`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 myquestions.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-updensity = the spin-down density . Which parameters are they monitoredto make these 2 densities equal. I have read that in this case theexchange magnetic potential will be equal to zero. I want to know ifit's so or not .Best regards -- Mr: A.Reggad Laboratoire de Génie Physique Université Ibn Khaldoun - Tiaret Algerie

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