Spin-orbit couples spin-up and dn wavefunctions via l.s
Both, GGA+U or EECE enter the calculations via an effective (orbital depended) potential (Vorbup/dn and the corresponding matrix elements in the Hamiltonian read (in case of applications to d-electrons) <psi(l=2)_up|Vorbup|psi'(l=2)_up> and the same for dn. This is done in both, in lapw1 and in lapwso. In the latter there is in principle also a spin-coupling term Vorbud , which couples up and dn spin electrons, but this is switched off by default. While for a case without inversion symmetry, there should not be any difference whether one applies Vorb in lapw1 or lapwso, in a case with inversion symmetry there is a BIG difference. Vorb can be complex (in particular with spin-orbit and a magnetic case, where it amplifies the orbital moment, i.e. the difference between the +m and -m components) and when you apply the complex Vorb in lapw1 with a real Hamiltonian, you simply throw away the imaginary parts of these matrix elements. The definition of the density matrix does not change with/without SO, except that without SO you have Dmatup=<psi_up|Psi_up>(l=2) and the same for the Psi-dn, while with SO each psi_nk had a Psi_up AND dn component, so you must project out the Dmatup from all states. Am 23.05.2015 um 18:27 schrieb Laurence Marks:
I am trying to understand exactly what spin-oribit & U (or eece) is doing, so a very simple question which does not appear to be cleanly spelt out in the user guide. When spin-orbit is included does the definition of the density matrices change to represent the presence of the mixed states? -- Professor Laurence Marks Department of Materials Science and Engineering Northwestern University www.numis.northwestern.edu <http://www.numis.northwestern.edu> Corrosion in 4D: MURI4D.numis.northwestern.edu <http://MURI4D.numis.northwestern.edu> Co-Editor, Acta Cryst A "Research is to see what everybody else has seen, and to think what nobody else has thought" Albert Szent-Gyorgi _______________________________________________ Wien mailing list Wien@zeus.theochem.tuwien.ac.at http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien SEARCH the MAILING-LIST at: http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html
-- ----------------------------------------- Peter Blaha Inst. Materials Chemistry, TU Vienna Getreidemarkt 9, A-1060 Vienna, Austria Tel: +43-1-5880115671 Fax: +43-1-5880115698 email: pbl...@theochem.tuwien.ac.at ----------------------------------------- _______________________________________________ Wien mailing list Wien@zeus.theochem.tuwien.ac.at http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien SEARCH the MAILING-LIST at: http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html
