Electron-energy-loss spectrum - Revision history

Huebsch at 08:45, 12 May 2025

2025-05-12T08:45:16Z

Pmelo: /* References */

2025-03-06T16:47:36Z

References

← Older revision		Revision as of 16:47, 6 March 2025
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	== References ==		== References ==

	[[Category:VASP\|Dielectric Functions]] [[Category:Linear response]] [[Category:Dielectric properties]] [[Category:~~HOWTO~~]]		[[Category:VASP\|Dielectric Functions]] [[Category:Linear response]] [[Category:Dielectric properties]] [[Category:Many-body perturbation theory]] [[Category:Howto]]

Pmelo: /* Calculations at finite momentum */

2025-03-06T16:43:54Z

Calculations at finite momentum

@@ Line 292: / Line 292: @@
 [[File:EELS bulk Si BSE TDHF Q2 py4vasp.png|thumbnail|400px|left|EELS plot for {{TAG|KPOINT_BSE}}=2 using py4vasp.]]
 <div style="clear:both;"></div>
 == References ==
-[[Category:VASP|Dielectric Functions]] [[Category:Linear response]][[Category:Dielectric properties]]
+[[Category:VASP|Dielectric Functions]] [[Category:Linear response]] [[Category:Dielectric properties]] [[Category:HOWTO]]

Pmelo: /* EELS from time-dependent density functional theory (TDDFT) */

2025-03-05T15:07:55Z

EELS from time-dependent density functional theory (TDDFT)

← Older revision		Revision as of 15:07, 5 March 2025
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	{{TAG\|HFSCREEN}} = 1.22		{{TAG\|HFSCREEN}} = 1.22

	At the end of the calculation the dielectric function can be extracted from the vasprum.xml or {{FILE\|vaspout.5}} files. Results are shown at the end of the next subsection, in order to compare the difference between the TDDFT and the many-body perturbation theory approaches.		At the end of the calculation the dielectric function can be extracted from the vasprum.xml or {{FILE\|vaspout.h5}} files. Results are shown at the end of the next subsection, in order to compare the difference between the TDDFT and the many-body perturbation theory approaches.

	==EELS from many-body perturbation theory (MBPT)==		==EELS from many-body perturbation theory (MBPT)==

Pmelo: /* EELS from many-body perturbation theory (MBPT) */

2025-03-05T14:33:45Z

EELS from many-body perturbation theory (MBPT)

← Older revision		Revision as of 14:33, 5 March 2025
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	plt.plot(energies, eels_bse, '', label='BSE')		plt.plot(energies, eels_bse, '', label='BSE')
	plt.plot(energies, eels_tdhf, '', label='TDHF')		plt.plot(energies, eels_tdhf, '', label='TDHF')
	plt.ylabel(r'Im[$\epsilon^{-1}_M$]')		plt.ylabel(r'-Im[$\epsilon^{-1}_M$]')
	plt.xlabel('Energy loss [eV]')		plt.xlabel('Energy loss [eV]')
	plt.legend()		plt.legend()

Pmelo: /* EELS from density functional theory (DFT) */

2025-03-05T14:33:32Z

EELS from density functional theory (DFT)

← Older revision		Revision as of 14:33, 5 March 2025
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	plt.plot(energies, eels, label='DFT')		plt.plot(energies, eels, label='DFT')
	plt.ylabel(r'Im[$\epsilon^{-1}_M$]')		plt.ylabel(r'-Im[$\epsilon^{-1}_M$]')
	plt.xlabel('Energy loss [eV]')		plt.xlabel('Energy loss [eV]')
	plt.legend()		plt.legend()

Pmelo: /* Micro-macro connection and relation to measured quantities */

2025-03-05T14:32:50Z

Micro-macro connection and relation to measured quantities

← Older revision		Revision as of 14:32, 5 March 2025
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	It is important to note that the actual measured quantity, <math>\epsilon_\mathrm{M}(\mathbf q, \omega)</math>, does not depend on the microscopic fields{{cite\|onida:revmodphys:2002}}. To connect both the microscopic and macroscopic quantities, an averaging procedure is taken out, so that		It is important to note that the actual measured quantity, <math>\epsilon_\mathrm{M}(\mathbf q, \omega)</math>, does not depend on the microscopic fields{{cite\|onida:revmodphys:2002}}. To connect both the microscopic and macroscopic quantities, an averaging procedure is taken out, so that
	::<math>		::<math>
	\~~epsilon_M~~(\mathbf q,\omega) = \frac{1}{\epsilon_{\mathbf G = 0, \mathbf G'=0}^{-1}(\mathbf q,\omega)}.		\epsilon_{\mathrm M}(\mathbf q,\omega) = \frac{1}{\epsilon_{\mathbf G = 0, \mathbf G'=0}^{-1}(\mathbf q,\omega)}.
	</math>		</math>
	Since VASP computes the macroscopic function, EELS can be extracted from the final result via		Since VASP computes the macroscopic function, EELS can be extracted from the final result via
	::<math>		::<math>
	\mathrm{EELS}(\omega) = -\mathrm{Im}\left[\frac{1}{\~~epsilon_M~~(\mathbf q,\omega)}\right]		\mathrm{EELS}(\omega) = -\mathrm{Im}\left[\frac{1}{\epsilon_{\mathrm M}(\mathbf q,\omega)}\right]
	</math>		</math>

Pmelo: /* Calculations at finite momentum */

2025-03-05T14:31:53Z

Calculations at finite momentum

← Older revision		Revision as of 14:31, 5 March 2025
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	Much like calculations at <math>\Gamma</math>, results from model TDDFT are very close to those from MBPT. The reduction in intensity for spectra away from <math>\Gamma</math> is normal, due to the fact that matrix elements are now away from the dipole approximation.		Much like calculations at <math>\Gamma</math>, results from model TDDFT are very close to those from MBPT. The reduction in intensity for spectra away from <math>\Gamma</math> is normal, due to the fact that matrix elements are now away from the dipole approximation.
	<div style="clear:both;"></div>		<div style="clear:both;"></div>
	To plot the same results with py4vasp, the new shape of the dielectric function has to be taken into account, and so no indexing is added to the epslion array		To plot the same results with {{py4vasp}}, the new shape of the dielectric function has to be taken into account, and so no indexing is added to the epslion array

	<syntaxhighlight lang="python" line>		<syntaxhighlight lang="python" line>

Pmelo: /* EELS from many-body perturbation theory (MBPT) */

2025-03-05T14:19:41Z

EELS from many-body perturbation theory (MBPT)

← Older revision		Revision as of 14:19, 5 March 2025
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	Both spectra look very similar, the differences coming from the treatment of the electron-hole interaction in both TDDFT and BSE case. This is both a consequence of the appropriate choice of {{TAG\|AEXX}} and {{TAG\|HFSCREEN}} parameters, as well as the fact that bulk Silicon is a centrosymmetric material, so the model dielectric function works well here. However, while the use of a model (diagonal) dielectric function is well suited for bulk Silicon, for systems with lower symmetry the off-diagonal elements that are ignored here will be important, and can lead to larger discrepancies in the results from TDDFT and MBPT.		Both spectra look very similar, the differences coming from the treatment of the electron-hole interaction in both TDDFT and BSE case. This is both a consequence of the appropriate choice of {{TAG\|AEXX}} and {{TAG\|HFSCREEN}} parameters, as well as the fact that bulk Silicon is a centrosymmetric material, so the model dielectric function works well here. However, while the use of a model (diagonal) dielectric function is well suited for bulk Silicon, for systems with lower symmetry the off-diagonal elements that are ignored here will be important, and can lead to larger discrepancies in the results from TDDFT and MBPT.

	To plot the EEL spectrum with {{py4vasp}}, it should be noted that the type of calculation has to be specified when reading the dielectric function. It is simply a matter of editing the following ~~lines~~		To plot the EEL spectrum with {{py4vasp}}, it should be noted that the type of calculation has to be specified when reading the dielectric function. It is simply a matter of editing the following script
	<syntaxhighlight lang="python" line>		<syntaxhighlight lang="python" line>
	import py4vasp		import py4vasp
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	calc_tdhf = py4vasp.Calculation.from_file('vaspout.TDHF_Q1.h5')		calc_tdhf = py4vasp.Calculation.from_file('vaspout.TDHF_Q1.h5')

			# The type of calculation must be specified, with the addition of the 'BSE' string
	energies = calc_bse_q1.dielectric_function.read('BSE')['energies']		energies = calc_bse_q1.dielectric_function.read('BSE')['energies']
	epsilon_bse = calc_bse.dielectric_function.read('BSE')['dielectric_function'][1][1][:]		epsilon_bse = calc_bse.dielectric_function.read('BSE')['dielectric_function'][1][1][:]
			# The type of calculation must be specified, with the addition of the 'TDHF' string
	epsilon_tdhf = calc_tdhf.dielectric_function.read('TDHF')['dielectric_function'][1][1][:]		epsilon_tdhf = calc_tdhf.dielectric_function.read('TDHF')['dielectric_function'][1][1][:]

Pmelo: /* EELS from many-body perturbation theory (MBPT) */

2025-03-05T14:16:03Z

EELS from many-body perturbation theory (MBPT)

← Older revision		Revision as of 14:16, 5 March 2025
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	<div style="clear:both;"></div>		<div style="clear:both;"></div>

	Both spectra look very similar, the differences coming from the treatment of the electron-hole interaction in both TDDFT and BSE case. ~~By varying the range separation parameters, TDDFT results can be brought up to match almost exactly those from BSE, but this will require more computing time, so it~~ is ~~advisable to test~~ the ~~best values~~ of {{TAG\|AEXX}} and {{TAG\|HFSCREEN}} ~~in lower settings~~, ~~away from convergence~~.		Both spectra look very similar, the differences coming from the treatment of the electron-hole interaction in both TDDFT and BSE case. This is both a consequence of the appropriate choice of {{TAG\|AEXX}} and {{TAG\|HFSCREEN}} parameters, as well as the fact that bulk Silicon is a centrosymmetric material, so the model dielectric function works well here. However, while the use of a model (diagonal) dielectric function is well suited for bulk Silicon, for systems with lower symmetry the off-diagonal elements that are ignored here will be important, and can lead to larger discrepancies in the results from TDDFT and MBPT.

	However, while the use of a model (diagonal) dielectric function is well suited for bulk Silicon, for systems with lower symmetry the off-diagonal elements that are ignored here will be important, and can lead to larger discrepancies in the results from TDDFT and MBPT.

	To plot the EEL spectrum with {{py4vasp}}, it should be noted that the type of calculation has to be specified when reading the dielectric function. It is simply a matter of editing the following lines		To plot the EEL spectrum with {{py4vasp}}, it should be noted that the type of calculation has to be specified when reading the dielectric function. It is simply a matter of editing the following lines
	<syntaxhighlight lang="python" line>		<syntaxhighlight lang="python" line>
	calc_bse = py4vasp.Calculation.from_file('vaspout.~~BSE~~.h5')		import py4vasp
	calc_tdhf = py4vasp.Calculation.from_file('vaspout.~~TDHF~~.h5')		import numpy as np
			import matplotlib.pyplot as plt

			calc_bse = py4vasp.Calculation.from_file('vaspout.BSE_Q1.h5')
			calc_tdhf = py4vasp.Calculation.from_file('vaspout.TDHF_Q1.h5')

			energies = calc_bse_q1.dielectric_function.read('BSE')['energies']
	epsilon_bse = calc_bse.dielectric_function.read('BSE')['dielectric_function'][1][1][:]		epsilon_bse = calc_bse.dielectric_function.read('BSE')['dielectric_function'][1][1][:]
	epsilon_tdhf = calc_tdhf.dielectric_function.read('TDHF')['dielectric_function'][1][1][:]		epsilon_tdhf = calc_tdhf.dielectric_function.read('TDHF')['dielectric_function'][1][1][:]

			eels_bse = -np.imag(1.0/epsilon_bse)
			eels_tdhf = -np.imag(1.0/epsilon_tdhf)

			plt.plot(energies, eels_bse, '', label='BSE')
			plt.plot(energies, eels_tdhf, '', label='TDHF')
			plt.ylabel(r'Im[$\epsilon^{-1}_M$]')
			plt.xlabel('Energy loss [eV]')
			plt.legend()
			plt.show()
	</syntaxhighlight>		</syntaxhighlight>
	which when used with the rest of the script will produce the following plot for EELS.		which when used with the rest of the script will produce the following plot for EELS.