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

[Stefano de Gironcoli]

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
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