[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  
wrote:
>
> On Thu, Jul 7, 2011 at 8:24 AM, Peter Blaha
>  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:> ?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. WhyI do notunderstand as
>>> I cannot write down a mathematical analysis to explainthis and do no

[Wien] Charge Convergence is not achieved

[shamik chakrabarti]

Dear Dr. Peter Blaha Sir,

Thank you very much for all your responses. I have
to think over all the discussions calmly and it should definitely help us to
understand the basics of this convergence problem.

Thank you very much Sir.

with best regards,

On Thu, Jul 7, 2011 at 6:58 PM, Peter Blaha wrote:

> The problem of "functional" could for instance happen for 4f-compounds.
>
> In LDA/GGA all 4f bands will be around EF (which is physically wrong) and
> convergence is naturally very different (14 extremely FLAT bands/atom !!).
>
> Using "open core" or LDA+U or Hybrid-DFT you remove the failure of GGA and
> immediately also convergence should improve (since you have only a FEW
> WIDE s,d-bands at EF).
>
> Am 07.07.2011 15:05, schrieb shamik chakrabarti:
>
>> Dear Laurence Marks Sir,
>>
>>   Thank you very much for your reply.yes the question may
>> not have a very good answerif in any calculation we are not getting the
>> desired convergence, it may
>> happen that:
>> (1) Our chosen functional is not appropriate for the system
>>
>> (2) The system (say while trying to predict a new material!) may not be
>> feasible at all..
>>
>> Probably all we can say that if we are able to achieve desired convergence
>> (say 0.0001) we can say that we have used the appropriate functional for the
>> system and the system is
>> (may be) feasible (at least theoretically!! ).
>>
>> Sir please correct me if I am wrong in my concept.
>>
>> with best regards,
>>
>> On Thu, Jul 7, 2011 at 6:12 PM, Laurence Marks > northwestern.edu> L-marks at northwestern.**edu >> wrote:
>>
>>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 may
>>disagree) always be good. With a very imperfect functional it is quite
>>possible that a DFT calculation will not converge, i.e. it is
>>unfeasible. Empirically many (but not all) metals do not converge well
>>with small numbers of k-points, but some others do. WhyI do not
>>understand as I cannot write down a mathematical analysis to explain
>>this and do not believe that there is a formal analysis in the
>>literature, it is just empirical knowledge (folklore).
>>
>>
>>--
>>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
>>__**_
>>Wien mailing list
>>Wien at zeus.theochem.tuwien.ac.**at > zeus.theochem.tuwien.ac.at>> Wien at zeus.theochem.**tuwien.ac.at >
>>
>>
>> http://zeus.theochem.tuwien.**ac.at/mailman/listinfo/wien
>>
>>
>>
>>
>> --
>> Shamik Chakrabarti
>> Research Scholar
>> Dept. of Physics & Meteorology
>> Material Processing & Solid State Ionics Lab
>> IIT Kharagpur
>> Kharagpur 721302
>> INDIA
>>
>>
>>
>> __**_
>> Wien mailing list
>> Wien at zeus.theochem.tuwien.ac.**at 
>> http://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.atWWW: http://info.tuwien.ac.at/**
> theochem/ 
> --**--**
> --
> __**_
> Wien mailing list
> Wien at zeus

[Wien] Charge Convergence is not achieved

[shamik chakrabarti]

Dear Laurence Marks Sir,

  Thank you very much for your reply.yes the question may
not have a very good answerif in any calculation we are not getting the
desired convergence, it may happen that:
(1) Our chosen functional is not appropriate for the system

(2) The system (say while trying to predict a new material!) may not be
feasible at all..

Probably all we can say that if we are able to achieve desired convergence
(say 0.0001) we can say that we have used the appropriate functional for the
system and the system is (may be) feasible (at least theoretically!! ).

Sir please correct me if I am wrong in my concept.

with best regards,

On Thu, Jul 7, 2011 at 6:12 PM, Laurence Marks wrote:

> 2011/7/7 Shamik Chakrabarti :
> > 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 may
> disagree) always be good. With a very imperfect functional it is quite
> possible that a DFT calculation will not converge, i.e. it is
> unfeasible. Empirically many (but not all) metals do not converge well
> with small numbers of k-points, but some others do. WhyI do not
> understand as I cannot write down a mathematical analysis to explain
> this and do not believe that there is a formal analysis in the
> literature, it is just empirical knowledge (folklore).
>
>
> --
> 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
> ___
> Wien mailing list
> Wien at zeus.theochem.tuwien.ac.at
> http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien
>



-- 
Shamik Chakrabarti
Research Scholar
Dept. of Physics & Meteorology
Material Processing & Solid State Ionics Lab
IIT Kharagpur
Kharagpur 721302
INDIA
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[Wien] Charge Convergence is not achieved

[Shamik Chakrabarti]

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?

Thanking you,
with best regards,

On Wed, Jul 6, 2011 at 6:13 PM, Peter Blaha wrote:

> For just 3 atoms/cell (and metallid ??) 1000 or 5000 k are still not much.
> Better k-mesh should improve convergence.
>
> And sometimes you cannot reach (easily) arbitrary convergence. What about
> E-tot, ... ?
>
>
> Am 06.07.2011 07:48, schrieb Shamik Chakrabarti:
>
>> Dear wien2k users,
>>
>> We have done volume optimization of a structure having space group no. 225
>> (Fm3m) and 3 inequivalent atoms per unit cell. We have taken the least
>> energy lattice parameters for
>> spin polarized SCF calculations. However, the last calculation (spin
>> polarized SCF) has not been converging at all. We have set the convergence
>> criteria of  charge to 0.0001and it
>> reached up to 0.006. After that its is fluctuating sinusoidally at this
>> value (even at around 400th iteration). We have also tried using the
>> fallowing steps, such as
>>
>> 1. increasing the RmaxKmax value from 7 to 9
>>
>> 2. changing mixer values ranging from 0.01 to 0.3 (using MSEC mixing
>> scheme...wien2k 10)
>>
>> 3. increasing the K-points from 1000 to 5000
>>
>> but unfortunately we haven't got the desired convergence yet. Therefore,
>> it is very helpful for us to have a suggestion for this problem.
>>
>> --
>> Shamik Chakrabarti
>> Research Scholar
>> Dept. of Physics & Meteorology
>> Material Processing & Solid State Ionics Lab
>> IIT Kharagpur
>> Kharagpur 721302
>> INDIA
>>
>>
>>
>> __**_
>> Wien mailing list
>>
>> Wien at zeus.theochem.tuwien.ac.**at 
>> http://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.atWWW: http://info.tuwien.ac.at/**
> theochem/ 
> --**--**
> --
> __**_
> Wien mailing list
>
> Wien at zeus.theochem.tuwien.ac.**at 
> http://zeus.theochem.tuwien.**ac.at/mailman/listinfo/wien
>



-- 
Shamik Chakrabarti
Research Scholar
Dept. of Physics & Meteorology
Material Processing & Solid State Ionics Lab
IIT Kharagpur
Kharagpur 721302
INDIA
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[Wien] Charge Convergence is not achieved

[Peter Blaha]

The problem of "functional" could for instance happen for 4f-compounds.

In LDA/GGA all 4f bands will be around EF (which is physically wrong) and
convergence is naturally very different (14 extremely FLAT bands/atom !!).

Using "open core" or LDA+U or Hybrid-DFT you remove the failure of GGA and
immediately also convergence should improve (since you have only a FEW
WIDE s,d-bands at EF).

Am 07.07.2011 15:05, schrieb shamik chakrabarti:
> Dear Laurence Marks Sir,
>
>Thank you very much for your reply.yes the question may 
> not have a very good answerif in any calculation we are not getting the 
> desired convergence, it may
> happen that:
> (1) Our chosen functional is not appropriate for the system
>
> (2) The system (say while trying to predict a new material!) may not be 
> feasible at all..
>
> Probably all we can say that if we are able to achieve desired convergence 
> (say 0.0001) we can say that we have used the appropriate functional for the 
> system and the system is
> (may be) feasible (at least theoretically!! ).
>
> Sir please correct me if I am wrong in my concept.
>
> with best regards,
>
> On Thu, Jul 7, 2011 at 6:12 PM, Laurence Marks  > wrote:
>
> 2011/7/7 Shamik Chakrabarti  >:
>  > 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 may
> disagree) always be good. With a very imperfect functional it is quite
> possible that a DFT calculation will not converge, i.e. it is
> unfeasible. Empirically many (but not all) metals do not converge well
> with small numbers of k-points, but some others do. WhyI do not
> understand as I cannot write down a mathematical analysis to explain
> this and do not believe that there is a formal analysis in the
> literature, it is just empirical knowledge (folklore).
>
>
> --
> 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
> ___
> Wien mailing list
> Wien at zeus.theochem.tuwien.ac.at  zeus.theochem.tuwien.ac.at>
> http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien
>
>
>
>
> --
> Shamik Chakrabarti
> Research Scholar
> Dept. of Physics & Meteorology
> Material Processing & Solid State Ionics Lab
> IIT Kharagpur
> Kharagpur 721302
> INDIA
>
>
>
> ___
> Wien mailing list
> Wien at zeus.theochem.tuwien.ac.at
> http://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.atWWW: http://info.tuwien.ac.at/theochem/
--

[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:>  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. WhyI 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
--

[Wien] Charge Convergence is not achieved

[Laurence Marks]

While what you say is probably right (it normally is), for this to
prevent convergence one has to hypothesize that these occupancy
changes correspond to excitation of different eigenvectors of the
charge density (not just the wavefunctions) with respect to the
appropriate dielectric response matrix, so near the solution the
mixing Jacobian only obtains information about the off-diagonal terms,
minimal information about the diagonal terms. (In effect the Jacobian
then become very ill-conditioned.) In effect this implies that in hard
cases this response matrix varies rapidly with k so needs to be finely
sampled to include all the different eigenvectors and avoid
ill-conditioning. While this is a very reasonable hypothesis, proving
it is not so simple

N.B., with respect to the comment by Shamik Chakrabarti, yes, if the
mixing has converged then this is a sufficient condition that you have
satisifed the KS equations for the functional used, i.e. found a
variational minimum and the problem is feasible. If the problem does
not converge it may be unfeasible, and all that is being found is a
trap not a fixed-point variational minimum. Or it is too hard for the
mixer.

On Thu, Jul 7, 2011 at 8:24 AM, Peter Blaha
 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:> ?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 q

[Wien] Charge Convergence is not achieved

[Laurence Marks]

2011/7/7 Shamik Chakrabarti :
> 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 may
disagree) always be good. With a very imperfect functional it is quite
possible that a DFT calculation will not converge, i.e. it is
unfeasible. Empirically many (but not all) metals do not converge well
with small numbers of k-points, but some others do. WhyI do not
understand as I cannot write down a mathematical analysis to explain
this and do not believe that there is a formal analysis in the
literature, it is just empirical knowledge (folklore).


-- 
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

[Wien] Charge Convergence is not achieved

[Peter Blaha]

For just 3 atoms/cell (and metallid ??) 1000 or 5000 k are still not much.
Better k-mesh should improve convergence.

And sometimes you cannot reach (easily) arbitrary convergence. What about 
E-tot, ... ?


Am 06.07.2011 07:48, schrieb Shamik Chakrabarti:
> Dear wien2k users,
>
> We have done volume optimization of a structure having space group no. 225 
> (Fm3m) and 3 inequivalent atoms per unit cell. We have taken the least energy 
> lattice parameters for
> spin polarized SCF calculations. However, the last calculation (spin 
> polarized SCF) has not been converging at all. We have set the convergence 
> criteria of  charge to 0.0001and it
> reached up to 0.006. After that its is fluctuating sinusoidally at this value 
> (even at around 400th iteration). We have also tried using the fallowing 
> steps, such as
>
> 1. increasing the RmaxKmax value from 7 to 9
>
> 2. changing mixer values ranging from 0.01 to 0.3 (using MSEC mixing 
> scheme...wien2k 10)
>
> 3. increasing the K-points from 1000 to 5000
>
> but unfortunately we haven't got the desired convergence yet. Therefore, it 
> is very helpful for us to have a suggestion for this problem.
>
> --
> Shamik Chakrabarti
> Research Scholar
> Dept. of Physics & Meteorology
> Material Processing & Solid State Ionics Lab
> IIT Kharagpur
> Kharagpur 721302
> INDIA
>
>
>
> ___
> Wien mailing list
> Wien at zeus.theochem.tuwien.ac.at
> http://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.atWWW: http://info.tuwien.ac.at/theochem/
--

[Wien] Charge Convergence is not achieved

[Shamik Chakrabarti]

Dear wien2k users,

We have done volume optimization of a structure having space group no. 225
(Fm3m) and 3 inequivalent atoms per unit cell. We have taken the least
energy lattice parameters for spin polarized SCF calculations. However, the
last calculation (spin polarized SCF) has not been converging at all. We
have set the convergence criteria of  charge to 0.0001and it reached up to
0.006. After that its is fluctuating sinusoidally at this value (even at
around 400th iteration). We have also tried using the fallowing steps, such
as

1. increasing the RmaxKmax value from 7 to 9

2. changing mixer values ranging from 0.01 to 0.3 (using MSEC mixing
scheme...wien2k 10)

3. increasing the K-points from 1000 to 5000

but unfortunately we haven't got the desired convergence yet. Therefore, it
is very helpful for us to have a suggestion for this problem.

-- 
Shamik Chakrabarti
Research Scholar
Dept. of Physics & Meteorology
Material Processing & Solid State Ionics Lab
IIT Kharagpur
Kharagpur 721302
INDIA
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