[Pw_forum] Normalization of the atomic wave functions

[degironc]

the atomic wavefunctions in the pseudopotential are normalized, and in 
the LDA+U they are used as such...
however for each k-point the code builds the bloch-type linear 
combination of atomic wavefunctions.
The norm of this bloch-like wfc depends on the overlap between wfc in 
neighboring cells AND on the wfc
spread. The 3d orbital are likely to be rather localized but the 4s wfc 
are probably very delocalized. this is why the
calculated norm of the bloch-type wfc is significantly different from 1.
The projection in LDA+U is however defined on the individual atoms (even 
if technically bloch states are involved) and these
wfc are normalized.
hope this helps,
stefano de Gironcoli, SISSA and DEMOCRITOS, Trieste (Italy)

Henning Glawe wrote:
> Moin,
> I am at the momemt trying to understand how the atomic states used in an
> LDA+U calculation are normalized. I inserted code to print out the
> normalization into the k-loop of the new_ns subroutine:
>
> [...]
>   COMPLEX(DP) :: hg_norm
> [...]
>   ALLOCATE(wfcatom(npwx,natomwfc))
>
>   DO ik = 1, nks
>      IF (lsda) current_spin = isk(ik)
>      IF (nks.GT.1) READ (iunigk) npw, igk
>      IF (nks.GT.1) CALL davcio (evc, nwordwfc, iunwfc, ik, - 1)
>
>      CALL davcio (swfcatom, nwordatwfc, iunsat, ik, - 1)
>      CALL davcio (wfcatom, nwordatwfc, iunat, ik, -1)
>      DO i = 1, natomwfc
>         hg_norm=ZDOTC(npw, wfcatom(1,i), 1, swfcatom(1,i), 1)
>         write( 43, '(i4.4,1x,i1.1,1x,i3.3,1x,2e20.10)') ik, current_spin, i, hg_norm
>      ENDDO
> [...]
>
> so basically I am calculating <\phi^I_k|S|\phi^I_k> (the S operator 
> being related to the relaxed norm conservation in the case of ultrasoft
> pseudopotentials).  I assumed this to be always 1.
>
> However, running the FeO example in the QE distribution, I obtain a spektrum
> of values, most of them between 0.9 and 1.1. The norm of one atomic state of
> the example system and its spin-counterpart are spread quite widely, between 
> 0.3 and 3.85 (?).
>
> So somehow I get the impression that I do not understand how the atomic 
> states are normalized in pwscf...
>
>