[Wien] When to add a U.

[Stefaan Cottenier]

A very interesting question, indeed. Here's my single eurocent:

We have been playing with LDA+U for a series of simple metals for which 
LDA+U wasn't designed in the first place (surfaces and multilayers 
involving Fe and Cr). Quite to our surprise, applying in a conservative 
way moderate values of U solves a series of deficiencies of LDA in those 
materials. At least in one case, the problem of LDA can be traced back 
to a single band that is incorrectly just above E_F, and LDA+U pushes it 
correctly just below it. Our hypothesis is that there isn't much physics 
in LDA+U for such materials, but that the additional freedom allowed by 
the U parameter can sometimes be sufficient to fix a nearly-miss of LDA. 
In this way, LDA+U can be a way to get more insight into a particular 
system, but still one can not say then that LDA+U 'works' for that 
system in the same way as LDA works.

I'm very interested to hear other opinions or experiences.

Stefaan



> I'm the guilty party for the question, which I agree with Georg is
> important. For instance, there is a paper by Fang and Terakura, Surf.Sci.
> 470, L75 (2000) where LDA+U is used for a SrTiO3 surface (a topic dear to
> my heart) where there are large effects and they argue that LDA+U is in
> better agreement with experiment.
> 
> Just to expand the scope of the discussion (?) further, for fun I did
> LDA+U for MgO. With U=6eV, J=0 there is a change of about 0.01 Ryd/Mg
> atom. Although MgO has no "d-electrons", it does have d-harmonics in the
> density and if I understand DFT/U correctly, there is no distinction
> between d-electrons and d-harmonics. This is probably similar to the
> effects in Ca....??
> 
> 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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>>
> 
> 
> -----------------------------------------------
> Laurence Marks
> Department of Materials Science and Engineering
> MSE Rm 2036 Cook Hall
> 2220 N Campus Drive
> Northwestern University
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> Tel: (847) 491-3996 Fax: (847) 491-7820
> email: L - marks @ northwestern . edu
> http://www.numis.northwestern.edu
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