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Summary

I wanted to calculate a density of states, which is projected onto the total angular momentum states j. As a test I made non-spin polarized calculations with spin-orbit coupling in the following way

1. Calculate a non-spinpolarized density with second variation SOC (in both cases)
2. Generate a spin polarised density with swsp="T"
3. Run 1 iteration and calculate a DOS with both second and first variation SOC

I used the following manually adjusted input files for the third step (see issues #384 and #389 (closed)).

inp_firstvariation.xml inp_secondvariation.xml

Kpoint set with no symmetry kpts.xml sym.xml

and obtain the following output and DOS files (DOS files only for one spin as they are still equivalent after the first iteration)

out_firstvariation;DOS_firstvariation

out_secondvariation;DOS_secondvariation

The resulting fDOS looks like this:

If you now take a closer look at the spectrum and the integral over the two peaks of the fDOS we get a weird behaviour. The integrals for second variation are approximately 3 for the lower peak and 4 for the upper peak. This is expected, because the lower peak should be the one with j=5/2 character, meaning 6 states in total. For first variation this is flipped. So the lower peak has an integral of 4 and the upper one 3. It seems like the j=5/2 and 7/2 states are flipped here. This can also be seen in the eigenvalues in the outfiles.

This is BUG because:

The j=5/2 state should be lower in energy regardless of first or second variation SOC

The problem only occurs if:

SOC, no change if no symmetries are used