About the equation used by non-collinear electronic structure calculation.

[hongyi-zhao]

I noticed the following description given by pyprocar documentation:

OTOH, I also noticed the following description on vaspwiki:

In case of non-collinear calculations, I want to know whether the two equations in the red box above are equivalent and can be derived from each other.

Any tips/comments on the differences and connections between them will be highly appreciated?

Here you can see some relevant discussions.

Regards, HZ

[fvmunoz]

Dear HZ,

I don't see any difference, just a typo psi -> phi

Best Francisco

On Wed, Mar 30, 2022, 5:59 AM hongyi-zhao @.***> wrote:

I noticed the following description given by pyprocar documentation https://romerogroup.github.io/pyprocar/:

[image: image] https://user-images.githubusercontent.com/11155854/160792208-81fccb03-d7db-4e6b-a6d5-e50f725f06c7.png

OTOH, I also noticed the following description on vaspwiki https://www.vasp.at/wiki/index.php/LORBIT:

[image: image] https://user-images.githubusercontent.com/11155854/160791960-14bea1ca-7e3e-478c-b8e8-899454d6fcd0.png

In case of non-collinear calculations, it seems that the forms of the two equations mentioned above do not correspond exactly.

Any tips/comments on the differences and connections between them?

Regards, HZ

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[hongyi-zhao]

I don't see any difference, just a typo psi -> phi

I can't see the above typo you mentioned. In detail, your version use \psi, while vaspwiki use \chi at the corresponding location as shown below:

What I don't understand is how the following parts correspond to each other in the formulae:

[uthpalaherath]

Dear Hongyi,

Thanks for pointing out the typo Francisco.

In the vaspwiki they are computing components of the density tensor. In the PyProcar docs description, the formula corresponds to the projection for a given Y(a,l,m).

In the PROCAR file for a non-collinear calculation, you see 4 projection blocks. These correspond to the total projection, x direction, y direction and z direction projections. The spin-up/spin-down directional projections are inseparable in this case (as opposed to the colinear spin case) as you see that the contributions are already summed up.

I think this would give you the description you're looking for: https://www.vasp.at/wiki/index.php/PROCAR

Hope that helps.

Best, Uthpala

On Wed, Mar 30, 2022 at 8:44 AM hongyi-zhao @.***> wrote:

I don't see any difference, just a typo psi -> phi

I can't see the above typo you mentioned. In detail, your version use \psi, while vaspwiki use \chi at the corresponding location as shown below:

[image: image] https://user-images.githubusercontent.com/11155854/160834942-95a3ae82-2d19-40ef-a624-92c8a31b0220.png

[image: image] https://user-images.githubusercontent.com/11155854/160834974-93105b38-8b7b-4de5-af9e-1dc22b483324.png

What I don't understand is how the following parts correspond to each other in the formulae:

[image: image] https://user-images.githubusercontent.com/11155854/160837124-88fd0a42-2b5f-4e02-a822-d96fdb4939a9.png

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Tel. (304) 216-2535 Email: @.*** @.***> Website: https://uthpalaherath.github.io/

[hongyi-zhao]

Thanks for pointing out the typo Francisco.

What do you mean by saying Francisco?

The spin-up/spin-down directional projections are inseparable in this case (as opposed to the colinear spin case) as you see that the contributions are already summed up.

Take the data used to interpret the PROCAR file on the VASP wiki as an example:

In this case, how to evaluate the respective contributions from spin-up/spin-down?

[hongyi-zhao]

Here are some related supplemental materials related to the questions discussed here:

• https://www.researchgate.net/post/How-can-I-decide-if-magnetic-calculation-should-be-collinear-or-noncollinear-from-DFT-using-VASP-or-any-other-code
• https://www.researchgate.net/post/Are_there_examples_of_collinear_and_non-collinear_magnetism
• https://people.sissa.it/~dalcorso/lectures/lecture_ncso_sb_2009.pdf
• The following description comes from the book Atomistic spin dynamics : foundations and applications: