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

"erroneous contribution" is erroneous. The contributions are what they
are, but the values we have are on the k-point grid, and that is where
the error can be estimated: there are in some sense "perfect" values
for the quadrature you choose, whose sum over discrete k would give
the exact continuous integral, but obviously we don't know what these
are, and the contributions we actually sum are in this sense
"erroneous".

The finite grid spacing gives an error, and, broadly speaking, the
smaller the k grid spacing the more precise your integral. And the
smallest grid spacing in k corresponds to the largest real space
vector.

Matthieu

On Tue, Apr 7, 2009 at 9:41 AM,  <hichem.bouderba@gmail.com> wrote:
> hello everybody,
> in the input file documentation in kptrlen entry we can read the following:
> " ... One can relate the error made by replacing the continuous integral by 
> a
> sum over k point lattice to the Fourier transform of the periodic quantity.
> Erroneous contributions will appear only for the vectors in real space that
> belong to the reciprocal of the k point lattice, except the origin. 
> Moreover,
> the expected size of these contributions usually decreases exponentially 
> with
> the distance. So, the length of the smallest of these real space vectors is 
> a
> measure of the accuracy of the k point grid."
>
> can somebody be more explicit about the relation between integrals and
> "erroneous contributions" ?
>



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

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