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THETA, PHI   1.57079632679490       0.955316618124509

and using your formula I get 0.927.

Bests

On 29/06/12 14:49, Gavin Abo wrote:
> 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.
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>>>>
>>>
>>>
>>>
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