[Pw_forum] inhomogenious k-points distribution

[Karoly Nemeth]

Dear Stefano and Nicola,

Thanks a lot for the valuable comments!
1. I still feel like a younger member of the forum though...
2. I use MATLAB to manipulate the bands extracted by pw2casino from PWSCF 
outputs. Of course it is quite simple to increase resolution of the bands 
by nice interpolations available in MATLAB. However interpolation of the 
wavefunction coefficients (crystal orbital coefficients) would be 
dangerous, e.g. because loss of normalization could happen, or there may 
be sign issues. My guess is though that it is perhaps not as dangerous as 
it might look like. As of longer term work on these transitions I can't 
tell much yet. Perhaps. Since the bands are normally smooth enough for 
interpolation (using a moderate but not too small number of k-points)
my best guess is that one should try to do some sort of interpolation, 
perhaps not on individual wavefunction coeffs, but on whole coeff vectors 
(wavefunctions). At least, numerically that seems to be the cheapest thing 
to do and perhaps not of too bad quality.
Cheers:

Karoly

***********************************************************************
Karoly Nemeth, Ph.D.
Argonne National Laboratory
9700 S. Cass Ave. Argonne, IL 60439.
Advanced Photon Source
X-Ray Science Division
Building 401, Room B4198
Tel. 630-252-5813
Fax: 630-252-3222
***********************************************************************

From: Stefano Baroni <baroni at sissa.it>
Subject: Re: [Pw_forum] inhomogenious k-points distribution
To: PWSCF Forum <pw_forum at pwscf.org>
Message-ID: <BFDC92FA-A976-4250-8BD7-7E5B132E9C6C at sissa.it>
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Hi! I think that would be useful, and not difficult to
implement.
At the very least, I think that it would be enough to pass
"manually" 
custom-defined sets of k points (with the associated weights) to
bands.x

Just a word of warning for the younger members of this forum.
NO transition (direct or indirect) ever occurs at a specific
point of 
the BZ. What Karoly meant is that in order to resolve the
contribution 
of "critical points" to the absorption intensity (which give
rise to 
Van Hove singularities in the spectrum), it would be useful to 
increase the k-point resulution in specific regions of the BZ.

Stefano

>
> Hi,
>
> I was wondering whether it would be possible to define
> sub-regions 
> in the
> Brillouin-zone where PWSCF would calculate bands at an
> increased
> resolution as compared to the rest of the Brillouin zone. This
> might 
> be
> useful in spectroscopy, when one wants to study direct
> transitions
> happening at a specific k-points region.
> Thanks:
>
> Karoly

Message: 3
Date: Thu, 23 Apr 2009 01:51:02 -0400
From: Nicola Marzari <marzari at MIT.EDU>
Subject: Re: [Pw_forum] inhomogenious k-points distribution
To: PWSCF Forum <pw_forum at pwscf.org>
Message-ID: <49F001C6.2080803 at mit.edu>
Content-Type: text/plain; charset=ISO-8859-1; format=flowed



Dear Karoly,


another option would be using Wannier functions to interpolate
the
bands - they capture van Hove singularities very well (Lee PRL
2007, 
Yates PRB 2007). Learning how to do this is a project in itself,
though,
so it would be worth only if you have a long term plan on
studying
transitions.

                         nicola