# Re: [Wien] What's the difference between the spin-polarized and the non spin-polarized calculations

```I guess the answer is basic calculus
B_eff = V_up - V_dn
is zero when V_up = V_dn and the equations in the spin polarized and the non
spinpolarized case become the same, isn't it.
(Note: V_up=V_up(rho_up) and V_dn=V_dn(rho_dn) is used for short, the densities
rho_up and rho_dn are calculated
from the Kohn-Sham wave functions the V(rho) depend on the used
exchange-correlation functional.)```
```
Just take a pencil and write down the equations given in the trancparencies or
textbooks and proof that I am right by
setting B_eff=0.

... or you finally did not understand what a selfconsistent field calculation
means,
then you have to attend some basic courses on mathematics or theoretical
physics.

Ciao
Gerhard

DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:
"I think the problem, to be quite honest with you,
is that you have never actually known what the question is."

====================================
Dr. Gerhard H. Fecher
Institut of Inorganic and Analytical Chemistry
Johannes Gutenberg - University
55099 Mainz
and
Max Planck Institute for Chemical Physics of Solids
01187 Dresden
________________________________________
Von: Wien [wien-boun...@zeus.theochem.tuwien.ac.at] im Auftrag von Gavin Abo
[gs...@crimson.ua.edu]
Gesendet: Donnerstag, 20. Oktober 2016 07:30
An: A Mailing list for WIEN2k users
Betreff: Re: [Wien] What's the difference between the spin-polarized and the
non spin-polarized calculations

You likely have to derive the Kohm–Sham equations and solve them for the
wavefunction solutions (and look into the WIEN2k source code) for the detailed
there.  I think the go to references for that were:

Planewaves, Pseudopotentials and the LAPW Method by David J. Singh and Lars
http://www.wien2k.at/reg_user/textbooks/double_counting.pdf
http://www.wien2k.at/reg_user/textbooks/DFT_and_LAPW_2nd.pdf

No parameters are monitored to make the 2 densities equal.  As seen on slide 21
of http://www.wien2k.at/events/ws2015/rolask_rela.pdf , there are two
equations, one for Psi_up and one for Psi_down, but for the non-spin polarized
case both equations are the same such that Psi_up = Psi_down = Psi.  So only
one equation for the wavefunction Psi needs to be solved for.  As seen on slide
66 in http://www.wien2k.at/events/ws2015/WS22-KS-DFT-LAPW.pdf , the calculation
is given an initial charge density (during init_lapw), then the charge (and
spin) density should be computed from the self consistent field (scf) cycles
(run_lapw).

On the other hand, the spin-polarized calculation (runsp_lapw) has to solve two
separate equations instead of one as shown on slide 24 in rolask_rela.pdf.
Which is why for example there is lapw1 -up and lapw1 -dn for the
spin-polarized calculation and only just lapw1 for the non-spin polarized.  The
simplified equations it uses for the spin-polarized case was made possible by
choosing the z-axis for the direction of the magnetic field [ Ab Initio Study
of NiO-Fe Interfaces: Electron States and Magnetic Configurations by L. D.
Giustino,
http://www.nano-phdschool.unimore.it/site/home/phd-students/documento102017667.html
(page 24) ].

The Bef term is crossed out on slide 21, so there should be no exchange
magnetic potential Bxc, since Bef = Bext + Bxc (from slide 19).  However,
whether Bef term is not there or how the Bef term is set to 0, I don't know and
someone else might; I didn't look into the source code to try to determine that.

On 10/19/2016 5:18 PM, Abderrahmane Reggad wrote:

questions.

I have checked the 2 presentations but I didn't find what I look for .

It's mentionned that in non spin-polarized calculation the spin-up density =
the spin-down density . Which parameters are they monitored to make these 2
densities equal. I have read that in this case the exchange magnetic potential
will be equal to zero. I want to know if it's so or not .

Best regards
--