[Wien] electronoccupancy in dmatup/dn

[Laurence Marks]

A little math/analysis may be helpful -- with the caveat that this is my
interpretation and I am currently on travel.

The density matrix (ignoring spin-orbit for simplicity) "D" is a conjugate
symmetric MxM matrix, M=5 for d electrons. From standard linear algebra it
can be decomposed as

    D = U^T L U

where "U" is the MxM unitary matrix of eigenvectors, and "L" is the
diagonal eigenvalue matrix. You can interpret the different eigenvectors as
pseudo orbitals of the different p, d, f, and the eigenvalues as the
occupancies. (Think about this please.) The total d (or p, f) occupancy is
the sum of the eigenvalues which is equal to the trace of D.

A small fortran, C or some other code such as matlab etc can be used to
generate U & L.

One can setup different density matrices by choosing different L values,
and recreating D. As Fabien said before one would use this in a +U method
to setup the values then run some cycles with fixed +U (i.e. -orbc) to
establish the particular spin state. Then let it run normally to see if the
spin state is stable. (One can also do this with -eece but it is trickier.)
You can either do this choosing your L values by hand, or even using a
random number generator to Monte Carlo explore the spin space. (I did this
once for 4f electrons.)

Warning: this is not completely trivial and you need to know how to
manipulate Wien2k, not just run it blackbox.

N.B., I suggested some time ago adding the decomposition to (I think)
lapwdm, but did not push. Any scientist who uses Wien2k should be capable
of doing this analysis themselves.

On Wed, Jul 31, 2019 at 5:29 PM prasad jayasena <prasad.j86 at yahoo.com>
wrote:

> Dear experts
>
> I am trying a test case to learn the correct procedure to check local
> minima.
> Dear experts
>
> I am sending this followup questions related to my previous post on "
> electron occupancy in dmatup/dn" in the mailing list.
>
>
> In the firt step I finished a "runsp_lapw" and saved. I checked
> case.dmatup/dn and they were empty.
> Then "runsp_lapw -orb -dm" is employed.
>
> the dmatup/dn both have values similar to the one in my previous email. I
> believe this work flow is corresponding to a random localization.
>
> I appreciate your support on following questions:
>
> (1)
> If I want to fix initial density matrix, is this the correct place to do
> it? Is the only file I have to edit case.dmatup/dn?
>
> Or,  do I have to do that without trying a random PBE+U as I have done?
> But in that case since the case.dmatup/dn from PBE is empty, I wonder how
> to create that file correctly.
>
> (2)
> If I need to include Spin orbital coupling, how I should proceed after
> this?
>
> (3)
> In my case I expected to have d-orbital electrons. But I do not see them
> in the case.dmatup/dn. Are there any special flow to find d-matrix in the
> output?
>
> Thank you in advance
>
> Prasad
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-- 
Professor Laurence Marks
Department of Materials Science and Engineering
Northwestern University
www.numis.northwestern.edu
Corrosion in 4D: www.numis.northwestern.edu/MURI
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
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