[Pw_forum] Convergence of dos near band edge

[Bo Qiu]

Never mind, I think a very dense grid is indeed required for correct DOS
near band edge and there is probably no other way around. Thanks

Bo

On Fri, Nov 30, 2012 at 10:01 PM, Bo Qiu <200210qb at gmail.com> wrote:

> 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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