Category:Hybrid functionals - Revision history

Ftran at 14:48, 11 June 2026

2026-06-11T14:48:31Z

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	== References ==		== References ==
			<references/>
	~~----~~

	[[Category:VASP\|Hybrids]][[Category:Exchange-correlation functionals]]		[[Category:VASP\|Hybrids]][[Category:Exchange-correlation functionals]]

Ftran at 14:42, 11 June 2026

2026-06-11T14:42:13Z

← Older revision		Revision as of 14:42, 11 June 2026
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	* {{NB\|mind\|		* {{NB\|mind\|
	*Evaluating the HF exchange is computationally very demanding, leading to '''a computational time that is one or several orders of magnitude larger than with semilocal functionals'''. Therefore, a proper assessment of the available computational resources and parallelization strategies becomes increasingly important.		*Evaluating the HF exchange is computationally very demanding, leading to '''a computational time that is one or several orders of magnitude larger than with semilocal functionals'''. Therefore, a proper assessment of the available computational resources and parallelization strategies becomes increasingly important.
	*Some properties cannot be computed using hybrid functionals because the corresponding implementations are not yet available. A non-exhaustive list includes [[Electron-phonon_interactions_theory\|~~Electron~~-phonon interactions]], [[Phonons from density-functional-perturbation theory\|~~Phonons~~ from density-functional-perturbation theory]]. However, note that the phonons ~~can be~~ calculated using the [[Phonons from finite differences\|finite differences method]].}}		*Some properties cannot be computed using hybrid functionals because the corresponding implementations are not yet available. A non-exhaustive list includes [[Electron-phonon_interactions_theory\|electron-phonon interactions]], [[Phonons from density-functional-perturbation theory\|phonons from density-functional-perturbation theory]], and [[Calculating_the_chemical_shieldings\|NMR shielding]]. However, note that hybrid functionals can be used if the phonons are calculated using the [[Phonons from finite differences\|finite differences method]].}}

	== Overview ==		== Overview ==
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	Details about the implementation of the unscreened hybrid functionals can be found in the work of Paier et al.,{{cite\|paier:jcp:05}} while details specific to the screened hybrid functionals can be found in Refs. {{cite\|paier:jcp:06}}{{cite\|angyan:jpa:2006}} Refs. {{cite\|cui2018doubly}}{{cite\|liu2019assessing}} report the development of dielectric-dependent hybrid functionals, which provide very accurate band gaps and are also available in VASP.		Details about the implementation of the unscreened hybrid functionals can be found in the work of Paier et al.,{{cite\|paier:jcp:05}} while details specific to the screened hybrid functionals can be found in Refs. {{cite\|paier:jcp:06}}{{cite\|angyan:jpa:2006}} Refs. {{cite\|cui2018doubly}}{{cite\|liu2019assessing}} report the development of dielectric-dependent hybrid functionals, which provide very accurate band gaps and are also available in VASP.

	Note that as in most other codes, hybrid functionals are implemented in VASP within the generalized KS scheme,{{cite\|seidl:prb:96}} which means that the total energy is minimized with respect to the orbitals (instead of the electron density~~) as in the HF theory~~.		Note that as in most other codes, hybrid functionals are implemented in VASP within the generalized KS scheme,{{cite\|seidl:prb:96}} which means that the total energy is minimized, as in the HF theory, with respect to the orbitals instead of the electron density.

	VASP offers a convenient way to generate the [[Band-structure calculation using hybrid functionals\|band structure with hybrid functionals]].		VASP offers a convenient way to generate the [[Band-structure calculation using hybrid functionals\|band structure with hybrid functionals]].
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	* The [[Downsampling of the Hartree-Fock operator\|Downsampling of the HF operator]] allows for the use of a coarser '''k''' point sampling for the HF operator, and therefore faster calculations.{{cite\|paier:jcp:06}} However, this option should be use with care for metals.		* The [[Downsampling of the Hartree-Fock operator\|Downsampling of the HF operator]] allows for the use of a coarser '''k''' point sampling for the HF operator, and therefore faster calculations.{{cite\|paier:jcp:06}} However, this option should be use with care for metals.

	* The Adaptively Compressed Exchange Operator,{{cite\|linlin:jctc:2016}} that allows for more efficient evaluation of the Fock operator, is used if the Davidson algorithm ({{TAG\|ALGO}} = Normal) is ~~used~~ (see {{TAG\|LFOCKACE}} for more details).		* The Adaptively Compressed Exchange Operator,{{cite\|linlin:jctc:2016}} that allows for a more efficient evaluation of the Fock operator, is used if the Davidson algorithm ({{TAG\|ALGO}} = Normal, the default) is selected (see {{TAG\|LFOCKACE}} for more details).

	== Additional resources ==		== Additional resources ==
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	=== How to ===		=== How to ===
	*[[Hybrid_functionals: formalism\|Formalism of the HF method and hybrids]]		*[[Hybrid_functionals: formalism\|Formalism of the HF method and hybrids]]. The various families are described.
	*[[List_of_hybrid_functionals\|List of available hybrid functionals]] and how to specify them in the {{FILE\|INCAR}} file.		*[[List_of_hybrid_functionals\|List of available hybrid functionals]] and how to specify them in the {{FILE\|INCAR}} file.
	*[[Downsampling_of_the_Hartree-Fock_operator\|Downsampling of the Hartree-Fock operator]] to reduce the computational cost.		*[[Downsampling_of_the_Hartree-Fock_operator\|Downsampling of the Hartree-Fock operator]] to reduce the computational cost.
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	In addition to the works already cited above, the selected publications listed below describe methodological developments or computational studies performed using the hybrid functionals implemented in VASP.		In addition to the works already cited above, the selected publications listed below describe methodological developments or computational studies performed using the hybrid functionals implemented in VASP.

	*The B3LYP functional applied to solid state systems and its failure for metals{{cite\|paier:jcp:07}}.		*The B3LYP functional applied to solid-state systems and its failure for metals{{cite\|paier:jcp:07}}.
	*Applications of hybrid functionals to selected materials: Ceria,{{cite\|juarez:prb:07}} lead chalcogenides,{{cite\|hummer:prb:07}} CO adsorption on metals,{{cite\|stroppa:prb:07}}{{cite\|stroppa:njp:08}} excitonic properties,{{cite\|paier:prb:08}} SrTiO and BaTiO, {{cite\|wahl:prb:08}} perovskites,{{cite\|franchini:jpcm:14}} and transition-metal oxides.{{cite\|gopidi:prb:26}}		*Applications of hybrid functionals to selected materials: Ceria,{{cite\|juarez:prb:07}} lead chalcogenides,{{cite\|hummer:prb:07}} CO adsorption on metals,{{cite\|stroppa:prb:07}}{{cite\|stroppa:njp:08}} excitonic properties,{{cite\|paier:prb:08}} SrTiO and BaTiO, {{cite\|wahl:prb:08}} perovskites,{{cite\|franchini:jpcm:14}} and transition-metal oxides.{{cite\|gopidi:prb:26}}
	*HSEsol hybrid functional.{{cite\|schimka:jcp:11}}		*HSEsol hybrid functional.{{cite\|schimka:jcp:11}}

Ftran at 10:45, 11 June 2026

2026-06-11T10:45:45Z

← Older revision		Revision as of 10:45, 11 June 2026
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	Depending on the type of systems or the property under consideration they can be more accurate than semilocal (GGA, meta-GGA) functionals. For instance, hybrid functionals are usually more suited for calculating the electronic and magnetic properties of nonmetallic systems. They are particularly recommended for bandgap calculations.{{cite\|heyd:jcp:05}}{{cite\|chen2018nonempirical}} Polarons{{cite\|franchini:nrm:21}} or defect states{{cite\|oba:prb:08}} are among properties that can also be better described by hybrid functionals.		Depending on the type of systems or the property under consideration they can be more accurate than semilocal (GGA, meta-GGA) functionals. For instance, hybrid functionals are usually more suited for calculating the electronic and magnetic properties of nonmetallic systems. They are particularly recommended for bandgap calculations.{{cite\|heyd:jcp:05}}{{cite\|chen2018nonempirical}} Polarons{{cite\|franchini:nrm:21}} or defect states{{cite\|oba:prb:08}} are among properties that can also be better described by hybrid functionals.
	Note that hybrid functionals are also often good at treating [[:Category:Strongly correlated electrons\|strongly correlated electrons]].{{cite\|liu2019assessing}}		Note that hybrid functionals are also often good at treating [[:Category:Strongly correlated electrons\|strongly correlated electrons]].{{cite\|liu2019assessing}}

			* {{NB\|mind\|
			*Evaluating the HF exchange is computationally very demanding, leading to '''a computational time that is one or several orders of magnitude larger than with semilocal functionals'''. Therefore, a proper assessment of the available computational resources and parallelization strategies becomes increasingly important.
			*Some properties cannot be computed using hybrid functionals because the corresponding implementations are not yet available. A non-exhaustive list includes [[Electron-phonon_interactions_theory\|Electron-phonon interactions]], [[Phonons from density-functional-perturbation theory\|Phonons from density-functional-perturbation theory]]. However, note that the phonons can be calculated using the [[Phonons from finite differences\|finite differences method]].}}

	== Overview ==		== Overview ==
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	== Technical points ==		== Technical points ==

	* {{NB\|mind\|Evaluating the HF exchange is computationally very demanding, leading to '''a computational time that is one or several orders of magnitude larger than with semilocal functionals'''. Therefore, a proper assessment of the available computational resources and parallelization strategies becomes increasingly important.}}

	* The unscreened Coulomb potential used to evaluate the exchange integral in HF has an integrable Coulomb singularity that leads to slow convergence with respect to supercell size (or equivalently '''k''' point sampling). To make the computations feasible requires special treatment of the [[Coulomb singularity]].		* The unscreened Coulomb potential used to evaluate the exchange integral in HF has an integrable Coulomb singularity that leads to slow convergence with respect to supercell size (or equivalently '''k''' point sampling). To make the computations feasible requires special treatment of the [[Coulomb singularity]].
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	* The Adaptively Compressed Exchange Operator,{{cite\|linlin:jctc:2016}} that allows for more efficient evaluation of the Fock operator, is used if the Davidson algorithm ({{TAG\|ALGO}} = Normal) is used (see {{TAG\|LFOCKACE}} for more details).		* The Adaptively Compressed Exchange Operator,{{cite\|linlin:jctc:2016}} that allows for more efficient evaluation of the Fock operator, is used if the Davidson algorithm ({{TAG\|ALGO}} = Normal) is used (see {{TAG\|LFOCKACE}} for more details).

	== Additional resources ==		== Additional resources ==
	=== Tutorials ===		=== Tutorials ===
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	*The B3LYP functional applied to solid state systems and its failure for metals{{cite\|paier:jcp:07}}.		*The B3LYP functional applied to solid state systems and its failure for metals{{cite\|paier:jcp:07}}.
	*Applications of hybrid functionals to selected materials: Ceria,{{cite\|juarez:prb:07}} lead chalcogenides,{{cite\|hummer:prb:07}} CO adsorption on metals,{{cite\|stroppa:prb:07}}{{cite\|stroppa:njp:08}} excitonic properties,{{cite\|paier:prb:08}} SrTiO and BaTiO, {{cite\|wahl:prb:08}} ~~and~~ perovskites.{{cite\|franchini:jpcm:14}}		*Applications of hybrid functionals to selected materials: Ceria,{{cite\|juarez:prb:07}} lead chalcogenides,{{cite\|hummer:prb:07}} CO adsorption on metals,{{cite\|stroppa:prb:07}}{{cite\|stroppa:njp:08}} excitonic properties,{{cite\|paier:prb:08}} SrTiO and BaTiO, {{cite\|wahl:prb:08}} perovskites,{{cite\|franchini:jpcm:14}} and transition-metal oxides.{{cite\|gopidi:prb:26}}
	*HSEsol hybrid functional.{{cite\|schimka:jcp:11}}		*HSEsol hybrid functional.{{cite\|schimka:jcp:11}}
	*Analysis of the HSE parameter space.{{cite\|moussa:jcp:12}}		*Analysis of the HSE parameter space.{{cite\|moussa:jcp:12}}

Ftran at 08:24, 11 June 2026

2026-06-11T08:24:56Z

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	* The unscreened Coulomb potential used to evaluate the exchange integral in HF has an integrable Coulomb singularity that leads to slow convergence with respect to supercell size (or equivalently '''k''' point sampling). To make the computations feasible requires special treatment of the [[Coulomb singularity]].		* The unscreened Coulomb potential used to evaluate the exchange integral in HF has an integrable Coulomb singularity that leads to slow convergence with respect to supercell size (or equivalently '''k''' point sampling). To make the computations feasible requires special treatment of the [[Coulomb singularity]].

	* The [[Downsampling of the Hartree-Fock operator\|Downsampling of the HF operator]] allows for the use of a coarser '''k''' point sampling for the HF operator, and therefore faster calculations.{{cite\|~~angyan~~:~~jpa~~:~~2006~~}} However, this option should be use with care for metals.		* The [[Downsampling of the Hartree-Fock operator\|Downsampling of the HF operator]] allows for the use of a coarser '''k''' point sampling for the HF operator, and therefore faster calculations.{{cite\|paier:jcp:06}} However, this option should be use with care for metals.

	* The Adaptively Compressed Exchange Operator,{{cite\|linlin:jctc:2016}} that allows for more efficient evaluation of the Fock operator, is used if the Davidson algorithm ({{TAG\|ALGO}} = Normal) is used (see {{TAG\|LFOCKACE}} for more details).		* The Adaptively Compressed Exchange Operator,{{cite\|linlin:jctc:2016}} that allows for more efficient evaluation of the Fock operator, is used if the Davidson algorithm ({{TAG\|ALGO}} = Normal) is used (see {{TAG\|LFOCKACE}} for more details).
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	=== Further reading ===		=== Further reading ===
	*A comprehensive study of the ~~performance of~~ the ~~HSE03/HSE06 functional compared to~~ the ~~PBE and PBE0~~ functionals~~{{cite\|paier:jcp:06}}~~.		In addition to the works already cited above, the selected publications listed below describe methodological developments or computational studies performed using the hybrid functionals implemented in VASP.

	*The B3LYP functional applied to solid state systems and its failure for metals{{cite\|paier:jcp:07}}.		*The B3LYP functional applied to solid state systems and its failure for metals{{cite\|paier:jcp:07}}.
	*Applications of hybrid functionals to selected materials: Ceria,{{cite\|juarez:prb:07}} lead chalcogenides,{{cite\|hummer:prb:07}} CO adsorption on metals,{{cite\|stroppa:prb:07}}{{cite\|stroppa:njp:08}} excitonic properties,{{cite\|paier:prb:08}} SrTiO and BaTiO.{{cite\|wahl:prb:08}}		*Applications of hybrid functionals to selected materials: Ceria,{{cite\|juarez:prb:07}} lead chalcogenides,{{cite\|hummer:prb:07}} CO adsorption on metals,{{cite\|stroppa:prb:07}}{{cite\|stroppa:njp:08}} excitonic properties,{{cite\|paier:prb:08}} SrTiO and BaTiO, {{cite\|wahl:prb:08}} and perovskites.{{cite\|franchini:jpcm:14}}
	*~~Various benchmark studies using hybrid functionals:~~ HSEsol hybrid functional,{{cite\|schimka:jcp:11}} Analysis of the HSE parameter space,{{cite\|moussa:jcp:12}}		*HSEsol hybrid functional.{{cite\|schimka:jcp:11}}
			*Analysis of the HSE parameter space.{{cite\|moussa:jcp:12}}
			*Automated workflow for non-empirical Wannier-localized optimal tuning of range-separated hybrid functionals.{{cite\|gant:cpc:26}}

	== References ==		== References ==

Ftran at 19:59, 10 June 2026

2026-06-10T19:59:35Z

← Older revision		Revision as of 19:59, 10 June 2026
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	Note that as in most other codes, hybrid functionals are implemented in VASP within the generalized KS scheme,{{cite\|seidl:prb:96}} which means that the total energy is minimized with respect to the orbitals (instead of the electron density) as in the HF theory.		Note that as in most other codes, hybrid functionals are implemented in VASP within the generalized KS scheme,{{cite\|seidl:prb:96}} which means that the total energy is minimized with respect to the orbitals (instead of the electron density) as in the HF theory.

	VASP offers a convenient way to generate the [band structure with hybrid functionals~~\|Bandstructure_calculation_using_hybrid_functionals~~]		VASP offers a convenient way to generate the [[Band-structure calculation using hybrid functionals\|band structure with hybrid functionals]].

	== Technical points ==		== Technical points ==

Ftran at 19:53, 10 June 2026

2026-06-10T19:53:00Z

← Older revision		Revision as of 19:53, 10 June 2026
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	where <math>a</math> is the mixing parameter that determines the relative weights of HF and semilocal exchange.		where <math>a</math> is the mixing parameter that determines the relative weights of HF and semilocal exchange.

	Depending on the type of systems or the property under consideration they can be more accurate than semilocal (GGA, meta-GGA) functionals. For instance, hybrid functionals are usually more suited for calculating the electronic and magnetic properties of nonmetallic systems. They are particularly recommended for bandgap calculations{{cite\|heyd:jcp:05}}{{cite\|chen2018nonempirical}}. Polarons{{cite\|franchini:nrm:21}} or defect states{{cite\|oba:prb:08}} are among properties that can also be better described by hybrid functionals.		Depending on the type of systems or the property under consideration they can be more accurate than semilocal (GGA, meta-GGA) functionals. For instance, hybrid functionals are usually more suited for calculating the electronic and magnetic properties of nonmetallic systems. They are particularly recommended for bandgap calculations.{{cite\|heyd:jcp:05}}{{cite\|chen2018nonempirical}} Polarons{{cite\|franchini:nrm:21}} or defect states{{cite\|oba:prb:08}} are among properties that can also be better described by hybrid functionals.
	Note that hybrid functionals are often good at treating [[:Category:Strongly correlated electrons\|strongly correlated electrons]].{{cite\|liu2019assessing}}		Note that hybrid functionals are also often good at treating [[:Category:Strongly correlated electrons\|strongly correlated electrons]].{{cite\|liu2019assessing}}

	However, be aware that evaluating the HF exchange is computationally very demanding, leading to '''a computational time that is one or several orders of magnitude larger than with semilocal functionals'''.

	== Overview ==		== Overview ==

	The hybrid functionals can be divided into families according to the type of semilocal approximation (LDA, GGA, or MGGA) or the interelectronic range at which the HF exchange is applied: at full range (unscreened hybrids) or either at short or long range (called screened or range-separated hybrids). From the practical point of view, the short-range hybrid functionals like HSE06{{cite\|krukau:jcp:06}} are preferable for periodic solids, since leading to faster convergence with respect to the number of k-points (or size of the unit cell).		The hybrid functionals can be divided into families according to the type of semilocal approximation that is used (LDA, GGA, or MGGA) and the interelectronic range at which the HF exchange is applied: at full range (unscreened hybrids) or either at short or long range (called screened or range-separated hybrids). From the practical point of view, the short-range hybrid functionals like HSE06{{cite\|krukau:jcp:06}} are preferable for periodic solids, since leading to faster convergence with respect to the number of k-points (or size of the unit cell).

	The different families of hybrid functionals available in VASP are described in details at [[Hybrid_functionals: formalism\|formalism of the HF method and hybrids]] along with examples and links to the corresponding {{TAG\|INCAR}} files.		The different families of hybrid functionals available in VASP are described in details at [[Hybrid_functionals: formalism\|formalism of the HF method and hybrids]] along with examples and links to the corresponding {{TAG\|INCAR}} files.

	Details about the implementation of the unscreened hybrid functionals can be found in the work of Paier et al.{{cite\|paier:jcp:05}}, while details specific to the screened hybrid functionals can be found in Refs. {{cite\|paier:jcp:06}}{{cite\|angyan:jpa:2006}}. Refs. {{cite\|cui2018doubly}}{{cite\|liu2019assessing}} report the development of dielectric-dependent hybrid functionals, which provide very accurate band gaps and are also available in VASP.		Details about the implementation of the unscreened hybrid functionals can be found in the work of Paier et al.,{{cite\|paier:jcp:05}} while details specific to the screened hybrid functionals can be found in Refs. {{cite\|paier:jcp:06}}{{cite\|angyan:jpa:2006}} Refs. {{cite\|cui2018doubly}}{{cite\|liu2019assessing}} report the development of dielectric-dependent hybrid functionals, which provide very accurate band gaps and are also available in VASP.

			Note that as in most other codes, hybrid functionals are implemented in VASP within the generalized KS scheme,{{cite\|seidl:prb:96}} which means that the total energy is minimized with respect to the orbitals (instead of the electron density) as in the HF theory.

			VASP offers a convenient way to generate the [band structure with hybrid functionals\|Bandstructure_calculation_using_hybrid_functionals]

			== Technical points ==

	~~Note that as in most other codes, hybrid functionals are implemented in VASP within the generalized KS scheme~~{{~~cite~~\|~~seidl:prb:96}}~~, ~~which means~~ that ~~the total energy~~ is ~~minimized~~ with ~~respect to the orbitals (instead~~ of the ~~electron density) as in the HF theory~~.		* {{NB\|mind\|Evaluating the HF exchange is computationally very demanding, leading to '''a computational time that is one or several orders of magnitude larger than with semilocal functionals'''. Therefore, a proper assessment of the available computational resources and parallelization strategies becomes increasingly important.}}

	~~On a technical side, the~~ unscreened Coulomb potential used to evaluate the exchange integral in HF has an integrable singularity that leads to slow convergence with respect to supercell size (or equivalently '''k''' point sampling).		* The unscreened Coulomb potential used to evaluate the exchange integral in HF has an integrable Coulomb singularity that leads to slow convergence with respect to supercell size (or equivalently '''k''' point sampling). To make the computations feasible requires special treatment of the [[Coulomb singularity]].
	To make the computations feasible requires special treatment of the [[Coulomb singularity]].

	~~Finally~~, ~~we mention that the~~ Adaptively Compressed Exchange Operator,{{cite\|linlin:jctc:2016}}) that allows for more efficient evaluation of the Fock operator, is used if the Davidson algorithm ({{TAG\|ALGO}} = Normal) is used (see {{TAG\|LFOCKACE}} for more details).		* The [[Downsampling of the Hartree-Fock operator\|Downsampling of the HF operator]] allows for the use of a coarser '''k''' point sampling for the HF operator, and therefore faster calculations.{{cite\|angyan:jpa:2006}} However, this option should be use with care for metals.

			* The Adaptively Compressed Exchange Operator,{{cite\|linlin:jctc:2016}} that allows for more efficient evaluation of the Fock operator, is used if the Davidson algorithm ({{TAG\|ALGO}} = Normal) is used (see {{TAG\|LFOCKACE}} for more details).


	== Additional resources ==		== Additional resources ==
	=== Tutorials ===		=== Tutorials ===
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	*The B3LYP functional applied to solid state systems and its failure for metals{{cite\|paier:jcp:07}}.		*The B3LYP functional applied to solid state systems and its failure for metals{{cite\|paier:jcp:07}}.
	*Applications of hybrid functionals to selected materials: Ceria,{{cite\|juarez:prb:07}} lead chalcogenides,{{cite\|hummer:prb:07}} CO adsorption on metals,{{cite\|stroppa:prb:07}}{{cite\|stroppa:njp:08}} excitonic properties,{{cite\|paier:prb:08}} SrTiO and BaTiO.{{cite\|wahl:prb:08}}		*Applications of hybrid functionals to selected materials: Ceria,{{cite\|juarez:prb:07}} lead chalcogenides,{{cite\|hummer:prb:07}} CO adsorption on metals,{{cite\|stroppa:prb:07}}{{cite\|stroppa:njp:08}} excitonic properties,{{cite\|paier:prb:08}} SrTiO and BaTiO.{{cite\|wahl:prb:08}}
	*Various benchmark studies using hybrid functionals: HSEsol hybrid functional,{{cite\|schimka:jcp:11}} Analysis of the HSE,{{cite\|moussa:jcp:12}}		*Various benchmark studies using hybrid functionals: HSEsol hybrid functional,{{cite\|schimka:jcp:11}} Analysis of the HSE parameter space,{{cite\|moussa:jcp:12}}
	~~parameter space~~

	== References ==		== References ==

Ftran at 15:35, 10 June 2026

2026-06-10T15:35:29Z

← Older revision		Revision as of 15:35, 10 June 2026
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	However, be aware that evaluating the HF exchange is computationally very demanding, leading to '''a computational time that is one or several orders of magnitude larger than with semilocal functionals'''.		However, be aware that evaluating the HF exchange is computationally very demanding, leading to '''a computational time that is one or several orders of magnitude larger than with semilocal functionals'''.

	== ~~Theoretical background~~ ==		== Overview ==

	The hybrid functionals can be divided into families according to the type of semilocal approximation (LDA, GGA, or MGGA) or the interelectronic range at which the HF exchange is applied: at full range (unscreened hybrids) or either at short or long range (called screened or range-separated hybrids). From the practical point of view, the short-range hybrid functionals like HSE06{{cite\|krukau:jcp:06}} are preferable for periodic solids, since leading to faster convergence with respect to the number of k-points (or size of the unit cell).		The hybrid functionals can be divided into families according to the type of semilocal approximation (LDA, GGA, or MGGA) or the interelectronic range at which the HF exchange is applied: at full range (unscreened hybrids) or either at short or long range (called screened or range-separated hybrids). From the practical point of view, the short-range hybrid functionals like HSE06{{cite\|krukau:jcp:06}} are preferable for periodic solids, since leading to faster convergence with respect to the number of k-points (or size of the unit cell).
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	The different families of hybrid functionals available in VASP are described in details at [[Hybrid_functionals: formalism\|formalism of the HF method and hybrids]] along with examples and links to the corresponding {{TAG\|INCAR}} files.		The different families of hybrid functionals available in VASP are described in details at [[Hybrid_functionals: formalism\|formalism of the HF method and hybrids]] along with examples and links to the corresponding {{TAG\|INCAR}} files.

	Note that as in most other codes, hybrid functionals are implemented in VASP within the generalized KS scheme{{cite\|seidl:prb:96}}, which means that the total energy is minimized with respect to the orbitals (instead of the electron density) as in the ~~Hartree-Fock~~ theory.		Details about the implementation of the unscreened hybrid functionals can be found in the work of Paier et al.{{cite\|paier:jcp:05}}, while details specific to the screened hybrid functionals can be found in Refs. {{cite\|paier:jcp:06}}{{cite\|angyan:jpa:2006}}. Refs. {{cite\|cui2018doubly}}{{cite\|liu2019assessing}} report the development of dielectric-dependent hybrid functionals, which provide very accurate band gaps and are also available in VASP.

			Note that as in most other codes, hybrid functionals are implemented in VASP within the generalized KS scheme{{cite\|seidl:prb:96}}, which means that the total energy is minimized with respect to the orbitals (instead of the electron density) as in the HF theory.

	On a technical side, the unscreened Coulomb potential used to evaluate the exchange integral in HF has an integrable singularity that leads to slow convergence with respect to supercell size (or equivalently '''k''' point sampling).		On a technical side, the unscreened Coulomb potential used to evaluate the exchange integral in HF has an integrable singularity that leads to slow convergence with respect to supercell size (or equivalently '''k''' point sampling).
	To make the computations feasible requires special treatment of the [[Coulomb singularity]].		To make the computations feasible requires special treatment of the [[Coulomb singularity]].

			Finally, we mention that the Adaptively Compressed Exchange Operator,{{cite\|linlin:jctc:2016}}) that allows for more efficient evaluation of the Fock operator, is used if the Davidson algorithm ({{TAG\|ALGO}} = Normal) is used (see {{TAG\|LFOCKACE}} for more details).


	== Additional resources ==		== Additional resources ==
Line 36:		Line 41:
	=== Further reading ===		=== Further reading ===
	*A comprehensive study of the performance of the HSE03/HSE06 functional compared to the PBE and PBE0 functionals{{cite\|paier:jcp:06}}.		*A comprehensive study of the performance of the HSE03/HSE06 functional compared to the PBE and PBE0 functionals{{cite\|paier:jcp:06}}.
	*The B3LYP functional applied to solid state systems{{cite\|paier:jcp:07}}.		*The B3LYP functional applied to solid state systems and its failure for metals{{cite\|paier:jcp:07}}.
	*Applications of hybrid functionals to selected materials: Ceria,{{cite\|juarez:prb:07}} lead chalcogenides,{{cite\|hummer:prb:07}} CO adsorption on metals,{{cite\|stroppa:prb:07}}{{cite\|stroppa:njp:08}} excitonic properties,{{cite\|paier:prb:08}} SrTiO and BaTiO.{{cite\|wahl:prb:08}}		*Applications of hybrid functionals to selected materials: Ceria,{{cite\|juarez:prb:07}} lead chalcogenides,{{cite\|hummer:prb:07}} CO adsorption on metals,{{cite\|stroppa:prb:07}}{{cite\|stroppa:njp:08}} excitonic properties,{{cite\|paier:prb:08}} SrTiO and BaTiO.{{cite\|wahl:prb:08}}
			*Various benchmark studies using hybrid functionals: HSEsol hybrid functional,{{cite\|schimka:jcp:11}} Analysis of the HSE,{{cite\|moussa:jcp:12}}
			parameter space

	== References ==		== References ==

Ftran at 14:29, 10 June 2026

2026-06-10T14:29:04Z

← Older revision		Revision as of 14:29, 10 June 2026
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	However, be aware that evaluating the HF exchange is computationally very demanding, leading to '''a computational time that is one or several orders of magnitude larger than with semilocal functionals'''.		However, be aware that evaluating the HF exchange is computationally very demanding, leading to '''a computational time that is one or several orders of magnitude larger than with semilocal functionals'''.

	== ~~Theory~~ ==		== Theoretical background ==

	The hybrid functionals can be divided into families according to the type of semilocal approximation (LDA, GGA, or MGGA) or the interelectronic range at which the HF exchange is applied: at full range (unscreened hybrids) or either at short or long range (called screened or range-separated hybrids). From the practical point of view, the short-range hybrid functionals like HSE06{{cite\|krukau:jcp:06}} are preferable for periodic solids, since leading to faster convergence with respect to the number of k-points (or size of the unit cell).		The hybrid functionals can be divided into families according to the type of semilocal approximation (LDA, GGA, or MGGA) or the interelectronic range at which the HF exchange is applied: at full range (unscreened hybrids) or either at short or long range (called screened or range-separated hybrids). From the practical point of view, the short-range hybrid functionals like HSE06{{cite\|krukau:jcp:06}} are preferable for periodic solids, since leading to faster convergence with respect to the number of k-points (or size of the unit cell).
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	=== How to ===		=== How to ===
			*[[Hybrid_functionals: formalism\|Formalism of the HF method and hybrids]]
	*[[List_of_hybrid_functionals\|List of available hybrid functionals]] and how to specify them in the {{FILE\|INCAR}} file.		*[[List_of_hybrid_functionals\|List of available hybrid functionals]] and how to specify them in the {{FILE\|INCAR}} file.
	*[[Downsampling_of_the_Hartree-Fock_operator\|Downsampling of the Hartree-Fock operator]] to reduce the computational cost.		*[[Downsampling_of_the_Hartree-Fock_operator\|Downsampling of the Hartree-Fock operator]] to reduce the computational cost.

Ftran at 14:18, 10 June 2026

2026-06-10T14:18:38Z

← Older revision		Revision as of 14:18, 10 June 2026
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	where <math>a</math> is the mixing parameter that determines the relative weights of HF and semilocal exchange.		where <math>a</math> is the mixing parameter that determines the relative weights of HF and semilocal exchange.

	Depending on the type of systems or the property under consideration they can be more accurate than semilocal (GGA, meta-GGA) functionals. For instance, hybrid functionals are usually more suited for calculating the electronic and magnetic properties of nonmetallic systems. They are particularly recommended for bandgap calculations{{cite\|heyd:jcp:05}}{{cite\|chen2018nonempirical~~}}{{cite\|liu2019assessing~~}}. Polarons{{cite\|franchini:nrm:21}} or defect states{{cite\|oba:prb:08}} are among properties that can also be better described by hybrid functionals.		Depending on the type of systems or the property under consideration they can be more accurate than semilocal (GGA, meta-GGA) functionals. For instance, hybrid functionals are usually more suited for calculating the electronic and magnetic properties of nonmetallic systems. They are particularly recommended for bandgap calculations{{cite\|heyd:jcp:05}}{{cite\|chen2018nonempirical}}. Polarons{{cite\|franchini:nrm:21}} or defect states{{cite\|oba:prb:08}} are among properties that can also be better described by hybrid functionals.
			Note that hybrid functionals are often good at treating [[:Category:Strongly correlated electrons\|strongly correlated electrons]].{{cite\|liu2019assessing}}

	However, be aware that evaluating the HF exchange is computationally very demanding, leading to '''a computational time that is one or several orders of magnitude larger than with semilocal functionals'''.		However, be aware that evaluating the HF exchange is computationally very demanding, leading to '''a computational time that is one or several orders of magnitude larger than with semilocal functionals'''.

	The hybrid functionals can be divided into families according to the interelectronic range at which the HF exchange is applied: at full range (unscreened hybrids) or either at short or long range (called screened or range-separated hybrids). From the practical point of view, the short-range hybrid functionals like HSE06{{cite\|krukau:jcp:06}} are preferable for periodic solids, since leading to faster convergence with respect to the number of k-points (or size of the unit cell).		== Theory ==

	~~Note that as in most other codes~~, hybrid functionals ~~are implemented in VASP within the generalized KS scheme~~{{cite\|~~seidl~~:~~prb~~:96}}, ~~which means that the total energy is minimized~~ with respect to the ~~orbitals~~ (~~instead~~ of the ~~electron density~~) ~~as in the Hartree-Fock theory~~.		The hybrid functionals can be divided into families according to the type of semilocal approximation (LDA, GGA, or MGGA) or the interelectronic range at which the HF exchange is applied: at full range (unscreened hybrids) or either at short or long range (called screened or range-separated hybrids). From the practical point of view, the short-range hybrid functionals like HSE06{{cite\|krukau:jcp:06}} are preferable for periodic solids, since leading to faster convergence with respect to the number of k-points (or size of the unit cell).

	~~It is important to mention that~~ hybrid functionals are ~~computationally more expensive than semilocal methods~~.		The different families of hybrid functionals available in VASP are described in details at [[Hybrid_functionals: formalism\|formalism of the HF method and hybrids]] along with examples and links to the corresponding {{TAG\|INCAR}} files.

	~~Read more about [[Hybrid_functionals~~: ~~formalism\|formalism~~ of the ~~HF method and hybrids]]~~.		Note that as in most other codes, hybrid functionals are implemented in VASP within the generalized KS scheme{{cite\|seidl:prb:96}}, which means that the total energy is minimized with respect to the orbitals (instead of the electron density) as in the Hartree-Fock theory.

	~~The~~ unscreened Coulomb potential used to evaluate the exchange integral in ~~Hartree-Fock~~ has an integrable singularity that leads to slow convergence with respect to supercell size (or equivalently '''k''' point sampling).		On a technical side, the unscreened Coulomb potential used to evaluate the exchange integral in HF has an integrable singularity that leads to slow convergence with respect to supercell size (or equivalently '''k''' point sampling).
	To make the computations feasible requires special treatment of the [[Coulomb singularity]].		To make the computations feasible requires special treatment of the [[Coulomb singularity]].
	~~{{NB\|mind\|Hybrid functionals are often good at treating [[:Category:Strongly correlated electrons\|strongly correlated electrons]].}}~~

	== Additional resources ==		== Additional resources ==
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	*A comprehensive study of the performance of the HSE03/HSE06 functional compared to the PBE and PBE0 functionals{{cite\|paier:jcp:06}}.		*A comprehensive study of the performance of the HSE03/HSE06 functional compared to the PBE and PBE0 functionals{{cite\|paier:jcp:06}}.
	*The B3LYP functional applied to solid state systems{{cite\|paier:jcp:07}}.		*The B3LYP functional applied to solid state systems{{cite\|paier:jcp:07}}.
	*Applications of hybrid functionals to selected materials: Ceria,{{cite\|juarez:prb:07}} lead chalcogenides,{{cite\|hummer:prb:07}} CO adsorption on metals,{{cite\|stroppa:prb:07}}{{cite\|stroppa:njp~~:08}} defects in ZnO,{{cite\|oba:prb~~:08}} excitonic properties,{{cite\|paier:prb:08}} SrTiO and BaTiO.{{cite\|wahl:prb:08}}		*Applications of hybrid functionals to selected materials: Ceria,{{cite\|juarez:prb:07}} lead chalcogenides,{{cite\|hummer:prb:07}} CO adsorption on metals,{{cite\|stroppa:prb:07}}{{cite\|stroppa:njp:08}} excitonic properties,{{cite\|paier:prb:08}} SrTiO and BaTiO.{{cite\|wahl:prb:08}}

	== References ==		== References ==

Ftran at 12:14, 10 June 2026

2026-06-10T12:14:43Z

← Older revision		Revision as of 12:14, 10 June 2026
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	where <math>a</math> is the mixing parameter that determines the relative weights of HF and semilocal exchange.		where <math>a</math> is the mixing parameter that determines the relative weights of HF and semilocal exchange.

	Depending on the type of systems or the property under consideration they can be more accurate than semilocal (GGA, meta-GGA) functionals. For instance, hybrid functionals are usually more suited for calculating the electronic and magnetic properties of nonmetallic systems. They are particularly recommended for bandgap calculations{{cite\|heyd:jcp:05}}{{cite\|chen2018nonempirical}}{{cite\|liu2019assessing}}. Polarons{{cite\|franchini:nrm:21}} ~~and~~ defect states can also be better described by hybrid functionals.		Depending on the type of systems or the property under consideration they can be more accurate than semilocal (GGA, meta-GGA) functionals. For instance, hybrid functionals are usually more suited for calculating the electronic and magnetic properties of nonmetallic systems. They are particularly recommended for bandgap calculations{{cite\|heyd:jcp:05}}{{cite\|chen2018nonempirical}}{{cite\|liu2019assessing}}. Polarons{{cite\|franchini:nrm:21}} or defect states{{cite\|oba:prb:08}} are among properties that can also be better described by hybrid functionals.

	However, be aware that evaluating the HF exchange is computationally very demanding, leading to '''a computational time that is one or several orders of magnitude larger than with semilocal functionals'''.		However, be aware that evaluating the HF exchange is computationally very demanding, leading to '''a computational time that is one or several orders of magnitude larger than with semilocal functionals'''.

	~~== Theoretical background ==~~		The hybrid functionals can be divided into families according to the interelectronic range at which the HF exchange is applied: at full range (unscreened hybrids) or either at short or long range (called screened or range-separated hybrids). From the practical point of view, the short-range hybrid functionals like HSE06{{cite\|krukau:jcp:06}} are preferable for periodic solids, since leading to faster convergence with respect to the number of k-points (or size of the unit cell).

	~~In hybrid functionals the exchange part consists of a linear combination of HF and semilocal (e.g., GGA) exchange:~~
	~~:<math>~~
	~~E_{\mathrm{xc}}^{\mathrm{hybrid}}=a E_{\mathrm{x}}^{\mathrm{HF}} + (1-a)E_{\mathrm{x}}^{\mathrm{GGA}} + E_{\mathrm{c}}^{\mathrm{GGA}}~~
	~~</math>~~
	~~where <math>a</math> determines the relative amount of HF and semilocal exchange.~~ The hybrid functionals can be divided into families according to the interelectronic range at which the HF exchange is applied: at full range (unscreened hybrids) or either at short or long range (called screened or range-separated hybrids). From the practical point of view, the short-range hybrid functionals like HSE06{{cite\|krukau:jcp:06}} are preferable for periodic solids, since leading to faster convergence with respect to the number of k-points (or size of the unit cell).

	Note that as in most other codes, hybrid functionals are implemented in VASP within the generalized KS scheme{{cite\|seidl:prb:96}}, which means that the total energy is minimized with respect to the orbitals (instead of the electron density) as in the Hartree-Fock theory.		Note that as in most other codes, hybrid functionals are implemented in VASP within the generalized KS scheme{{cite\|seidl:prb:96}}, which means that the total energy is minimized with respect to the orbitals (instead of the electron density) as in the Hartree-Fock theory.

← Older revision		Revision as of 14:42, 11 June 2026
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	* {{NB\|mind\|		* {{NB\|mind\|
	*Evaluating the HF exchange is computationally very demanding, leading to '''a computational time that is one or several orders of magnitude larger than with semilocal functionals'''. Therefore, a proper assessment of the available computational resources and parallelization strategies becomes increasingly important.		*Evaluating the HF exchange is computationally very demanding, leading to '''a computational time that is one or several orders of magnitude larger than with semilocal functionals'''. Therefore, a proper assessment of the available computational resources and parallelization strategies becomes increasingly important.
	*Some properties cannot be computed using hybrid functionals because the corresponding implementations are not yet available. A non-exhaustive list includes [[Electron-phonon_interactions_theory\|~~Electron~~-phonon interactions]], [[Phonons from density-functional-perturbation theory\|~~Phonons~~ from density-functional-perturbation theory]]. However, note that the phonons ~~can be~~ calculated using the [[Phonons from finite differences\|finite differences method]].}}		*Some properties cannot be computed using hybrid functionals because the corresponding implementations are not yet available. A non-exhaustive list includes [[Electron-phonon_interactions_theory\|electron-phonon interactions]], [[Phonons from density-functional-perturbation theory\|phonons from density-functional-perturbation theory]], and [[Calculating_the_chemical_shieldings\|NMR shielding]]. However, note that hybrid functionals can be used if the phonons are calculated using the [[Phonons from finite differences\|finite differences method]].}}

	== Overview ==		== Overview ==
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	Details about the implementation of the unscreened hybrid functionals can be found in the work of Paier et al.,{{cite\|paier:jcp:05}} while details specific to the screened hybrid functionals can be found in Refs. {{cite\|paier:jcp:06}}{{cite\|angyan:jpa:2006}} Refs. {{cite\|cui2018doubly}}{{cite\|liu2019assessing}} report the development of dielectric-dependent hybrid functionals, which provide very accurate band gaps and are also available in VASP.		Details about the implementation of the unscreened hybrid functionals can be found in the work of Paier et al.,{{cite\|paier:jcp:05}} while details specific to the screened hybrid functionals can be found in Refs. {{cite\|paier:jcp:06}}{{cite\|angyan:jpa:2006}} Refs. {{cite\|cui2018doubly}}{{cite\|liu2019assessing}} report the development of dielectric-dependent hybrid functionals, which provide very accurate band gaps and are also available in VASP.

	Note that as in most other codes, hybrid functionals are implemented in VASP within the generalized KS scheme,{{cite\|seidl:prb:96}} which means that the total energy is minimized with respect to the orbitals (instead of the electron density~~) as in the HF theory~~.		Note that as in most other codes, hybrid functionals are implemented in VASP within the generalized KS scheme,{{cite\|seidl:prb:96}} which means that the total energy is minimized, as in the HF theory, with respect to the orbitals instead of the electron density.

	VASP offers a convenient way to generate the [[Band-structure calculation using hybrid functionals\|band structure with hybrid functionals]].		VASP offers a convenient way to generate the [[Band-structure calculation using hybrid functionals\|band structure with hybrid functionals]].
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	* The [[Downsampling of the Hartree-Fock operator\|Downsampling of the HF operator]] allows for the use of a coarser '''k''' point sampling for the HF operator, and therefore faster calculations.{{cite\|paier:jcp:06}} However, this option should be use with care for metals.		* The [[Downsampling of the Hartree-Fock operator\|Downsampling of the HF operator]] allows for the use of a coarser '''k''' point sampling for the HF operator, and therefore faster calculations.{{cite\|paier:jcp:06}} However, this option should be use with care for metals.

	* The Adaptively Compressed Exchange Operator,{{cite\|linlin:jctc:2016}} that allows for more efficient evaluation of the Fock operator, is used if the Davidson algorithm ({{TAG\|ALGO}} = Normal) is ~~used~~ (see {{TAG\|LFOCKACE}} for more details).		* The Adaptively Compressed Exchange Operator,{{cite\|linlin:jctc:2016}} that allows for a more efficient evaluation of the Fock operator, is used if the Davidson algorithm ({{TAG\|ALGO}} = Normal, the default) is selected (see {{TAG\|LFOCKACE}} for more details).

	== Additional resources ==		== Additional resources ==
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	=== How to ===		=== How to ===
	*[[Hybrid_functionals: formalism\|Formalism of the HF method and hybrids]]		*[[Hybrid_functionals: formalism\|Formalism of the HF method and hybrids]]. The various families are described.
	*[[List_of_hybrid_functionals\|List of available hybrid functionals]] and how to specify them in the {{FILE\|INCAR}} file.		*[[List_of_hybrid_functionals\|List of available hybrid functionals]] and how to specify them in the {{FILE\|INCAR}} file.
	*[[Downsampling_of_the_Hartree-Fock_operator\|Downsampling of the Hartree-Fock operator]] to reduce the computational cost.		*[[Downsampling_of_the_Hartree-Fock_operator\|Downsampling of the Hartree-Fock operator]] to reduce the computational cost.
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	In addition to the works already cited above, the selected publications listed below describe methodological developments or computational studies performed using the hybrid functionals implemented in VASP.		In addition to the works already cited above, the selected publications listed below describe methodological developments or computational studies performed using the hybrid functionals implemented in VASP.

	*The B3LYP functional applied to solid state systems and its failure for metals{{cite\|paier:jcp:07}}.		*The B3LYP functional applied to solid-state systems and its failure for metals{{cite\|paier:jcp:07}}.
	*Applications of hybrid functionals to selected materials: Ceria,{{cite\|juarez:prb:07}} lead chalcogenides,{{cite\|hummer:prb:07}} CO adsorption on metals,{{cite\|stroppa:prb:07}}{{cite\|stroppa:njp:08}} excitonic properties,{{cite\|paier:prb:08}} SrTiO and BaTiO, {{cite\|wahl:prb:08}} perovskites,{{cite\|franchini:jpcm:14}} and transition-metal oxides.{{cite\|gopidi:prb:26}}		*Applications of hybrid functionals to selected materials: Ceria,{{cite\|juarez:prb:07}} lead chalcogenides,{{cite\|hummer:prb:07}} CO adsorption on metals,{{cite\|stroppa:prb:07}}{{cite\|stroppa:njp:08}} excitonic properties,{{cite\|paier:prb:08}} SrTiO and BaTiO, {{cite\|wahl:prb:08}} perovskites,{{cite\|franchini:jpcm:14}} and transition-metal oxides.{{cite\|gopidi:prb:26}}
	*HSEsol hybrid functional.{{cite\|schimka:jcp:11}}		*HSEsol hybrid functional.{{cite\|schimka:jcp:11}}

← Older revision		Revision as of 19:53, 10 June 2026
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	where <math>a</math> is the mixing parameter that determines the relative weights of HF and semilocal exchange.		where <math>a</math> is the mixing parameter that determines the relative weights of HF and semilocal exchange.

	Depending on the type of systems or the property under consideration they can be more accurate than semilocal (GGA, meta-GGA) functionals. For instance, hybrid functionals are usually more suited for calculating the electronic and magnetic properties of nonmetallic systems. They are particularly recommended for bandgap calculations{{cite\|heyd:jcp:05}}{{cite\|chen2018nonempirical}}. Polarons{{cite\|franchini:nrm:21}} or defect states{{cite\|oba:prb:08}} are among properties that can also be better described by hybrid functionals.		Depending on the type of systems or the property under consideration they can be more accurate than semilocal (GGA, meta-GGA) functionals. For instance, hybrid functionals are usually more suited for calculating the electronic and magnetic properties of nonmetallic systems. They are particularly recommended for bandgap calculations.{{cite\|heyd:jcp:05}}{{cite\|chen2018nonempirical}} Polarons{{cite\|franchini:nrm:21}} or defect states{{cite\|oba:prb:08}} are among properties that can also be better described by hybrid functionals.
	Note that hybrid functionals are often good at treating [[:Category:Strongly correlated electrons\|strongly correlated electrons]].{{cite\|liu2019assessing}}		Note that hybrid functionals are also often good at treating [[:Category:Strongly correlated electrons\|strongly correlated electrons]].{{cite\|liu2019assessing}}

	However, be aware that evaluating the HF exchange is computationally very demanding, leading to '''a computational time that is one or several orders of magnitude larger than with semilocal functionals'''.

	== Overview ==		== Overview ==

	The hybrid functionals can be divided into families according to the type of semilocal approximation (LDA, GGA, or MGGA) or the interelectronic range at which the HF exchange is applied: at full range (unscreened hybrids) or either at short or long range (called screened or range-separated hybrids). From the practical point of view, the short-range hybrid functionals like HSE06{{cite\|krukau:jcp:06}} are preferable for periodic solids, since leading to faster convergence with respect to the number of k-points (or size of the unit cell).		The hybrid functionals can be divided into families according to the type of semilocal approximation that is used (LDA, GGA, or MGGA) and the interelectronic range at which the HF exchange is applied: at full range (unscreened hybrids) or either at short or long range (called screened or range-separated hybrids). From the practical point of view, the short-range hybrid functionals like HSE06{{cite\|krukau:jcp:06}} are preferable for periodic solids, since leading to faster convergence with respect to the number of k-points (or size of the unit cell).

	The different families of hybrid functionals available in VASP are described in details at [[Hybrid_functionals: formalism\|formalism of the HF method and hybrids]] along with examples and links to the corresponding {{TAG\|INCAR}} files.		The different families of hybrid functionals available in VASP are described in details at [[Hybrid_functionals: formalism\|formalism of the HF method and hybrids]] along with examples and links to the corresponding {{TAG\|INCAR}} files.

	Details about the implementation of the unscreened hybrid functionals can be found in the work of Paier et al.{{cite\|paier:jcp:05}}, while details specific to the screened hybrid functionals can be found in Refs. {{cite\|paier:jcp:06}}{{cite\|angyan:jpa:2006}}. Refs. {{cite\|cui2018doubly}}{{cite\|liu2019assessing}} report the development of dielectric-dependent hybrid functionals, which provide very accurate band gaps and are also available in VASP.		Details about the implementation of the unscreened hybrid functionals can be found in the work of Paier et al.,{{cite\|paier:jcp:05}} while details specific to the screened hybrid functionals can be found in Refs. {{cite\|paier:jcp:06}}{{cite\|angyan:jpa:2006}} Refs. {{cite\|cui2018doubly}}{{cite\|liu2019assessing}} report the development of dielectric-dependent hybrid functionals, which provide very accurate band gaps and are also available in VASP.

			Note that as in most other codes, hybrid functionals are implemented in VASP within the generalized KS scheme,{{cite\|seidl:prb:96}} which means that the total energy is minimized with respect to the orbitals (instead of the electron density) as in the HF theory.

			VASP offers a convenient way to generate the [band structure with hybrid functionals\|Bandstructure_calculation_using_hybrid_functionals]

			== Technical points ==

	~~Note that as in most other codes, hybrid functionals are implemented in VASP within the generalized KS scheme~~{{~~cite~~\|~~seidl:prb:96}}~~, ~~which means~~ that ~~the total energy~~ is ~~minimized~~ with ~~respect to the orbitals (instead~~ of the ~~electron density) as in the HF theory~~.		* {{NB\|mind\|Evaluating the HF exchange is computationally very demanding, leading to '''a computational time that is one or several orders of magnitude larger than with semilocal functionals'''. Therefore, a proper assessment of the available computational resources and parallelization strategies becomes increasingly important.}}

	~~On a technical side, the~~ unscreened Coulomb potential used to evaluate the exchange integral in HF has an integrable singularity that leads to slow convergence with respect to supercell size (or equivalently '''k''' point sampling).		* The unscreened Coulomb potential used to evaluate the exchange integral in HF has an integrable Coulomb singularity that leads to slow convergence with respect to supercell size (or equivalently '''k''' point sampling). To make the computations feasible requires special treatment of the [[Coulomb singularity]].
	To make the computations feasible requires special treatment of the [[Coulomb singularity]].

	~~Finally~~, ~~we mention that the~~ Adaptively Compressed Exchange Operator,{{cite\|linlin:jctc:2016}}) that allows for more efficient evaluation of the Fock operator, is used if the Davidson algorithm ({{TAG\|ALGO}} = Normal) is used (see {{TAG\|LFOCKACE}} for more details).		* The [[Downsampling of the Hartree-Fock operator\|Downsampling of the HF operator]] allows for the use of a coarser '''k''' point sampling for the HF operator, and therefore faster calculations.{{cite\|angyan:jpa:2006}} However, this option should be use with care for metals.

			* The Adaptively Compressed Exchange Operator,{{cite\|linlin:jctc:2016}} that allows for more efficient evaluation of the Fock operator, is used if the Davidson algorithm ({{TAG\|ALGO}} = Normal) is used (see {{TAG\|LFOCKACE}} for more details).


	== Additional resources ==		== Additional resources ==
	=== Tutorials ===		=== Tutorials ===
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	*The B3LYP functional applied to solid state systems and its failure for metals{{cite\|paier:jcp:07}}.		*The B3LYP functional applied to solid state systems and its failure for metals{{cite\|paier:jcp:07}}.
	*Applications of hybrid functionals to selected materials: Ceria,{{cite\|juarez:prb:07}} lead chalcogenides,{{cite\|hummer:prb:07}} CO adsorption on metals,{{cite\|stroppa:prb:07}}{{cite\|stroppa:njp:08}} excitonic properties,{{cite\|paier:prb:08}} SrTiO and BaTiO.{{cite\|wahl:prb:08}}		*Applications of hybrid functionals to selected materials: Ceria,{{cite\|juarez:prb:07}} lead chalcogenides,{{cite\|hummer:prb:07}} CO adsorption on metals,{{cite\|stroppa:prb:07}}{{cite\|stroppa:njp:08}} excitonic properties,{{cite\|paier:prb:08}} SrTiO and BaTiO.{{cite\|wahl:prb:08}}
	*Various benchmark studies using hybrid functionals: HSEsol hybrid functional,{{cite\|schimka:jcp:11}} Analysis of the HSE,{{cite\|moussa:jcp:12}}		*Various benchmark studies using hybrid functionals: HSEsol hybrid functional,{{cite\|schimka:jcp:11}} Analysis of the HSE parameter space,{{cite\|moussa:jcp:12}}
	~~parameter space~~

	== References ==		== References ==