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

[Ben Palmer]

Hi Emine,

Thank you for clearing up what I should be converging.  I wasn't too 
sure if I should be trying to converge the smearing and k-point 
combinations to a single value.  I'll give your technique a go, and also 
incorporate the forces as mentioned by Nicola.  I'm just on my 
university library and should have Stefano's paper soon.

All the best,

Ben
> 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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