[Wien] Charge Convergence is not achieved

[Peter Blaha]

Basically, for a metal the convergence depends on the details of the
bandstructure around EF and on the method to determine EF and the occupation
of all eigenvalues.

Suppose you have two bands crossing EF, one has A character, the other one B.
Now you start with a coarse k-mesh and represent the band with only a few k-points,
such that the weight (number of electrons) for each eigenvalue E_n_k is large (e.g 0.1 e)

At some iteration it can happen that E_n1_k1 is just a tiny little bit lower than E_n2_k2
(k1 and k2 come from different bands) and both are close to EF. Than E_n1_k1 is
"fully" occupied", while E_n2_k2" is completely empty when using the TETRA method (because this
interpolates only within the same band n!) and thus you get more charge
at atom A.
Even when the mixer now adds only very little of this new density, it may lead to a potential where
E_n_k1 is now HIGHER than E_n_k2, and thus in the next iteration we get a density
which has 0.1 e more at site B (and not A). Thus the newly generated charge densities
differ by a huge (0.1 e) amount from the previous one.

If you now increase the k-mesh, the weight of an individual k-point will go down
(eg. be only 0.01 e) and thus such oszillations will be an order of magnitude smaller.
In addition, an integration (TETRAHEDRON method) becomes better with more sample
points and convergence will be better.....

On the other hand when using TEMP(S) instead of TETRA, you may be able to damp these
oszillations, since the occupation depends only on the energy, but not on the
"topology" of the bands (i.e. which eigenvalues are connected to each other via band n
and k-index k). This is a clear advantage of TEMP, however, you run into the problem
that a final solution eventually has ALWAYS some occupation of "unoccupied" states,
which should be zero for an "exact method" (and you may even loose or greatly reduce
your magnetic moment).

Basically, there is no absolute rule and convergence has to be checked for each individual
case because you do not know the band-details.

Of coarse there are general considerations like:

bad           -           good convergence
metal         -           nonmetal
flat bands    -           steep bands   at EF, or equivalently
elements with f,d-states at EF -         no d,f states at EF
many non-equivalent atoms of the same type -    onyl ONE equivalent atom on nuclear charge Z

Some examples derived from those rules:

fcc Cu converges very quick (only ONE very STEEP S-like band at EF), bcc V is more difficult
(MANY D-BANDS cross EF).
fcc Ni is even worse, because of spin polarization you DOUBLE the number of bands at EF
and one can easily shuffle electrons from spin-up to dn,...

A supercell or surface of Ni becomes even worse, because you may have several different
Ni atoms (surface, sub-surface,.... bulk) and thus have with X-layers X-TIMES as many bands
around EF, all of them VERY SIMILAR (because they are all Ni), but still clearly distinct
(surface,....).....



Am 07.07.2011 14:42, schrieb Laurence Marks:
> 2011/7/7 Shamik Chakrabarti<shamikiitkgp at gmail.com>:>  Dear Peter Blaha Sir,>                          Indeed by increasing number of K points we got the>  convergence. Sir I have now some basic queries on this topic. You have said>  that>                       "sometimes you cannot reach (easily) arbitrary>  convergence">  why in some cases we can not reach convergence up to our desired limit?...is>  it the limitation of DFT?....or it means that the feasibility of the>  solution is only up to the achieved convergence?
> This is in fact a deep, and very good question, at least in my opinion.
> Unfortunately that does not mean that there is a good answer to it!
> With the perfect functional convergence should (I believe, others maydisagree) always be good. With a very imperfect functional it is quitepossible that a DFT calculation will not converge, i.e. it isunfeasible. Empirically many (but not all) metals do not converge wellwith small numbers of k-points, but some others do. Why....I do notunderstand as I cannot write down a mathematical analysis to explainthis and do not believe that there is a formal analysis in theliterature, it is just empirical knowledge (folklore).
>
> -- Laurence MarksDepartment of Materials Science and EngineeringMSE Rm 2036 Cook Hall2220 N Campus DriveNorthwestern UniversityEvanston, IL 60208, USATel: (847) 491-3996 Fax: (847) 491-7820email: L-marks at northwestern dot eduWeb: www.numis.northwestern.eduChair, Commission on Electron Crystallography of IUCRwww.numis.northwestern.edu/Research is to see what everybody else has seen, and to think whatnobody else has thoughtAlbert Szent-Gyorgi_______________________________________________Wien mailing listWien at zeus.theochem.tuwien.ac.athttp://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien

-- 

                                       P.Blaha
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Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-1-58801-15671             FAX: +43-1-58801-15698
Email: blaha at theochem.tuwien.ac.at    WWW: http://info.tuwien.ac.at/theochem/
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