[Pw_forum] Technique for converging Ecut and K-points?

Tue Feb 26 11:47:23 CET 2013

Dear Ben,

I would also like to contribute my 5 cents to the discussion.
There are two main questions to answer prior to any convergence study.

1) What quantity is of interest?

If you can answer this question, you can save a lot of time and
computational resources, because different
quantities require different parameters (cut-offs, BZ-sampling, etc.) to
converge. Converging total energies
is not always a good idea.

2) How much precision do I really need?

Answering this question depends on the problem you are trying to solve. For
instance, if you are trying to
identify which of two phases of some substance is most stable at 0K
(according to DFT), and the difference
in the free energies of these phases is big, then you would need rather
coarse parameters to figure out the answer
to your problem. It might happen though, that the difference is tiny, then
you would have to tune the parameters
till a reliable distinction is achieved.

Best regards,
Maxim.

2013/2/25 Ali KACHMAR <kachmar_ali at hotmail.fr>

>  Dear Stefano,
>
> That's great. In any case, I learnt too much from you and from many others
> on this forum.
>
> Thank you,
> Ali
>
> > Date: Mon, 25 Feb 2013 15:05:14 +0100
> > From: degironc at sissa.it
> > To: pw_forum at pwscf.org
> > Subject: Re: [Pw_forum] Technique for converging Ecut and K-points?
>
> >
> > Dear All,
> > My previous post was actually more intended as an answer to Ben
> > Palmer question than a comment to
> > Ali Kachmar contribution. Sorry.
> > best regards,
> > stefano
> >
> >
> > On 02/25/2013 02:58 PM, Stefano de Gironcoli wrote:
> > > Dear Ali Kachmar,
> > >
> > > convergence w.r.t. ecutwfc (and ecutrho) and convergence w.r.t.
> > > k-points sampling are rather independent issues and can be tested to a
> > > large extent separately
> > >
> > > - convergence w.r.t. ecutwfc and ecutrho is a property depending on
> > > the highest Fourier components that are needed to describe the
> > > wavefunctions and the density of your system. his depends on the
> > > pseudopotentials that are present in the calculation and do not depend
> > > strongly, for a given set of pseudopotentials, on the particular
> > > configuration because it depends mostly on the behaviour of the wfc in
> > > the core region which is quite insensitive (in terms of shape) on the
> > > environment.
> > > So each pseudopotential has a required cutoff. An upperbound to this
> > > value can be determined from any system that contains that pseudo.
> > > The cutoff needed for a system containing several species is the
> > > highest among those needed for each element.
> > > Moreover, in US pseudo or PAW the charge density has contributions
> > > from localized terms that may (an usually do in USPP) require quite
> > > higher cutoff than the one needed for psi**2 (4*ecutwfc) ... hence the
> > > possibility to vary and test independently for ecutrho ...
> > >
> > > My recommended strategy to fix ecutwfc and ecutrho is to perform total
> > > energy (and possibly, force and stress) covergence test increasing
> > > ecutwfc keeping ecutrho at its default vaule (=4*ecutwfc) until
> > > satisfactory stability is reached (typically ~1 mry/atom in the
> > > energy, 1.d-4 ry/au in the forces, a fraction of a KBar in the stress)
> > > ... this fixes the converged value of ecutrho to 4 times the
> > > resulting ecutwfc.
> > > Now keeping this value for ecutrho one can try to reduce ecutwfc and
> > > see how much this can be done without deteriorating the convergence.
> > >
> > > -convergence with respect to k-points is a property of the band
> > > structure.
> > > I would study it after the ecutwfc/ecutrho issue is settled but some
> > > fairly accurate parameters can be obtained even with reasonable but
> > > not optimal cutoff parameters.
> > >
> > > There is a big difference between convergence in a band insulator or
> > > in a metal.
> > >
> > > In an insulator bands are completely occupied or empty across the BZ
> > > and charge density can be written in terms of wannier functions that
> > > are exponentially localized in real space.
> > > Hence the convergence w.r.t the density of point in the different
> > > directions in the BZ should be exponentially fast and anyway quite
> > > quick...
> > >
> > > In a metal the need to sample only a portion of the BZ would require
> > > an extremely dense set of k points in order to locate accurately the
> > > Fermi surface. This induces to introduce a smearing width that smooth
> > > the integral to be performed... the larger the smearing width, the
> > > smoother the function, and the faster the convergence results...
> > > however the larger the smearing width the farther the result is going
> > > to be from the accurate, zero smearing width, result that one would
> > > desire.
> > > Therefore different shapes fro the smearing functions have been
> > > proposed to alleviate this problem and
> > > Marzari-Vanderbilt and Methfessel-Paxton smearing functions give a
> > > quite mild dependence of the (k-point converged) total energy as a
> > > function of the smearing width thus being good choices for metals.
> > >
> > > My recommended strategy for fix the k-point sampling in metals is
> > > 1) chose the smearing function type (mv or mp, recomended)
> > > 2) for decreasing values of the smearing width (let's say from an high
> > > value of 0.1 ry = 1.36 eV to a low value of 0.01 - 0.005 ry =
> > > 0.136-0.068 eV if feasable) CONVERGE the total energy w.r.t to
> > > smearing well within the global desired tolerance (of 1 mry/atom, for
> > > instance)
> > > 3) by examining the behaviour of the CONVERGED Energy vs smearing
> > > width curve E(sigma) identify the smearing width for which E(sigma) is
> > > within tolerance w.r.t. E(sigma==0) keeping in mind that for
> > > methfessel-paxton E(sigma) ~ E(0) + A*sigma**4 + o(sigma**6) while for
> > > marzari-vanderbilt the dependence is more likely E(sigma) ~ E(0)
> > > +A*sigma**3 + o(sigma**4).
> > > 4) select that value of the smearing width and the smallest set of
> > > k-points for which this is converged.
> > >
> > > HTH
> > >
> > > stefano
> > >
> > >
> > >
> > > On 02/24/2013 06:54 PM, Ali KACHMAR wrote:
> > >> Hi,
> > >>
> > >> as far as I know, there is no any techinques for choosing ecut and
> > >> k-points. Please have a look at the pwscf archive and make up a
> > >> conclusion.
> > >>
> > >> Best,
> > >> Ali
> > >>
> > >>> Date: Sat, 23 Feb 2013 19:55:51 +0000
> > >>> From:benpalmer1983 at gmail.com
> > >>> To:pw_forum at pwscf.org
> > >>> Subject: [Pw_forum] Technique for converging Ecut and K-points?
> > >>>
> > >>> Hi everyone,
> > >>>
> > >>> I just wanted to ask if users have any techniques for choosing ecut
> and
> > >>> k-points? I've read that one way would be to start with a high number
> > >>> of k-points and high energy cutoff, and use that energy as an almost
> > >>> true value. Then adjust k-points and energy cutoff from a lower
> > >>> number/cutoff until it converges to the true value. Would you try to
> > >>> converge energy cutoff first, or k-points? Does it matter which you
> > >>> converge first?
> > >>>
> > >>> Thanks
> > >>>
> > >>> Ben Palmer
> > >>> Student @ University of Birmingham
> > >>> _______________________________________________
> > >>> Pw_forum mailing list
> > >>> Pw_forum at pwscf.org
> > >>> http://pwscf.org/mailman/listinfo/pw_forum
> > >>
> > >>
> > >>
> > >> _______________________________________________
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> > >
> >
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-- 
Best regards, Max Popov
Ph.D. student
Materials center Leoben (MCL), Leoben, Austria.
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