[Pw_forum] question about spinors

[Alexey Akimov]

Dear all,

I try to understand the format of the wavefunction in case of spin-polarization (nspin=4, spinorb=.true. (or something similar)) without digging into code (what may take some longer time). First of all I print the wavefunction in the ascii format (text) using the post-processing utilities, that is the coefficients c_ig in expansion: psi_i = sum_over_g {c_ig * exp(u*g*r)}  (assuming Gamma-point case, so k=0). So when i compute overlap of 2 orbitals <psi_i|psi_j> it is delta_ij (Kronecker) (almost) for non-spin polarized case or with spin-polarized case but without spin-orbit. However, in spin-orbit case i have something like: <phi_1|psi_1> = 1, <psi_2|psi_2> = 0, <psi_3|psi_3> = 1, etc. Also the eigenvalues of the even orbitals look the same as those of odd orbitals (e.g. e_1 = e2, e3 = e4, etc.) 

So my question is what are the even wavefunctions, why their overlap is not 1, but is 0 while for odd orbitals the normal expectation of overlap being close to 1 is satisfied? More specifically, what is the interpretation of the output wavefunctions (bands) in such calculations? I tried to look tutorial and presentations about spin-orbit coupling calculations in QE. They say about spinors, but what is what in the output and how the (ortho)normalization is expressed in term of the outputs? 


Thank you,
Alexey



-- 
Dr. Alexey V. Akimov

Postdoctoral Research Associate
Department of Chemistry
University of Rochester

aakimov at z.rochester.edu