List of hybrid functionals: Difference between revisions

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A certain number of [[Hybrid functionals: formalism|unscreened and screened hybrid functionals]] are available in VASP, and furthermore if VASP is [[Makefile.include#Libxc_.28optional.29|compiled]] with the library of exchange-correlation functionals Libxc, then most of the existing hybrid functionals can be used{{cite|libxc_list}}. Examples of {{FILE|INCAR}} files are shown below. Since VASP.6.4.0 it is possible to use hybrid functionals that mix meta-GGA and Hartree-Fock exchange. Note that it is in general recommended to use the PBE {{FILE|POTCAR}} files for hybrid functionals.
=== Range-separated hybrid functionals ===
<span id="HSE06">
*HSE06{{cite|krukau:jcp:06}}
{{TAG|LHFCALC}} = .TRUE.
{{TAG|GGA}} = PE
{{TAG|HFSCREEN}} = 0.2
:with the default values {{TAG|AEXX}}=0.25, {{TAG|AGGAX}}=1-{{TAG|AEXX}}=0.75, {{TAG|AGGAC}}=1, and {{TAG|ALDAC}}=1.
</span>
<span id="HSE03">
<span id="HSE03">
*HSE03<ref name="heyd:jcp:03"/><ref name="heyd:jcp:04"/><ref name="heyd:jcp:06"/>
*HSE03{{cite|heyd:jcp:03}}{{cite|heyd:jcp:04}}{{cite|heyd:jcp:06}}
  {{TAG|LHFCALC}} = .TRUE.
{{TAG|LHFCALC}} = .TRUE.
  {{TAG|HFSCREEN}} = 0.3
{{TAG|GGA}} = PE
{{TAG|HFSCREEN}} = 0.3
 
:with the default values {{TAG|AEXX}}=0.25, {{TAG|AGGAX}}=1-{{TAG|AEXX}}=0.75, {{TAG|AGGAC}}=1, and {{TAG|ALDAC}}=1.
</span>
 
<span id="HSEsol">
*HSEsol{{cite|schimka:jcp:11}}
  {{TAG|LHFCALC}} = .TRUE.
{{TAG|GGA}} = PS
  {{TAG|HFSCREEN}} = 0.2


:With the default values {{TAG|AEXX}}=0.25, {{TAG|AGGAX}}=1-{{TAG|AEXX}}=0.75, {{TAG|AGGAC}}=1.0 and {{TAG|ALDAC}}=1.0, and using the PBE {{FILE|POTCAR}} files or with the following additional entry in the {{FILE|INCAR}} file:
:with the default values {{TAG|AEXX}}=0.25, {{TAG|AGGAX}}=1-{{TAG|AEXX}}=0.75, {{TAG|AGGAC}}=1, and {{TAG|ALDAC}}=1.
</span>


<span id="RS-DDH">
*Dielectric-dependent hybrid (DDH) RS-DDH{{cite|skone:prb:2016}}
{{TAG|LHFCALC}} = .TRUE.
{{TAG|LMODELHF}} = .TRUE.
{{TAG|AEXX}} = <math>\varepsilon_{\infty}^{-1}</math>
{{TAG|BEXX}} = 0.25
{{TAG|HFSCREEN}} = <math>\mu</math>
  {{TAG|GGA}} = PE
  {{TAG|GGA}} = PE
:where <math>\varepsilon_{\infty}^{-1}</math> is the inverse dielectric constant and <math>\mu</math> is the range-separation parameter. See a detailed description of the DDH functionals in the documentation for the {{TAG|LMODELHF}} tag as well as [[Hybrid_functionals:_formalism#HF_exchange_at_short_range_and_long_range_%28error-function_screening%29_with_different_mixings|here]].
</span>
</span>


<span id="HSE06">
<span id="DD-RSH-CAM">
*HSE06<ref name="krukau:jcp:06"/>
*Dielectric-dependent hybrid (DDH) DD-RSH-CAM,{{cite|chen2018nonempirical}}DSH{{cite|cui2018doubly}}
  {{TAG|LHFCALC}}  = .TRUE.
  {{TAG|LHFCALC}} = .TRUE.
  {{TAG|HFSCREEN}} = 0.2
  {{TAG|LMODELHF}} = .TRUE.
{{TAG|AEXX}} = <math>\varepsilon_{\infty}^{-1}</math>
  {{TAG|HFSCREEN}} = <math>\mu</math>
{{TAG|GGA}} = PE
 
:with the default value {{TAG|BEXX}}=1 and where <math>\varepsilon_{\infty}^{-1}</math> is the inverse dielectric constant and <math>\mu</math> is the range-separation parameter. See a detailed description of the DDH functionals in the documentation for the {{TAG|LMODELHF}} tag as well as [[Hybrid_functionals:_formalism#HF_exchange_at_short_range_and_long_range_%28error-function_screening%29_with_different_mixings|here]].
</span>


:With the defaults: {{TAG|AEXX}}=0.25, {{TAG|AGGAX}}=1-{{TAG|AEXX}}=0.75, {{TAG|AGGAC}}=1.0 and {{TAG|ALDAC}}=1.0
<span id="RSHXLDA">
:Using PBE {{FILE|POTCAR}} files or with the following additional entry in the {{FILE|INCAR}} file:
*RSHXLDA{{cite|gerber:jcp:2007}}
{{TAG|LHFCALC}} = .TRUE.
{{TAG|LRHFCALC}} = .TRUE.
{{TAG|GGA}} = CA (or PZ)
{{TAG|HFSCREEN}} = 0.75 # Optimal value for solids
{{TAG|ALDAC}} = 1.0     # Necessary since correlation is by default not included when {{TAG|AEXX}}=1


:with the default value {{TAG|AEXX}}=1.
</span>
<span id="RSHXPBE">
*RSHXPBE{{cite|gerber:cpl:2005}}
{{TAG|LHFCALC}} = .TRUE.
{{TAG|LRHFCALC}} = .TRUE.
  {{TAG|GGA}} = PE
  {{TAG|GGA}} = PE
{{TAG|HFSCREEN}} = 0.91 # Optimal value for the enthalpies of formation of molecules
{{TAG|ALDAC}} = 1.0    # Necessary since correlation is by default not included when {{TAG|AEXX}}=1
{{TAG|AGGAC}} = 1.0    # Necessary since correlation is by default not included when {{TAG|AEXX}}=1
:with the default values {{TAG|AEXX}}=1.
</span>
</span>


*PBE0
<span id="sX-LDA">
*sX-LDA{{cite|bylander:prb:90}}
  {{TAG|LHFCALC}} = .TRUE.
  {{TAG|LHFCALC}} = .TRUE.
:With the defaults: {{TAG|AEXX}}=0.25, {{TAG|AGGAX}}=1-{{TAG|AEXX}}=0.75, {{TAG|AGGAC}}=1.0 and {{TAG|ALDAC}}=1.0
{{TAG|LTHOMAS}} = .TRUE.
:Using PBE {{FILE|POTCAR}} files or with the following additional entry in the {{FILE|INCAR}} file:
{{TAG|GGA}} = CA (or PZ)
{{TAG|HFSCREEN}} = <math>k_{\rm TF}</math>
{{TAG|ALDAC}} = 1.0    # Necessary since correlation is by default not included when {{TAG|AEXX}}=1
{{TAG|AGGAC}} = 1.0     # Necessary since correlation is by default not included when {{TAG|AEXX}}=1
 
:with the default value {{TAG|AEXX}}=1 and where <math>k_{\rm TF}</math> is the Thomas-Fermi screening. More details can be found at {{TAG|LTHOMAS}} as well as [[Hybrid_functionals:_formalism#HF_exchange_at_short_range_(exponential_screening)|here]].
</span>
 
=== Unscreened hybrid functionals ===


<span id="PBE0">
*PBE0 (PBEh){{cite|perdew:jcp:1996}}{{cite|ernzerhof:jcp:99}}{{cite|adamo:jcp:1999}}
{{TAG|LHFCALC}} = .TRUE.
  {{TAG|GGA}} = PE
  {{TAG|GGA}} = PE


*B3LYP
:with the default values {{TAG|AEXX}}=0.25, {{TAG|AGGAX}}=1-{{TAG|AEXX}}=0.75, {{TAG|AGGAC}}=1, and {{TAG|ALDAC}}=1.
</span>
 
<span id="B3LYP">
*B3LYP{{cite|stephens:jpc:94}} with VWN3 (or VWN5) for LDA correlation
  {{TAG|LHFCALC}} = .TRUE.  
  {{TAG|LHFCALC}} = .TRUE.  
  {{TAG|GGA}}    = B3  
  {{TAG|GGA}}    = B3 (or B5)
  {{TAG|AEXX}}    = 0.2
  {{TAG|AEXX}}    = 0.2
  {{TAG|AGGAX}}  = 0.72  
  {{TAG|AGGAX}}  = 0.72  
Line 35: Line 107:
  {{TAG|ALDAC}}  = 0.19
  {{TAG|ALDAC}}  = 0.19


:Using PBE {{FILE|POTCAR}} files
:with the default value {{TAG|ALDAX}}=1-{{TAG|AEXX}}=0.8.
</span>


*Hartree-Fock
<span id="B3PW91">
*B3PW91{{cite|becke:jcp:93}} (using Libxc, see the tag {{TAG|LIBXC1}})
{{TAG|LHFCALC}} = .TRUE.
{{TAG|GGA}} = LIBXC
{{TAG|LIBXC1}} = HYB_GGA_XC_B3PW91 # or 401
{{TAG|AEXX}} = 0.2
</span>
 
<span id="B1-WC">
*B1-WC{{cite|bilc:prb:08}} (using Libxc, see the tag {{TAG|LIBXC1}})
{{TAG|LHFCALC}} = .TRUE.
{{TAG|GGA}} = LIBXC
{{TAG|LIBXC1}} = HYB_GGA_XC_B1WC # or 412
{{TAG|AEXX}} = 0.16
</span>
 
<span id="SCAN0">
*SCAN0
{{TAG|LHFCALC}} = .TRUE.
{{TAG|METAGGA}} = SCAN
 
:with the default values {{TAG|AEXX}}=0.25, {{TAG|AMGGAX}}=1-{{TAG|AEXX}}=0.75, and {{TAG|AMGGAC}}=1.
</span>
 
<span id="Hartree-Fock">
*Hartree-Fock (no correlation)
  {{TAG|LHFCALC}} = .TRUE.  
  {{TAG|LHFCALC}} = .TRUE.  
  {{TAG|AEXX}}    = 1.0
  {{TAG|AEXX}}    = 1
{{TAG|ALDAC}}  = 0.0
</span>
{{TAG|AGGAC}}  = 0.0


:With the default: {{TAG|AGGAX}}=1-{{TAG|AEXX}}=0.0
:with the default values {{TAG|AGGAX}}=1-{{TAG|AEXX}}=0, {{TAG|ALDAC}}=0, and {{TAG|AGGAC}}=0.
:Using PBE {{FILE|POTCAR}} files


{{sc|Specific hybrid functionals|Examples|Examples that use this tag}}
{{NB|mind|Note the default values when {{TAG|LHFCALC}}{{=}}.TRUE.:
*{{TAG|ALDAX}}, {{TAG|AGGAX}} and {{TAG|AMGGAX}} are set to 1-{{TAG|AEXX}}.
*{{TAG|ALDAC}}, {{TAG|AGGAC}} and {{TAG|AMGGAC}} are set to 0 if {{TAG|AEXX}}{{=}}1 or to 1 if {{TAG|AEXX}}<math>\neq</math>1.}}
 
== Related tags and articles ==
{{TAG|GGA}},
{{TAG|METAGGA}},
{{TAG|LIBXC1}},
{{TAG|LIBXC2}},
{{TAG|AEXX}},
{{TAG|BEXX}},
{{TAG|ALDAX}},
{{TAG|ALDAC}},
{{TAG|AGGAX}},
{{TAG|AGGAC}},
{{TAG|AMGGAX}},
{{TAG|AMGGAC}},
{{TAG|LHFCALC}},
{{TAG|HFSCREEN}},
{{TAG|LMODELHF}},
{{TAG|LTHOMAS}},
{{TAG|LRHFCALC}},
[[Hybrid_functionals:_formalism|Hybrid functionals: formalism]]


== References ==
== References ==
<references>
<references/>
<ref name="heyd:jcp:03">[http://dx.doi.org/10.1063/1.1564060 J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 118, 8207 (2003).]</ref>
 
<ref name="heyd:jcp:04">[http://dx.doi.org/10.1063/1.1760074 J. Heyd and G. E. Scuseria, J. Chem. Phys. 121, 1187 (2004).]</ref>
<ref name="heyd:jcp:06">[http://dx.doi.org/10.1063/1.2204597 J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 124, 219906 (2006).]</ref>
<ref name="krukau:jcp:06">[http://dx.doi.org/10.1063/1.2404663 A. V. Krukau , O. A. Vydrov, A. F. Izmaylov, and G. E. Scuseria, J. Chem. Phys. 125, 224106 (2006).]</ref>
</references>
----
----
[[The_VASP_Manual|Contents]]
[[Category:Exchange-correlation functionals]][[Category:Hybrid_functionals]][[Category:Howto]]
[[Category:Exchange-correlation functionals]][[Category:Hybrids]]

Latest revision as of 11:25, 9 February 2026

A certain number of unscreened and screened hybrid functionals are available in VASP, and furthermore if VASP is compiled with the library of exchange-correlation functionals Libxc, then most of the existing hybrid functionals can be used[1]. Examples of INCAR files are shown below. Since VASP.6.4.0 it is possible to use hybrid functionals that mix meta-GGA and Hartree-Fock exchange. Note that it is in general recommended to use the PBE POTCAR files for hybrid functionals.

Range-separated hybrid functionals

LHFCALC = .TRUE.
GGA = PE
HFSCREEN = 0.2
with the default values AEXX=0.25, AGGAX=1-AEXX=0.75, AGGAC=1, and ALDAC=1.

LHFCALC = .TRUE.
GGA = PE
HFSCREEN = 0.3
with the default values AEXX=0.25, AGGAX=1-AEXX=0.75, AGGAC=1, and ALDAC=1.

LHFCALC = .TRUE.
GGA = PS
HFSCREEN = 0.2
with the default values AEXX=0.25, AGGAX=1-AEXX=0.75, AGGAC=1, and ALDAC=1.

  • Dielectric-dependent hybrid (DDH) RS-DDH[7]
LHFCALC = .TRUE.
LMODELHF = .TRUE.
AEXX = [math]\displaystyle{ \varepsilon_{\infty}^{-1} }[/math]
BEXX = 0.25
HFSCREEN = [math]\displaystyle{ \mu }[/math]
GGA = PE
where [math]\displaystyle{ \varepsilon_{\infty}^{-1} }[/math] is the inverse dielectric constant and [math]\displaystyle{ \mu }[/math] is the range-separation parameter. See a detailed description of the DDH functionals in the documentation for the LMODELHF tag as well as here.

  • Dielectric-dependent hybrid (DDH) DD-RSH-CAM,[8]DSH[9]
LHFCALC = .TRUE.
LMODELHF = .TRUE.
AEXX = [math]\displaystyle{ \varepsilon_{\infty}^{-1} }[/math]
HFSCREEN = [math]\displaystyle{ \mu }[/math]
GGA = PE
with the default value BEXX=1 and where [math]\displaystyle{ \varepsilon_{\infty}^{-1} }[/math] is the inverse dielectric constant and [math]\displaystyle{ \mu }[/math] is the range-separation parameter. See a detailed description of the DDH functionals in the documentation for the LMODELHF tag as well as here.

LHFCALC = .TRUE.
LRHFCALC = .TRUE.
GGA = CA (or PZ)
HFSCREEN = 0.75 # Optimal value for solids
ALDAC = 1.0     # Necessary since correlation is by default not included when AEXX=1
with the default value AEXX=1.

LHFCALC = .TRUE.
LRHFCALC = .TRUE.
GGA = PE
HFSCREEN = 0.91 # Optimal value for the enthalpies of formation of molecules
ALDAC = 1.0     # Necessary since correlation is by default not included when AEXX=1
AGGAC = 1.0     # Necessary since correlation is by default not included when AEXX=1
with the default values AEXX=1.

LHFCALC = .TRUE.
LTHOMAS = .TRUE.
GGA = CA (or PZ)
HFSCREEN = [math]\displaystyle{ k_{\rm TF} }[/math]
ALDAC = 1.0     # Necessary since correlation is by default not included when AEXX=1
AGGAC = 1.0     # Necessary since correlation is by default not included when AEXX=1
with the default value AEXX=1 and where [math]\displaystyle{ k_{\rm TF} }[/math] is the Thomas-Fermi screening. More details can be found at LTHOMAS as well as here.

Unscreened hybrid functionals

LHFCALC = .TRUE.
GGA = PE
with the default values AEXX=0.25, AGGAX=1-AEXX=0.75, AGGAC=1, and ALDAC=1.

  • B3LYP[16] with VWN3 (or VWN5) for LDA correlation
LHFCALC = .TRUE. 
GGA     = B3 (or B5)
AEXX    = 0.2
AGGAX   = 0.72 
AGGAC   = 0.81 
ALDAC   = 0.19
with the default value ALDAX=1-AEXX=0.8.

LHFCALC = .TRUE.
GGA = LIBXC
LIBXC1 = HYB_GGA_XC_B3PW91 # or 401
AEXX = 0.2


LHFCALC = .TRUE.
GGA = LIBXC
LIBXC1 = HYB_GGA_XC_B1WC # or 412
AEXX = 0.16

  • SCAN0
LHFCALC = .TRUE.
METAGGA = SCAN
with the default values AEXX=0.25, AMGGAX=1-AEXX=0.75, and AMGGAC=1.

  • Hartree-Fock (no correlation)
LHFCALC = .TRUE. 
AEXX    = 1

with the default values AGGAX=1-AEXX=0, ALDAC=0, and AGGAC=0.


Mind: Note the default values when LHFCALC=.TRUE.:

Related tags and articles

GGA, METAGGA, LIBXC1, LIBXC2, AEXX, BEXX, ALDAX, ALDAC, AGGAX, AGGAC, AMGGAX, AMGGAC, LHFCALC, HFSCREEN, LMODELHF, LTHOMAS, LRHFCALC, Hybrid functionals: formalism

References

  1. ↑ https://libxc.gitlab.io/functionals/
  2. ↑ A. V. Krukau , O. A. Vydrov, A. F. Izmaylov, and G. E. Scuseria, J. Chem. Phys. 125, 224106 (2006).
  3. ↑ J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 118, 8207 (2003).
  4. ↑ J. Heyd and G. E. Scuseria, J. Chem. Phys. 121, 1187 (2004).
  5. ↑ J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 124, 219906 (2006).
  6. ↑ L. Schimka, J. Harl, and G. Kresse, J. Chem. Phys. 134, 024116 (2011).
  7. ↑ J. H. Skone, M. Govoni, and G. Galli, Nonempirical range-separated hybrid functionals for solids and molecules, Phys. Rev. B 93, 235106 (2016).
  8. ↑ W. Chen, G. Miceli, G.M. Rignanese, and A. Pasquarello, Nonempirical dielectric-dependent hybrid functional with range separation for semiconductors and insulators, Phys. Rev. Mater. 2, 073803 (2018).
  9. ↑ Z.H. Cui, Y.C. Wang, M.Y. Zhang, X. Xu, and H. Jiang, Doubly Screened Hybrid Functional: An Accurate First-Principles Approach for Both Narrow- and Wide-Gap Semiconductors J. Phys. Chem. Lett., 9, 2338-2345 (2018).
  10. ↑ I. C. Gerber, J. G. Ángyán, M. Marsman, and G. Kresse, Range separated hybrid density functional with long-range Hartree-Fock exchange applied to solids, J. Chem. Phys. 127, 054101 (2007).
  11. ↑ I. C. Gerber and J. G. Ángyán, Hybrid functional with separated range, Chem. Phys. Lett. 415, 100 (2005).
  12. ↑ D. M. Bylander and L. Kleinman, Phys. Rev. B 41, 7868 (1990).
  13. ↑ J. P. Perdew, M. Ernzerhof, and K. Burke, J. Chem. Phys. 105, 9982 (1996).
  14. ↑ M. Ernzerhof and G. E. Scuseria, J. Chem. Phys. 110, 5029 (1999).
  15. ↑ C. Adamo and V. Barone, Phys. Rev. Lett., 110, 6158 (1999).
  16. ↑ P. J. Stephens, F. J. Devlin, C. F. Chabalowski, and M. J. Frisch, J. Phys. Chem. 98, 11623 (1994).
  17. ↑ A. D. Becke, J. Chem. Phys. 98, 5648 (1993).
  18. ↑ D. I. Bilc, R. Orlando, R. Shaltaf, G.-M. Rignanese, J. Iniguez, and P. Ghosez, Phys. Rev. B 77, 165107 (2008).
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