Category:Hybrid functionals - Revision history

Csheldon at 13:23, 24 March 2026

2026-03-24T13:23:40Z

← Older revision		Revision as of 13:23, 24 March 2026
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	To make the computations feasible requires special treatment of the [[Coulomb singularity]].		To make the computations feasible requires special treatment of the [[Coulomb singularity]].

	== ~~How to~~ ==		== Additional resources ==
			=== Tutorials ===
			*Tutorial for {{Tutorial\|hybrids:part1\|hybrid calculations}}.

			=== Lectures ===
			*Lecture on {{Video\|hybrid:henrique:2022\|hybrid functionals}}.

			=== How to ===
	*[[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.
	*[[Band-structure calculation using hybrid functionals\|band-structure calculation using hybrid functionals]].		*[[Band-structure calculation using hybrid functionals\|band-structure calculation using hybrid functionals]].

	=~~= Tutorials ==~~		=== Further reading ===
	*Tutorial for [https://vasp.at/tutorials/latest/hybrids/part1/ hybrid calculations].
	*Lecture for [https://youtu.be/zNc0bx8FTlU hybrid functionals].

	== 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{{cite\|paier:jcp:07}}.
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	== References ==		== References ==
	~~<references/>~~

	----		----

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

Ftran at 21:14, 23 October 2025

2025-10-23T21:14:44Z

← Older revision		Revision as of 21:14, 23 October 2025
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	In hybrid functionals the exchange part consists of a linear combination of HF and semilocal (e.g., GGA) exchange:		In hybrid functionals the exchange part consists of a linear combination of HF and semilocal (e.g., GGA) exchange:
	:<math>		:<math>
	E_{\mathrm{xc}}^{\mathrm{hybrid}}=~~\alpha~~ E_{\mathrm{x}}^{\mathrm{HF}} + (1-~~\alpha~~)E_{\mathrm{x}}^{\mathrm{GGA}} + E_{\mathrm{c}}^{\mathrm{GGA}}		E_{\mathrm{xc}}^{\mathrm{hybrid}}=a E_{\mathrm{x}}^{\mathrm{HF}} + (1-a)E_{\mathrm{x}}^{\mathrm{GGA}} + E_{\mathrm{c}}^{\mathrm{GGA}}
	</math>		</math>
	where <math>~~\alpha~~</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).		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.

Csheldon: /* Tutorials */

2025-09-22T10:08:13Z

Tutorials

← Older revision		Revision as of 10:08, 22 September 2025
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	== Tutorials ==		== Tutorials ==
	*Tutorial for [https://vasp.at/tutorials/latest/hybrids/part1/ hybrid calculations].		*Tutorial for [https://vasp.at/tutorials/latest/hybrids/part1/ hybrid calculations].
			*Lecture for [https://youtu.be/zNc0bx8FTlU hybrid functionals].

	== Further reading ==		== Further reading ==

Csheldon at 13:22, 28 May 2025

2025-05-28T13:22:51Z

← Older revision		Revision as of 13:22, 28 May 2025
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	*[[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.
	*[[Band-structure calculation using hybrid functionals\|band-structure calculation using hybrid functionals]].		*[[Band-structure calculation using hybrid functionals\|band-structure calculation using hybrid functionals]].

			== Tutorials ==
			*Tutorial for [https://vasp.at/tutorials/latest/hybrids/part1/ hybrid calculations].

	== Further reading ==		== Further reading ==

Ftran at 14:15, 6 March 2025

2025-03-06T14:15:02Z

← Older revision		Revision as of 14:15, 6 March 2025
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	E_{\mathrm{xc}}^{\mathrm{hybrid}}=\alpha E_{\mathrm{x}}^{\mathrm{HF}} + (1-\alpha)E_{\mathrm{x}}^{\mathrm{GGA}} + E_{\mathrm{c}}^{\mathrm{GGA}}		E_{\mathrm{xc}}^{\mathrm{hybrid}}=\alpha E_{\mathrm{x}}^{\mathrm{HF}} + (1-\alpha)E_{\mathrm{x}}^{\mathrm{GGA}} + E_{\mathrm{c}}^{\mathrm{GGA}}
	</math>		</math>
	where <math>\alpha</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 ~~HSE~~ are preferable for periodic solids, since leading to faster convergence with respect to the number of k-points (or size of the unit cell).		where <math>\alpha</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.

Ftran at 14:11, 25 February 2025

2025-02-25T14:11:28Z

← Older revision		Revision as of 14:11, 25 February 2025
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	E_{\mathrm{xc}}^{\mathrm{hybrid}}=\alpha E_{\mathrm{x}}^{\mathrm{HF}} + (1-\alpha)E_{\mathrm{x}}^{\mathrm{GGA}} + E_{\mathrm{c}}^{\mathrm{GGA}}		E_{\mathrm{xc}}^{\mathrm{hybrid}}=\alpha E_{\mathrm{x}}^{\mathrm{HF}} + (1-\alpha)E_{\mathrm{x}}^{\mathrm{GGA}} + E_{\mathrm{c}}^{\mathrm{GGA}}
	</math>		</math>
	where <math>\alpha</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 at long range (called screened or range-separated hybrids). From the practical point of view, the short-range hybrid functionals like HSE are preferable for periodic solids, since leading to faster convergence with respect to the number of k-points (or size of the unit cell).		where <math>\alpha</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 HSE 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.

Ftran at 14:00, 25 February 2025

2025-02-25T14:00:15Z

← Older revision		Revision as of 14:00, 25 February 2025
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	== How to ==		== How to ==

	[[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.		*[[Band-structure calculation using hybrid functionals\|band-structure calculation using hybrid functionals]].

	~~How to do a~~ [[Band-structure calculation using hybrid functionals\|band-structure calculation using hybrid functionals]].

	== Further reading ==		== Further reading ==

Ftran at 12:30, 19 October 2023

2023-10-19T12:30:43Z

← Older revision		Revision as of 12:30, 19 October 2023
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	'''Hybrid functionals''' mix the Hartree-Fock (HF) and Kohn-Sham theories{{cite\|becke:jcp:93}} and can be more accurate than semilocal methods, e.g., {{TAG\|GGA}}, in particular for nonmetallic systems. They are for instance suited for band-gap calculations. ~~There are several~~ hybrid functionals ~~that~~ are available in VASP.		'''Hybrid functionals''' mix the Hartree-Fock (HF) and Kohn-Sham theories{{cite\|becke:jcp:93}} and can be more accurate than semilocal methods, e.g., {{TAG\|GGA}}, in particular for nonmetallic systems. They are for instance suited for band-gap calculations. Several hybrid functionals are available in VASP.

	== Theoretical background ==		== Theoretical background ==

Miranda.henrique: /* Theoretical background */

2022-07-19T20:35:47Z

Theoretical background

← Older revision		Revision as of 20:35, 19 July 2022
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	Read more about [[Hybrid_functionals: formalism\|formalism of the HF method and hybrids]].		Read more about [[Hybrid_functionals: formalism\|formalism of the HF method and hybrids]].

			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).
			To make the computations feasible requires special treatment of the [[Coulomb singularity]].

	== How to ==		== How to ==

Huebsch at 13:02, 11 May 2022

2022-05-11T13:02:28Z

← Older revision		Revision as of 13:02, 11 May 2022
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	Hybrid functionals~~, which~~ mix the Hartree-Fock (HF) and Kohn-Sham theories{{cite\|becke:jcp:93}}, can be more accurate than semilocal methods ~~like~~ GGA, in particular for nonmetallic systems. They are suited for band gap calculations ~~for instance~~. ~~Hybrid~~ functionals are available in VASP.		'''Hybrid functionals''' mix the Hartree-Fock (HF) and Kohn-Sham theories{{cite\|becke:jcp:93}} and can be more accurate than semilocal methods, e.g., {{TAG\|GGA}}, in particular for nonmetallic systems. They are for instance suited for band-gap calculations. There are several hybrid functionals that are available in VASP.

	== Theoretical background ==		== Theoretical background ==
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	E_{\mathrm{xc}}^{\mathrm{hybrid}}=\alpha E_{\mathrm{x}}^{\mathrm{HF}} + (1-\alpha)E_{\mathrm{x}}^{\mathrm{GGA}} + E_{\mathrm{c}}^{\mathrm{GGA}}		E_{\mathrm{xc}}^{\mathrm{hybrid}}=\alpha E_{\mathrm{x}}^{\mathrm{HF}} + (1-\alpha)E_{\mathrm{x}}^{\mathrm{GGA}} + E_{\mathrm{c}}^{\mathrm{GGA}}
	</math>		</math>
	where <math>\alpha</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 at long range (called screened or range-separated hybrids). From the practical point of view the short-range hybrid functionals like HSE are preferable for periodic solids, since leading to faster convergence with respect to the number of k-points (or size of the unit cell).		where <math>\alpha</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 at long range (called screened or range-separated hybrids). From the practical point of view, the short-range hybrid functionals like HSE 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.
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	It is important to mention that hybrid functionals are computationally more expensive than semilocal methods.		It is important to mention that hybrid functionals are computationally more expensive than semilocal methods.

	~~More details~~ about ~~the~~ formalism of the HF method and hybrids ~~can be found [[Hybrid_functionals: formalism\|here~~]].		Read more about [[Hybrid_functionals: formalism\|formalism of the HF method and hybrids]].

	== How to ==		== How to ==

	[[List_of_hybrid_functionals\|List of available hybrid functionals]] and how to specify them in {{FILE\|INCAR}}.		[[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]].		[[Downsampling_of_the_Hartree-Fock_operator\|Downsampling of the Hartree-Fock operator]] to reduce the computational cost.

			How to do a [[Band-structure calculation using hybrid functionals\|band-structure calculation using hybrid functionals]].

	== Further reading ==		== Further reading ==