[Pw_forum] Technique for converging Ecut and K-points?
Ben Palmer
benpalmer1983 at gmail.com
Wed Feb 27 00:41:37 CET 2013
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
>>>> _______________________________________________
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>>>
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