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Spin-orbit interaction and electron structure in NCDFT
Date: 2017/10/25 05:43
Name: Daniil

Dear developers,

We are trying to reproduce the atomic state of Niobium with the OpenMX package. However, it seems that the spin-orbit interaction does not work like expected. For comparison, we performed 4 calculations: with two programs (openmx and turbomole) with and without spin-orbit interaction for each case. We used default VPS and PAO for openmx calculations, and our pseudopotential and basis for turbomole. (We also tried our pseudopotential and basis embedded in openmx format, and results were quite close to the default ones).

Both programs gave similar results in case of no so-interaction, but when the latter was enabled, in both programs orbital energies were split, but only in turbomole it resulted in change of electron distribution.
1. We calculated LJ-occupancies and for d-electrons results are:
|D,1.5> 1.60
|D,2.5> 2.40
for openmx-noso, openmx-so and turbomole-noso, and
|D,1.5> 1.74
|D,2.5> 2.26
for turbomole-so
2. We compared spin density (or "magnetization" for turbomole) cube files, and they were of exact cubic symmetry for openmx-noso, openmx-so and turbomole-noso and distorted for turbomole-so.

So, the question is if it is possible to achieve the change of electronic distribution in OpenMX with spin-orbit interaction enabled?

All essential files, including cube files and images are shared at the folder.
dm_ljm.mat file is density matrix, converted to N/L/J/MJ basis.

Best regards,
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Re: Spin-orbit interaction and electron structure in NCDFT ( No.1 )
Date: 2018/01/07 07:48
Name: Daniil


Any information or advices about this case?

Best regards,
Re: Spin-orbit interaction and electron structure in NCDFT ( No.2 )
Date: 2018/01/08 13:36
Name: Chi-Cheng Lee  <>

Hi Daniil,

From a user's point of view, I guess the default energy cutoff is too small to give a noticeable
distorted charge density from the cubic one. The charge density could also not converge very well.
This might not be due to the difference between openmx and turbomole.
Could you try to add the following parameter?

scf.energycutoff 200

and also try to change 200 to 300, 400, or 500 to see if there is any difference in the spin density?
For me, I would also add

Atoms.UnitVectors.Unit Ang
10 0 0
0 10 0
0 0 10

to specify the unit cell size and I will also set k point to 1 1 1, such as

scf.Kgrid 1 1 1

to save time.


Re: Spin-orbit interaction and electron structure in NCDFT ( No.3 )
Date: 2018/01/08 14:43
Name: T. Ozaki


I checked "nb.out" and "nb.sden.cube" stored in "openmx-so", and found that
the charge distribution deviates from the cubic one. It can be seen that the Mulliken
populations violate the cubic symmetry. In addition to this, if you carefully look at
isosurface of the cube file, the distribution looks like tetragonal rather than cubic,
while "nb.sden.cube" stored in "openmx-noso" remains cubic.
Also, please be careful that there is freedom in the distribution due to degeneracy
of the spin-orbit states, which may cause the difference between OpenMX and TURBOMOLE.


Re: Spin-orbit interaction and electron structure in NCDFT ( No.4 )
Date: 2018/01/16 04:52
Name: Daniil

Thank you for answers.

I tried to increase scf.energycutoff, but with only small, if any, effect. Yes, under close study cube files are slightly distorted from cubic symmetry, but much less than in turbomole case.

As for LJ-distribution:
Correct me, if I am wrong, but in first order, SO interaction is proportional to l*s, so that degeneracy between j=l±s states should disappear.
Thus, electrons must redistribute, which can be seen in case of Turbomole calculations: initial non-so distribution is 1.6:2.4 = 4:6, where 4 and 6 are total numbers of j=1.5 and j=2.5 states for D-shell, while under SO interaction j=1.5 states become lower by energy and their total occupation increases to 1.74.

Best regards,
Re: Spin-orbit interaction and electron structure in NCDFT ( No.5 )
Date: 2018/03/05 23:48
Name: Daniil


Can you please comment on LJ-distribution? The D1/3-D3/2 degeneracy should vanish with SO enabled.

Best regards,
Re: Spin-orbit interaction and electron structure in NCDFT ( No.6 )
Date: 2018/03/23 00:44
Name: T. Ozaki


In OpenMX the population of each state is determined by the Fermi-Dirac function, which is not a proper treatment
for an isolate system like atom especially with a high temperature.
With the spin-orbit coupling I found that the populations vary depending on the electronic temperature as follows:

At 10 K
spin up spin down
d3z^2-r^2 0 0.370180785 0.001097401
dx^2-y^2 0 0.826992544 0.000216028
dxy 0 0.802166556 0.000220739
dxz 0 0.999197203 0.000354755
dyz 0 0.999197364 0.000354753
sum over m 3.997734451 0.002243677

At 300 K

d3z^2-r^2 0 0.822098488 0.000719802
dx^2-y^2 0 0.789486124 0.000154999
dxy 0 0.769269179 0.000157835
dxz 0 0.808441550 0.000555007
dyz 0 0.808446917 0.000555006
sum over m 3.997742258 0.002142649

This would be responsible for the problem.


Re: Spin-orbit interaction and electron structure in NCDFT ( No.7 )
Date: 2018/03/24 07:15
Name: Daniil

Thanks for your explanation.

I tried to perform low-temperature calculations, but scf seems to be very unstable with 10K. How did you achieve convergence? I tried to increase scf.Mixing.History and scf.Mixing.StartPulay, but with no effect.

And are there any other drawbacks to using low temperature, except for scf instability?

Best regards,
Re: Spin-orbit interaction and electron structure in NCDFT ( No.8 )
Date: 2018/03/24 09:09
Name: T. Ozaki


The following is a set of parameters I used:

scf.SpinOrbit.Coupling on
scf.SpinPolarization NC # On|Off
scf.maxIter 300 # default=40
scf.ElectronicTemperature 10.0 # default=300 (K)
scf.energycutoff 1000.0 # default=150 (Ry)
scf.EigenvalueSolver Cluster # Recursion|Cluster|Band
scf.Kgrid 1 1 1 # means 4x4x4
scf.Mixing.Type rmm-diish # Simple|Rmm-Diis|Gr-Pulay|Kerker|Rmm-Diisk
scf.Init.Mixing.Weight 0.01 # default=0.30
scf.Min.Mixing.Weight 0.001 # default=0.001
scf.Max.Mixing.Weight 0.200 # default=0.40
scf.Mixing.History 20 # default=5
scf.Mixing.StartPulay 15 # default=6
scf.criterion 1.0e-8 # default=1.0e-6 (Hartree)


Re: Spin-orbit interaction and electron structure in NCDFT ( No.9 )
Date: 2018/03/24 21:30
Name: Daniil

Thanks! With your parameters, calculation did converge, with occupations similar to yours:
d3z^2-r^2 0 0.365803842 0.001118400 0.366922242 0.364685441 0.0004 -37.0934
dx^2-y^2 0 0.829987864 0.000217503 0.830205368 0.829770361 0.0004 -35.8720
dxy 0 0.803548928 0.000222626 0.803771554 0.803326302 0.0004 -35.8685
dxz 0 0.999177628 0.000357497 0.999535125 0.998820132 0.0005 -34.0179
dyz 0 0.999177633 0.000357496 0.999535129 0.998820136 0.0005 -37.1983
sum over m 3.997695895 0.002273522 3.999969417 3.995422373
But, unfortunately, it still yielded 1.6/2.4 ratio for d-electrons.

Best regards,
Re: Spin-orbit interaction and electron structure in NCDFT ( No.10 )
Date: 2018/04/19 04:02
Name: Daniil


Is it possible to perform 0K calculations in OpenMX? I tried to increase scf parameters, but convergence was not achieved yet. So, does it make sense to continue, or there are some fundamental restrictions in scf algorithms?

Best regards,

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