I need to plot projected band structure like the figure I have attached below. According to the ELK manual, "tasks = 21" does this but it is only for s, p, d, and f orbitals.
I want to plot band structure including d_xy, d_yz, d_zx, d_x2-y2, and d_z2 characters. However I have no idea how to do this in Elk. Could anyone help me, please?
The tasks for the band structure are 20, 21, 22 and 23:
20 : regular band structure
21 : l-resolved band structure, l = 0...3
22: (l,m)-resolved band structure (l,m) arranged in order (0,0), (1,-1), (1,0), (1,1), (2,-2), (2,-1), ...
23: spin-resolved band structure, arranged as spin-up and spin-down
To obtain your specific characters, you'll have to run task=22 and take appropriate linear combinations of the (l,m) characters.
Regards,
Kay.
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Thank you so much for your expert explanation. I read some articles and books about the conversion from the spherical harmonic representation to the cartesian polynomial representation, they say it in different way,
Some say Y(l,m) = Y(1, -1) = p_x; Y( 2, 1) = d_zx; etc
Other say p_x=[ Y(1, -1) + Y(1, +1) ]/sqrt(2); d_zx = [Y(2, -1) -Y(2, +1)]/sqrt(2); etc.
It is quite confusing. I don't know how to properly combine the (l,m) characters to get the Cartesian orbital projected DoS/Band Structure from the results of task=22. It would be very helpful to our ELK users if you can add another task or a switch in the future ELK release, to export the cartesian characters by combining the (l,m) characters obtained from task=22.
Again many thanks
Best
Jerry
Last edit: Jerry Li 2023-07-25
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The difference in the notations comes from the choice of using real or complex spherical harmonics to represent the orbital. You can see this for yourself by comparing the l=2 complex and real cases from the table link you posted.
Here you are using the complex spherical harmonics and the table tells you directly which linear combinations you should take.
Best,
Kari
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Dear Jerry,
Have you figured it out? How is it working?
Can you please explain how to work it out in some detail?
Another question is: Is it complex spherical harmonics that ELK give us in the PDOS file? or is it real/tesseral spherical harmonic projections in the PDOS file?
Best,
Zhiwei
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As Kay and Karti suggested, you need to calculate the band structure using the Method 22 in your ELK computation.
You will get (l,m)-resolved band structure (l,m) files like BAND_S01_A0001.OUT in which columns arrange in order k, E, (0,0), (1,-1), (1,0), (1,1), (2,-2), (2,-1), ...
Then you can take appropriate linear combinations of these (l,m) characters using Microsoft Excel (or other software like OriginPro) by referring to the link https://en.wikipedia.org/wiki/Table_of_spherical_harmonics#Real_spherical_harmonics
Of course, you also need to summerize all elements together if you want to present the project band structure from all elements.
Sorry for my late resonse.
Attached please find the projected Band structure calculation: elk.in input file, one of 3 Ni output, and excel spreadsheet for projected orbit calculation.
Hope they are helpful.
The band structure and PDOS projections are not completely consistent.
For the PDOS:
* if lmirep is .true. then the PDOS is in the irreducible representation of the site symmetry group
* the spin quantization axis (SQA) can be specified with sqados
* if dosmsum is .true. then the PDOS is summed over m so that only the l (and spin) character remain
* if dosssum is .true. then the PDOS is summed over spin so that only l (and m) remain
For the band structure:
* task=20 is the regular band structure
* task=21 contains the l character of the bands arranged l = 0,1, 2, ...
* task=22 contains the (l,m) character of the bands arranged (l,m) = (0,0), (1,-1), (1,0), (1,1), (2,-2),...
* task=23 contains the spin character of the bands arranged as spin-up and spin-down
The basis for both the PDOS and band structure are the complex spherical harmonics Y_lm with the Condon-Shortley phase. If lmirep is .true. then a linear combination of the spherical harmonic coefficients is made to generate the irreducible representation, but only for the PDOS.
The real spherical harmonics (R_lm) are used internally in the code for real valued functions.
If there is a need then we could also generate band structure characters in the irreducible representations. The same is true for setting the SQA. Currently, if you need a SQA different from the z-axis then you'll have to rotate the crystal.
Regards,
Kay.
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
Dear ELK developers and ELK users
I need to plot projected band structure like the figure I have attached below. According to the ELK manual, "tasks = 21" does this but it is only for s, p, d, and f orbitals.
I want to plot band structure including d_xy, d_yz, d_zx, d_x2-y2, and d_z2 characters. However I have no idea how to do this in Elk. Could anyone help me, please?
Best Regards,
Jerry
Hi Jerry,
The tasks for the band structure are 20, 21, 22 and 23:
20 : regular band structure
21 : l-resolved band structure, l = 0...3
22: (l,m)-resolved band structure (l,m) arranged in order (0,0), (1,-1), (1,0), (1,1), (2,-2), (2,-1), ...
23: spin-resolved band structure, arranged as spin-up and spin-down
To obtain your specific characters, you'll have to run task=22 and take appropriate linear combinations of the (l,m) characters.
Regards,
Kay.
Hi Dr. Dewhurst,
Thank you so much for your expert explanation. I read some articles and books about the conversion from the spherical harmonic representation to the cartesian polynomial representation, they say it in different way,
https://cs.dartmouth.edu/wjarosz/publications/dissertation/appendixB.pdf
https://en.wikipedia.org/wiki/Atomic_orbital
https://en.wikipedia.org/wiki/Table_of_spherical_harmonics
Some say Y(l,m) = Y(1, -1) = p_x; Y( 2, 1) = d_zx; etc
Other say p_x=[ Y(1, -1) + Y(1, +1) ]/sqrt(2); d_zx = [Y(2, -1) -Y(2, +1)]/sqrt(2); etc.
It is quite confusing. I don't know how to properly combine the (l,m) characters to get the Cartesian orbital projected DoS/Band Structure from the results of task=22. It would be very helpful to our ELK users if you can add another task or a switch in the future ELK release, to export the cartesian characters by combining the (l,m) characters obtained from task=22.
Again many thanks
Best
Jerry
Last edit: Jerry Li 2023-07-25
Hi Jerry,
The difference in the notations comes from the choice of using real or complex spherical harmonics to represent the orbital. You can see this for yourself by comparing the l=2 complex and real cases from the table link you posted.
Here you are using the complex spherical harmonics and the table tells you directly which linear combinations you should take.
Best,
Kari
Thank you Kari,
I think I figured it out with your explanation.
Dear Jerry,
Have you figured it out? How is it working?
Can you please explain how to work it out in some detail?
Another question is: Is it complex spherical harmonics that ELK give us in the PDOS file? or is it real/tesseral spherical harmonic projections in the PDOS file?
Best,
Zhiwei
Hi Zhiwei,
As Kay and Karti suggested, you need to calculate the band structure using the Method 22 in your ELK computation.
You will get (l,m)-resolved band structure (l,m) files like BAND_S01_A0001.OUT in which columns arrange in order k, E, (0,0), (1,-1), (1,0), (1,1), (2,-2), (2,-1), ...
Then you can take appropriate linear combinations of these (l,m) characters using Microsoft Excel (or other software like OriginPro) by referring to the link
https://en.wikipedia.org/wiki/Table_of_spherical_harmonics#Real_spherical_harmonics
Of course, you also need to summerize all elements together if you want to present the project band structure from all elements.
After that you can plot the projected band structure data in OriginPro by following the instruction in https://vaspkit.com/tutorials.html#band-structure
In this way, I got my projected ELK band structure results which are consistent very well with those obtained from VASP, and WIEN2k.
Hope the above procedure are helpful to you.
Best
Jerry
Last edit: Jerry Li 2023-08-12
Dear Jerry,
Could you provide an example file ? Thank you !
Best
Long Yu
Last edit: Long Yu 2023-12-28
Sorry for my late resonse.
Attached please find the projected Band structure calculation: elk.in input file, one of 3 Ni output, and excel spreadsheet for projected orbit calculation.
Hope they are helpful.
Last edit: Jerry Li 2024-02-22
Dear Zhiwei,
its tesseral spherical harmonic, so it is consistent with all other usage in the code.
best wishes
Michael
PS: Remember that if you use the switch lmirep the columns are done with the adapted projections!
Hi All,
The band structure and PDOS projections are not completely consistent.
For the PDOS:
* if lmirep is .true. then the PDOS is in the irreducible representation of the site symmetry group
* the spin quantization axis (SQA) can be specified with sqados
* if dosmsum is .true. then the PDOS is summed over m so that only the l (and spin) character remain
* if dosssum is .true. then the PDOS is summed over spin so that only l (and m) remain
For the band structure:
* task=20 is the regular band structure
* task=21 contains the l character of the bands arranged l = 0,1, 2, ...
* task=22 contains the (l,m) character of the bands arranged (l,m) = (0,0), (1,-1), (1,0), (1,1), (2,-2),...
* task=23 contains the spin character of the bands arranged as spin-up and spin-down
The basis for both the PDOS and band structure are the complex spherical harmonics Y_lm with the Condon-Shortley phase. If lmirep is .true. then a linear combination of the spherical harmonic coefficients is made to generate the irreducible representation, but only for the PDOS.
The real spherical harmonics (R_lm) are used internally in the code for real valued functions.
If there is a need then we could also generate band structure characters in the irreducible representations. The same is true for setting the SQA. Currently, if you need a SQA different from the z-axis then you'll have to rotate the crystal.
Regards,
Kay.