[Wien] [wien2wannier] unit of |w(r)|^2 in case.xsf and case.psink

[Elias Assmann]

Dear Wenhu Xu,

On 12/12/2016 08:10 PM, Xu Wenhu wrote:
> Then I want to check the normalization of the wannier function, so I
> integrate the grid and assume the unit of |w(r)|^2 to be 1/A^3, as
> the unit parameter set in my case.inwplot file. But the number turns
> to be ~450, too much larger than the expected 1.

The most important factor is likely the number of k-points.  You are
probably using wien2wannier 1.0 (as included in Wien2k 14.2), where an
erroneous factor of sqrt(#k-points) was included in the WFs (see
wien2wannier issue #2 at https://git.io/wf-norm).  To fix this issue,
best upgrade to the brand-new Wien2k 16.1
<http://susi.theochem.tuwien.ac.at/reg_user/updates/>.

Then, depending on what you did, you might see a remaining factor of
Å/Bohr.  To get that right, keep in mind:

 * the unit of distance you selected in case.inwplot (in the template,
   Å is selected, contrary to Wien2k convention);

 * the proper “dV” factor (in the header of case_i.psink, the lengths
   of the plot axes are always given in Bohr, regardless of the units
   option -- I should probably change that).

> Please see below the case.inwplot I used. The length of grid axes is
> twice of the lattice vectors, and the number of mesh points is
> 100x100x100.

Normally, you do not need to worry about WF normalization.  If for
some reason you do, then you need to be very careful about the
integration.  In my experience from one project [1], you may need to
go to surprisingly large plot regions (2×2×2 may or may not suffice,
depending on your unit cell and the shape of your WFs).

But to do a convergence study in the r-mesh, you also have to make
sure your r-meshes are commensurate.  That is to say, if the r-points
are slightly shifted from one mesh to another, you will pick up
contributions from different regions of the (sharply peaked) WFs and
converge to a different integral.

In summary: If possible, it is best to treat the r-integral over the
WFs as an arbitrary constant.


	Elias


[1] T. Ribic, E. Assmann, A. Tóth, and K. Held, Phys. Rev. B 90,
165105 (2014)

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