# Re: [Wien] Spin-orbit coupling SCF not converging

```As Peter has already responded, TETRA is not appropriate for 2D structures.
You got away with it without SOC, as that exactly solves the eigenproblem
for RKMAX etc. However, SOC uses the finite set of lapw1 eigenvectors.
There will therefore be something similar to telegraph noise as which
eigenvectors are used changes with iterations. This leads to
ill-conditioning which is amplified by the use of TETRA which I suspect can
also introduce something similar to telegraph noise. The total conditioning
of a particular case is a product of the condition numbers of different
parts. As nband--> infinity the SOC calculation should be better
conditioned.```
```
Small values of Beta and the total step are clear indicators that the
problem is ill-conditioned. I would guesstimate that values smaller than
0.5 are an indicator of ill-conditioning if they persist; an occasional
value is OK. Small GREED may also be an indicator of problems, particularly
near convergence. However, GREED is more complicated and can legitimately
be small far from the fixed-point solution.

Wikipedia seems to have a reasonable page,
https://en.wikipedia.org/wiki/Condition_number . I have never tried to
calculate these for different parts of Wien2k, my understanding is somewhat
empirical experience. Peter has more experience so has a better feel,
although I am not sure he has ever tried to actually calculate the numbers.
(A good project for someone.)

On Wed, Nov 27, 2019 at 9:54 AM Luigi Maduro - TNW <l.a.mad...@tudelft.nl>
wrote:

> I am using WIEN2k_19.1 and Using grep MULTISECANT *.scfm I get the
> following:
>
>
>
> * MULTISECANT MIXING VER9 RELEASE 10.4.0
>
>
>
> For the input of the SCF calculation with SOC the output of a SCF
> calculation without SOC was used (with TETRA). For the SCF calculation with
> SOC the following criteria were used: RKmax = 7.0, 21 k-points in IBZ,
> charge convergence of 0.001e and energy convergence of 0.0001 Ry. These are
> the same criteria as the original SCF calculation without SOC.
>
>
> If I understood correctly, then looking at the size GREED and Beta should
> be sufficient for determining if the calculation has converged, if so then
> how small is too small for these parameters?
>
>
>
>
>
> *From:* Laurence Marks [mailto:laurence.ma...@gmail.com]
> *Sent:* dinsdag 26 november 2019 18:19
> *To:* A Mailing list for WIEN2k users
> *Cc:* Luigi Maduro - TNW
> *Subject:* Re: [Wien] Spin-orbit coupling SCF not converging
>
>
>
> What version of Wien2k are you using, particularly the mixer (grep
> MULTISECANT *.scfm)?
>
>
>
> Your calculations are "starving to death". The step size is so small (both
> the GREED and Beta) that it is bouncing around on numerical noise. It may
> well have already converged to the limits of the noise/conditioning in your
> calculation, which is linked to RKMAX and the k-mesh and also (Peter's
> response) from TETRA. The iterative diagonalizations also introduce some
> noise.
>
>
>
> For the specific case I would remove the prior history (rm *.broyd*) and
> continue it.
>
>
>
> On Tue, Nov 26, 2019 at 11:01 AM Luigi Maduro - TNW <l.a.mad...@tudelft.nl>
> wrote:
>
> Hello Laurence,
>
>
>
> This is the result I get when using Check-mixing (this is with the
> thinnest slab model, and using SCALA with Emax = 10.0 Ry)
>
>
>
>
>
> :DIRQ :  |MSR1|= 1.472E-06 |PRATT|= 3.852E-03 ANGLE=  79.0 DEGREES
>
> :DIRT :  |MSR1|= 1.516E-06 |PRATT|= 4.100E-03 ANGLE=  79.2 DEGREES
>
> :MIX  :   MSE1   REGULARIZATION:  9.15E-04 GREED: 0.00200  Newton 1.00
> 0.0004
>
> :ENE  : ********** TOTAL ENERGY IN Ry =       -58196.30065156
>
> :DIS  :  CHARGE DISTANCE       ( 0.0046033 for atom    7 spin 1)
> 0.0009683
>
> :PLANE:  PW TOTAL      6.0026 DISTAN   3.20E-03  5.33E-02 %
>
> :CHARG:  CLM/ATOM     74.0417 DISTAN   5.58E-04  7.54E-04 %
>
> :RANK :  ACTIVE  14.44/16 =  90.26 % ; YY RANK  14.44/16 =  90.25 %
>
> :DIRM :  MEMORY 16/12 SCALE   1.000 RED  2.57 PRED  0.95 NEXT  0.95 BETA
> 0.05
>
> :DIRP :  |MSR1|= 1.024E-06 |PRATT|= 3.198E-03 ANGLE= 102.9 DEGREES
>
> :DIRQ :  |MSR1|= 4.046E-06 |PRATT|= 1.005E-02 ANGLE=  82.5 DEGREES
>
> :DIRT :  |MSR1|= 4.174E-06 |PRATT|= 1.054E-02 ANGLE=  84.0 DEGREES
>
> :MIX  :   MSE1   REGULARIZATION:  1.33E-03 GREED: 0.00500  Newton 1.00
> 0.0004
>
> :ENE  : ********** TOTAL ENERGY IN Ry =       -58196.30346394
>
> :DIS  :  CHARGE DISTANCE       ( 0.0012891 for atom    8 spin 1)
> 0.0002073
>
> :PLANE:  PW TOTAL      6.0026 DISTAN   1.51E-03  2.51E-02 %
>
> :CHARG:  CLM/ATOM     74.0417 DISTAN   2.13E-04  2.88E-04 %
>
> :RANK :  ACTIVE  15.31/16 =  95.68 % ; YY RANK  15.31/16 =  95.72 %
>
> :DIRM :  MEMORY 16/12 SCALE   1.000 RED  0.39 PRED  0.95 NEXT  0.95 BETA
> 0.05
>
> :DIRP :  |MSR1|= 3.562E-07 |PRATT|= 1.508E-03 ANGLE=  72.0 DEGREES
>
> :DIRQ :  |MSR1|= 1.479E-06 |PRATT|= 3.835E-03 ANGLE=  80.1 DEGREES
>
> :DIRT :  |MSR1|= 1.522E-06 |PRATT|= 4.121E-03 ANGLE=  79.5 DEGREES
>
> :MIX  :   MSE1   REGULARIZATION:  9.97E-04 GREED: 0.00200  Newton 1.00
> 0.0004
>
> :ENE  : ********** TOTAL ENERGY IN Ry =       -58196.29908151
>
> :DIS  :  CHARGE DISTANCE       ( 0.0007022 for atom    7 spin 1)
> 0.0001661
>
> :PLANE:  PW TOTAL      6.0026 DISTAN   8.27E-04  1.38E-02 %
>
> :CHARG:  CLM/ATOM     74.0417 DISTAN   1.39E-04  1.87E-04 %
>
> :RANK :  ACTIVE  14.56/15 =  97.05 % ; YY RANK  14.56/15 =  97.07 %
>
> :DIRM :  MEMORY 15/12 SCALE   1.000 RED  0.64 PRED  0.95 NEXT  0.97 BETA
> 0.05
>
> :DIRP :  |MSR1|= 1.020E-06 |PRATT|= 8.274E-04 ANGLE=  53.5 DEGREES
>
> :DIRQ :  |MSR1|= 4.021E-06 |PRATT|= 2.497E-03 ANGLE=  54.9 DEGREES
>
> :DIRT :  |MSR1|= 4.149E-06 |PRATT|= 2.630E-03 ANGLE=  54.9 DEGREES
>
> :MIX  :   MSE1   REGULARIZATION:  9.23E-04 GREED: 0.00289  Newton 1.00
> 0.0016
>
> :ENE  : ********** TOTAL ENERGY IN Ry =       -58196.29797368
>
> :DIS  :  CHARGE DISTANCE       ( 0.0051635 for atom    7 spin 1)
> 0.0011664
>
> :PLANE:  PW TOTAL      6.0026 DISTAN   4.15E-03  6.91E-02 %
>
> :CHARG:  CLM/ATOM     74.0417 DISTAN   6.89E-04  9.31E-04 %
>
> :RANK :  ACTIVE  13.83/16 =  86.45 % ; YY RANK  13.82/16 =  86.38 %
>
> :DIRM :  MEMORY 16/12 SCALE   1.000 RED  4.97 PRED  0.97 NEXT  0.94 BETA
> 0.06
>
> :DIRP :  |MSR1|= 7.019E-07 |PRATT|= 4.150E-03 ANGLE=  88.8 DEGREES
>
> :DIRQ :  |MSR1|= 2.677E-06 |PRATT|= 1.240E-02 ANGLE=  83.7 DEGREES
>
> :DIRT :  |MSR1|= 2.768E-06 |PRATT|= 1.308E-02 ANGLE=  84.1 DEGREES
>
> :MIX  :   MSE1   REGULARIZATION:  1.18E-03 GREED: 0.00220  Newton 1.00
> 0.0002
>
> :ENE  : ********** TOTAL ENERGY IN Ry =       -58196.30074694
>
>
>
>
>
> Cheers,
>
> Luigi
>
> PhD candidate
> Kavli Institute of Nanoscience
>
> Department of Quantum Nanoscience
>
> Faculty of Applied Sciences
>
> Delft University of Technology
>
>
>
>
>
>
> --
>
> Professor Laurence Marks
> Department of Materials Science and Engineering
> Northwestern University
> www.numis.northwestern.edu
> <https://urldefense.proofpoint.com/v2/url?u=http-3A__www.numis.northwestern.edu_&d=DwMFaQ&c=XYzUhXBD2cD-CornpT4QE19xOJBbRy-TBPLK0X9U2o8&r=5iw1V7arTSY2eHCQ6TNB1SAega4fD0MesZICD9uK0wU&m=hamjemBMYgbNdOdCG4mRH4Xmk0EfJOart2itbDm_hk4&s=Ck5yDqstMy0tovzK1Kn9CExxP9dUo1z1vHJh_qpevi8&e=>
>
> Corrosion in 4D: www.numis.northwestern.edu/MURI
> <https://urldefense.proofpoint.com/v2/url?u=http-3A__www.numis.northwestern.edu_MURI&d=DwMFaQ&c=XYzUhXBD2cD-CornpT4QE19xOJBbRy-TBPLK0X9U2o8&r=5iw1V7arTSY2eHCQ6TNB1SAega4fD0MesZICD9uK0wU&m=hamjemBMYgbNdOdCG4mRH4Xmk0EfJOart2itbDm_hk4&s=e72Py5kM2xQ7EFAXObZ6gBQdthRgCZAKXEz5fjUBowE&e=>
> 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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