[Pw_forum] Question on the wsweight subroutine

[Lorenzo Paulatto]

On 03/29/2013 05:27 PM, Aaditya Manjanath wrote:
I would like to know, what is the purpose/logic of this subroutine, 
since I see that this is an essential part in calculating the dynamical 
matrices at arbitrary q-points.
>
> I would be grateful if you could shed some light on this problem.

Dear Aaditya,
wsweights does a very simple task in a very complicated way. It assigns 
this weights:
1) if a point is inside the Wigner-Seitz cell: weight=1
2) if a point is outside the WS cell: weight=0
3) 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

I.e. if a point is on the surface of the WS cell of a cubic lattice 
it'll have weight 1/2, on the vertex of the WS it would be 1/8; the K 
point of an hexagonal lattice has weight 1/3 and so on.

It takes some thought and some time to understand wsweight; if I 
remember correctly, Schwarz inequality is used < 
http://en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality> 
<http://en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality>

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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