That should be because the equation is not sqrt(x**2 + y**2 + z**2). The equation that it seems to use is sin(theta)*(cos(phi)*x+sin(phi)*y)+cos(theta)*z for both ORBxxx and SPIxxx.
So, sin(theta)*(cos(phi)*0.46560+sin(phi)*0.80642)+cos(theta)*0.53749 = 1.075 (projection on the M axis). What are the values of phi and theta? I believe they are given in case.outputdm(up/dn). Hopefully the values satisfy the equation, else I must have overlooked something. On 6/29/2012 1:54 AM, Kateryna Foyevtsova wrote: > Dear Gavin, > > thanks a lot for your detailed answer and the very useful links! > > If ORBxxx and SPIxxx are in CCS, how to explain the fact that for, eg, > SPI005 in the first iteration > > sqrt(0.46560**2 + 0.80642**2 + 0.53749**2) = 1.075 > > ie, exactly the projection on the M axis. I would not expect that if > 0.46560, 0.80642 and 0.53749 were projections on the non-orthogonal > axes. That is for me the hardest thing to understand. > > Best regards, > Kateryna > > > On 29/06/12 04:49, Gavin Abo wrote: >> 1) In which coordinate system are SPI005 and ORB005 given? >> >> In Appendix C (http://www.wien2k.at/reg_user/textbooks/) of "New notes >> about Hyperfinefield calculations (ps)", it mentions that the subroutine >> /couplx/ (of lapwdm) now calculates matrices of all components of spin >> and orbital momentum in the "crystal coordinate system >> (sx,sy,sz,lx,ly,lz)". Therefore, *I believe the x, y, and z values of >> SPIxxx and ORBxxx are also in the crystal coordinate system (CCS), while >> the M values ("PROJECTION ON M" values) are parallel to the >> magnetization. * >> >> If your good with reading fortan, you can look into the code. I don't >> full understand what is going on in the code, but I believe the >> "direction to M" (in your case: 1 1 -1) specified in case.inso is read >> in SRC_lapwdm/lapwdm.f. Then, the angles theta and phi between the >> "direction to M" and CCS are calculated in SRC_lapwdm/angle.f. Next, the >> x, y, and z values of SPIxxx and ORBxxx are calculated in the CCS. The >> x, y, and z values are written to case.outputdm(up/dn) and >> case.scfdm(up/dn), while a Cartesian to spherical equation [r = >> sin(theta)*(cos(phi)*x+sin(phi)y)+cos(theta)*z] is used to calculate the >> radius (M) using the x, y, and z, theta, and phi values before writing >> to the same output files as performed by SRC_lapwdm/output.f. >> >> 2) Why for the first iteration MMI005 is not even roughly equal to >> SPI005 + ORB005? >> >> SPIxxx is the spin moment calculated from selected electrons only >> (usually d or f). >> >> MMIxxx is the sum from all electrons (s, p, d and f states) inside the >> atomic sphere xxx. >> >> ORBxxx is the orbital magnetic moment. >> >> So*MMIxxx = SPIxxx + ORBxxx is not necessarily true.* >> >> See the reference links below for more information: >> >> http://zeus.theochem.tuwien.ac.at/pipermail/wien/2011-September/015296.html >> http://zeus.theochem.tuwien.ac.at/pipermail/wien/2008-April/010820.html >> http://zeus.theochem.tuwien.ac.at/pipermail/wien/2005-January/004399.html >> >> On 6/28/2012 9:18 AM, Kateryna Foyevtsova wrote: >>> Dear Wien2k developers, >>> >>> I use wien2k version 11.1 to run spin-polarized GGA+U calculations with >>> SO coupling for a molibdenum oxide. >>> The symmetry of the system is the following >>> >>> blebleble s-o calc. M|| 1.00 1.00 -1.00 >>> P 15 2 P- >>> RELA >>> 13.669712 13.669712 13.669712 60.000000 60.000000 60.000000 >>> >>> As you see, I set magnetization axis to 1 1 -1, which should be in terms >>> of (non-orthogonal) lattice vectors. >>> With the help of xcrysden and case.outsymso, I can deduce that this >>> direction corresponds to the 0.577350, 0.816497, 0 direction in terms of >>> the cartesian global coordinate system. >>> >>> When I converge the electron density with (without using any previously >>> converged non-relativistic calculation) >>> >>> runsp_lapw -p -orb -so -dm >>> >>> I get the following data for the first and the last iteration on one of >>> the Mo atoms: >>> >>> 1. iteration: >>> :SPI005: SPIN MOMENT: 0.46560 0.80642 -0.53749 PROJECTION ON M >>> 1.07518 >>> :ORB005: ORBITAL MOMENT: -0.08361 -0.01872 0.02851 PROJECTION ON M >>> -0.06454 >>> :MMI005: MAGNETIC MOMENT IN SPHERE 5 = 1.86180 >>> >>> last iteration (converged solution): >>> :SPI005: SPIN MOMENT: 0.61653 1.06239 -0.70860 PROJECTION ON M >>> 1.41804 >>> :ORB005: ORBITAL MOMENT: -0.08361 -0.01872 0.02851 PROJECTION ON M >>> -0.06454 >>> :MMI005: MAGNETIC MOMENT IN SPHERE 5 = 1.43149 >>> >>> Now, I am struggling to understand two things: >>> 1) In which coordinate system are SPI005 and ORB005 given? >>> If they were given in the global cartesian coordinate system, they would >>> be parallel to 0.577350, 0.816497, 0, but they are not. >>> >>> 2) Why for the first iteration MMI005 is not even roughly equal to >>> SPI005 + ORB005? >>> >>> Thank you very much! >>> Kateryna Foyevtsova >>> >>> P.S. When I perform relativistic calculations starting with a >>> preconverged electron density of the non-relativistic solution I get the >>> same final result. >>> _______________________________________________ >>> Wien mailing list >>> Wien at zeus.theochem.tuwien.ac.at >>> http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien >>> >> >> >> >> _______________________________________________ >> Wien mailing list >> Wien at zeus.theochem.tuwien.ac.at >> http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien > _______________________________________________ > Wien mailing list > Wien at zeus.theochem.tuwien.ac.at > http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien >