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.ma...@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....@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 >> _______________________________________________ >> Wien mailing list >> Wien@zeus.theochem.tuwien.ac.at >> >> https://urldefense.proofpoint.com/v2/url?u=http-3A__zeus.theochem.tuwien.ac.at_mailman_listinfo_wien&d=DwICAg&c=yHlS04HhBraes5BQ9ueu5zKhE7rtNXt_d012z2PA6ws&r=U_T4PL6jwANfAy4rnxTj8IUxm818jnvqKFdqWLwmqg0&m=JsiPLhhnGY5vWjIHSTaErXCmOUvmmcdRuaraV6JWK24&s=Ja--Kl05WF99HyMK2Quj7Vyc9Du2dPeJS3oF5nd85vA&e= >> SEARCH the MAILING-LIST at: >> https://urldefense.proofpoint.com/v2/url?u=http-3A__www.mail-2Darchive.com_wien-40zeus.theochem.tuwien.ac.at_index.html&d=DwICAg&c=yHlS04HhBraes5BQ9ueu5zKhE7rtNXt_d012z2PA6ws&r=U_T4PL6jwANfAy4rnxTj8IUxm818jnvqKFdqWLwmqg0&m=JsiPLhhnGY5vWjIHSTaErXCmOUvmmcdRuaraV6JWK24&s=t-_GN5vjxe2Z9BCic3AZSLz1Rz8lTy19azdsfr7982E&e= >> > > > -- > 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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