[Pw_forum] k point grid hybrid functionals

["Valentina Dellacà C.R.F. S.C.p.A."]

Dear Lorenzo,
thanks for your answer. I still have some doubts; when you say that

'In the limit where the {q} grid contains only the Gamma point, than
     each k-point exchanges only with itself (not with Gamma!).'

it means that the q+k grid will end up to be the k grid. But then,

'In the
     opposite limit where the {q} grid has the same spacing as the {k}
     one (which may include a shift) then the {k} grid becomes equivalent
     to the {k+q} one, for every k. I.e.  the {k} grid and any {k+q} grid
     are just shifted and re-indexed w.r.t each other. '

which is the difference with this second case? I have thought that when 
q grid and the k grid have the same spacing, the number of k+q points is 
larger than that of the k points, so they could not be equivalent.
As you see, I am a beginner and a bit confused about this topic, do you 
have any paper to recommend me?
Thank you very much,
regards

Valentina


Il 04/15/2013 01:08 PM, Lorenzo Paulatto ha scritto:
> On 04/15/2013 12:23 PM, "Valentina Dellacà C.R.F. S.C.p.A." wrote:
>> Hi,
>> I am having some doubts concerning nqx1,2,3 and K points grid when 
>> using hybrid functionals. As I understand, please let me know if I am 
>> wrong, there is no specific rule in how to choose the q point grid, 
>> for a given k point grid. The advice is to choose them to be the 
>> same, in order to avoid convergence issues. My question now is, since 
>> I read in hybrid functional README, that a shift in the q point grid 
>> is not implemented, can I pick a shifted k-point grid and a non 
>> shifted q point grid? Would it be better to pick two unshifted grids?
>
> Dear Valentina,
> the grids are {k} and {k+q}, where the {q} grid is always 
> Gamma-centered. In other words, for each k point there is a 
> corresponding {k+q} grid centered around it.
>
> There is the additional constraint that each k+q point (for every k 
> and q) must be related to one of the initial k points by a G vector of 
> the reciprocal lattice and eventually a symmetry operation. I think 
> this condition should not cause any problem if the {k} grid is 
> shifted, but I'm not 100% sure.
>
> In the limit where the {q} grid contains only the Gamma point, than 
> each k-point exchanges only with itself (not with Gamma!). In the 
> opposite limit where the {q} grid has the same spacing as the {k} one 
> (which may include a shift) then the {k} grid becomes equivalent to 
> the {k+q} one, for every k. I.e.  the {k} grid and any {k+q} grid are 
> just shifted and re-indexed w.r.t each other.
>
> I hope this helps, it is a bit confusing but it makes sense eventually.
>
> bests
>
> -- 
> Dr. Lorenzo Paulatto
> IdR @ IMPMC -- CNRS&  Université Paris 6
> phone:+33 (0)1 44275 084 / skype: paulatz
> www:http://www-int.impmc.upmc.fr/~paulatto/
> mail: 23-24/4é16 Boîte courrier 115, 4 place Jussieu 75252 Paris Cédex 5


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