[Pw_forum] Two More Questions on k-points Generation

[Gabriele Sclauzero]

Dear Paul

Paul M. Grant wrote:
> In Example 01, the number of k-points for Al is 60 in the scf step.I would
> have thought it would have been a power of 3 for an fcc cell (eg.,
> 4x4x4=64).  

Not necessarily, since some k-points are equivalent to others because of symmetry. Only 
the first non-equivalent k-point in a list of uniformly spaced k-points is considered and 
its weight is proportional to the number of equivalent points.

> How was this and the respective weights generated?
First the uniform grid is generated, eventually shifted according to the Monkhorst-Pack 
scheme (you should find plenty of discussion about that on the forum archive). Then each 
symmetry of the system is applied to each vector in the grid and if the transformed vector 
is already in the list (and has already been considered), then the starting vector is 
considered as equivalent to that prevoiusly checked and retained in the list.

> 
> What subroutine in the pw.x compiled and linked executable actually calls
> the input NAMELIST, in particular to generate the kpoints array passing
> appropriate arguments (e.g., Automatic)?

The automatic generation of k-points is performed by subroutine setupkpoint or 
kpoint_grid, which are called by setup. Some missing point might be added later by 
irreducible_BZ if the symmetry of the crystal (lattice+basis) is lower than that of the 
lattice alone.

If you know the correct weights, you can give a k-point list explicitly (as done in the 
example you mentioned - BTW, the weights are renormalized so that the total sum gives 1 or 
2, depending if you're using nspin=2 or 1, resp.). A k-point grid equivalent to that in 
the example could have been obtained automatically by specifying

K_POINTS automatic
8 8 8 1 1 1

The coordinates of k-point are very different from those given explicitly in the example, 
but the result you get (i.e. total energy) is exactly the same.

You may want to play a bit with the kpoints.x tool, which also generates grids of k-point 
and also optionally shows you the full list of points, telling you which is equivalent to 
which.

Best regards,

Gabriele Sclauzero


> 
> -Paul
> 
> Paul M. Grant, PhD
> Principal, W2AGZ Technologies
> Visiting Scholar, Applied Physics, Stanford (2005-2008)
> EPRI Science Fellow (Retired)
> IBM Research Staff Member Emeritus
> w2agz at pacbell.net
> http://www.w2agz.com <http://www.w2agz.com/> 
>  
>  
> 
> 
> 
> 
> 
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