Category:Hybrid functionals - Revision history

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

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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 ==

Ftran at 07:31, 10 May 2022

2022-05-10T07:31:54Z

← Older revision		Revision as of 07:31, 10 May 2022
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	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. It is important to mention that hybrid functionals are computationally more expensive than semilocal methods.		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.

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

Ftran at 07:29, 10 May 2022

2022-05-10T07:29:34Z

← Older revision		Revision as of 07:29, 10 May 2022
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	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 ~~as in the Hartree-Fock theory~~ the total energy is minimized with respect to the orbitals instead of the electron density. It is important to mention that hybrid functionals are computationally more expensive than semilocal methods.		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. 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]].		More details about the formalism of the HF method and hybrids can be found [[Hybrid_functionals: formalism\|here]].

Ftran at 07:28, 10 May 2022

2022-05-10T07:28:15Z

← Older revision		Revision as of 07:28, 10 May 2022
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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 as in the Hartree-Fock theory the total energy is minimized with respect to the orbitals instead of the electron density. It is important to mention that hybrid functionals are computationally more expensive than semilocal methods.		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 as in the Hartree-Fock theory the total energy is minimized with respect to the orbitals instead of the electron density. It is important to mention that hybrid functionals are computationally more expensive than semilocal methods.

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

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