[Wien] Charge Convergence is not achieved

[Laurence Marks]

In addition to what Peter said (use more k-points and/or TEMP or
TEMPS, perhaps just 0.0018 or even 0.001 for the later), in principle
it might help a little to:
a) Reduce the Greed (mixing factor) to 0.1
b) Increase the number of memory steps (nuse) to 16 (the code will not
let you go too high)
c) At least in version 11.1 with MSEC3 you can increase the
regularization, for instance with
DIAG XXX

where XXX can be increased to 1E-3 or perhaps even 1e-2 (but please be careful).

On Thu, Jul 7, 2011 at 9:24 AM, Laurence Marks <L-marks at northwestern.edu> wrote:
>
> On Thu, Jul 7, 2011 at 8:24 AM, Peter Blaha
> <pblaha at theochem.tuwien.ac.at> wrote:
>> 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
>> --------------------------------------------------------------------------
>> 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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>>
>
>
>
> --
> Laurence Marks
> Department of Materials Science and Engineering
> MSE Rm 2036 Cook Hall
> 2220 N Campus Drive
> Northwestern University
> Evanston, IL 60208, USA
> Tel: (847) 491-3996 Fax: (847) 491-7820
> email: L-marks at northwestern dot edu
> Web: www.numis.northwestern.edu
> Chair, Commission on Electron Crystallography of IUCR
> www.numis.northwestern.edu/
> Research is to see what everybody else has seen, and to think what
> nobody else has thought
> Albert Szent-Gyorgi
>



-- 
Laurence Marks
Department of Materials Science and Engineering
MSE Rm 2036 Cook Hall
2220 N Campus Drive
Northwestern University
Evanston, IL 60208, USA
Tel: (847) 491-3996 Fax: (847) 491-7820
email: L-marks at northwestern dot edu
Web: www.numis.northwestern.edu
Chair, Commission on Electron Crystallography of IUCR
www.numis.northwestern.edu/
Research is to see what everybody else has seen, and to think what
nobody else has thought
Albert Szent-Gyorgi