[Pw_forum] Question on the wsweight subroutine

[Aaditya Manjanath]

Dear Dr. Paulatto,

Thanks for your reply. However:

a) I still do not understand why this subroutine is necessary.
b) "if a point q is on the border of the WS cell, it finds the number N
of translationally equivalent point q+G  (where G is a lattice vector)
that are also on the border of the cell. Than, weight = 1/N".
What I do not understand from the above mentioned statement is, in this
wsweight subroutine, the expanded Wigner-Seitz cell is constructed in the
REAL space keeping in mind a finite no. of nearest neighbors. The weights
are subsequently calculated based on the distance between the atoms. If
that is the case, how does the concept of q-point fit here, since q-points
belong to the RECIPROCAL space.
c) Is it possible to obtain Fourier interpolation of dynamical matrices
without the use of wsweight?

I would really appreciate if you could shed some light on these issues.

Many thanks once again! :-)

Cheers,

Aaditya



   5. Question on the wsweight subroutine (Aaditya Manjanath)
>    6. Re: Question on the wsweight subroutine (Lorenzo Paulatto)
>
>
>
> Message: 5
> Date: Fri, 29 Mar 2013 21:57:33 +0530
> From: Aaditya Manjanath <aadipotter at gmail.com>
> Subject: [Pw_forum] Question on the wsweight subroutine
> To: pw_forum at pwscf.org
> Message-ID:
>         <
> CALcVMZKdB5iKjujb6nsNC2bT215UeZcOmuStB-6NdfXqKejnpg at mail.gmail.com>
> Content-Type: text/plain; charset="iso-8859-1"
>
> Dear all,
>
> I was looking through the matdyn program wherein the dynamical matrices are
> calculated at any q-point through Fourier interpolation and I came across
> the wsweight subroutine.
>
> I know that this subroutine calculates the weight factors that are used in
> the Fourier interpolation formula.I tried calculating the dynamical matrix
> at a point (0 0.6667 0, say) without using the weight factors and
> interestingly, I found that the values of the dynamical matrix obtained
> through matdyn do not match with those calculated directly.
>
> I would like to know, what is the purpose/logic of this subroutine, since I
> see that this is an essential part in calculating the dynamical matrices at
> arbitrary q-points.
>
> I would be grateful if you could shed some light on this problem.
>
> Cheers,
>
> Aaditya
>
> --
> "Stay hungry. Stay Foolish" - Steve Jobs
>
> Om Sri Sairam
> Best Regards,
> Aaditya Manjanath
> PhD Engineering Programme
> Interdisciplinary Program - Nanoscience and Engineering
> Indian Institute of Science
> Bangalore - 560012
>
> Webpage - http://mrc.iisc.ernet.in/~abhishek/Aaditya.html
> Email ID -  aadipotter at gmail.com, aaditya.m at cense.iisc.ernet.in
> Skype - aadipotter
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>
> Message: 6
> Date: Fri, 29 Mar 2013 17:52:45 +0100
> From: Lorenzo Paulatto <lorenzo.paulatto at impmc.upmc.fr>
> Subject: Re: [Pw_forum] Question on the wsweight subroutine
> To: PWSCF Forum <pw_forum at pwscf.org>
> Message-ID: <5155C6DD.4090807 at impmc.upmc.fr>
> Content-Type: text/plain; charset="iso-8859-1"
>
> On 03/29/2013 05:27 PM, Aaditya Manjanath wrote:
> I would like to know, what is the purpose/logic of this subroutine,
> since I see that this is an essential part in calculating the dynamical
> matrices at arbitrary q-points.
> >
> > I would be grateful if you could shed some light on this problem.
>
> Dear Aaditya,
> wsweights does a very simple task in a very complicated way. It assigns
> this weights:
> 1) if a point is inside the Wigner-Seitz cell: weight=1
> 2) if a point is outside the WS cell: weight=0
> 3) if a point q is on the border of the WS cell, it finds the number N
> of translationally equivalent point q+G  (where G is a lattice vector)
> that are also on the border of the cell. Than, weight = 1/N
>
> I.e. if a point is on the surface of the WS cell of a cubic lattice
> it'll have weight 1/2, on the vertex of the WS it would be 1/8; the K
> point of an hexagonal lattice has weight 1/3 and so on.
>
> It takes some thought and some time to understand wsweight; if I
> remember correctly, Schwarz inequality is used <
> http://en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality>
> <http://en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality>
>
> bests
>
>
> --
> Dr. Lorenzo Paulatto
> IdR @ IMPMC -- CNRS & Universit? Paris 6
> phone: +33 (0)1 44275 084 / skype: paulatz
> www:   http://www-int.impmc.upmc.fr/~paulatto/
> mail:  23-24/4?16 Bo?te courrier 115, 4 place Jussieu 75252 Paris C?dex 05
>
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-- 
"Stay hungry. Stay Foolish" - Steve Jobs

Om Sri Sairam
Best Regards,
Aaditya Manjanath
PhD Engineering Programme
Interdisciplinary Program - Nanoscience and Engineering
Indian Institute of Science
Bangalore - 560012

Webpage - http://mrc.iisc.ernet.in/~abhishek/Aaditya.html
Email ID -  aadipotter at gmail.com, aaditya.m at cense.iisc.ernet.in
Skype - aadipotter
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