I have some questions concerning the x-ray absorption spectra (XANES) in BSE implemented in the elk-code:
We know that in the XANES, by a x-ray photon, a core electron of a single atom, such as 1s electron of a single N atom in BN, is excited to the conduction states. It seems that in x-ray absorption calculation in the elk, the 1s electrons of all the N atoms in BN crystal absorb the x-ray (not a single N atom)!
By attention to above point: Can one compare this type of calculation with the corresponding energy loss near edge structure (ELNES) spectrum (N 1s edge ELNES)?? As you know, ELNES and XANES spectra nearly have the same dispersion, but in ELNES, the incident beam is electron. In the ELNES, the incident electron excites a core electron (such as 1s electron of N) to the conduction states and a hole is left by the electron transition. Again as you know, in the wien2k, one removes 1s electron of a single atom (not all N atoms) and adds that to the background, and with the corehole approximation, one makes supercell in order to reducing the mutual interaction of coreholes (a result of the periodic boundary). Now, I think that the XANES in elk does not consider this point: I mean that the final absorption spectrum in elk-code is due to the absorption by all the N atoms. In the other words, why you don't get supercell in calculating XANES within BSE?
By considering above points, I think that I cannot compare the XANES of elk-code with the corresponding ELNES.
Please clarify these point for me.
All the best for you
Ahmad Abdolmaleki
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the answer has two parts:
a) The supercell in the core-hole approximation is required to compute the relaxed electron density after core-hole excitation. In the BSE, this is treated directly in terms of many-body perturbation theory. It appeared to me that the spectra matched experiments very well, so I have not done further investigation with supercells to study interaction effects.
b) You can of course do BSE in a supercell. However, your calculation will become prohibitively slow! On the one hand, you have to compute the screening and the BSE matrix elements with the supercell. On the other hand, the BSE hamiltonian itself blows up because you need many more final states (which are degenerate with the number of your atoms in the supercell) to reach the same maximum energy above threshold. Finally, this will quickly make you run out of memory. Consider this example:
L2,3 edge: 6 initial bands, 40 final bands, 8x8x8 k-point mesh. This means you hold a 30,000 x 30,000 matrix in your memory. Each elements is a complex double precision number, so it has 240GB. BSE is expensive...
By the way, a similar procedure as you describe for wien2k is also possible in elk. See the example ELNES/BN-ELNES. Strictly speaking, here it is the Z+1 approximation.
Regards
Markus
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Dear elk users and developers,
I have some questions concerning the x-ray absorption spectra (XANES) in BSE implemented in the elk-code:
We know that in the XANES, by a x-ray photon, a core electron of a single atom, such as 1s electron of a single N atom in BN, is excited to the conduction states. It seems that in x-ray absorption calculation in the elk, the 1s electrons of all the N atoms in BN crystal absorb the x-ray (not a single N atom)!
By attention to above point: Can one compare this type of calculation with the corresponding energy loss near edge structure (ELNES) spectrum (N 1s edge ELNES)?? As you know, ELNES and XANES spectra nearly have the same dispersion, but in ELNES, the incident beam is electron. In the ELNES, the incident electron excites a core electron (such as 1s electron of N) to the conduction states and a hole is left by the electron transition. Again as you know, in the wien2k, one removes 1s electron of a single atom (not all N atoms) and adds that to the background, and with the corehole approximation, one makes supercell in order to reducing the mutual interaction of coreholes (a result of the periodic boundary). Now, I think that the XANES in elk does not consider this point: I mean that the final absorption spectrum in elk-code is due to the absorption by all the N atoms. In the other words, why you don't get supercell in calculating XANES within BSE?
By considering above points, I think that I cannot compare the XANES of elk-code with the corresponding ELNES.
Please clarify these point for me.
All the best for you
Ahmad Abdolmaleki
Dear Ahmad,
the answer has two parts:
a) The supercell in the core-hole approximation is required to compute the relaxed electron density after core-hole excitation. In the BSE, this is treated directly in terms of many-body perturbation theory. It appeared to me that the spectra matched experiments very well, so I have not done further investigation with supercells to study interaction effects.
b) You can of course do BSE in a supercell. However, your calculation will become prohibitively slow! On the one hand, you have to compute the screening and the BSE matrix elements with the supercell. On the other hand, the BSE hamiltonian itself blows up because you need many more final states (which are degenerate with the number of your atoms in the supercell) to reach the same maximum energy above threshold. Finally, this will quickly make you run out of memory. Consider this example:
L2,3 edge: 6 initial bands, 40 final bands, 8x8x8 k-point mesh. This means you hold a 30,000 x 30,000 matrix in your memory. Each elements is a complex double precision number, so it has 240GB. BSE is expensive...
By the way, a similar procedure as you describe for wien2k is also possible in elk. See the example ELNES/BN-ELNES. Strictly speaking, here it is the Z+1 approximation.
Regards
Markus
Thank you Markus