[Pw_forum] k points

[Axel Kohlmeyer]

On Mon, May 12, 2014 at 9:20 AM, Caroline <katesedate at gmail.com> wrote:

> Dear all,
>
> I am trying to understand the significance of k points in the input file.
> Can you please help me with the following questions:
>
> 1) How k points are selected? Dos it have to with the dimension of the
> crystal? Say for 2 dimension crystal only two lines in K point section is
> defined?
>
> 2) Or k points have to do with the numerical solution of integrals? I am
> confused how to define these values, and how they are important.
>
> 3) Is there a relation between number of k points and number of atoms in
> the lattice crystal?
>
>
> I have read text books on this, and learned that k points need to selected
> in such a way that total energy is converged.
>

​you obviously have either not read enough, or need to discuss with
somebody local to clear up some fundamental issues. explaining them
(thoroughly) in an e-mail ​would simply result in another textbook-like
text.

as a starting point, the k-points result automatically from the
reformulation of the schroedinger equation for periodic systems and the
resulting condition that the solution has to be commensurate with the
periodicity of the system, i.e. it has to be bounded by the simulation box
or be periodic over one or more primitive cells in each direction.

a second simple relation to keep in mind is, that a solution where you
double the system in one direction, is equivalent to a calculation where
you keep the system but sample over two evenly spaces k-points in that same
direction.

​i think with these rather general descriptions, you should re-read your
textbook(s) (and perhaps try a different one, e.g. this one which i find
particularly suited for somebody at your level of understanding:
http://www.amazon.com/Electronic-Structure-Calculations-Solids-Molecules/dp/0521815916
) and then discuss with your colleagues, adviser, professor etc. a mailing
list is a bad replacement for these kind of discussions and they are
essential for a proper insight into the methods)


axel.
​



>
> Please help me with this.
> Thanks a lot,
> C.
>
>
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-- 
Dr. Axel Kohlmeyer  akohlmey at gmail.com  http://goo.gl/1wk0
College of Science & Technology, Temple University, Philadelphia PA, USA
International Centre for Theoretical Physics, Trieste. Italy.
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