[Pw_forum] question about spinors

[Alexey Akimov]

Dear Paolo,

I'm not sure that i completely understand what you mean by empty coefficients. Also what is npwx, how is it different from npw? Let say npw = 3 and npwx = 4 (very small basis :)) then the overlap of orbital i and orbital j will be:
c_i0^* * c_j0 + c_i1^* * c_j1 + c_i2^* * c_j2 + c_i3^* * c_j3 (four terms as npwx). If, as you say, some coefficients are empty (lets say c_i3 and c_j3) we still have some non-zero terms. I'm not sure if the previous sentence have any sense at all, so sorry if this is something terribly wrong :) - that is why i'm asking. 
(^* - means complex conjugate)

Also am i correct that the spin-up and spin-down orbitals are orthogonal not because of the artificial convention <alpha|beta> = 0, but rather by construction of the corresponding plane wave expansions (given by coefficients c_gi )? What i mean is that in localized orbitals e.g. Gaussians the spatial parts of the alpha and beta orbitals are practically the same (exactly in restricted HF or KS approaches), but the orthogonality is then introduced by convention: psi_i_alpa = phi_i * sigma_alpha, psi_j_beta = phi_j * sigma_beta => <psi_i_alpha|psi_j_beta> = <phi_i|phi_j> * <sigma_alpha|sigma_beta>, so even if <phi_i|phi_j> != 0 the orbitals are still orthogonal because <sigma_alpha|sigma_beta> = 0 by convention. So in spin-orbital case do we still need to consider these artificial sigma_alpha, sigma_beta spin-functions or the orthogonality is already included in "spatial" part (so <phi_i|phi_j> = 0 for alpha and beta spin-orbitals)?

Thank you,
Alexey


----- Original Message -----
From: "Paolo Giannozzi" <giannozz at democritos.it>
To: "PWSCF Forum" <pw_forum at pwscf.org>
Sent: Wednesday, August 22, 2012 8:27:59 AM
Subject: Re: [Pw_forum] question about spinors


On Aug 21, 2012, at 23:55 , Alexey Akimov wrote:

> I try to understand the format of the wavefunction in case of spin- 
> polarization
> (nspin=4, spinorb=.true. (or something similar))

KS orbitals  for the spin-orbit case have coefficient on a basis of  
NPW plane
waves with spin up, NPW plane waves with spin down. The dimension of the
orbitals is 2*NPWX >= 2*NPW, so there can be empty coefficients in the
middle.

P.
---
Paolo Giannozzi, Dept of Chemistry&Physics&Environment,
Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222




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-- 
Dr. Alexey V. Akimov

Postdoctoral Research Associate
Department of Chemistry
University of Rochester

aakimov at z.rochester.edu