[Pw_forum] k point grid hybrid functionals

[Lorenzo Paulatto]

On 04/15/2013 02:33 PM, "Valentina Dellacà C.R.F. S.C.p.A." wrote:
> 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,

No, it does not. In fact there is not a single {k+q} grid, there is one 
for each k point. In the first case each of these grids contain a single 
point: k itself. In the second case, each of this grids contain all the 
k points, but in a different order and eventually translated by a G vector.

The second condition I stated before guarantees that k+q = Sk'+G, for 
every k and q, where k' is a point in the {k} grid, S a symmetry 
operation and G a vector of the reciprocal lattice. If you ignore 
symmetry, you can restate the condition as, it must be possible to 
express any q as q= k-k'+G, same definitions as before.

This allows to store all the {k+q} grids very efficiently, but you 
should still think of them as many different grids.
> As you see, I am a beginner and a bit confused about this topic, do 
> you have any paper to recommend me?
>
I do not have any paper where this is mechanism is explained in 
detail... maybe someone else who's reading this thread can recommend 
some reading?

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 05

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