[QE-users] [projwfc.x]

[박기명]

Thank you for your reply.

Looking at the projwfc.x output, the projected atomic states are labeled by l, j, and mj, for example :
     state #   1: atom   1 (Cs ), wfc  1 (l=0 j=0.5 m_j=-0.5)
     state #   2: atom   1 (Cs ), wfc  1 (l=0 j=0.5 m_j= 0.5)
     state #   3: atom   1 (Cs ), wfc  2 (l=1 j=1.5 m_j=-1.5)
     state #   4: atom   1 (Cs ), wfc  2 (l=1 j=1.5 m_j=-0.5)
     state #   5: atom   1 (Cs ), wfc  2 (l=1 j=1.5 m_j= 0.5)
     state #   6: atom   1 (Cs ), wfc  2 (l=1 j=1.5 m_j= 1.5)
     state #   7: atom   1 (Cs ), wfc  3 (l=1 j=0.5 m_j=-0.5)
     state #   8: atom   1 (Cs ), wfc  3 (l=1 j=0.5 m_j= 0.5)
...

Further below, each Bloch state is decomposed in terms of these projected states,
e.g.
==== e(   1) =  -159.62902077 eV ====
     psi = 0.499*[#  11]+0.499*[#  12]
    |psi|^2 = 1.000
==== e(   2) =  -159.62902077 eV ====
     psi = 0.499*[#  11]+0.499*[#  12]
    |psi|^2 = 1.000
==== e(   3) =  -109.66866690 eV ====
     psi = 0.500*[#  17]+0.500*[#  18]
    |psi|^2 = 1.000
...

So, is it correct to interpret this as |C_n,k,l,j,mj|^2=|<phi_n,k,l,j,mj|psi_q.e>|^2
rather than in |l,m,s> basis ?

In other words, when spin-orbit coupling is included, should the projwfc.x output be understood in the coupled angular momentum basis |l, j, mj>?

Best regards,
Gi Myung Park
Yonsei University
-----Original Message-----
From: "Giovanni Cantele via users"<users at lists.quantum-espresso.org>
To: "Quantum ESPRESSO users Forum"<users at lists.quantum-espresso.org>;
Cc:
Sent: 2026-04-04 (토) 23:33:58 (GMT+09:00)
Subject: Re: [QE-users] [projwfc.x]

Hi,
in the presence of spin-orbit coupling, as specified here:
https://www.quantum-espresso.org/Doc/INPUT_PROJWFC.html
this is what projwfc.x does:

In the non-collinear, spin-orbit case (i.e. if there is at least one
fully relativistic pseudopotential) wavefunctions are projected
onto eigenstates of the total angular-momentum.
Projected DOS are written to file "filpdos".pdos_atm#N(X)_wfc#M(l_j),
where N = atom number , X = atom symbol, M = wfc number, l=s,p,d,f
and j is the value of the total angular momentum.
In this case the format is:
    E LDOS(E) PDOS_1(E) ... PDOS_2j+1(E)
    ...


The presence of the perturbing spin-robit potential L.S merges spatial orbitals
with spin orbitals to produce eigenstates of the total angular momentum eigenstates`
and mz --> Lz, ms --> Sz are no longer good quantum numbers (L.S = (J^2-L^2-S^2)/2 and
the eigenstates of J^2 and Jz are also eigenstates of L^2 and S^2 but not of Lz and Sz).

Giovanni
-- 

Prof. Giovanni Cantele
Dipartimento di Fisica "Ettore Pancini"
Universita' degli Studi di Napoli "Federico II"
Complesso Universitario M. S. Angelo - Ed. 6
Via Cintia, I-80126, Napoli, Italy
e-mail: giovanni.cantele at unina.it
Phone: +39 081 676910

Web page: https://sites.google.com/view/giovanni-cantele/home


Il giorno sab 4 apr 2026 alle ore 12:34 박기명 <knppkm at naver.com> ha scritto:

Dear users,

When performing calculations using projwfc.x, results for "j" and "mj" are obtained.
Are "j" and "mj" the total angular moment and the corresponding mj (j, j-1, ..., -j)?
Is there a reason why the values ​​for "l" and "m" are not provided?

Best regards,
Gi Myung Park
Yonsei University



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