List of hybrid functionals: Difference between revisions

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

HSE06^[2]

LHFCALC = .TRUE.
GGA = PE
HFSCREEN = 0.2

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

HSE03^[3]^[4]^[5]

LHFCALC = .TRUE.
GGA = PE
HFSCREEN = 0.3

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

HSEsol^[6]

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 =  $\varepsilon^{-1}$ 
HFSCREEN =  $\mu$ 
GGA = PE

where

\varepsilon^{-1}

is the inverse dielectric constant and

\mu

is the range-separation parameter. See a detailed description of the DDH functionals in the documentation for the LMODELHF tag.

RSHXLDA^[9]

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.

RSHXPBE^[10]

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

PBEh (PBE0)^[11]^[12]^[13]

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.

B3PW91^[15] (using Libxc, see the tag LIBXC1)

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

B1-WC^[16] (using Libxc, see the tag LIBXC1)

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.:

ALDAX, AGGAX and AMGGAX are set to 1-AEXX.
ALDAC, AGGAC and AMGGAC are set to 0 if AEXX=1 or to 1 if AEXX $\neq$ 1.

References

[libxc_list-1] ttps://libxc.gitlab.io/functionals/

[krukau:jcp:06-2] A. V. Krukau , O. A. Vydrov, A. F. Izmaylov, and G. E. Scuseria, J. Chem. Phys. 125, 224106 (2006).

[heyd:jcp:03-3] J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 118, 8207 (2003).

[heyd:jcp:04-4] J. Heyd and G. E. Scuseria, J. Chem. Phys. 121, 1187 (2004).

[heyd:jcp:06-5] J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 124, 219906 (2006).

[schimka:jcp:11-6] L. Schimka, J. Harl, and G. Kresse, J. Chem. Phys. 134, 024116 (2011).

[chen2018nonempirical-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).

[cui2018doubly-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).

[gerber:jcp:2007-9] 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).

[gerber:cpl:2005-10] I. C. Gerber and J. G. Ángyán, Hybrid functional with separated range, Chem. Phys. Lett. 415, 100 (2005).

[perdew:jcp:1996-11] J. P. Perdew, M. Ernzerhof, and K. Burke, J. Chem. Phys. 105, 9982 (1996).

[ernzerhof:jcp:99-12] M. Ernzerhof and G. E. Scuseria, J. Chem. Phys. 110, 5029 (1999).

[adamo:jcp:1999-13] C. Adamo and V. Barone, Phys. Rev. Lett., 110, 6158 (1999).

[stephens:jpc:94-14] P. J. Stephens, F. J. Devlin, C. F. Chabalowski, and M. J. Frisch, J. Phys. Chem. 98, 11623 (1994).

[becke:jcp:93-15] A. D. Becke, J. Chem. Phys. 98, 5648 (1993).

[bilc:prb:08-16] 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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[16]

@@ Line 1: / Line 1: @@
-*PBE0
+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.
-:With the defaults: {{TAG|AEXX}}=0.25, {{TAG|AGGAX}}=1-{{TAG|AEXX}}=0.75, {{TAG|AGGAC}}=1.0 and {{TAG|ALDAC}}=1.0
+ {{TAG|GGA}} = PE
-:Using PBE {{FILE|POTCAR}} files or with the following additional entry in the {{FILE|INCAR}} file:
+ {{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">
+*HSE03{{cite|heyd:jcp:03}}{{cite|heyd:jcp:04}}{{cite|heyd:jcp:06}}
+ {{TAG|LHFCALC}} = .TRUE.
   {{TAG|GGA}} = PE
+ {{TAG|HFSCREEN}} = 0.3
-<span id="HSE03">
+:with the default values {{TAG|AEXX}}=0.25, {{TAG|AGGAX}}=1-{{TAG|AEXX}}=0.75, {{TAG|AGGAC}}=1, and {{TAG|ALDAC}}=1.
-*HSE03<ref name="heyd:jcp:03"/><ref name="heyd:jcp:04"/><ref name="heyd:jcp:06"/>
+</span>
-  {{TAG|LHFCALC}}  = .TRUE.
-  {{TAG|HFSCREEN}} = 0.3
+<span id="HSEsol">
+*HSEsol{{cite|schimka:jcp:11}}
+  {{TAG|LHFCALC}} = .TRUE.
+ {{TAG|GGA}} = PS
+  {{TAG|HFSCREEN}} = 0.2
-:With the defaults: {{TAG|AEXX}}=0.25, {{TAG|AGGAX}}=1-{{TAG|AEXX}}=0.75, {{TAG|AGGAC}}=1.0 and {{TAG|ALDAC}}=1.0
+:with the default values {{TAG|AEXX}}=0.25, {{TAG|AGGAX}}=1-{{TAG|AEXX}}=0.75, {{TAG|AGGAC}}=1, and {{TAG|ALDAC}}=1.
-:Using PBE {{FILE|POTCAR}} files or with the following additional entry in the {{FILE|INCAR}} file:
+</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
+: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 id="HSE06">
+<span id="RSHXLDA">
-*HSE06<ref name="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 defaults: {{TAG|AEXX}}=0.25, {{TAG|AGGAX}}=1-{{TAG|AEXX}}=0.75, {{TAG|AGGAC}}=1.0 and {{TAG|ALDAC}}=1.0
+:with the default values {{TAG|AEXX}}=1, {{TAG|AGGAX}}=1-{{TAG|AEXX}}=0, {{TAG|AGGAC}}=1, and {{TAG|ALDAC}}=1.
-:Using PBE {{FILE|POTCAR}} files or with the following additional entry in the {{FILE|INCAR}} file:
+</span>
+<span id="RSHXPBE">
+*RSHXPBE{{cite|gerber:cpl:2005}}
+ {{TAG|LHFCALC}} = .TRUE.
+ {{TAG|LRHFCALC}} = .TRUE.
   {{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>
-*B3LYP
+=== Unscreened hybrid functionals ===
+*PBEh (PBE0){{cite|perdew:jcp:1996}}{{cite|ernzerhof:jcp:99}}{{cite|adamo:jcp:1999}}
+ {{TAG|LHFCALC}} = .TRUE.
+ {{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{{cite|stephens:jpc:94}} with VWN3 (or VWN5) for LDA correlation
   {{TAG|LHFCALC}} = .TRUE.
-  {{TAG|GGA}}     = B3
+  {{TAG|GGA}}     = B3 (or B5)
   {{TAG|AEXX}}    = 0.2
   {{TAG|AGGAX}}   = 0.72
@@ Line 36: / Line 76: @@
   {{TAG|ALDAC}}   = 0.19
-: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|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: {{TAG|AGGAX}}=1-{{TAG|AEXX}}=0.0
+{{NB|mind|Note the default values when {{TAG|LHFCALC}}{{=}}.TRUE.:
-:Using PBE {{FILE|POTCAR}} files
+*{{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>
+<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]]