[Pw_forum] Shifted_Vs_Unshifted

[Ari P Seitsonen]

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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