Band-structure calculation using hybrid functionals - Revision history

Huebsch: /* Step-by-step instructions */

2025-02-28T08:25:39Z

Step-by-step instructions

← Older revision		Revision as of 08:25, 28 February 2025
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	'''Step 4:''' Set {{TAG\|HFRCUT}} in the {{FILE\|INCAR}} file and restart the hybrid calculation from the DFT {{FILE\|WAVECAR}} file.		'''Step 4:''' Set {{TAG\|HFRCUT}} in the {{FILE\|INCAR}} file and restart the hybrid calculation from the DFT {{FILE\|WAVECAR}} file.

	'''Step 5:''' Plot the band structure, e.g., using {{py4vasp\|url=calculation/band/#py4vasp.calculation._band.Band.to_graph}}.		'''Step 5:''' Plot the band structure, e.g., using {{py4vasp\|url=calculation/band/#py4vasp.calculation._band.Band.to_graph}}. In a python notebook in the directory of the calculation, you can execute
			<syntaxhighlight lang="python">
			import py4vasp as pv
			calc = pv.Calculation.from_path(".")
			calc.band.plot()
			# calc.band.plot("kpoints_opt") # if the high-symmetry path is in KPOINTS_OPT
			</syntaxhighlight>

	== Recommendations and advice ==		== Recommendations and advice ==

Schlipf: /* Step-by-step instructions */

2024-06-10T10:07:54Z

Step-by-step instructions

← Older revision		Revision as of 10:07, 10 June 2024
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	'''Step 4:''' Set {{TAG\|HFRCUT}} in the {{FILE\|INCAR}} file and restart the hybrid calculation from the DFT {{FILE\|WAVECAR}} file.		'''Step 4:''' Set {{TAG\|HFRCUT}} in the {{FILE\|INCAR}} file and restart the hybrid calculation from the DFT {{FILE\|WAVECAR}} file.

	'''Step 5:''' Plot the band structure, e.g., using ~~[https://www.vasp.at/~~py4vasp~~/latest/data~~/band/#py4vasp.~~data~~.Band.~~plot\| py4vasp]~~.		'''Step 5:''' Plot the band structure, e.g., using {{py4vasp\|url=calculation/band/#py4vasp.calculation._band.Band.to_graph}}.

	== Recommendations and advice ==		== Recommendations and advice ==

Ftran at 09:15, 18 October 2023

2023-10-18T09:15:55Z

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	==Related tags and articles==		==Related tags and articles==
	{{FILE\| KPOINTS}}, {{FILE\| KPOINTS_OPT}}, [[list_of_hybrid_functionals\|List of hybrid functionals]], [[Hybrid functionals: formalism]]		{{FILE\| KPOINTS}}, {{FILE\| KPOINTS_OPT}}, [[list_of_hybrid_functionals\|List of hybrid functionals]], [[Hybrid functionals: formalism]], [[Coulomb singularity]]

	== References ==		== References ==

Ftran at 09:05, 18 October 2023

2023-10-18T09:05:21Z

← Older revision		Revision as of 09:05, 18 October 2023
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	==Related tags and articles==		==Related tags and articles==
	{{FILE\| KPOINTS}}, {{FILE\| KPOINTS_OPT}}, [[Hybrid functionals: formalism]]		{{FILE\| KPOINTS}}, {{FILE\| KPOINTS_OPT}}, [[list_of_hybrid_functionals\|List of hybrid functionals]], [[Hybrid functionals: formalism]]

	== References ==		== References ==

Huebsch at 09:03, 10 October 2023

2023-10-10T09:03:50Z

← Older revision		Revision as of 09:03, 10 October 2023
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	'''Step 4:''' Set {{TAG\|HFRCUT}} in the {{FILE\|INCAR}} file and restart the hybrid calculation from the DFT {{FILE\|WAVECAR}} file.		'''Step 4:''' Set {{TAG\|HFRCUT}} in the {{FILE\|INCAR}} file and restart the hybrid calculation from the DFT {{FILE\|WAVECAR}} file.

			'''Step 5:''' Plot the band structure, e.g., using [https://www.vasp.at/py4vasp/latest/data/band/#py4vasp.data.Band.plot\| py4vasp].

	== Recommendations and advice ==		== Recommendations and advice ==

Huebsch at 08:27, 10 October 2023

2023-10-10T08:27:44Z

← Older revision		Revision as of 08:27, 10 October 2023
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	The {{FILE\|KPOINTS_OPT}} method is more convenient because it allows using the automatic generation modes for the '''k''' points. The computational cost and memory requirement can vary for the two methods due to the scaling behaviour with the number of '''k''' points.		The {{FILE\|KPOINTS_OPT}} method is more convenient because it allows using the automatic generation modes for the '''k''' points. The computational cost and memory requirement can vary for the two methods due to the scaling behaviour with the number of '''k''' points.

	'''Step 3:''' Supply a regular '''k''' mesh and '''k''' points along a high-symmetry path either using the explicit list including zero-weighted '''k''' points or using a {{FILE\|KPOINTS_OPT}} file and restart the hybrid calculation from the DFT {{FILE\|WAVECAR}} file.		'''Step 3:''' Supply a regular '''k''' mesh and '''k''' points along a high-symmetry path either using the explicit list including zero-weighted '''k''' points or using a {{FILE\|KPOINTS_OPT}} file.

			By default VASP uses auxiliary functions ({{TAG\|HFALPHA}}) for the truncation of the [[Coulomb singularity]], but this method leads to discontinuities in band-structure calculations. We recommend using the Coulomb truncation ({{TAG\|HFRCUT}}) instead. In particular, {{TAG\|HFRCUT}}=-1 converges best for systems with a band gap.

			'''Step 4:''' Set {{TAG\|HFRCUT}} in the {{FILE\|INCAR}} file and restart the hybrid calculation from the DFT {{FILE\|WAVECAR}} file.

	== Recommendations and advice ==		== Recommendations and advice ==
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	{{NB\|warning\| The electronic charge density must not be fixed for any hybrid calculation, i.e., never set {{TAG\|ICHARG}}{{=}}11!}}		{{NB\|warning\| The electronic charge density must not be fixed for any hybrid calculation, i.e., never set {{TAG\|ICHARG}}{{=}}11!}}
	{{NB\|tip\|To understand how the two methods work in practice, try using them with a DFT calculation as if it were a hybrid calculation.}}		{{NB\|tip\|To understand how the two methods work in practice, try using them with a DFT calculation as if it were a hybrid calculation.}}
			If you forgot setting {{TAG\|HFRCUT}} you may be able to mitigate the band structure. Semi-core states can be assumed to be dispersionless but you will see the same discontinuities featured on the semi core states. By subtracting the faulty dispersion of the semi-core state from all bands, you can recover the true dispersion of the conduction bands.
	== Example of '''k''' points for hybrid band-structure calculation==		== Example of '''k''' points for hybrid band-structure calculation==

Miranda.henrique: /* Related tags and articles */

2022-07-19T11:45:11Z

Ftran at 14:47, 18 May 2022

2022-05-18T14:47:15Z

← Older revision		Revision as of 14:47, 18 May 2022
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	==Related tags and articles==		==Related tags and articles==
	{{FILE\| KPOINTS}}, {{FILE\| KPOINTS_OPT}}, [[:~~Category:Hybrid functionals\|Hybrid functionals~~]]		{{FILE\| KPOINTS}}, {{FILE\| KPOINTS_OPT}}, [[Hybrid_functionals:_formalism]]

	== References ==		== References ==

Huebsch: Huebsch moved page Construction:Band-structure calculation using hybrid functionals to Band-structure calculation using hybrid functionals without leaving a redirect

2022-05-11T12:52:19Z

Huebsch moved page Construction:Band-structure calculation using hybrid functionals to Band-structure calculation using hybrid functionals without leaving a redirect

← Older revision	Revision as of 12:52, 11 May 2022
(No difference)

Huebsch at 09:56, 11 May 2022

2022-05-11T09:56:17Z

← Older revision		Revision as of 08:27, 10 October 2023
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	The {{FILE\|KPOINTS_OPT}} method is more convenient because it allows using the automatic generation modes for the '''k''' points. The computational cost and memory requirement can vary for the two methods due to the scaling behaviour with the number of '''k''' points.		The {{FILE\|KPOINTS_OPT}} method is more convenient because it allows using the automatic generation modes for the '''k''' points. The computational cost and memory requirement can vary for the two methods due to the scaling behaviour with the number of '''k''' points.

	'''Step 3:''' Supply a regular '''k''' mesh and '''k''' points along a high-symmetry path either using the explicit list including zero-weighted '''k''' points or using a {{FILE\|KPOINTS_OPT}} file and restart the hybrid calculation from the DFT {{FILE\|WAVECAR}} file.		'''Step 3:''' Supply a regular '''k''' mesh and '''k''' points along a high-symmetry path either using the explicit list including zero-weighted '''k''' points or using a {{FILE\|KPOINTS_OPT}} file.

			By default VASP uses auxiliary functions ({{TAG\|HFALPHA}}) for the truncation of the [[Coulomb singularity]], but this method leads to discontinuities in band-structure calculations. We recommend using the Coulomb truncation ({{TAG\|HFRCUT}}) instead. In particular, {{TAG\|HFRCUT}}=-1 converges best for systems with a band gap.

			'''Step 4:''' Set {{TAG\|HFRCUT}} in the {{FILE\|INCAR}} file and restart the hybrid calculation from the DFT {{FILE\|WAVECAR}} file.

	== Recommendations and advice ==		== Recommendations and advice ==
Line 35:		Line 39:
	{{NB\|warning\| The electronic charge density must not be fixed for any hybrid calculation, i.e., never set {{TAG\|ICHARG}}{{=}}11!}}		{{NB\|warning\| The electronic charge density must not be fixed for any hybrid calculation, i.e., never set {{TAG\|ICHARG}}{{=}}11!}}
	{{NB\|tip\|To understand how the two methods work in practice, try using them with a DFT calculation as if it were a hybrid calculation.}}		{{NB\|tip\|To understand how the two methods work in practice, try using them with a DFT calculation as if it were a hybrid calculation.}}
			If you forgot setting {{TAG\|HFRCUT}} you may be able to mitigate the band structure. Semi-core states can be assumed to be dispersionless but you will see the same discontinuities featured on the semi core states. By subtracting the faulty dispersion of the semi-core state from all bands, you can recover the true dispersion of the conduction bands.
	== Example of '''k''' points for hybrid band-structure calculation==		== Example of '''k''' points for hybrid band-structure calculation==

← Older revision		Revision as of 11:45, 19 July 2022
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	==Related tags and articles==		==Related tags and articles==
	{{FILE\| KPOINTS}}, {{FILE\| KPOINTS_OPT}}, [[~~Hybrid_functionals~~:~~_formalism~~]]		{{FILE\| KPOINTS}}, {{FILE\| KPOINTS_OPT}}, [[Hybrid functionals: formalism]]

	== References ==		== References ==

← Older revision		Revision as of 09:56, 11 May 2022
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	== Step-by-step instructions ==		== Step-by-step instructions ==

	For [[:Category:Hybrid functionals \|hybrid functionals]], the Hamiltonian cannot be expressed in terms of the electronic charge density alone. Instead, the Kohn-Sham orbitals on a regular '''k''' mesh are required for any calculation within the [[Hybrid functionals: formalism\|formalism of hybrid functionals]]. The regular '''k''' mesh must be supplied in the {{FILE\|KPOINTS}} file. Consequently, restarting a hybrid calculation requires the {{FILE\|WAVECAR}} file of the previous self-consistent-field (SCF) run. This is in contrast to [[GGA\|density-functional theory]] (DFT), where the electronic charge density written to the {{FILE\|CHGCAR}} file suffices to restart a DFT calculation.		For [[:Category:Hybrid functionals \|hybrid functionals]], the Hamiltonian cannot be expressed in terms of the electronic charge density alone. Instead, the Kohn-Sham orbitals on a regular '''k''' mesh are required for any calculation within the [[Hybrid functionals: formalism\|formalism of hybrid functionals]]. The regular '''k''' mesh must be supplied in the {{FILE\|KPOINTS}} file. Consequently, restarting a hybrid calculation requires the {{FILE\|WAVECAR}} file of the previous self-consistent-field (SCF) run. This is in contrast to [[GGA\|density-functional theory]] (DFT), where the electronic charge density written to the {{FILE\|CHGCAR}} file suffices to restart a DFT calculation. In order to reach convergence more quickly, it is good practice to first compute the DFT result in a SCF calculation.

	'''Step 1:''' Run an SCF calculation to obtain a converged {{FILE\|WAVECAR}} file.		'''Step 1 (optional):''' Run an SCF calculation to obtain a converged {{FILE\|WAVECAR}} file for DFT.

	[[:Category:Band structure \|Band-structure calculations]] generally compute the Kohn-Sham orbitals and eigenenergies along a path in reciprocal space which usually connects high-symmetry points in the first Brillouin zone. Some external tools{{cite\|bilbao:kvec}}{{cite\|seekpath}} help to identify the high-symmetry points and '''k''' points along a high-symmetry path for materials of any symmetry.		[[:Category:Band structure \|Band-structure calculations]] generally compute the Kohn-Sham orbitals and eigenenergies along a path in reciprocal space which usually connects high-symmetry points in the first Brillouin zone. Some external tools{{cite\|bilbao:kvec}}{{cite\|seekpath}} help to identify the high-symmetry points and '''k''' points along a high-symmetry path for materials of any symmetry.

	'''Step 2:''' Determine the high-symmetry ~~points~~ along which VASP should compute the band structure.		'''Step 2:''' Determine the high-symmetry path along which VASP should compute the band structure.

	There are two options to simultaneously supply a regular '''k''' mesh and '''k''' points along a high-symmetry path to VASP.		There are two options to simultaneously supply a regular '''k''' mesh ''and'' '''k''' points along a high-symmetry path to VASP.
	:;1. ~~Read~~ an [[KPOINTS#Explicit_k-point_mesh\|explicit list of '''k''' points]] with zero-weighted '''k''' points.		:;1. Provide an [[KPOINTS#Explicit_k-point_mesh\|explicit list of '''k''' points]] with zero-weighted '''k''' points.
	::Here, the explicit list of the irreducible '''k''' points of the regular '''k''' mesh can be copied from the {{FILE\|IBZKPT}} file of a previous run to the {{FILE\|KPOINTS}} file. These irreducible '''k''' points must be weighted by their multiplicity according to the system's symmetry. Additionally, the '''k''' points along a high-symmetry path must be added to the {{FILE\|KPOINTS}} file with the value of all weights set to zero.		::Here, the explicit list of the irreducible '''k''' points of the regular '''k''' mesh can be copied from the {{FILE\|IBZKPT}} file of a previous run to the {{FILE\|KPOINTS}} file. For instance, use the {{FILE\|IBZKPT}} file of step 1. These irreducible '''k''' points must be weighted by their multiplicity according to the system's symmetry. Additionally, the '''k''' points along a high-symmetry path must be added to the {{FILE\|KPOINTS}} file with the value of all weights set to zero.

	:;2. ~~Read~~ an additional {{FILE\|KPOINTS_OPT}} file that can specify the [[KPOINTS#Band-structure_calculations\|high-symmetry path in line mode]].		:;2. Provide an additional {{FILE\|KPOINTS_OPT}} file that can specify the [[KPOINTS#Band-structure_calculations\|high-symmetry path in line mode]].
	::Generally, the {{FILE\|KPOINTS}} file and the {{FILE\|KPOINTS_OPT}} file accept the same format. But again, the regular '''k''' mesh needs to be supplied in the {{FILE\|KPOINTS}} file and the high-symmetry path in the {{FILE\|KPOINTS_OPT}} file. We therefore recommend using the [[KPOINTS#Regular_k-point_mesh\|Γ-centered mesh or Monkhorst-Pack mesh]] and ~~providing the~~ [[KPOINTS#Band-structure_calculations\|~~high-symmetry path in~~ line mode]], respectively.		::Generally, the {{FILE\|KPOINTS}} file and the {{FILE\|KPOINTS_OPT}} file accept the same format. But again, the regular '''k''' mesh needs to be supplied in the {{FILE\|KPOINTS}} file and the high-symmetry path in the {{FILE\|KPOINTS_OPT}} file. We therefore recommend using the [[KPOINTS#Regular_k-point_mesh\|Γ-centered mesh or Monkhorst-Pack mesh]], and [[KPOINTS#Band-structure_calculations\|line mode]], respectively.

	The {{FILE\|KPOINTS_OPT}} method is more convenient because it allows using the automatic generation modes for the '''k''' points. The computational cost and memory requirement can vary for the two methods due to the scaling with the number of '''k''' points.		The {{FILE\|KPOINTS_OPT}} method is more convenient because it allows using the automatic generation modes for the '''k''' points. The computational cost and memory requirement can vary for the two methods due to the scaling behaviour with the number of '''k''' points.

	'''Step 3:''' Supply a regular '''k''' mesh and '''k''' points along a high-symmetry path either using the explicit list including zero-weighted '''k''' points or using a {{FILE\|KPOINTS_OPT}} file and restart the hybrid calculation from the ~~converged~~ {{FILE\|WAVECAR}} file.		'''Step 3:''' Supply a regular '''k''' mesh and '''k''' points along a high-symmetry path either using the explicit list including zero-weighted '''k''' points or using a {{FILE\|KPOINTS_OPT}} file and restart the hybrid calculation from the DFT {{FILE\|WAVECAR}} file.

	== Recommendations and advice ==		== Recommendations and advice ==

	~~The~~ {{FILE\|KPOINTS_OPT}} file ~~can also be provided when starting an SCF calculation from scratch. In that case~~, VASP computes the band energies for the '''k''' points of the {{FILE\|KPOINTS_OPT}} file after SCF is reached. ~~While this seems~~ to ~~make step 1 obsolete~~, ~~mind that it affects how VASP can treat~~ the ~~Coulomb-convergence during the SCF~~ calculation~~. That~~ is~~, {{TAG\| FOCKCORR}}=2 cannot be used when computing the band structure with either option of supplying the '''k''' points~~.		In case a {{FILE\|KPOINTS_OPT}} file is present, VASP computes the band energies for the '''k''' points of the {{FILE\|KPOINTS_OPT}} file after SCF is reached within the same submitted job. Their convergence is checked independently by requiring the sum over occupied band energies not to change in two successive iterations. Hence, for the computational time, there is no advantage to restart from a converged hybrid calculation, but in principle it is possible.

	~~The~~ method using an explicit list including zero-weighted '''k''' points ~~should not be used from scratch~~ for ~~performance reasons~~. ~~Constructing~~ the ~~Fock exchange dominates the computational cost~~ and ~~memory requirement and it scales with~~ the ~~number~~ of '''k''' points. ~~Thus~~, each SCF step ~~will get unnecessarily~~ expensive when including zero-weighted '''k''' points.		In contrast, the method using an explicit list including zero-weighted '''k''' points computes the band energies for all '''k''' points at each SCF step. The convergence criterion considers the total energy and, thus, does not account for convergence of KS orbitals at zero-weighted '''k''' points. Taking the KS orbitals of the zero-weighted '''k''' points along the entire SCF run makes their convergence highly likely. However, restarting from a converged hybrid calculation can result in premature stopping. This can be counteracted by setting the {{TAG\|NELMIN}} tag to a higher value. Especially if the hybrid calculation needs many SCF steps to reach convergence and each SCF step is very expensive when including zero-weighted '''k''' points, one may consider to restart from a converged hybrid calculation with {{TAG\|NELMIN}} set to a large number. We recommend carefully checking the convergence of the band structure in this case.
	{{NB\|tip\|For ~~both methods~~, ~~restart~~ from a converged hybrid ~~SCF calculation to seize all available options for optimal performance~~.}}		{{NB\|tip\|For a band-structure calculation with an explicit list including zero-weighted '''k''' points, avoid restarting from a converged hybrid {{FILE\|WAVECAR}} file.}}

	As mentioned, the computational cost and memory requirement can vary for the two methods due to the scaling with the number of '''k''' points. ~~It is still possible to achieve very fine sampling along the '''k''' path with both methods:~~ For the {{FILE\|KPOINTS_OPT}} method, ~~set an appropriate batch size, i.e.,~~ the {{TAG\|KPOINTS_OPT_NKBATCH}} tag. For the explicit list including zero-weighted '''k''' points, VASP may exceed the available memory if the number of zero-weighted '''k''' points is large. In that case, split the hybrid band-structure calculation into multiple calculations. For each calculation, add part of the zero-weighted '''k''' points.		It is possible to achieve very fine sampling along the '''k''' path with both methods, but there are some aspects to take into account. As mentioned, the computational cost and memory requirement can vary for the two methods due to the scaling with the number of '''k''' points. For the {{FILE\|KPOINTS_OPT}} method, the number of '''k''' points treated simultaneously can be controlled by means of the {{TAG\|KPOINTS_OPT_NKBATCH}} tag. For the explicit list including zero-weighted '''k''' points, VASP may exceed the available memory if the number of zero-weighted '''k''' points is large. In that case, split the hybrid band-structure calculation into multiple calculations. For each calculation, add part of the zero-weighted '''k''' points.
	{{NB\|tip\|Make fine sampling computationally feasible using the {{TAG\|KPOINTS_OPT_NKBATCH}} tag or splitting the calculation with part of the zero-weighted '''k''' points.}}		{{NB\|tip\|Make fine sampling computationally feasible using the {{TAG\|KPOINTS_OPT_NKBATCH}} tag or splitting the calculation with part of the zero-weighted '''k''' points.}}

	~~To understand how the two methods work in practice, try using them with a DFT calculation as if it were a hybrid calculation.~~		Let us stress a significant difference between hybrid band-structure calculations and DFT band-structure calculations. The electronic charge density suffices for density functionals to define the Hamiltonian, and no regular '''k''' mesh is required during DFT band-structure calculations. However, if no regular '''k''' mesh is provided, the electronic charge density must be fixed during the DFT band-structure calculation by setting {{TAG\|ICHARG}}=11 in the {{FILE\|INCAR}} file.

	~~Finally, let~~ us stress a significant difference between hybrid band-structure calculations and DFT band-structure calculations. The electronic charge density suffices for density functionals to define the Hamiltonian, and no regular '''k''' mesh is required during DFT band-structure calculations. However, if no regular '''k''' mesh is provided, the electronic charge density must be fixed during the DFT band-structure calculation by setting {{TAG\|ICHARG}}=11 in the {{FILE\|INCAR}} file.
	{{NB\|warning\| The electronic charge density must not be fixed for any hybrid calculation, i.e., never set {{TAG\|ICHARG}}{{=}}11!}}		{{NB\|warning\| The electronic charge density must not be fixed for any hybrid calculation, i.e., never set {{TAG\|ICHARG}}{{=}}11!}}
			{{NB\|tip\|To understand how the two methods work in practice, try using them with a DFT calculation as if it were a hybrid calculation.}}
	== Example of '''k''' points for hybrid band-structure calculation==		== Example of '''k''' points for hybrid band-structure calculation==