[Pw_forum] Convergence of dos near band edge

[Bo Qiu]

Dear Dr. Baroni,

Thanks a lot for the reply. I understand the DOS dependence in 1d/2d/3d and
unfortunately that's not what surprised me. I used tetrahedron method (a
technique intrinsically able to account for the singularity as you
mentioned). I did study grids of different sizes for convergence, not only
nk=30 30 30, but all the way up to nk = 60 60 60 and even more. I did
observe the resemblance of DOS to \sqrt{E-E_0) in the case of 60 60 60
grid. What surprised me was that I didn't see people report they used grids
as dense as such to get DOS for transport calculations, especially for
silicon. That's why I wondered if the requirement of such dense grid was
normal practice or it was because I missed something when computing the
DOS. Thanks

Bo

On Fri, Nov 30, 2012 at 3:41 PM, Stefano Baroni <baroni at sissa.it> wrote:

> Dear Bo Qu,
>
> the \sqrt{E-E_0) behavior of the DOS results from a rather singular
> integral in k space. So singular, that in 2D the same integral gives a
> constant at E=E_0, and even a divergence in 1D. If this statement comes as
> a surprise to you, I advise you to go through the (simple) calculus leading
> to the limiting behaviors of the DOS for parabolic bands in 1/2/3D. If you
> like the exercise, you may want to repeat it for phonons, for which the
> dispersion is linear, rather than quadratic.
>
> This being said (and understood), if you want to calculate numerically a
> singular integral, basically you have two choices: you either choose a
> technique intrinsically able to account for the singularity, or you use
> "any" technique, but in that case you'd better carefully check the
> convergence (a single calculation done with whatever k-point mesh,
> [30,30,30], or even [10^30,10^30,10^30] does not look exactly as a
> convergence test ...).
>
> An example of the first choice is to use the tetrahedron method; if you
> want to use standard k-point sampling with Gaussian (or whatever) smearing,
> keep first the broadening fixed and choose a k-point mesh fine enough so as
> to have a converged DOS *for that smearing*. Repeat the procedure for ever
> finer Gaussian smearings, until the DOS looks "square-root-like" enough ...
>
> I know, it's lengthy and possibly boring, but that's the hard researcher's
> life ...
>
> If you make any progress, let us know (or even if you don't).
>
> Take care,
> SB
>
>
>
> On Nov 30, 2012, at 7:53 PM, Bo Qiu wrote:
>
> Dear developers and users,
>
> I'm testing the electron dos of silicon near conduction band minimum
> following the example came with the package. The produced band structure
> compares well with literature.  The overall shape of DOS also compares well
> with literature.  However, to my great surprise, the dos near the CBM
> doesn't follow the expected DOS ~ E^1/2 dependence at all (see attachment),
> this wrong dependence leads to disaster when trying to compute transport
> properties. The grid I chose for scf is 16 16 16 1 1 1, while for nscf is
> 30 30 30 0 0 0. The rest of the input pretty much follows the example input
> files. I wonder if there is any part I missed or should I just keep
> increasing the nscf grid? Thanks a lot!
>
> Please let me know if I need to attach the input files too.
>
> Bo
> <dos_silicon.jpg><bandstr.jpg>
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>
> ---
> Stefano Baroni -  http://stefano.baroni.me, stefanobaroni (skype)
> on leave of absence from SISSA, Trieste, presently at the Department of
> Materials, EPF Lausanne (untill March 2013)
>
> I believe in the despotism of human life and happiness against the liberty
> of money and possessions - John Steinbeck
>
>
>
>
>
>
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