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

Ali KACHMAR kachmar_ali at hotmail.fr
Mon Feb 25 21:59:58 CET 2013 

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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