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[matthieu verstraete <matthieu.jean.verstraete@gmail.com>]

Right: a general grid of k-points in the Brillouin Zone is defined by
the k-grid lattice vectors (different from the G vectors of the
reciprocal space unit cell) and the origin of the grid. The grid does
not need to contain Gamma, which is why shiftk are necessary. This can
be much better for integration in the BZ (see Baldereschi and then
Monkhorst & Pack). For each shiftk, a basic grid, determined as a
uniform grid (dimensioned by ngkpt) along the G recip space lattice
vectors, is replicated, shifted in the BZ with respect to the origin.

This is well described in DFT reviews, solid state books, and in
particular Richard Martin's book on dft.

The optimal grids are not necessarily ones which follow the G vector
directions with a simple geometry. Depending on unit cell symmetry,
other grids of k-points may be better (M&P). In practice, the best
grids are usually evenly spaced in _cartesian_ reciprocal space
coordinates, whereas the default ones (generated with ngkpt and 1
shift, and those used in just about all other codes) are restricted to
even spacing in _reduced_ reciprocal space coordinates.

In your specific case, it looks like you generate the same grid with
your 4 shifts as with the default, which is 1 shift of 1/2 1/2 1/2.
This is somewhat of a coincidence, and with a less cubic system will
not happen. Try with nshift 1 shiftk 0 0 0 and you will see a
difference in the energy.

Matthieu

On Thu, Jun 18, 2009 at 9:39 AM, Rob<spamrefuse@yahoo.com> wrote:
>
>
> Hi,
>
> Tutorial 3.1 introduces the variables nshiftk and shiftk.
> This is quite confusing to me. I don't see what is shifted?
>
> Moreover:
> The total energy is EXACTLY the same as when I remove
> these two variables from the input file t31.in:
>
> With
>    nshiftk 4
>    shiftk 0.5 0.5 0.5
>             0.5 0.0 0.0
>             0.0 0.5 0.0
>             0.0 0.0 0.5
> I get
>    etotal   -8.8662238960E+00
>
> When I change it into the default values:
>      nshiftk 1
>      shiftk 0.5 0.5 0.5
> I get:
>      etotal   -8.8662238960E+00  (EXACTLY the same energy).
>
>
> I have tried the above for different ngkpt values (2 2 2, 4 4 4, 6 6 6)
> with the same conclusion!
>
> What is then the purpose of this tutorial 3.1?
> This confuses me quite a bit, since I tried to understand nshiftk and 
> shiftk.
>
> Thanks,
> Rob.
>
>
>
>
>



-- 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Dr. Matthieu Verstraete

European Theoretical Spectroscopy Facility (ETSF)
Dpto. Fisica de Materiales,
U. del Pais Vasco,
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Mail : matthieu.jean.verstraete@gmail.com
http://www-users.york.ac.uk/~mjv500