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

[Stefano de Gironcoli]

Dear Ben,

    2x2x2 k-points with a 0.02 Ry width looks to me quite a daring small 
k-points set ... I would start with a somewhat denser 6x6x6 or 8x8x8 one...

    the first check of convergence with respect to ecutwfc/ecutrho is 
fine BUT your interpretation is not.
    what you conclude from there is that ecutwf=35  and ecutrho=140  are 
enough to converge the energy
    in particular ecutrho=140 is enough !

    The second stage is therefore to fix ecutrho=140 and check whether 
it is possible to REDUCE ecutwfc.

     As for the convergence w.r.t. to k-points i would make a more 
systematic study...
     reordering the data that you present...  and examining results for 
decreasing values of the smearing width

width = 0.03
9956.6765:   K-point: 6,  Degauss: 0.03, energy: -154.05968822, time: 
0m46.50s
9956.6735:   K-point: 8,  Degauss: 0.03, energy: -154.06335682, time: 
1m20.19s     ?
there is not enough information to decide what grid would be enough here...
definitely you should test for 12, 16 (23 if needed) etc

width = 0.02
9956.6754:   K-point: 6,  Degauss: 0.02, energy: -154.05986685, time: 
0m46.42s
9956.6720:   K-point: 8,  Degauss: 0.02, energy: -154.06351667, time: 1m 
8.18s
9956.6473:   K-point: 12, Degauss: 0.02, energy: -154.06227228, time: 
3m59.45s  *
9956.6243:   K-point: 16, Degauss: 0.02, energy: -154.0622109, time: 
6m41.03s
a nicely complete series of calculations
12x12x12 is converged within a fraction of mry  ...

width = 0.015
9956.6191:   K-point: 16, Degauss: 0.015, energy: -154.06218801, time: 
6m40.66s     *
9956.6122:   K-point: 24, Degauss: 0.015, energy: -154.06234325, time: 
27m28.22s
16x16x16 is converged withinn a fraction of mry... maybe 12 (or less) is 
enough but you didn't check

width = 0.01
9956.6358:   K-point: 12, Degauss: 0.01, energy: -154.06191016, time: 
3m47.69s
9956.6064:   K-point: 24, Degauss: 0.01, energy: -154.06231018, time: 
27m31.26s  ?*
who knows if (as probable) 24x24x24 is converged ...or even 
overkilling...  missing data at 16 and 20 would help to understand

width = 0.005
9956.6004:   K-point: 24, Degauss: 0.005, energy: -154.06230709, time: 
25m21.81s  ?
again... no clue whether this is converged or not... data at 12,16,20... 
(and 28,32 if needed) are missing

once converged results as function of smearing width are obtained
you can decide which is the largest width that is still accurate and 
then what is the smallest k-point set that
integrates it correctly...

width     converged energy     converged grid
0.03             ?
0.02         -154.06227228, *         12
0.015       -154.06234325, *         16
0.01         -154.06231018, ?*       24 ?
0.005            ?

looks like 0.02 and 12x12x12 is fine within a fraction of mry...
maybe also 0.03 or larger with a smaller grid but there is no info to tell.

HTH

stefano

> 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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