[Pw_forum] What is the difference between Q points mesh and k points mesh

[Stefano Baroni]

On Jan 8, 2012, at 6:51 PM, Paolo Giannozzi wrote:

just a few more more words

> On Jan 8, 2012, at 17:43 , Caloma Trumica wrote:
> 
>> why do we need to have such an additional setting of q points
>> rather than just using k points mesh for both?
> 
> because they refer to different quantities and have different
> convergence criteria. The "k-point" grid is used to perform the
> integral over the Brillouin Zone;

... for electronic properties (squared Bloch states -> charge density, 1-electron energies -> sum thereof, etc.)

> the "q-point" grid is used to
> perform integrals over phonon wave vectors,

... which is also a sum over the Brillouin zone, but of quantities belonging to a different class of properties, which usually display different convergence properties (as pointed out by Paolo)

> or to obtain
> Interatomic Force Constants in real space.

as above ...

Also, q-point meshes usually include the gamma point (both because technically they often appear as differences between "k-points" q=k2-k1, hence if k2 and k1 both belong to a same mesh, q can be equal to zero; and also because one is often interested in zone-center phonons per se); k-points, instead, are often offset from the origin, because the sum over points of a regular grid of a periodic function converges slightly better as a function of the number of points if the grid is offset (this the somewhat obscure logics behind the construction of the Monkhorst-Pack sets of "special points").

SB

---
Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center - Trieste
http://stefano.baroni.me [+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)

La morale est une logique de l'action comme la logique est une morale de la pensée - Jean Piaget

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