[Pw_forum] inhomogeneous K-point sampling

[Aritz Leonardo Liceranzu]

Dear prof. Baroni,

Thanks for your prompt answer.

"Ever read a textbook on numerical integration? This and similar  
issues are treated, I think, in many textbooks on numerical analysis."

Up to know the integrals I calculated were performed in real space  
using Simpson's rule and was enough. To build the (k,q) momentum  
dependent F_kq(r,r',w) matrix, I have to pick with caution  
wavefunctions and their corresponding weights. It is not that I have  
to integrate them but build a matrix and diagonalize it. As I said in  
my 1st email choosing a uniform small  K-grid to build F does not  
assure me convergence, that is why I would like to add points close  
to the Gamma point.

For this purpose, I need to be able to construct nonuniform  
reciprocal grids in the IBZ with their corresponding wafunctions and  
weights. I am trying to figure out how to do this so I guess that  
first I will need to understand how Monkhorst-Pack grids are  
generated and more precisely the corresponding the weights of each  
kpoint.

ANY REFERENCE AND/OR TEXTBOOK IS REALLY APPRECIATED. (I just printed  
the original M-P paper so I can read it... )

Thanks again
Aritz

On 09-mai-27, at 14:23, Stefano Baroni wrote:

>
> On May 27, 2009, at 8:44 PM, Aritz Leonardo Liceranzu wrote:
>
>> Hi all,
>
> Hi Leonardo:
>
>> So, the question would be, is it stupid to do the following?
>>
>> Take a huge grid, let us say (14,14,14) and get rid of points that  
>> are
>> at farther than a certain threshold from Gamma, normalizing the
>> weights of the "new" grid so that they sum one.
>
> This not stupid, of course. It may be wrong, though. There are many  
> different ways of "normalizing the new wights of the new grid so  
> that they sum to one". Some of them correct (within a given  
> accuracy), others plain wrong. It all depends on how you choose the  
> weights and on the specific integral you aim at approximating with  
> a weighted sum. Ever read a textbook on numerical integration? This  
> and similar issues are treated, I think, in many textbooks on  
> numerical analysis. Please, take a glance at one of them and then  
> revert to us.
>
> S.
>
> ---
> Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center -  
> Trieste
> http://stefano.baroni.me [+39] 040 3787 406 (tel) -528 (fax) /  
> stefanobaroni (skype)
>
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