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For LNONCOLLINEAR=.TRUE. three additional projections for each ion are printed in PROCAR, as described here:



But I have some questions about this situation:

1. In this case, spin-up/spin-down is entanglement together and thus non-orthogonal/inseparable. How to evaluate the respective contributions from spin-up/spin-down?
2. What does the "s" column mean, and what is the difference between it and the "tot" column?

Regards,
HZ

Dear HZ,

Thank you for bringing up these questions.

Ad 1, in fact, also in case of non-relativistic calculations with LNONCOLLINEAR=T one can define a local spin axis and separate the KS orbitals in spin-up and spin-down. This is an important insight by Kuebler et al, Journal of Applied Physics 63, 3482 (1988).

Ad 2, the columns correspond to the angular-momentum quantum number l. We follow the usual naming convention, where l=0 are s orbitals, l=1 are p orbitals, etc. Finally, tot is the sum over l in each row or the sum over ions in each column.

Best regards,
Marie-Therese

marie-therese.huebsch wrote: ↑Thu Mar 31, 2022 7:28 am Ad 1, in fact, also in case of non-relativistic calculations with LNONCOLLINEAR=T one can define a local spin axis and separate the KS orbitals in spin-up and spin-down. This is an important insight by Kuebler et al, Journal of Applied Physics 63, 3482 (1988).

1. Why does it have to be a non-relativistic calculation?
2. What's the parameter/option to define a local spin axis for this purpose?

Ad 2, the columns correspond to the angular-momentum quantum number l. We follow the usual naming convention, where l=0 are s orbitals, l=1 are p orbitals, etc. Finally, tot is the sum over l in each row or the sum over ions in each column.

Do you mean the difference between "tot" and the corresponding columns/rows is rounding errors:

0.144 + 0.291*2 = 0.726 != 0.727

Regards,
HZ

Ad 1, when spin-orbit coupling is invoked, s and l are technically not good quantum numbers anymore. Still you can perform a projection of the KS orbitals onto an on-center basis that is given in terms of s and l. But your claim that s and l are not good quantum numbers for noncollinear magnetism in general is wrong.

Ad 2, the local spin axis is determined self-consistently. This is underlying the LNONCOLLINEAR tag. If you want to set the direction of the magnetic moment manually, it is possible to perform a calculation with constrained magnetic moments, se e.g.. I_CONSTRAINED_M. Perhaps, you want to read the paper about the implementation of noncollinear magnetism in VASP by D. Hobbs, G. Kresse, and J. Hafner PRB 62, 11556 (2000).

Ad 3, yes.

Cheers,
Marie-Therese

marie-therese.huebsch wrote: ↑Thu Mar 31, 2022 10:01 am Ad 1, when spin-orbit coupling is invoked, s and l are technically not good quantum numbers anymore. Still you can perform a projection of the KS orbitals onto an on-center basis that is given in terms of s and l. But your claim that s and l are not good quantum numbers for noncollinear magnetism in general is wrong.

So, you mean, for specific relativistic based calculation, i.e., somewhat rooted on Dirac equation and its alternatives/variants, the s and l are technically not good quantum numbers anymore. But this also implies that p, d or f is still good quantum numbers. This gives me an impression that heavy or transition elements and their compounds may be still can be studied by this method in some scenarios. Am I right?

Regards,
HZ

Dear HZ,

Spin-orbit coupling is a relativistic correction derived from Dirac theory. But this has nothing to do with the content of the PROCAR file and is even a general topic not specifically related to using VASP.

But this also implies that p, d or f is still good quantum numbers.

I do not understand this statement. p, d or f are just names for specific value of the angular momentum quantum number l. So, p, d and f are not quantum numbers. Maybe it would help if you study the solutions of a hydrogen atom. This is usually discussed well in many quantum mechanics text books. And also spin-orbit coupling is discussed in many text books.

Regarding the applicability of VASP to compounds featuring heavy elements or transition metals: You will find many peer-reviewed publications that use VASP to describe the properties of such compounds. Of course, there are caveats depending on the specific property you are interested in. For instance, open 3d and 4f orbitals can observe strong electronic correlation that is not well captured in density-functional theory and there are varies approaches to deal with this issue, e.g., including an on-site Coulomb interaction (so-called DFT+U), or the use of Hybrid functionals. If you are interested in noncollinear magnetism you may be interested in this high-throughput benchmark calculation, which we published last year M.-T. Huebsch, T. Nomoto, M.-T. Suzuki, and R. Arita, Phys. Rev. X 11, 011031 (2021).

Did this answer your questions about the PROCAR file? I am happy to answer further questions in a new thread with the appropriate title, but would like to try to stay on topic here. Thank you for understanding.

Best regards,
Marie-Therese

Thank you very much for your kindly help and reply again.

1. I misunderstood your previously used symbols s and l. In fact, you should mean the following as described here:

Azimuthal quantum number (ℓ)
Spin quantum number (m_s)

2. Thank you very much for letting me know your group's recently work: "Benchmark for Ab Initio Prediction of Magnetic Structures Based on Cluster-Multipole Theory" .

3. The questions about the PROCAR file originally posted in this topic has been answered completely. Thank you again.

Regards,
HZ

Glad I could help!

I see how the name of the l=0 orbital "s" and the spin-quantum number "s" can be easily mixed up. And yes, spin-up and spin-down then correspond to the spin-magnetic quantum number m_s=+1/2 and -1/2.

Best regards,
Marie-Therese