[QE-users] normalization of wfcs (wfck2r)

[Davide Ceresoli]

Dear Chris,
     you don't need the volume, just to divide by (n1*n2*n3).

Best,
D.


On 8/26/21 6:24 AM, Christoph Wolf wrote:
> Dear all,
> 
> I am converting a wave-function from k to R space using wfck2r.x. There is only 
> 1 k-point (particle in a box of 15*15*15 Ang) and the wfc looks like:
> 
> ==== e(   8) =    -4.84501 eV ====
>       psi = 0.998*[#   2]
>      |psi|^2 = 0.999
> 
> state #   2: atom   1 (Fe ), wfc  2 (l=0 m= 1)
> 
> So this is a "pure s state"; i converte the wfc into real space by using:
> 
>     first_k = 1,
>     last_k = 1,
>     first_band = 8
>     last_band = 8
> 
> and I get an ".oct" (plain text) file containing on a grid of 144 x 144 x144:
> 
> (*-0.885667802907E+01*,  0.607695317678E-16)
> ( *-0.627285985227E+01*, -0.418670474801E-15)
> ( -0.291716024900E+01, -0.436306625693E-15)
> ....
> ..
> 
> if I  understood the manual correctly the order is such that the real part for 
> example:
> 
> re[:,:,0]= [ *-8.85667803, * *-6.02698044, * -2.39305522, ..., -12.45808728,  
>   -11.95557896, -10.79190254]
> 
> that is the first 144*144 elements belong to z=0, the next to z=1, z=2, ...z=144.
> 
> my volume element would be: (15/0.529)**3/144**3=0.0076 (au^3/grid^3)
> 
> if I take the dot product of the complex wfc 
> <psi*|psi>*0.076=25733.51243066387+0j, but should this not be the same as 
> |psi|^2 = 0.999?
> 
> This is probably a very stupid and obvious mistake but I have been looking at 
> this for a while now and don't get it...
> 
> Best,
> Chris
> -- 
> Group Leader "Theory of Quantum Systems at Surfaces"
> IBS Center for Quantum Nanoscience
> Seoul, South Korea

-- 
+--------------------------------------------------------------+
   Davide Ceresoli
   CNR - Istituto di Scienze e Tecnologie Chimiche (SCITEC)
   c/o University of Milan, via Golgi 19, 20133 Milan, Italy
   Email: davide.ceresoli at cnr.it
   Phone: +39-02-50314276, +39-347-1001570 (mobile)
   Skype: dceresoli
   Website: http://sites.google.com/site/dceresoli/
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