[Pw_forum] Question on the wsweight subroutine

[Lorenzo Paulatto]

On 04/19/2013 11:28 PM, Aaditya Manjanath wrote:
> Dear Dr. Paulatto,
>
> Thanks for your reply. However:
>
> a) I still do not understand why this subroutine is necessary.

if you don't use it the fourier interpolation will produce crap.. if you 
don't recenter the force constants you can have higher harmonics in the 
interpolation, if you do not consider equivalent points you will break 
symmetry

> b) "if a point q is on the border of the WS cell, it finds the number N
> of translationally equivalent point q+G  (where G is a lattice vector)
> that are also on the border of the cell. Than, weight = 1/N".
> What I do not understand from the above mentioned statement is, in 
> this wsweight subroutine, the expanded Wigner-Seitz cell is 
> constructed in the REAL space keeping in mind a finite no. of nearest 
> neighbors. The weights are subsequently calculated based on the 
> distance between the atoms. If that is the case, how does the concept 
> of q-point fit here, since q-points belong to the RECIPROCAL space.

you are right, everything is done in real space
> c) Is it possible to obtain Fourier interpolation of dynamical 
> matrices without the use of wsweight?
yes, but you must still respect these 2 rules:
1. always consider the smallest possible distance between all the 
possible periodic images (to prevent aliasing)
2. when N choices are equivalents, consider all of them with weight 1/N 
(to avoid breaking symmetry)

there are many ways to enforce these 2 simple rules, wsweights is just 
the most complicated
>
> I would really appreciate if you could shed some light on these issues.
>
> Many thanks once again!

you can find a longer explanation in appendix C of this pre-print: 
http://arxiv.org/abs/1304.2626

cheers

-- 
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