# [QE-users] Wavefunction Overlap for Different K-space Samplings (repost)

```Hi,

I’m currently computing wave function overlap of some KS-wave functions
produced by QE for monolayer MoS2 with SOC enabled. The wave functions are read
with HDF5 in Fortran. However, something is bothering me. When computing```
```
< nk | nk’ > = delta_kk’ sum_{G_nk} C*_nk(G_nk) C_nk’(G_nk) ,

O_nk_nk' = sum_{G_nk} C*_nk(G_nk) C_nk’(G_nk),

for k = (0.0 , 0.0 , 0.0) and k’ = (1/3, 1/3, 0) in crystal coordinates, and
some fixed band, n (I choose the top valence band in this example), I get
wildly different values depending on the k-space sampling. In the equation C_nk
and C_nk’ denotes the plane wave coefficients stored in the .hdf5 output files.

I’ve attached a figure, displaying the absolute value of O_nk_nk’ for different
k-space samplings.

I would have imagined, that the values of O_nk_nk’ should either be identical
or at least look smooth when plotted against the k-space sampling. Can you
clarify on this behaviour?

As a note, the wave function stored in your .hdf5 files have four times the
length of the number of planewaves (npw). Therefore, I rearrange the wave
function as (Fortran version)

psi_up_r = psi_k(1        :npw_   ,:),
psi_up_i = psi_k(npw_+1   :2*npw_ ,:),
psi_dw_r = psi_k(2*npw_+1 :3*npw_ ,:),
psi_dw_i = psi_k(3*npw_+1 :4*npw_ ,:),

where r denotes the real part and vice versa for i. Moreover, I am aware that
the G-basis varies for each k-point, and I took care of this as well.

Attached figure:
https://www.dropbox.com/s/m70kwhg0wir7eh1/wf.png?dl=0

Sorry for reposting, but I did not realise that figures should be attached
externally.

Kind regards

Carl Emil Mørch Nielsen

---------------------------------------------------------
MSc. Carl Emil Mørch Nielsen
Universität Hamburg
HARBOR, Geb. 610
Luruper Chaussee 149
D-22761 Hamburg
---------------------------------------------------------

```
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