List of hybrid functionals: Difference between revisions

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A certain number of hybrid functionals are available in VASP. How to select an hybrid functional in the {{FILE|INCAR}} file is shown below for a certain number of them, including examples with Libxc.
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{{cite|heyd:jcp:03}}{{cite|heyd:jcp:04}}{{cite|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:
: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="DDH (dielectric-dependent hybrid)">
*Dielectric-dependent hybrid (DDH) functional{{cite|chen2018nonempirical}}{{cite|cui2018doubly}}
{{TAG|LMODELHF}} = .TRUE.
{{TAG|AEXX}} = <math>\varepsilon^{-1}</math>
{{TAG|HFSCREEN}} = <math>\mu</math>
  {{TAG|GGA}} = PE
  {{TAG|GGA}} = PE
:where <math>\varepsilon^{-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.
</span>
</span>


<span id="HSE06">
<span id="RSHXLDA">
*HSE06{{cite|krukau:jcp:06}}
*RSHXLDA{{cite|gerber:jcp:2007}}
  {{TAG|LHFCALC}}  = .TRUE.
  {{TAG|LHFCALC}} = .TRUE.
  {{TAG|HFSCREEN}} = 0.2
  {{TAG|LRHFCALC}} = .TRUE.
{{TAG|GGA}} = CA (or PZ)
  {{TAG|HFSCREEN}} = 0.75 # Optimal value for solids


: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:
:with the default values {{TAG|AEXX}}=1, {{TAG|AGGAX}}=1-{{TAG|AEXX}}=0, {{TAG|AGGAC}}=1, and {{TAG|ALDAC}}=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
:with the default values {{TAG|AEXX}}=1, {{TAG|AGGAX}}=1-{{TAG|AEXX}}=0, {{TAG|AGGAC}}=1, and {{TAG|ALDAC}}=1.
</span>
</span>


*PBE0
=== Unscreened hybrid functionals ===
 
*PBEh (PBE0){{cite|perdew:jcp:1996}}{{cite|ernzerhof:jcp:99}}{{cite|adamo:jcp:1999}}
  {{TAG|LHFCALC}} = .TRUE.
  {{TAG|LHFCALC}} = .TRUE.
: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:
{{TAG|GGA}} = PE


{{TAG|GGA}} = PE
:with the default values {{TAG|AEXX}}=0.25, {{TAG|AGGAX}}=1-{{TAG|AEXX}}=0.75, {{TAG|AGGAC}}=1, and {{TAG|ALDAC}}=1.


*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 76:
  {{TAG|ALDAC}}  = 0.19
  {{TAG|ALDAC}}  = 0.19


:and using PBE {{FILE|POTCAR}} files.
:with the default value {{TAG|ALDAX}}=1-{{TAG|AEXX}}=0.8.
 
*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
 
*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
 
*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.


*Hartree-Fock
*Hartree-Fock (no correlation)
  {{TAG|LHFCALC}} = .TRUE.  
  {{TAG|LHFCALC}} = .TRUE.  
  {{TAG|AEXX}}    = 1.0
  {{TAG|AEXX}}    = 1
{{TAG|ALDAC}}   = 0.0
 
{{TAG|AGGAC}}   = 0.0
:with the default values {{TAG|AGGAX}}=1-{{TAG|AEXX}}=0, {{TAG|ALDAC}}=0, and {{TAG|AGGAC}}=0.


:with the default values {{TAG|AGGAX}}=1-{{TAG|AEXX}}=0.0, and using the PBE {{FILE|POTCAR}} files.
{{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.}}


{{sc|Specific hybrid functionals|Examples|Examples that use this tag}}
== Related tags and articles ==
{{TAG|GGA}},
{{TAG|METAGGA}},
{{TAG|LIBXC1}},
{{TAG|LIBXC2}},
{{TAG|AEXX}},
{{TAG|ALDAX}},
{{TAG|ALDAC}},
{{TAG|AGGAX}},
{{TAG|AGGAC}},
{{TAG|AMGGAX}},
{{TAG|AMGGAC}},
{{TAG|LHFCALC}},
{{TAG|HFSCREEN}},
{{TAG|LMODELHF}},
{{TAG|LRHFCALC}},
[[Hybrid_functionals:_formalism|Hybrid functionals: formalism]]


== References ==
== References ==
Line 51: Line 129:


----
----
[[The_VASP_Manual|Contents]]
[[Category:Exchange-correlation functionals]][[Category:Hybrid_functionals]][[Category:Howto]]
[[Category:Exchange-correlation functionals]][[Category:Hybrids]]

Latest revision as of 11:52, 14 June 2024

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) functional[7][8]
LMODELHF = .TRUE.
AEXX = 
HFSCREEN = 
GGA = PE
where is the inverse dielectric constant and is the range-separation parameter. See a detailed description of the DDH functionals in the documentation for the LMODELHF tag.

LHFCALC = .TRUE.
LRHFCALC = .TRUE.
GGA = CA (or PZ)
HFSCREEN = 0.75 # Optimal value for solids
with the default values AEXX=1, AGGAX=1-AEXX=0, AGGAC=1, and ALDAC=1.

LHFCALC = .TRUE.
LRHFCALC = .TRUE.
GGA = PE
HFSCREEN = 0.91 # Optimal value for the enthalpies of formation of molecules
with the default values AEXX=1, AGGAX=1-AEXX=0, AGGAC=1, and ALDAC=1.

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[14] 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, ALDAX, ALDAC, AGGAX, AGGAC, AMGGAX, AMGGAC, LHFCALC, HFSCREEN, LMODELHF, 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. 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).
  8. 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).
  9. 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).
  10. I. C. Gerber and J. G. Ángyán, Hybrid functional with separated range, Chem. Phys. Lett. 415, 100 (2005).
  11. J. P. Perdew, M. Ernzerhof, and K. Burke, J. Chem. Phys. 105, 9982 (1996).
  12. M. Ernzerhof and G. E. Scuseria, J. Chem. Phys. 110, 5029 (1999).
  13. C. Adamo and V. Barone, Phys. Rev. Lett., 110, 6158 (1999).
  14. P. J. Stephens, F. J. Devlin, C. F. Chabalowski, and M. J. Frisch, J. Phys. Chem. 98, 11623 (1994).
  15. A. D. Becke, J. Chem. Phys. 98, 5648 (1993).
  16. D. I. Bilc, R. Orlando, R. Shaltaf, G.-M. Rignanese, J. Iniguez, and P. Ghosez, Phys. Rev. B 77, 165107 (2008).