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

[Paolo Giannozzi]

Plane-wave coefficients are complex: the real part is followed by 
imaginary part. The first 2*npw coefficients are for the "up" components 
of the spinor; the following 2*npw are for the "down" component

Paolo
-- 
Paolo Giannozzi, DMIF, Univ. Udine, Italy
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On 12/12/23 11:25, Alireza Shabani via users wrote:
> 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 <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 
> <http://www.researcherid.com/rid/A-1951-2009>
> Web page: https://sites.google.com/view/giovanni-cantele/home 
> <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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