[Wannier] Question over the Amn(k) matrix

[Hung Pham]

Dear Wannier90 developers,

Firstly, I do apologize for my long email. Thank you for your patience.

I have implemented the interface between Wannier90 and PySCF.
I have a question over Amn(k) matrix. I just recall the formula of Amn(k)
[image: image.png]

* In my 1st implementation, | psi_m^k(r)> is represented by a uniform grid
of the *unit cell*. The gn(r) is similarly described in a similar way (only
computed at the grid points in the unit cell). And Amn(k) is calculated in
a numerical manner. Here, I assume that gn(r) is not k-dependent.
There is a concern over this. If we put a p orbital, for example, as a
guess at (0.0,0.0,0.0), then we will lose the partially information of the
gn(r), i.e. the part outside the unit cell (only grid points in the unit
cell is considered).

* In my 2nd implementation, the gn(r) is represented by a uniform grid for
the *supercell *that is consistent with the k-mesh used. Then gn(r) is
Fourier-transformed to the k-space representation gn*^k*(r). This
implementation is backed up by the fact that one wants gn(r), as a guessed
function, is close to the WFs (the Fourier-transformed functions of Block
states).

Personally, I think the 2nd scheme should be more reasonable.
However, in fact, the 1st scheme often results in more localized WFs (the
img/real ratios are smaller).
Is there anything wrong with these both schemes?

I would appreciate any comments, especially developer for QE_wannier90.

Thank you,
Hung Pham








-- 

Hung Q. Pham
Gagliardi Group
Office: Smith 101
Email: phamx494 at umn.edu

Department of Chemistry
University of Minnesota - Twin Cities, Minneapolis, MN 55455
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