[Pw_forum] k point grid hybrid functionals

[Lorenzo Paulatto]

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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