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

[Kucukbenli Emine]

Hi Ben,

the idea is to calculate the "converged energy" wrt "smearing width."
So, the procedure as I understand is
1.choose a smearing width
2.converge the energy at that smearing width with by choosing an appropriate k mesh
3.repeat it for other values of smearing width.

You need to be quite generous with the range of smearing width you explore.
Your values span a very narrow range where smearing is _very_ small.
Although it depends on the material, I find a range of 0.1 to 0.005 is generally a good starting point.
Guess I would do calculations at around 0.1, 0.05, 0.03, 0.02, 0.01, 0.005 if i was exploring the correct behaviour here..

An example:
To understand if you have spanned a good range for the k point grids you can afford,
look for "merging lines":
As you increase the smearing, the convergence is gonna get to be more easily reached with even smaller k point meshes. so you would be able to see
* lines for 18, 16 to merge to same value lets say -154.062, at width 0.005 ;
* then as you increase smearing width further to 0.02 you would see 18 16 14 12 mesh lines will all merge to same value of -154.061,
* and continuing, at width 0.1 all lines 18 16 14 12 8 4 will converge to energy value -154.058

that is what we mean by "converged energy" at each width:
when k point lines merge it means that you have reached convergence wrt k mesh for that width.

in the above made-up example,
smearing width versus converged energy would look like:

0.005 -154.062 (18,16 merged)
0.01  -154.062 (18 16 )
0.02  -154.062 (18 16 14)
0.03  -154.061 (18 16 14 12)
0.05  -154.060 (18 16 14 12 8)
0.1   -154.058 (18 16 14 12 8 4)

so 0.02 width and 14 kmesh could be considered converged with the given precision here.

if you have chosen a very small width range (for the k grids you can afford), you will see separate, flat lines as you do in your figure instead. Anyways, next time such separate flat lines can be your cue to explore wider ranges of smearing width.

Note that in the above example, i have always reduced the energy as i reduced the smearing width. this does not have to be so. Indeed in Nicola's thesis and Stefano's paper on phonons w metallic systems, you can see how different ways of smearing would depend differently on the shape of the density of states at the fermi level to determine this behaviour.

Also note that in the above example i have used energy as a convergence criterion but you could have as well used forces as Nicola suggested.

You already have Nicola's thesis link, and here is Stefano's paper: http://prb.aps.org/abstract/PRB/v51/i10/p6773_1

best
emine kucukbenli, postdoc at theos, epfl, switzerland
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