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 answers to your questions. I haven't done it myself, so I
cannot help you there. I think the go to references for that were:
Planewaves, Pseudopotentials and the LAPW Method by David J. Singh and
Lars Nordström [
http://link.springer.com/book/10.1007%2F978-0-387-29684-5 ]
http://www.wien2k.at/reg_user/textbooks/double_counting.pdf
http://www.wien2k.at/reg_user/textbooks/DFT_and_LAPW_2nd.pdf
My attempt at general answers:
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:
Thank you Dr Gavin for your reply and also for your interesting for my
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
--
Mr: A.Reggad
Laboratoire de Génie Physique
Université Ibn Khaldoun - Tiaret
Algerie
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