[Wien] electronoccupancy in dmatup/dn

[Laurence Marks]

N.B., I should of course have said Hermitian, not symmetric.

N.N.B., the extension to include spin-orbit is simple.

On Wed, Jul 31, 2019 at 11:24 PM Laurence Marks <laurence.marks at gmail.com>
wrote:

> 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
>


-- 
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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