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

Wed Feb 27 07:15:18 CET 2013

Dear Stefano and Paolo,
I think that information from this thread should be placed into the User
Manual and FAQ. :)

2013/2/27 Ben Palmer <benpalmer1983 at gmail.com>

> Dear Stefano,
>
> I have had a go at converging for Aluminium.  I wasn't too sure what to
> do with the K-points, but I've had a go anyway.  This is what I have
> done, step by step, with some results from the calculations.
>
> First I set k-points to 2, smearing as MV and a width of 0.02 for the
> energy convergence.  I varied the energy from 10 to 50 (taking 50 as the
> 'true' value), and selected the first within 1mRy of the 'true' energy.
>
> 113.2226:   K points: 2, ecut: 10, energy: -153.984951, time: 4.05s
> 113.2237:   K points: 2, ecut: 15, energy: -153.99949084, time: 4.31s
> 113.2251:   K points: 2, ecut: 20, energy: -154.00496366, time: 4.96s
> 113.2261:   K points: 2, ecut: 25, energy: -154.00841338, time: 5.49s
> 113.2268:   K points: 2, ecut: 30, energy: -154.00937872, time: 6.52s
> 113.2283:   K points: 2, ecut: 35, energy: -154.01004897, time: 8.31s
> 113.2292:   K points: 2, ecut: 40, energy: -154.01057988, time: 8.17s
> 113.2306:   K points: 2, ecut: 45, energy: -154.01066204, time: 10.91s
> 113.2314:   K points: 2, ecut: 50, energy: -154.01083456, time: 12.83s
> 113.2315:   Converged energy cutoff ecutwfc: 35
>
> I then lowered ecutrho until, and selected the lowest value that fell
> within 1mRy of the 'true' energy.
>
> 218.6003:   K points: 2, ecutwfc: 35, ecutrho: 252, energy:
> -154.01105461, time: 10.98s
> 218.6014:   K points: 2, ecutwfc: 35, ecutrho: 224, energy:
> -154.01104417, time: 11.67s
> 218.6031:   K points: 2, ecutwfc: 35, ecutrho: 196, energy:
> -154.01069558, time: 8.82s
> 218.604:   K points: 2, ecutwfc: 35, ecutrho: 168, energy:
> -154.01054112, time: 9.99s
> 218.6052:   K points: 2, ecutwfc: 35, ecutrho: 140, energy:
> -154.01004897, time: 8.46s
> 218.6064:   K points: 2, ecutwfc: 35, ecutrho: 112, energy:
> -154.00962358, time: 7.22s
> 218.6076:   K points: 2, ecutwfc: 35, ecutrho: 84, energy:
> -154.00782952, time: 5.80s
> 218.6082:   Converged energy cutoff ecutrho: 140
>
> At this point, I've got ecutwfc = 35 and ecutrho = 140, but I wasn't too
> sure how to progress, so I attempted the following.  I set a large
> number of k-points, 24x24x24, with a narrow smearing of 0.005.  I used
> the energy cutoffs to then calculate a new reference energy for
> convergence.
>
> I increased the smear width and decreased the k-points in quite
> arbitrary combinations, and looked for the combination that executed
> fastest, while keeping within 1mRy of the new reference energy.
>
> 9956.6004:   K-point: 24, Degauss: 0.005, energy: -154.06230709, time:
> 25m21.81s
> 9956.6064:   K-point: 24, Degauss: 0.01, energy: -154.06231018, time:
> 27m31.26s
> 9956.6122:   K-point: 24, Degauss: 0.015, energy: -154.06234325, time:
> 27m28.22s
> 9956.6191:   K-point: 16, Degauss: 0.015, energy: -154.06218801, time:
> 6m40.66s
> 9956.6243:   K-point: 16, Degauss: 0.02, energy: -154.0622109, time:
> 6m41.03s
> 9956.6358:   K-point: 12, Degauss: 0.01, energy: -154.06191016, time:
> 3m47.69s
> 9956.6473:   K-point: 12, Degauss: 0.02, energy: -154.06227228, time:
> 3m59.45s
> 9956.672:   K-point: 8, Degauss: 0.02, energy: -154.06351667, time: 1m
> 8.18s
> 9956.6735:   K-point: 8, Degauss: 0.03, energy: -154.06335682, time:
> 1m20.19s
> 9956.6754:   K-point: 6, Degauss: 0.02, energy: -154.05986685, time:
> 0m46.42s
> 9956.6765:   K-point: 6, Degauss: 0.03, energy: -154.05968822, time:
> 0m46.50s
>
>  From this, I'd choose K-points 12x12x12 and smearing width 0.01 or 0.02.
>
> My final convergence settings were:
>
> ecutwfc = 35,
> ecutrho = 140,
> k points 12x12x12
> smearing mv 0.01
>
> Would this be an acceptable way to chose the settings, or could I speed
> up the end part?
>
> All the best,
>
> Ben Palmer, Student @ University of Birmingham
>
> > 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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-- 
С уважением,
Дмитрий Коротин

Best regards,
Dr. Dmitry Korotin

Institute of Metal Physics
S. Kovalevskaya, 18
620990 Yekaterinburg
Russia
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