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Dear Stefano,<br>
<br>
I've just finished running the calculations, and I've quickly put
the results into excel. K-points were 6,8,10,12,14,16,18.<br>
<br>
Energy v K-points:<br>
<br>
<img src="cid:part1.00020506.02020203@gmail.com" alt=""><br>
<br>
The horizontal lines are +/- 1mRy from the energy with 18x18x18
k-points.<br>
<br>
PWscf runtime v K-points:<br>
<br>
<img src="cid:part2.03080000.03050308@gmail.com" alt=""><br>
<br>
Would it be reasonable to choose k-points 10, maybe even 8, and any
smearing width? I could try higher k-points, but it may take a
while as my computer is a bit slow.<br>
<br>
All the best,<br>
<br>
Ben<br>
<br>
<br>
<br>
On 27/02/2013 10:40, Stefano de Gironcoli wrote:
<blockquote cite="mid:512DE29C.1050704@sissa.it" type="cite">
<pre wrap="">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
</pre>
<blockquote type="cite">
<pre wrap="">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
</pre>
<blockquote type="cite">
<pre wrap="">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:
</pre>
<blockquote type="cite">
<pre wrap="">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:
</pre>
<blockquote type="cite">
<pre wrap="">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
</pre>
<blockquote type="cite">
<pre wrap="">Date: Sat, 23 Feb 2013 19:55:51 +0000
<a class="moz-txt-link-abbreviated" href="mailto:From:benpalmer1983@gmail.com">From:benpalmer1983@gmail.com</a>
<a class="moz-txt-link-abbreviated" href="mailto:To:pw_forum@pwscf.org">To:pw_forum@pwscf.org</a>
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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