LMODELHF - Revision history

Ftran at 11:18, 2 March 2026

2026-03-02T11:18:41Z

← Older revision		Revision as of 11:18, 2 March 2026
Line 1:		Line 1:
	{{TAGDEF\|LMODELHF\|.TRUE. {{!}} .FALSE.\|.FALSE.}}		{{TAGDEF\|LMODELHF\|.TRUE. {{!}} .FALSE.\|.FALSE.}}

	Description: {{TAG\|LMODELHF}} selects dielectric-dependent hybrid functionals with ~~full exchange in the short-range,~~ and {{TAG\|~~AEXX~~}} in the long-range.		Description: {{TAG\|LMODELHF}} selects dielectric-dependent range-separated hybrid functionals with {{TAG\|AEXX}} and {{TAG\|BEXX}} for the exact Hartree-Fock exchange at long- and short-range, respectively.
	----		----
	{{TAG\|LMODELHF}}=.TRUE. ~~selects the~~ range separated hybrid ~~functional suggested in Ref~~. {{~~cite~~\|~~chen2018nonempirical~~}}		By setting {{TAG\|LMODELHF}}=.TRUE. various types of range-separated hybrid functionals using the error function for the screening can be specified. The general form of hybrid functionals that can be constructed with {{TAG\|LMODELHF}} is given by
	and ~~Ref~~. {{~~cite~~\|~~cui2018doubly~~}} ~~under~~ the ~~name dielectric-dependent hybrid functionals~~ (~~DDH~~) and ~~doubly screened hybrid~~ (~~DSH~~) functionals~~, respectively~~. These ~~two~~ hybrid functionals are ~~both~~ based on a common model for the dielectric function, but differ in the way how the range-separation parameters are obtained from first principles calculations. Their connection and performance have been discussed for instance in Ref. {{cite\|liu2019assessing}}. In principle,
			:<math>E_{\mathrm{xc}}^{\mathrm{hybrid}}=a_{\mathrm{SR}} E_{\mathrm{x,SR}}^{\mathrm{HF}}(\mu) + a_{\mathrm{LR}} E_{\mathrm{x,LR}}^{\mathrm{HF}}(\mu) + (1-a_{\mathrm{SR}})E_{\mathrm{x,SR}}^{\mathrm{SL}}(\mu) + (1-a_{\mathrm{LR}})E_{\mathrm{x,LR}}^{\mathrm{SL}}(\mu) + E_{\mathrm{c}}^{\mathrm{SL}}</math>

			where
			*<math>a_{\mathrm{SR}}</math> ({{TAG\|BEXX}}) and <math>a_{\mathrm{LR}}</math> ({{TAG\|AEXX}}) are the '''mixing parameters (fraction of HF exchange) at short and long range''', respectively.
			*<math>\mu</math> ({{TAG\|HFSCREEN}}) is the '''screening parameter''' that determines the separation between short range (SR) and long range (LR).

			Examples of such functionals are those proposed in Refs. {{cite\|skone:prb:2016}}{{cite\|chen2018nonempirical}}{{cite\|cui2018doubly}}. These hybrid functionals are based on a common model for the dielectric function, but differ in the way how the range-separation parameters are obtained from first-principles calculations. Their connection and performance have been discussed for instance in Ref. {{cite\|liu2019assessing}}. In principle,
	they can be considered to be a smartly constructed approximation to COH-SEX (local Coulomb hole plus screened exchange),		they can be considered to be a smartly constructed approximation to COH-SEX (local Coulomb hole plus screened exchange),
	albeit fulfilling many important constraints that the exact exchange correlation functional must observe.		albeit fulfilling many important constraints that the exact exchange correlation functional must observe.
Line 10:		Line 17:
	The corresponding functional has been available in VASP since VASP.5.2 released in 2009 (before the two publications), although the gradient contribution had been erroneously implemented in all VASP.5 releases and is only correct in VASP.6. The related bug fix has been made available by the authors of Ref. {{cite\|cui2018doubly}}. The nonlocal exchange part of the functional has also been used and documented in Ref. {{cite\|bokdam:scr:2016}} and is covered in [[Improving the dielectric function]].		The corresponding functional has been available in VASP since VASP.5.2 released in 2009 (before the two publications), although the gradient contribution had been erroneously implemented in all VASP.5 releases and is only correct in VASP.6. The related bug fix has been made available by the authors of Ref. {{cite\|cui2018doubly}}. The nonlocal exchange part of the functional has also been used and documented in Ref. {{cite\|bokdam:scr:2016}} and is covered in [[Improving the dielectric function]].

	~~Typically the user will need~~ to ~~set the following tags~~ in the INCAR file:		An example of tags to specify in the [[INCAR]] file is given for the DD-RSH-CAM functional:{{cite\|chen2018nonempirical}}{{cite\|cui2018doubly}}

	{{TAGBL\|LHFCALC}} = .TRUE.		{{TAGBL\|LHFCALC}} = .TRUE.
	{{TAGBL\|LMODELHF}} = .TRUE.		{{TAGBL\|LMODELHF}} = .TRUE.
	{{TAGBL\|~~HFSCREEN~~}} = 1.26		{{TAGBL\|AEXX}} = <math>\varepsilon_{\infty}^{-1}</math>
	{{TAGBL\|AEXX}} = 0.1		{{TAGBL\|BEXX}} = 1.0 #The default value. Available since VASP.6.6.0.
			{{TAGBL\|HFSCREEN}} = <math>\mu</math>
			{{TAGBL\|GGA}} = PE

			where <math>\varepsilon_{\infty}^{-1}</math> is the inverse dielectric constant and <math>\mu</math> is the screening parameter.
			{{TAG\|AEXX}} and {{TAG\|BEXX}} specify the amount of exact exchange in the long and short range, respectively, that is for short (<math> \mathbf{G} \to 0 </math>) and large (<math> \mathbf{G} \to \infty </math>) wave vectors, respectively. The screening parameter {{TAG\|HFSCREEN}} determines how quickly the nonlocal exchange changes from {{TAG\|AEXX}} to {{TAG\|BEXX}}.

	~~In this case,~~ {{~~TAG~~\|~~AEXX~~}} specifies the amount of exact exchange in the long range, that is for short wave vectors (<math> \mathbf{G} \to 0 </math>). In the short range, that is for large wave vectors, always the full nonlocal exchange is used. The {{~~TAG~~\|~~HFSCREEN~~}} ~~determines how quickly the nonlocal exchange changes from~~ {{~~TAG~~\|~~AEXX~~}} ~~to 1~~.		Other examples of dielectric-dependent range-separated functionals proposed in the literature{{cite\|skone:prb:2016}}{{cite\|chen2018nonempirical}}{{cite\|cui2018doubly}} can be found [[Hybrid_functionals:_formalism#HF_exchange_at_short_range_and_long_range_%28error-function_screening%29_with_different_mixings\|here]] and their corresponding INCAR files at [[list_of_hybrid_functionals\|list of hybrid functionals]].
	{{NB\|mind\|If {{TAG\|LMODELHF}}{{=}}.TRUE., then {{TAG\|LHFCALC}}{{=}}.TRUE. is automatically set.}}		{{NB\|mind\|
			*If {{TAG\|LMODELHF}}{{=}}.TRUE., then {{TAG\|LHFCALC}}{{=}}.TRUE. is automatically set.
			*The {{TAG\|BEXX}} tag is available only since VASP.6.6.0. {{TAG\|BEXX}} was hard-coded to 1 in versions prior to VASP.6.6.0.
			}}

	Specifically, in VASP, the Coulomb kernel <math> 4 \pi e^2 / (\mathbf{q}+\mathbf{G})^2</math> in the exact exchange is multiplied by a model for the dielectric function <math> \epsilon^{-1} (\mathbf{q}+\mathbf{G})</math>:		Specifically, in VASP, the Coulomb kernel <math> 4 \pi e^2 / (\mathbf{q}+\mathbf{G})^2</math> in the exact exchange is multiplied by a model for the dielectric function <math> \epsilon^{-1} (\mathbf{q}+\mathbf{G})</math>:

	:<math> \epsilon^{-1} (\mathbf{q}+\mathbf{G})=1-(1-{{\varepsilon}_{\infty}^{-1}})\text{exp}(-\frac{\|\mathbf{q+G}\|^2}{4{\mu}^2})</math>.		:<math> \epsilon^{-1} (\mathbf{q}+\mathbf{G})=1-(1-{{\varepsilon}_{\infty}^{-1}})\text{exp}\left(-\frac{\|\mathbf{q+G}\|^2}{4{\mu}^2}\right)</math>.

	where <math> \mu </math> corresponds to {{TAG\|HFSCREEN}}, and <math> {{\varepsilon}_{\infty}^{-1}} </math> is specified by {{TAG\|AEXX}}. In real space this correspond to a Coulomb kernel		where <math> \mu </math> corresponds to {{TAG\|HFSCREEN}}, and <math> {{\varepsilon}_{\infty}^{-1}} </math> is specified by {{TAG\|AEXX}}. In real space this correspond to a Coulomb kernel
	:<math> V(r) =(1-(1-{{\varepsilon}_{\infty}^{-1}})\text{erf}( {\mu} r)) \frac{e^2}{r} </math>.		:<math> V(r) =\left[1-\left(1-{{\varepsilon}_{\infty}^{-1}}\right)\text{erf}( {\mu} r)\right] \frac{e^2}{r} </math>.


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	{{TAG\|HFSCREEN}},		{{TAG\|HFSCREEN}},
	{{TAG\|AEXX}},		{{TAG\|AEXX}},
			{{TAG\|BEXX}},
			{{TAG\|LTHOMAS}},
	{{TAG\|LRHFCALC}},		{{TAG\|LRHFCALC}},
	~~{{TAG\|LTHOMAS}},~~
	[[list_of_hybrid_functionals\|List of hybrid functionals]],		[[list_of_hybrid_functionals\|List of hybrid functionals]],
	[[Hybrid_functionals:_formalism\|Hybrid functionals: formalism]],		[[Hybrid_functionals:_formalism\|Hybrid functionals: formalism]],

Ftran: Undo revision 33829 by Ftran (talk)

2026-02-03T15:56:18Z

Undo revision 33829 by Ftran (talk)

← Older revision		Revision as of 15:56, 3 February 2026
Line 62:		Line 62:
	{{TAG\|HFSCREEN}},		{{TAG\|HFSCREEN}},
	{{TAG\|AEXX}},		{{TAG\|AEXX}},
	~~{{TAG\|BEXX}},~~
	{{TAG\|LRHFCALC}},		{{TAG\|LRHFCALC}},
	{{TAG\|LTHOMAS}},		{{TAG\|LTHOMAS}},

Ftran at 16:39, 2 February 2026

2026-02-02T16:39:10Z

← Older revision		Revision as of 16:39, 2 February 2026
Line 62:		Line 62:
	{{TAG\|HFSCREEN}},		{{TAG\|HFSCREEN}},
	{{TAG\|AEXX}},		{{TAG\|AEXX}},
			{{TAG\|BEXX}},
	{{TAG\|LRHFCALC}},		{{TAG\|LRHFCALC}},
	{{TAG\|LTHOMAS}},		{{TAG\|LTHOMAS}},

Ftran at 21:11, 21 October 2025

2025-10-21T21:11:46Z

← Older revision		Revision as of 21:11, 21 October 2025
Line 57:		Line 57:
	ZnTe 1.12		ZnTe 1.12
	These values have been obtained from fits of the dielectric function using the Nanoquanta kernel and partially self-consistent GW calculations as used in Ref. {{cite\|grueneis2014ionization}}. The values can be also estimated from simple dimensional scaling relations of the valence electron density. Furthermore band gap predictions are not very sensitive to the choice of {{TAG\|HFSCREEN}}.		These values have been obtained from fits of the dielectric function using the Nanoquanta kernel and partially self-consistent GW calculations as used in Ref. {{cite\|grueneis2014ionization}}. The values can be also estimated from simple dimensional scaling relations of the valence electron density. Furthermore band gap predictions are not very sensitive to the choice of {{TAG\|HFSCREEN}}.

	== Related tags and articles ==		== Related tags and articles ==
	{{TAG\|LHFCALC}},		{{TAG\|LHFCALC}},
	{{TAG\|HFSCREEN}},		{{TAG\|HFSCREEN}},
	{{TAG\|AEXX}},		{{TAG\|AEXX}},
	~~[[Hybrid functionals: formalism#Thomas-Fermi exponential screening with short-range Hartree-Fock exchange~~\|~~Thomas-Fermi screening]]~~,		{{TAG\|LRHFCALC}},
			{{TAG\|LTHOMAS}},
	[[list_of_hybrid_functionals\|List of hybrid functionals]],		[[list_of_hybrid_functionals\|List of hybrid functionals]],
	[[Hybrid_functionals:_formalism\|Hybrid functionals: formalism]],		[[Hybrid_functionals:_formalism\|Hybrid functionals: formalism]],

Huebsch: /* References */

2024-05-23T07:29:35Z

References

← Older revision		Revision as of 07:29, 23 May 2024
Line 68:		Line 68:
	<references/>		<references/>

	~~----~~
	[[Category:INCAR tag]][[Category:Exchange-correlation functionals]][[Category:Hybrid_functionals]]		[[Category:INCAR tag]][[Category:Exchange-correlation functionals]][[Category:Hybrid_functionals]]

Huebsch: /* References */

2024-05-23T07:29:25Z

References

← Older revision		Revision as of 07:29, 23 May 2024
Line 67:		Line 67:
	== References ==		== References ==
	<references/>		<references/>
	~~----~~
	~~{{sc\|LMODELHF\|Examples\|Examples that use this tag}}~~
	----		----
	[[Category:INCAR tag]][[Category:Exchange-correlation functionals]][[Category:Hybrid_functionals]]		[[Category:INCAR tag]][[Category:Exchange-correlation functionals]][[Category:Hybrid_functionals]]

Huebsch at 06:30, 21 February 2024

2024-02-21T06:30:29Z

← Older revision		Revision as of 06:30, 21 February 2024
Line 70:		Line 70:
	{{sc\|LMODELHF\|Examples\|Examples that use this tag}}		{{sc\|LMODELHF\|Examples\|Examples that use this tag}}
	----		----
	[[Category:INCAR tag]][[Category:Exchange-correlation functionals]][[Category:Hybrid_functionals~~]][[Category:VASP6~~]]		[[Category:INCAR tag]][[Category:Exchange-correlation functionals]][[Category:Hybrid_functionals]]

Ftran at 11:40, 19 October 2023

2023-10-19T11:40:47Z

← Older revision		Revision as of 11:40, 19 October 2023
Line 18:		Line 18:

	In this case, {{TAG\|AEXX}} specifies the amount of exact exchange in the long range, that is for short wave vectors (<math> \mathbf{G} \to 0 </math>). In the short range, that is for large wave vectors, always the full nonlocal exchange is used. The {{TAG\|HFSCREEN}} determines how quickly the nonlocal exchange changes from {{TAG\|AEXX}} to 1.		In this case, {{TAG\|AEXX}} specifies the amount of exact exchange in the long range, that is for short wave vectors (<math> \mathbf{G} \to 0 </math>). In the short range, that is for large wave vectors, always the full nonlocal exchange is used. The {{TAG\|HFSCREEN}} determines how quickly the nonlocal exchange changes from {{TAG\|AEXX}} to 1.
			{{NB\|mind\|If {{TAG\|LMODELHF}}{{=}}.TRUE., then {{TAG\|LHFCALC}}{{=}}.TRUE. is automatically set.}}

	Specifically, in VASP, the Coulomb kernel <math> 4 \pi e^2 / (\mathbf{q}+\mathbf{G})^2</math> in the exact exchange is multiplied by a model for the dielectric function <math> \epsilon^{-1} (\mathbf{q}+\mathbf{G})</math>:		Specifically, in VASP, the Coulomb kernel <math> 4 \pi e^2 / (\mathbf{q}+\mathbf{G})^2</math> in the exact exchange is multiplied by a model for the dielectric function <math> \epsilon^{-1} (\mathbf{q}+\mathbf{G})</math>:

Ftran at 12:57, 18 October 2023

2023-10-18T12:57:25Z

← Older revision		Revision as of 12:57, 18 October 2023
Line 60:		Line 60:
	{{TAG\|HFSCREEN}},		{{TAG\|HFSCREEN}},
	{{TAG\|AEXX}},		{{TAG\|AEXX}},
	[[Hybrid functionals: formalism#~~Thomas_Fermi~~\|Thomas-Fermi screening]],		[[Hybrid functionals: formalism#Thomas-Fermi exponential screening with short-range Hartree-Fock exchange\|Thomas-Fermi screening]],
	[[list_of_hybrid_functionals\|List of hybrid functionals]],		[[list_of_hybrid_functionals\|List of hybrid functionals]],
	[[Hybrid_functionals:_formalism\|Hybrid functionals: formalism]],		[[Hybrid_functionals:_formalism\|Hybrid functionals: formalism]],

Ftran at 09:26, 18 October 2023

2023-10-18T09:26:04Z

← Older revision		Revision as of 09:26, 18 October 2023
Line 61:		Line 61:
	{{TAG\|AEXX}},		{{TAG\|AEXX}},
	[[Hybrid functionals: formalism#Thomas_Fermi\|Thomas-Fermi screening]],		[[Hybrid functionals: formalism#Thomas_Fermi\|Thomas-Fermi screening]],
	[[list_of_hybrid_functionals\|List of hybrid functionals]]		[[list_of_hybrid_functionals\|List of hybrid functionals]],
			[[Hybrid_functionals:_formalism\|Hybrid functionals: formalism]],

	== References ==		== References ==

← Older revision		Revision as of 11:18, 2 March 2026
Line 1:		Line 1:
	{{TAGDEF\|LMODELHF\|.TRUE. {{!}} .FALSE.\|.FALSE.}}		{{TAGDEF\|LMODELHF\|.TRUE. {{!}} .FALSE.\|.FALSE.}}

	Description: {{TAG\|LMODELHF}} selects dielectric-dependent hybrid functionals with ~~full exchange in the short-range,~~ and {{TAG\|~~AEXX~~}} in the long-range.		Description: {{TAG\|LMODELHF}} selects dielectric-dependent range-separated hybrid functionals with {{TAG\|AEXX}} and {{TAG\|BEXX}} for the exact Hartree-Fock exchange at long- and short-range, respectively.
	----		----
	{{TAG\|LMODELHF}}=.TRUE. ~~selects the~~ range separated hybrid ~~functional suggested in Ref~~. {{~~cite~~\|~~chen2018nonempirical~~}}		By setting {{TAG\|LMODELHF}}=.TRUE. various types of range-separated hybrid functionals using the error function for the screening can be specified. The general form of hybrid functionals that can be constructed with {{TAG\|LMODELHF}} is given by
	and ~~Ref~~. {{~~cite~~\|~~cui2018doubly~~}} ~~under~~ the ~~name dielectric-dependent hybrid functionals~~ (~~DDH~~) and ~~doubly screened hybrid~~ (~~DSH~~) functionals~~, respectively~~. These ~~two~~ hybrid functionals are ~~both~~ based on a common model for the dielectric function, but differ in the way how the range-separation parameters are obtained from first principles calculations. Their connection and performance have been discussed for instance in Ref. {{cite\|liu2019assessing}}. In principle,
			:<math>E_{\mathrm{xc}}^{\mathrm{hybrid}}=a_{\mathrm{SR}} E_{\mathrm{x,SR}}^{\mathrm{HF}}(\mu) + a_{\mathrm{LR}} E_{\mathrm{x,LR}}^{\mathrm{HF}}(\mu) + (1-a_{\mathrm{SR}})E_{\mathrm{x,SR}}^{\mathrm{SL}}(\mu) + (1-a_{\mathrm{LR}})E_{\mathrm{x,LR}}^{\mathrm{SL}}(\mu) + E_{\mathrm{c}}^{\mathrm{SL}}</math>

			where
			*<math>a_{\mathrm{SR}}</math> ({{TAG\|BEXX}}) and <math>a_{\mathrm{LR}}</math> ({{TAG\|AEXX}}) are the '''mixing parameters (fraction of HF exchange) at short and long range''', respectively.
			*<math>\mu</math> ({{TAG\|HFSCREEN}}) is the '''screening parameter''' that determines the separation between short range (SR) and long range (LR).

			Examples of such functionals are those proposed in Refs. {{cite\|skone:prb:2016}}{{cite\|chen2018nonempirical}}{{cite\|cui2018doubly}}. These hybrid functionals are based on a common model for the dielectric function, but differ in the way how the range-separation parameters are obtained from first-principles calculations. Their connection and performance have been discussed for instance in Ref. {{cite\|liu2019assessing}}. In principle,
	they can be considered to be a smartly constructed approximation to COH-SEX (local Coulomb hole plus screened exchange),		they can be considered to be a smartly constructed approximation to COH-SEX (local Coulomb hole plus screened exchange),
	albeit fulfilling many important constraints that the exact exchange correlation functional must observe.		albeit fulfilling many important constraints that the exact exchange correlation functional must observe.
Line 10:		Line 17:
	The corresponding functional has been available in VASP since VASP.5.2 released in 2009 (before the two publications), although the gradient contribution had been erroneously implemented in all VASP.5 releases and is only correct in VASP.6. The related bug fix has been made available by the authors of Ref. {{cite\|cui2018doubly}}. The nonlocal exchange part of the functional has also been used and documented in Ref. {{cite\|bokdam:scr:2016}} and is covered in [[Improving the dielectric function]].		The corresponding functional has been available in VASP since VASP.5.2 released in 2009 (before the two publications), although the gradient contribution had been erroneously implemented in all VASP.5 releases and is only correct in VASP.6. The related bug fix has been made available by the authors of Ref. {{cite\|cui2018doubly}}. The nonlocal exchange part of the functional has also been used and documented in Ref. {{cite\|bokdam:scr:2016}} and is covered in [[Improving the dielectric function]].

	~~Typically the user will need~~ to ~~set the following tags~~ in the INCAR file:		An example of tags to specify in the [[INCAR]] file is given for the DD-RSH-CAM functional:{{cite\|chen2018nonempirical}}{{cite\|cui2018doubly}}

	{{TAGBL\|LHFCALC}} = .TRUE.		{{TAGBL\|LHFCALC}} = .TRUE.
	{{TAGBL\|LMODELHF}} = .TRUE.		{{TAGBL\|LMODELHF}} = .TRUE.
	{{TAGBL\|~~HFSCREEN~~}} = 1.26		{{TAGBL\|AEXX}} = <math>\varepsilon_{\infty}^{-1}</math>
	{{TAGBL\|AEXX}} = 0.1		{{TAGBL\|BEXX}} = 1.0 #The default value. Available since VASP.6.6.0.
			{{TAGBL\|HFSCREEN}} = <math>\mu</math>
			{{TAGBL\|GGA}} = PE

			where <math>\varepsilon_{\infty}^{-1}</math> is the inverse dielectric constant and <math>\mu</math> is the screening parameter.
			{{TAG\|AEXX}} and {{TAG\|BEXX}} specify the amount of exact exchange in the long and short range, respectively, that is for short (<math> \mathbf{G} \to 0 </math>) and large (<math> \mathbf{G} \to \infty </math>) wave vectors, respectively. The screening parameter {{TAG\|HFSCREEN}} determines how quickly the nonlocal exchange changes from {{TAG\|AEXX}} to {{TAG\|BEXX}}.

	~~In this case,~~ {{~~TAG~~\|~~AEXX~~}} specifies the amount of exact exchange in the long range, that is for short wave vectors (<math> \mathbf{G} \to 0 </math>). In the short range, that is for large wave vectors, always the full nonlocal exchange is used. The {{~~TAG~~\|~~HFSCREEN~~}} ~~determines how quickly the nonlocal exchange changes from~~ {{~~TAG~~\|~~AEXX~~}} ~~to 1~~.		Other examples of dielectric-dependent range-separated functionals proposed in the literature{{cite\|skone:prb:2016}}{{cite\|chen2018nonempirical}}{{cite\|cui2018doubly}} can be found [[Hybrid_functionals:_formalism#HF_exchange_at_short_range_and_long_range_%28error-function_screening%29_with_different_mixings\|here]] and their corresponding INCAR files at [[list_of_hybrid_functionals\|list of hybrid functionals]].
	{{NB\|mind\|If {{TAG\|LMODELHF}}{{=}}.TRUE., then {{TAG\|LHFCALC}}{{=}}.TRUE. is automatically set.}}		{{NB\|mind\|
			*If {{TAG\|LMODELHF}}{{=}}.TRUE., then {{TAG\|LHFCALC}}{{=}}.TRUE. is automatically set.
			*The {{TAG\|BEXX}} tag is available only since VASP.6.6.0. {{TAG\|BEXX}} was hard-coded to 1 in versions prior to VASP.6.6.0.
			}}

	Specifically, in VASP, the Coulomb kernel <math> 4 \pi e^2 / (\mathbf{q}+\mathbf{G})^2</math> in the exact exchange is multiplied by a model for the dielectric function <math> \epsilon^{-1} (\mathbf{q}+\mathbf{G})</math>:		Specifically, in VASP, the Coulomb kernel <math> 4 \pi e^2 / (\mathbf{q}+\mathbf{G})^2</math> in the exact exchange is multiplied by a model for the dielectric function <math> \epsilon^{-1} (\mathbf{q}+\mathbf{G})</math>:

	:<math> \epsilon^{-1} (\mathbf{q}+\mathbf{G})=1-(1-{{\varepsilon}_{\infty}^{-1}})\text{exp}(-\frac{\|\mathbf{q+G}\|^2}{4{\mu}^2})</math>.		:<math> \epsilon^{-1} (\mathbf{q}+\mathbf{G})=1-(1-{{\varepsilon}_{\infty}^{-1}})\text{exp}\left(-\frac{\|\mathbf{q+G}\|^2}{4{\mu}^2}\right)</math>.

	where <math> \mu </math> corresponds to {{TAG\|HFSCREEN}}, and <math> {{\varepsilon}_{\infty}^{-1}} </math> is specified by {{TAG\|AEXX}}. In real space this correspond to a Coulomb kernel		where <math> \mu </math> corresponds to {{TAG\|HFSCREEN}}, and <math> {{\varepsilon}_{\infty}^{-1}} </math> is specified by {{TAG\|AEXX}}. In real space this correspond to a Coulomb kernel
	:<math> V(r) =(1-(1-{{\varepsilon}_{\infty}^{-1}})\text{erf}( {\mu} r)) \frac{e^2}{r} </math>.		:<math> V(r) =\left[1-\left(1-{{\varepsilon}_{\infty}^{-1}}\right)\text{erf}( {\mu} r)\right] \frac{e^2}{r} </math>.


Line 62:		Line 77:
	{{TAG\|HFSCREEN}},		{{TAG\|HFSCREEN}},
	{{TAG\|AEXX}},		{{TAG\|AEXX}},
			{{TAG\|BEXX}},
			{{TAG\|LTHOMAS}},
	{{TAG\|LRHFCALC}},		{{TAG\|LRHFCALC}},
	~~{{TAG\|LTHOMAS}},~~
	[[list_of_hybrid_functionals\|List of hybrid functionals]],		[[list_of_hybrid_functionals\|List of hybrid functionals]],
	[[Hybrid_functionals:_formalism\|Hybrid functionals: formalism]],		[[Hybrid_functionals:_formalism\|Hybrid functionals: formalism]],

← Older revision		Revision as of 15:56, 3 February 2026
Line 62:		Line 62:
	{{TAG\|HFSCREEN}},		{{TAG\|HFSCREEN}},
	{{TAG\|AEXX}},		{{TAG\|AEXX}},
	~~{{TAG\|BEXX}},~~
	{{TAG\|LRHFCALC}},		{{TAG\|LRHFCALC}},
	{{TAG\|LTHOMAS}},		{{TAG\|LTHOMAS}},

← Older revision		Revision as of 16:39, 2 February 2026
Line 62:		Line 62:
	{{TAG\|HFSCREEN}},		{{TAG\|HFSCREEN}},
	{{TAG\|AEXX}},		{{TAG\|AEXX}},
			{{TAG\|BEXX}},
	{{TAG\|LRHFCALC}},		{{TAG\|LRHFCALC}},
	{{TAG\|LTHOMAS}},		{{TAG\|LTHOMAS}},

← Older revision		Revision as of 21:11, 21 October 2025
Line 57:		Line 57:
	ZnTe 1.12		ZnTe 1.12
	These values have been obtained from fits of the dielectric function using the Nanoquanta kernel and partially self-consistent GW calculations as used in Ref. {{cite\|grueneis2014ionization}}. The values can be also estimated from simple dimensional scaling relations of the valence electron density. Furthermore band gap predictions are not very sensitive to the choice of {{TAG\|HFSCREEN}}.		These values have been obtained from fits of the dielectric function using the Nanoquanta kernel and partially self-consistent GW calculations as used in Ref. {{cite\|grueneis2014ionization}}. The values can be also estimated from simple dimensional scaling relations of the valence electron density. Furthermore band gap predictions are not very sensitive to the choice of {{TAG\|HFSCREEN}}.

	== Related tags and articles ==		== Related tags and articles ==
	{{TAG\|LHFCALC}},		{{TAG\|LHFCALC}},
	{{TAG\|HFSCREEN}},		{{TAG\|HFSCREEN}},
	{{TAG\|AEXX}},		{{TAG\|AEXX}},
	~~[[Hybrid functionals: formalism#Thomas-Fermi exponential screening with short-range Hartree-Fock exchange~~\|~~Thomas-Fermi screening]]~~,		{{TAG\|LRHFCALC}},
			{{TAG\|LTHOMAS}},
	[[list_of_hybrid_functionals\|List of hybrid functionals]],		[[list_of_hybrid_functionals\|List of hybrid functionals]],
	[[Hybrid_functionals:_formalism\|Hybrid functionals: formalism]],		[[Hybrid_functionals:_formalism\|Hybrid functionals: formalism]],

← Older revision		Revision as of 12:57, 18 October 2023
Line 60:		Line 60:
	{{TAG\|HFSCREEN}},		{{TAG\|HFSCREEN}},
	{{TAG\|AEXX}},		{{TAG\|AEXX}},
	[[Hybrid functionals: formalism#~~Thomas_Fermi~~\|Thomas-Fermi screening]],		[[Hybrid functionals: formalism#Thomas-Fermi exponential screening with short-range Hartree-Fock exchange\|Thomas-Fermi screening]],
	[[list_of_hybrid_functionals\|List of hybrid functionals]],		[[list_of_hybrid_functionals\|List of hybrid functionals]],
	[[Hybrid_functionals:_formalism\|Hybrid functionals: formalism]],		[[Hybrid_functionals:_formalism\|Hybrid functionals: formalism]],