[Wien] Spin-orbit coupling SCF not converging

[Laurence Marks]

As general information, Beta is a scaling of the predicted step. Earlier
versions of the mixer used an algorithm based upon improvements for this,
in the more recent version (improved in the next one, 10.5) it is estimated
from the previous history. A value of 0.05 means that the mixer thinks that
the predicted step is very inaccurate.

The specific case (deleted for size limits on emails) was taking very small
steps (e.g. "Newton 1.00  0.0016") which are ~1E-3 of the a Pratt step,
which is already small as the calculation is closed to converged (:DIS <
1D-3). With a GREED of 0.002 this means that the unpredicted step is also
small, and both are ~1D-6 (:DIRT :  |MSR1|= 2.768E-06). Very small steps
are susceptible to numerical noise and ill-conditioning. All mixers employ
Simplex differentiation which is a form of numerical differentiation so
susceptible to such problems.

I have not analyzed in detail myself the conditioning/noise of SOC in
Wien2k. Peter's recommendations are almost certainly ones which improve the
conditioning.

-- 
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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