[Wien] question about ISPLIT and orbital degeneracy

[Peter Blaha]

The eigenvalues at equivalent k-points are the same, but the
wavefunction is not (how should a Bloch-function be identically for
different k).

Take eg. a cubic symmetry, than px,py and pz orbitals must be degenerate
and the total density from p-states must be spherical.

When plotting the density of a k-point (x,0,0) it will NOT be spherical,
but show eg. px symmetry, but the k-point (0,x,0) will have identical
eigenvaliues, but a density with py-character and (0,0,x) ...

Only the sum of those 3 has the correct symmetry.
Alternatively, one can make a symmetry-projection, then one can get out of
ONE k-point the proper "symmetrized" density. But this requires, that you stick
to the WIEN2k inputs and do not look at px,py,pz individually.

A similar situation happens with the LM expansion of the density (as listed
in case.in2). In principle, other LM-values should be zero by symmetry, but that
would only be fulfilled when using a summation over the full BZ, not the IBZ.
Thus you MUST NOT modify the LM-list.



Am 12.10.2011 10:59, schrieb Georg Eickerling:
> Dear WIEN users,
>
> I have a question concerning the ISPLIT option:
> Assuming a cubic (non-magnetic/non spin-polarized) NiO as example,
> the default ISPLIT after init_lapw is "2" which results in the
> expected eg/t2g splitting of the Ni d-orbitals in the projected DOS.
>
> What I now did was
>
> change ISPLIT to 8
> run lapw2 -qtl (or qtl itself with QSPLIT 2)
>
> in order to see the same eg/t2g degenracy for the five individual
> d-orbitals. However, this produces a partial d-DOS in which none of
> the orbitals are degenerate.
>
> I only obtain the correct degeneracy with ISPLIT 8/QSPLIT 2 when
> first calculating a "P1" k-list by
>
> removing all symmetry operations apart from the identity from the struct
> generating a new klist
> run lapw1
> run lapw2 -qtl (or qtl itself)
>
> So my question is: Why do I need the "P1" k-list in this case,
> should not the eigenvalues on the original k-points show the
> degeneracies as well?
>
> Thank you in advance for your help,
>
> Georg Eickerling
>
>
>
>

-- 

                                       P.Blaha
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Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-1-58801-15671             FAX: +43-1-58801-15698
Email: blaha at theochem.tuwien.ac.at    WWW: http://info.tuwien.ac.at/theochem/
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