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<div class="moz-cite-prefix">angle (M,z) and angle (M,x) deg are
THETA and PHI, respectively.<br>
<br>
Here is how the code calculates the Projection of M (for your
crystal system).<br>
<br>
Your lattice constants a = b = c = 13.6697120 angstrom<br>
Your crystal angles alpha = beta = gamma = 60 deg =
1.04719755119660 rad<br>
M|| XMS1 = 1.000 XMS2 = 1.000 XMS3 = -1.000<br>
<br>
XA=XMS1*a*sin(gamma)<br>
XB=XMS1*a*cos(gamma)+b*XMS2<br>
XC=c*XMS3<br>
<br>
XX=sqrt(XA**2+XB**2+XC**2)<br>
theta=acos(XC/XX)<br>
XX=sqrt(XA^2+XB^2)<br>
<br>
if XX < 1e-5<br>
phi=0;<br>
else<br>
phi=acos(XA/XX)<br>
if abs(XB) > 1e-5 <br>
phi=phi*XB/abs(XB)<br>
end<br>
end<br>
<br>
M = sin(theta)*(cos(phi)*x+sin(phi)*y)+cos(theta)*z (equation from
line 168 of code in $WIENROOT/SRC_lapwdm/output.f)<br>
<br>
Example for <br>
<pre wrap="">:ORB005: ORBITAL MOMENT: -0.03637 -0.06090 0.04160 PROJECTION ON M -0.08224</pre>
XA=1*13.6697120*sin(1.04719755119660) = 11.8383179<br>
XB=1*13.6697120*cos(1.04719755119660)+13.6697120*1 = 20.504568<br>
XC=13.6697120*-1 = -13.669712<br>
<br>
XX=sqrt(11.8383179**2+20.504568**2+(-13.669712)**2) = 27.339424<br>
theta=acos(-13.669712/27.339424) = 2.0943951 rad =<b> 120 deg</b><br>
XX=sqrt(11.8383179**2+20.504568**2) = 23.6766357<br>
<br>
phi=acos(XA/XX) = acos(11.8383179/23.6766357) = 1.04719755<br>
phi=phi*XB/abs(XB)
= 1.04719755*20.504568/abs(20.504568) = 1.04719755 rad = <b>60
deg</b><br>
<br>
M = <b>sin(2.0943951)*(cos(1.04719755)*-0.03637+sin(1.04719755)*-0.06090)+cos(2.0943951)*0.04160</b>
= <b>-0.82223672</b> (has slight but acceptable round off error)<br>
<br>
Now you can confirm for yourself that all ORBxxx and SPIxxx are
satisfied. <br>
<br>
On 7/1/2012 4:29 AM, <a class="moz-txt-link-abbreviated" href="mailto:foyevtsova@th.physik.uni-frankfurt.de">foyevtsova@th.physik.uni-frankfurt.de</a> wrote:<br>
</div>
<blockquote
cite="mid:b72c13710d4b856fa7832d44098f19a3.squirrel@th.physik.uni-frankfurt.de"
type="cite">
<pre wrap="">Dear Gavin,
in case.outputdmup, for instance, I find only this information on angles:
120.0 60.0 angle (M,z), angle (M,x) deg
Here below is a passage where this line comes from:
SUBSTANCE = blebleble
s-o calc. M|| 1.00 1.00 -1.00
LATTICE = P
LATTICE CONSTANTS ARE = 13.6697120 13.6697120 13.6697120
NUMBER OF ATOMS IN UNITCELL = 15
MODE OF CALCULATION IS = RELA
BR1, BR2
0.56295 -0.18765 -0.18765 0.56295 -0.18765 -0.18765
0.00000 0.53075 -0.26537 0.00000 0.53075 -0.26537
0.00000 0.00000 0.45964 0.00000 0.00000 0.45964
alpha test 1.04719755119660 1.04719755119660
1.04719755119660
SO= T
Spin-polarized + s-o calculation, M|| 1.000 1.000 -1.000
alpha test 1.04719755119660 1.04719755119660
1.04719755119660
LATTICE:P
alpha test 1.04719755119660 1.04719755119660
1.04719755119660
120.0 60.0 angle (M,z), angle (M,x) deg
SYMMETRY OPERATIONS IN SPIN COORD. SYSTEM
There is no information on THETA and PHI.
</pre>
<blockquote type="cite">
<pre wrap="">Do you have a case.outputdm, case.outputdmup, or case.outputdmdn file?
Can you see if the THETA and PHI is different from that in case.outsymso?
How to explain the 1st iteration ORB005, since sqrt((-0.08361)**2 +
(-0.01872)**2 + (0.02851)**2) = +0.0903 != -0.06454
</pre>
</blockquote>
<pre wrap="">
Sorry, this is my mistake: what you see is the last iteration. The true
first iteration is
:ORB005: ORBITAL MOMENT: -0.03637 -0.06090 0.04160 PROJECTION ON M -0.08224
For these values, sqrt(x**2 + y**2 + z**2) indeed holds. Then, in the
converged solution the orbital moment deviates from M.
Could it be that something is wrong in the code?
</pre>
<blockquote type="cite">
<pre wrap="">
For those angles, I also get 0.927 for SPI005 and -0.06356 for ORB005.
If THETA and PHI in case.outputdm are slightly different, then both
calculations could work out.
Kind Regards
On 6/29/2012 7:36 AM, Kateryna Foyevtsova wrote:
</pre>
<blockquote type="cite">
<pre wrap="">Dear Gavin,
that's the point: sqrt(x**2 + y**2 + z**2) works! I indeed get 1.075
when I insert my x, y and z into this equation!
>From case.outsymso:
THETA, PHI 1.57079632679490 0.955316618124509
and using your formula I get 0.927.
Bests
On 29/06/12 14:49, Gavin Abo wrote:
</pre>
<blockquote type="cite">
<pre wrap="">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:
</pre>
<blockquote type="cite">
<pre wrap="">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:
</pre>
<blockquote type="cite">
<pre wrap="">1) In which coordinate system are SPI005 and ORB005 given?
In Appendix C (<a class="moz-txt-link-freetext" href="http://www.wien2k.at/reg_user/textbooks/">http://www.wien2k.at/reg_user/textbooks/</a>) 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:
<a class="moz-txt-link-freetext" href="http://zeus.theochem.tuwien.ac.at/pipermail/wien/2011-September/015296.html">http://zeus.theochem.tuwien.ac.at/pipermail/wien/2011-September/015296.html</a>
<a class="moz-txt-link-freetext" href="http://zeus.theochem.tuwien.ac.at/pipermail/wien/2008-April/010820.html">http://zeus.theochem.tuwien.ac.at/pipermail/wien/2008-April/010820.html</a>
<a class="moz-txt-link-freetext" href="http://zeus.theochem.tuwien.ac.at/pipermail/wien/2005-January/004399.html">http://zeus.theochem.tuwien.ac.at/pipermail/wien/2005-January/004399.html</a>
On 6/28/2012 9:18 AM, Kateryna Foyevtsova wrote:
</pre>
<blockquote type="cite">
<pre wrap="">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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