[Pw_forum] Convergence of dos near band edge

[Stefano Baroni]

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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