[Wien] state normalization problem violates correct spin expectation value :: modified w2w code

[Martin Gmitra]

Dear Wien2k users,

I have modified w2w code to calculate overlaps and consequently spin
expectation values for states of interest.

For the tests I consider an artificial system -- a flat germanene with
spin-orbit coupling without RLO. The system has inversion and thus all
the states are spin degenerated. Spin-expectation values are obtained
by diagonalizing (rotating) a generalized spin matrix. As the spin
should follow certain symmetry constrains I have observed tiny
violations.

Further inspection of the violations points to the normalization of
the states that shows that the states are not perfectly
othonormalnormali. For instance the overlaps for a degenerate band (n)
close to Fermi level at the K point are:

<n, K | n, K> = 0.999990071859
<n+1, G| n, G> = 0.0
<n+1, K | n+1, K> = 0.999990071859

The w2w code works only with spherical potential. Looking into lapwso,
non-spherical contributions to the Hamiltonian are added only if RLO
is included in vnsrint.F. Therefore I suggest that the non-spherical
contribution should not matter in my case once diagonalization of the
Hamiltonian in lapwso should provide orthonormal states.

My question is -- do you have any hints what could be missing to get
perfectly normalized state?

Best regards,
Martin Gmitra
Uni Regensburg