[Pw_forum] Shifted_Vs_Unshifted

[Mofrad, Amir Mehdi (MU-Student)]

Thank you all for your replies. 

Amir M. Mofrad
Graduate Research Assistant
Chemical Engineering Department
University of Missouri

________________________________________
From: pw_forum-bounces at pwscf.org <pw_forum-bounces at pwscf.org> on behalf of Ari P Seitsonen <Ari.P.Seitsonen at iki.fi>
Sent: Tuesday, March 8, 2016 3:50 PM
To: PWSCF Forum
Subject: Re: [Pw_forum] Shifted_Vs_Unshifted

Dear Amir-who-is-missing-the-affiliation-in-the-post,

   A small clarification to Lorenzo's-who-did-not-even-sign-the-post
answer, in principle both would mathematically give the same accuracy, but
due to the pecularities in the density of states in particular regions of
the Brillouin zone one or the other could lead to faster convergence, like
Lorenzo wrote. Traditionally one tries to avoid the Gamma point, as one
thinks that it is an "extreme point" in the band structure (it is a local
minimum or maximum of each band, as their derivatives with respect to any
direction in k space is zero). Earlier this was of more importance, when
one could afford few k points and/or the systems were small, nowadays
choosing one or the other is no longer that important, as the increased
computing power makes the inclusion of more k points or larger cell
easier.

   And just to bore all the reader of the Forum, I remind you that in
hexagonal cell it is better to keep a Gamma-centred Monkhorst-Pack grid,
as otherwise the k point grid will get symmetrised (if this would not be
done, the grid would have a lower symmetry than the hexagonal cell
itself).

   And for historical note, the original Monkhorst-Pack grid corresponds to
the case "1 1 1", the shift was actually introduced later (when they were
indeed notified about the problem in the hexagonal case; references are a
Comment and Reply to Comment to the original Article of Monkhorst and
Pack). So in this sense the convention in QE of "shifted" and "unshifted"
k point sets are opposite to the ones of the original literature. :)

     Greetings from Paris,

        apsi

-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-
   Ari Paavo Seitsonen / Ari.P.Seitsonen at iki.fi / http://www.iki.fi/~apsi/
     Ecole Normale Supérieure (ENS), Département de Chimie, Paris
     Mobile (F) : +33 789 37 24 25    (CH) : +41 79 71 90 935


On Tue, 8 Mar 2016, Lorenzo Paulatto wrote:

>
> If you use 1's the grid will be shifted by half its step, this makes the integrals of the grid convergence faster in some cases.
>
> On 8 Mar 2016 8:51 p.m., "Mofrad, Amir Mehdi (MU-Student)" <amzf5 at mail.missouri.edu> wrote:
>
>       Dear all QE users and developers,
>
>
>       I have a question about the K_POINTS card in the input file. What is the difference between using shifted (1 1 1) and unshifted (0 0 0)?
>
>
>       Best,
>
>
>
>       Amir M. Mofrad
>
>
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