[QE-users] Spatial dependency of the wave functions for the spin-orbit coupling calculation

[Alireza Shabani]

Dear Giovanni,

Thank you for your explanation. Yes, I think for the number of KS states, you are right, as the spin-orbit coupled states are twice the non-spin-orbit coupled states. But I am going to focus on just one of these states and calculate the wave function using the information in the .hdf5 file and equation psi = sigma (C_real + i C_imag) * exp(iG.r), which I know I must change a little bit because of the two-component spinor.

My question is, is it right to say for every single 'Miller Indices' in the .hdf5, we have four complex 'evc'? If so, how should we write the vector to form the desired wave function? Is it a vector with two complex components like this: (c_1 + j c_2       c_3 +j c_4) * exp(iG.r)   ,here c_i are the 'evc'.

Unfortunately, I didn’t find the mathematical description for constructing the spinor plane wave in QE, so I would appreciate it if anybody could introduce a reference for it.

Thank you for your suggestions.
Alireza Shabani
Postdoc researcher,
Denmark Technical University
Copenhagen, Denmark


From: Giovanni Cantele <giovanni.cantele at spin.cnr.it>
Sent: Monday, December 11, 2023 2:14 PM
To: Alireza Shabani <alsha at dtu.dk>; Quantum ESPRESSO users Forum <users at lists.quantum-espresso.org>
Subject: Re: [QE-users] Spatial dependency of the wave functions for the spin-orbit coupling calculation

I'm not expert about HDF5 files, however because you are seeking for wave function coefficients, the answer might be that, as explained for example here
https://www.quantum-espresso.org/Doc/pw_user_guide/node10.html#SECTION00043030000000000000
when spin-orbit is turned on the wave functions are two-component spinors.
This also reflect the fact that, with nelec electrons, the ground-state density suffices nelec/2 Kohn-Sham states (using spin degeneracy) in the absence of spin-orbit
coupling, whereas including the latter you need to compute (for semiconductors) at least nelec states.

Giovanni

--

Giovanni Cantele, PhD
CNR-SPIN
c/o Dipartimento di Fisica
Universita' di Napoli "Federico II"
Complesso Universitario M. S. Angelo - Ed. 6
Via Cintia, I-80126, Napoli, Italy
e-mail: giovanni.cantele at spin.cnr.it<mailto:giovanni.cantele at spin.cnr.it>
Phone: +39 081 676910
Skype contact: giocan74

ResearcherID: http://www.researcherid.com/rid/A-1951-2009
Web page: https://sites.google.com/view/giovanni-cantele/home


Il giorno lun 11 dic 2023 alle ore 13:49 Alireza Shabani via users <users at lists.quantum-espresso.org<mailto:users at lists.quantum-espresso.org>> ha scritto:
Dear QE users,
I am going to calculate the spatial dependency of the wave function from the output HDF5 files from QE (for one specific k-point, such as Gamma). I know that the number 'evc' should be twice the 'Miller Indices' because it includes real and imaginary coefficients in the wave function: psi = sigma (C_real + i C_imag) * exp(iG.r).
Everything looks fine, and I can calculate the wave function in a normal DFT calculation (I mean without spin-orbit coupling!!). But, when I use spin-orbit coupling, the number of 'evc' in the final .hdf5 file becomes four times the 'Miller Indices.' For instance, if I have 100 'Miller Indices, ' I will have 400 'evc' which is a bit confusing. Does anybody know how we can interpret it?
Thank you for your suggestions.

Kind regards,
Alireza Shabani
Postdoc researcher,
Denmark Technical University
Copenhagen, Denmark

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