# [Wannier] charge of wannier function

Hu Shuanglin hushuanglin at gmail.com
Fri Jun 29 12:19:37 CEST 2012

```Dear all,

I am new to wannier90, and try to use wannier90 and vasp together.
I thought since wannier function is the unitary transfromation of
Bloch functions,
1, each wannier centers here should correspond to one charge center,
and each could
be occupied by 2 electrons (without spin-polarization).
2, from the occupied wannier functions, I can do summation to get the
overall charge
density that equal to vasp CHGCAR data.
Is this understanding correct?

Then in order to test this, I added some lines like following in the
plot.F90 file:

wann_rho(nxx,nyy,nzz,loop_w)=
wann_func(nxx,nyy,nzz,loop_w)*conjg(wann_func(nxx,nyy,nzz,loop_w)
wann_chg(nxx,nyy,nzz)= wann_chg(nxx,nyy,nzz)+wann_rho(nxx,nyy,nzz,loop_w)
sum_rho(loop_w)=sum_rho(loop_w)+wann_rho(nxx,nyy,nzz,loop_w)

After the summation, the "electron number of each wannier function" is
printed out
sum_rho(loop_w)=sum_rho(loop_w)/(ngs*ngx*ngs*ngy*ngs*ngz)

I am studying a insulator LiOH, in which there are 16 valence
electrons in one unit cell,
and vasp gave a default num_wann=8 in the .win file. The loop_w is
looped over all the 8
occupied band in this model, and only Gamma point is used in k-space.
However, I get a number lower than 1 for one wannier band, and they do
not equal to each
other between wannier bands.

Wannier Function Num:    1       Number of Charge =  0.843700E+00
Wannier Function Num:    2       Number of Charge =  0.843700E+00
Wannier Function Num:    3       Number of Charge =  0.833333E+00
Wannier Function Num:    4       Number of Charge =  0.832989E+00
Wannier Function Num:    5       Number of Charge =  0.832841E+00
Wannier Function Num:    6       Number of Charge =  0.810597E+00
Wannier Function Num:    7       Number of Charge =  0.833188E+00
Wannier Function Num:    8       Number of Charge =  0.810594E+00

In this case, the total number of electrons will certainly not to be 8*2=16.

Is there anything wring in my understanding or inplementation? Any
Thank you!

Best Regards,
Shuanglin Hu
--
Department of Chemistry - the Angstrom Lab
Uppsala University
Box 538, SE 751-21
Uppsala, Sweden

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