[Pw_forum] k point generation

[MMS]

Dear all,

I have been trying to understand the sampling of the Brillouin Zone for
integration in the k-space.  The method adopted in the automatic generation
scheme in Espresso is the Monkhorst-Pack one. I have been reading the file
kpoints.f90  in

espresso-5.0/PW/tools/

and I went through some of the forum archives
http://www.democritos.it/pipermail/pw_forum/2012-February/023321.html to
understand this.

I think the algorithm follows these lines

1. generate a shifted uniform grid in *crystal space* of *the reciprocal
lattice* and associating a weight of 1/(total no: of k points)
2. use symmetry of the reciprocal lattice to reduce the list
                Here the weights of the eliminated points are accumulated
on to the remaining ones

This is what I was hoping to find
a) Some sort of check that ensures that k points fall within the
Wigner-Seitz Cell (first Brillouin Zone).
b) During the generation of the k point mesh, the sampling seems to not
extend in all quadrants of the crystal space, i.e., I am not able to find
negative crystal vectors. I expect them because the Brillouin zone extends
in all quadrants.

Can someone please explain this to me?

Regards
Meenakshi Sundaram M
Grad Student
Mechanical and Aerospace Engineering
Ithaca
Cornell
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