[Pw_forum] more about K points of the whole BZ or the irreducible part?

[Stefano de Gironcoli]

When you chose to provide manually the k-point for a given structure
the code trusts you and assumes that you knows that the k-points you
provide are a good-sampling for the BRAVAIS LATTICE of your system.

IF the actual crystal symmetry of your system is LOWER that the one of the
Bravais lattice then the k-points given in input are expanded with those 
that
would be equivalent to the original ones for the full symmetry but 
aren't due
to the lower symmetry.

example:

In a system with cubic Bravais lattice but where x,y, and z direction are
inequivalent due to the positions of the atom in the unit cell.
the single k-point  (1.0, 0.0, 0.0) is expanded in the three points
(1.0,0.0,0.0),(0.0,1.0,0.0),(0.0,0.0,1.0).
If the crystal symmetry is instead cubic the original k-point is kept.
The code correctly takes into account the multiplicity of the points in
the star of equivalent k-points and rescales the weights accordingly.

>Sorry, I still don't quite understand here. What does
>it mean by  "all required k-points "? Those outside
>the irreducible part of the BZ? 
>  
>
those outside the Bravais Lattice Irrreducible part of the BZ but inside
the irreducible part of "your crystal" BZ

>>if the symmetry of
>>the system is lower than the symmetry of the Bravais
>>lattice."
>>    
>>
>
>What's the meaning of "the symmetry of the system is
>lower than the symmetry of the Bravais lattice"? Are
>there other occasions when the code doesn't need to
>generate all the other k-points?
>  
>
what matters for the symmetrization is the point group of your CRYSTAL
which is a sub group of the point group of your Bravais lattice.

>By the way, I know there is a small tool called
>kpoints which generate kpoints according to the
>convention of Monkhorst and Pack. But it seems the PW
>automatically generated kpoints are not always the
>same as those by this program. Do they use the same
>scheme?  
>
>How did the following 10 kpoints in example2
>generated? It doesn't seems to be generated either by
>kpoints tool or the PW automatic generating code.
>Either non-shifted or shifted.
>  
>
4 4 4 1 1 1
in a fcc generates 10 points that are equivalent to them.
They are probably taken from some other k-point generation code
of from the original Monkhorst and Pack or Chadi and Cohen papers.

Stefano de Gironcoli

>10
>   0.1250000  0.1250000  0.1250000   1.00
>   0.1250000  0.1250000  0.3750000   3.00
>   0.1250000  0.1250000  0.6250000   3.00
>   0.1250000  0.1250000  0.8750000   3.00
>   0.1250000  0.3750000  0.3750000   3.00
>   0.1250000  0.3750000  0.6250000   6.00
>   0.1250000  0.3750000  0.8750000   6.00
>   0.1250000  0.6250000  0.6250000   3.00
>   0.3750000  0.3750000  0.3750000   1.00
>   0.3750000  0.3750000  0.6250000   3.00
>
>
>  
>