[Pw_forum] Understanding projwfc.x output and atomic_proj.xml

[Tobias Frank]

Dear quantum espresso users,
I'm currently trying to calculate the orbital resolved DOS of a system
which has very small spin-orbit splittings. As projwfc.x (v. 5.1) outputs
total angular momentum eigenstates (j,mj) in case of a noncollinear
spin-orbit calculation, I want to use the complex projections in
atomic_proj.xml to convert via Clebsch-Gordan coefficients to the l,lm,ms
basis and then to let's say px,py,pz orbitals.

My question is the following: What is the meaning of coefficients in
projwfc.out/atomic_proj.xml?:

For example (in projwfc.out):

-------------------------------------------
     state #  1: atom   1 (C  ), wfc  1 (j=0.5 l=0 m_j=-0.5)
     state #  2: atom   1 (C  ), wfc  1 (j=0.5 l=0 m_j= 0.5)
...
 k =   0.0000000000  0.0000000000  0.0000000000
==== e(   1) =   -21.24315 eV ====
     psi = ...+0.004*[#  1]+0.004*[#  2]+...
--------------------------------------------

I suppose those are the absolutes of the projections. Those two values for
example seem reasonable, as they are s orbitals of the same atom and should
have the same value.

If I take the corresponding complex coefficients out of atomic_proj.xml:

--------------------------------------------
    <K-POINT.1>
      <ATMWFC.1 type="complex" size="484">
-6.626669451678283E-002,-4.909240025179520E-002
...
      <ATMWFC.2 type="complex" size="484">
 6.173950333767936E-003,-1.379861858681805E-002
--------------------------------------------

When I take the norm of both, I get 0.0825 and 0.0015 respectively. Why are
they not the same and consistent with "projwfc.out", or in other words,
what am I doing wrong?

Thank you for your answers,
Tobias Frank
PhD. Student,
University of Regensburg
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