[Wien] what mesh (real space) is used in WIEN2k? (Artem Urubkov)

[Stefaan Cottenier]

>  I did following experiment. I created two .struct files for Ni2MnGa
> (cubic fcc, 225 symmetry spacegroup) with equal arrangements of atoms,
> equal MT-radia, equal RKmax and all other parameters, but: for one
> case I set the lattice parameter 5.85A, and for another case the
> lattice parameter was 15A. To my mind, the result was not obvious: the
> calculation time for the second case became above 100 times greater
> than for the first case. How to explain it? The numders of k-points in
> IBZ for both of these cases are equal (10), gmax and Kmax are equal
> too-- so, according to accessfull for me UGs (WIEN UG and "DFT and
> the Family of (L)APW-methods: a step-by-step introduction"), matrixes
> of expansion of wave functions must be equal by size and the
> calculation times must be equal. If no meshes are used in real space
> than I must have been mistaked. And, as far as I know,
> "Gmax"-parameter is to control potential expansion in WIEN-code.
>  Tell me, please, where is the mistake?

This is a nice question. You are right that Kmax plays a role in determining
the matrix size, but it is not the only factor. The matrix size is
determined by the number of K-points (capital K = reciprocal lattice
vectors) that are smaller than Kmax. For a big unit cell, there are much
more such K than for a smaller one, because the reciprocal unit cell size is
inversely dependent on the size of the direct unit cell (see e.g. App. A.3
of the "Family of  (L)APW...." text). As you have one basis state for every
such K (see eq. 5.1 of the "Family..." text), your basis set will be much
larger for your larger cell.

You can check in your :RKM lines that the matrix size will be larger for the
larger cell. Bigger matrix = much longer calculation time, and that's the
factor 100 you find.

If you find places in the "Family ..." text where confusion is possible
(does it somewhere say that from Kmax alone you find the basis set size?),
then please let me know the exact location of these lines in the latest
version (since August, there is an update on the web where a few minor
errors have been corrected).

Stefaan