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

[Stefano de Gironcoli]

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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