# 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 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:
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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```
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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).
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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) ].
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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.
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On 10/19/2016 5:18 PM, Abderrahmane Reggad wrote:
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I have checked the 2 presentations but I didn't find what I look for .

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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 .
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Best regards
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