Jan 2005 georg at chem.au.dk wrote:

> 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
>
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