[Pw_forum] Orbital order in the non-collinear relativistic case... again!

[Rodrigo Neumann]

Dear QE users and developers,

This issue has already been raised before, but no matter how many times I
read the available info I cannot conclude what is the final answer to it.
So, I kindly ask you to go back to this subject, once and for all.

In a previous post to the pw_forum (
http://www.democritos.it/pipermail/pw_forum/2011-February/019281.html) it
was suggested that the several columns present in the
"X.pdos_atm#1(X)_wfc#Y(d_j2.5)" file were directly related to the
eigenvalues of J^2 and Jz, that is, the total angular momentum quantum
number "j" and its projection "m_j" (j, m_j). So the header line could be
interpreted as:

# E  ldos  (5/2,-5/2)  (5/2,-3/2) (5/2,-1/2)  (5/2,+1/2)  (5/2,+3/2)
 (5/2,+5/2)


However, the in-place documentation on
espresso-5.0/PP/src/atomic_wfc_nc_proj.f90 (
http://qe-forge.org/scm/viewvc.php/trunk/espresso/PP/src/atomic_wfc_nc_proj.f90?view=markup&root=q-e&pathrev=8404),
suggests otherwise:
  ! If lspinorb=.TRUE. it makes linear combinations of eigenstates of
  ! the atomic total angular momenta j and j_z; otherwise, of eigenstates of
  ! the orbital angular momenta l, l_z and of s_z (the z-component of the
spin).


The "Orbital Order" entry on the INPUT_PROJWFC documentation (
http://www.quantum-espresso.org/wp-content/uploads/Doc/INPUT_PROJWFC.html#id485086,
by the way, there's a minor typo regarding dxy) further strengthens the
"linear combination hypothesis". From where I stand, it seems to suggest
that the order is actually something like:

# E   ldos   "(5/2,+1/2)+(5/2,-1/2)"   "(5/2,+1/2)-(5/2,-1/2)"
"(5/2,+3/2)+(5/2,-3/2)"   "(5/2,+3/2)-(5/2,-3/2)" ...the same for
m_j=+-5/2...
where the + and - operation between eigenstates means (loosely) "linear
combinations".


I hope I was clear enough while presenting the issue. Maybe, if I could
read FORTRAN, I'd be able to figure it out for myself. But I can't, and
that's why I'm asking for you help. I also suggest that whatever answer we
come up to in this thread should be written explicitly on INPUT_PROJWFC in
order to prevent this issue from surfacing again in a few months.

So, for once and for all, are those the columns related to the eigenstates
of J^2 and Jz or to their linear combinations?

Thanks in advance!

Best regards,
Rodrigo Neumann

--------------------------------------------------------
Rodrigo Neumann Barros Ferreira
PhD Student
Departamento de Física dos Sólidos - Instituto de Física
Universidade Federal do Rio de Janeiro
Cx.Postal 68.528
21945-972, Rio de Janeiro - RJ - BRASIL

Tel: [+55] (21) 2562-7341
http://www.if.ufrj.br/~neumann/
http://tmc.if.ufrj.br/
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