GGA: Difference between revisions

Latest revision as of 15:20, 19 December 2024

GGA = PE | RP | PS | AM | LIBXC | ...

Default: The functional specified by LEXCH in the POTCAR if METAGGA and XC are also not specified.

Description: Selects a LDA or GGA exchange-correlation functional.

Important: VASP recalculates the exchange-correlation energy inside the PAW sphere and corrects the atomic energies given by the POTCAR file. For this to work, the original LEXCH tag must not be modified in the POTCAR file.

Mind:

When the OR, BO, MK, ML or CX GGA is used in combination with the nonlocal vdW-DF functional of Dion et al.^[1], the GGA component of the correlation should in principle be turned off with AGGAC=0 (see nonlocal vdW-DF functionals).
The XC tag, available since VASP.6.4.3, can be used to specify any linear combination of LDA, GGA and METAGGA exchange-correlation functionals.

Available functionals

This table lists the LDA and GGA functionals available in VASP. The names of functionals which end with "_X" and "_C" correspond to exchange-only and correlation functionals, respectively.

GGA=	Type	Description
LIBXC (or LI)	LDA/GGA	Any LDA or GGA from the external library Libxc.^[2]^[3]^[4] It is necessary to have Libxc >= 5.2.0 installed and VASP.6.3.0 or higher compiled with precompiler options. The LIBXC1 and LIBXC2 tags (where examples are shown) are also required.
CA (or PZ)⁽¹⁾	LDA	Slater exchange^[5] + Perdew-Zunger parametrization of Ceperley-Alder Monte Carlo correlation data.^[6]^[7]
PW92⁽¹⁾	LDA	Slater exchange^[5] + Perdew-Wang parametrization of Ceperley-Alder Monte Carlo correlation data.^[6]^[8]
SL⁽¹⁾	LDA	Slater exchange only.^[5] Available since VASP.6.4.3.
CA_C (or PZ_C)	LDA	Correlation-only Perdew-Zunger parametrization of Ceperley-Alder Monte Carlo correlation data.^[6]^[7] Available since VASP.6.4.3.
PW92_C	LDA	Correlation-only Perdew-Wang parametrization of Ceperley-Alder Monte Carlo correlation data.^[6]^[8] Available since VASP.6.5.0.
VW⁽¹⁾	LDA	Slater exchange^[5] + Vosko-Wilk-Nusair correlation (VWN5).^[9]
HL⁽¹⁾	LDA	Slater exchange^[5] + Hedin-Lundqvist correlation.^[10]
WI⁽¹⁾	LDA	Slater exchange^[5] + Wigner correlation^[11] (Eq. (3.2) in Ref. ^[12]).
PE	GGA	Perdew-Burke-Ernzerhof (PBE).^[13]
PBE_X	GGA	Exchange-only Perdew-Burke-Ernzerhof.^[13] Available since VASP.6.4.3.
PBE_C	GGA	Correlation-only Perdew-Burke-Ernzerhof.^[13] Available since VASP.6.4.3.
RE	GGA	Revised PBE from Zhang and Yang (revPBE).^[14]
RP	GGA	Revised PBE from Hammer et al. (RPBE).^[15]
PS	GGA	Revised PBE for solids (PBEsol).^[16]
AM	GGA	Armiento-Mattsson (AM05).^[17]^[18]^[19]
91⁽¹⁾	GGA	Perdew-Wang (PW91).^[20]
B3⁽¹⁾	GGA	B3LYP^[21] with VWN3^[9] for LDA correlation.
B5⁽¹⁾	GGA	B3LYP^[21] with VWN5^[9] for LDA correlation.
OR⁽²⁾	GGA	optPBE exchange^[22] + PBE correlation.^[13]
BO⁽²⁾	GGA	optB88 exchange^[22] + PBE correlation.^[13] PARAM1=0.1833333333 for $\beta$ and PARAM2=0.22 for $\mu$ also need to be specified.
MK⁽²⁾	GGA	optB86b exchange^[23] + PBE correlation.^[13] The PARAM1 and PARAM2 tags can be used to modify the parameters $\mu$ and $\kappa$ , respectively.
ML⁽²⁾	GGA	PW86R exchange^[24] + PBE correlation.^[13]
CX⁽²⁾	GGA	CX (LV-PW86r) exchange^[25] + PBE correlation.^[13]
BF	GGA	BEEF (requires VASP compiled with -Dlibbeef).^[26]

(1) The Slater LDA exchange includes relativistic effects.^[27]

(2) The exchange component was designed in particular to be used as the exchange component of Nonlocal vdW-DF functionals and with AGGAC=0 such that only LDA is used for the local correlation, see list of nonlocal vdW-DF functionals.

References

[dion:prl:2004-1] M. Dion, H. Rydberg, E. Schröder, D. C. Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004).

[marques:cpc:2012-2] M. A. L. Marques, M. J. T. Oliveira, and T. Burnus, Comput. Phys. Commun., 183, 2272 (2012).

[lehtola:sx:2018-3] S. Lehtola, C. Steigemann, M. J. T. Oliveira, and M. A. L. Marques, SoftwareX, 7, 1 (2018).

[libxc-4] ttps://libxc.gitlab.io

[dirac:mpcps:1930-5] ↑ ^a ^b ^c ^d ^e ^f P. A. M. Dirac, Math. Proc. Cambridge Philos. Soc. 26, 376 (1930).

[ceperley1980-6] D. M. Ceperley and B. J. Alder, Phys. Rev. Lett. 45, 566 (1980).

[perdewzunger1981-7] J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981).

[perdew1992-8] J. P. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992).

[vosko1980-9] S. H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys. 58, 1200 (1980).

[hedin1971-10] L. Hedin and B. I. Lundqvist, J. Phys. C 4, 2064 (1971).

[Wigner:tfs:1938-11] E. Wigner, Trans. Faraday Soc. 34, 678 (1938).

[pines:ssp:1955-12] D. Pines, in Solid State Physics, edited by F. Seitz and D. Turnbull (Academic, New York, 1955), Vol. I, p. 367.

[perdew:prl:1996-13] ↑ ^a ^b ^c ^d ^e ^f ^g ^h J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett., 77, 3865 (1996).

[zhang1998-14] Y. Zhang and W. Yang, Phys. Rev. Lett. 80, 890 (1998).

[hammer1999-15] B. Hammer, L. B. Hansen, and J. K. Nørskov, Phys. Rev. B 59, 7413 (1999).

[perdew:prl:2008-16] J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Phys. Rev. Lett. 100, 136406 (2008).

[armiento:prb:05-17] R. Armiento and A. E. Mattsson, Phys. Rev. B 72, 085108 (2005).

[mattson:jcp:08-18] A. E. Mattsson, R. Armiento, J. Paier, G. Kresse, J. M. Wills, and T. R. Mattsson, J. Chem. Phys. 128, 084714 (2008).

[mattson:prb:09-19] A. E. Mattsson and R. Armiento, Phys. Rev. B 79, 155101 (2009).

[perdew:prb:1991-20] J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, and C. Fiolhais, Phys. Rev. B 46, 6671 (1992).

[stephens:jpc:1994-21] P. J. Stephens, F. J. Devlin, C. F. Chabalowski, and M. J. Frisch, J. Phys. Chem. 98, 11623 (1994).

[klimes:jpcm:2010-22] J. Klimeš, D. R. Bowler, and A. Michaelides, J. Phys.: Condens. Matter 22, 022201 (2010).

[klimes:prb:2011-23] J. Klimeš, D. R. Bowler, and A. Michaelides, Phys. Rev. B 83, 195131 (2011).

[lee:prb:2010-24] K. Lee, E. D. Murray, L. Kong, B. I. Lundqvist, and D. C. Langreth, Phys. Rev. B 82, 081101(R) (2010).

[berland:prb:2014-25] K. Berland and P. Hyldgaard, Phys. Rev. B 89, 035412 (2014).

[beef2012-26] J. Wellendorff, K. T. Lundgaard, A. Møgelhøj, V. Petzold, D. D. Landis, Jens K. Nørskov, T. Bligaard, and K. W. Jacobsen, Phys. Rev. B 85, 235149 (2012).

[macdonald:jpc:1979-27] A. H. MacDonald and S. H. Vosko, A relativistic density functional formalism, J. Phys. C 12, 2977 (1979).

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[6]

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[11]

[12]

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@@ Line 1: / Line 1: @@
-{{TAGDEF|GGA|PE {{!}} RP {{!}} PS {{!}} AM {{!}} LIBXC {{!}} ...| exchange-correlation functional in accordance with the {{FILE|POTCAR}} file}}
+{{TAGDEF|GGA|PE {{!}} RP {{!}} PS {{!}} AM {{!}} LIBXC {{!}} ...}}
-Description: {{TAG|GGA}} specifies a LDA or GGA exchange-correlation functional.
+Default: The functional specified by {{TAG|LEXCH}} in the {{FILE|POTCAR}} if {{TAG|METAGGA}} and {{TAG|XC}} are also not specified.
+Description: Selects a LDA or GGA [[Exchange-correlation_functionals|exchange-correlation functional]].
 ----
+<!--
 This tag was added to perform GGA calculations with pseudopotentials generated with conventional LDA reference configurations.
+-->
 {{NB| important| VASP recalculates the exchange-correlation energy inside the PAW sphere and corrects the atomic energies given by the {{FILE|POTCAR}} file. For this to work, the original LEXCH tag must not be modified in the {{FILE|POTCAR}} file.}}
+{{NB|mind|
+*When the OR, BO, MK, ML or CX GGA is used in combination with the nonlocal vdW-DF functional of Dion ''et al.''{{cite|dion:prl:2004}}, the GGA component of the correlation should in principle be turned off with {{TAG|AGGAC}}{{=}}0 (see {{TAG|nonlocal vdW-DF functionals}}).
+*The {{TAG|XC}} tag, available since VASP.6.4.3, can be used to specify any linear combination of LDA, {{TAG|GGA}} and {{TAG|METAGGA}} exchange-correlation functionals.}}
+<!--
+*The options in the last table allow to select range-separated ACFDT calculations, where a short-range local (DFT-like) exchange and correlation kernel is added to the long-range exchange and RPA correlation energy.
+-->
-The possible options for the {{TAG|GGA}} tag are:
+==  Available functionals  ==
-:'''No functional:'''
+This table lists the LDA and GGA functionals available in VASP. The names of functionals which end with "_X" and "_C" correspond to exchange-only and correlation functionals, respectively.
-:{| border="1" cellspacing="0" cellpadding="5"
+{| class="sortable wikitable"
 |-
-|CO  || No exchange-correlation
+! style="text-align:center;" style=width:6em | GGA= !! style="text-align:center;" style=width:3.5em | Type !! class="unsortable" | Description
 |-
-|}
+| style="text-align:center;"| LIBXC (or LI) || style="text-align:center;"| LDA/GGA || Any LDA or GGA from the external library Libxc.{{cite|marques:cpc:2012}}{{cite|lehtola:sx:2018}}{{cite|libxc}} It is necessary to have [[Makefile.include#Libxc_.28optional.29|Libxc >= 5.2.0 installed]] and VASP.6.3.0 or higher compiled with [[Precompiler_options#-DUSELIBXC|precompiler options]]. The {{TAG|LIBXC1}} and {{TAG|LIBXC2}} tags (where examples are shown) are also required.
-:'''LDA functionals:'''
-:{| border="1" cellspacing="0" cellpadding="5"
-|WI  || Slater exchange{{cite|dirac:mpcps:1930}} + Wigner correlation{{cite|Wigner:tfs:1938}} (Eq. (3.2) in Ref. {{cite|pines:ssp:1955}})
 |-
-|HL  || Slater exchange{{cite|dirac:mpcps:1930}} + Hedin-Lundqvist correlation{{cite|hedin1971}}
+| style="text-align:center;"| CA (or PZ)<span style="color:blue"><sup>(1)</sup></span> || style="text-align:center;"| LDA || Slater exchange{{cite|dirac:mpcps:1930}} + Perdew-Zunger parametrization of Ceperley-Alder Monte Carlo correlation data.{{cite|ceperley1980}}{{cite|perdewzunger1981}}
 |-
-|PZ (or CA)  || Slater exchange{{cite|dirac:mpcps:1930}} + Perdew-Zunger parametrization of Ceperley-Alder Monte-Carlo correlation data{{cite|ceperley1980}}{{cite|perdewzunger1981}}
+| style="text-align:center;"| PW92<span style="color:blue"><sup>(1)</sup></span> || style="text-align:center;"| LDA || Slater exchange{{cite|dirac:mpcps:1930}} + Perdew-Wang parametrization of Ceperley-Alder Monte Carlo correlation data.{{cite|ceperley1980}}{{cite|perdew1992}}
 |-
-|VW  || Slater exchange{{cite|dirac:mpcps:1930}} + Vosko-Wilk-Nusair correlation (VWN5){{cite|vosko1980}}
+| style="text-align:center;"| SL<span style="color:blue"><sup>(1)</sup></span> || style="text-align:center;"| LDA || Slater exchange only.{{cite|dirac:mpcps:1930}} Available since VASP.6.4.3.
 |-
-|LIBXC (or LI)  || Any LDA from Libxc{{cite|marques:cpc:2012}}{{cite|lehtola:sx:2018}}{{cite|libxc}} (the {{TAG|LIBXC1}} and {{TAG|LIBXC2}} tags are also required)
+| style="text-align:center;"| CA_C (or PZ_C) || style="text-align:center;"| LDA || Correlation-only Perdew-Zunger parametrization of Ceperley-Alder Monte Carlo correlation data.{{cite|ceperley1980}}{{cite|perdewzunger1981}} Available since VASP.6.4.3.
 |-
-|}
+| style="text-align:center;"| PW92_C || style="text-align:center;"| LDA || Correlation-only Perdew-Wang parametrization of Ceperley-Alder Monte Carlo correlation data.{{cite|ceperley1980}}{{cite|perdew1992}} Available since VASP.6.5.0.
-:'''GGA functionals:'''
-:{| border="1" cellspacing="0" cellpadding="5"
-<!-- these first three options have been obsolete since VASP.4.X
-|PB  || Perdew - Becke
 |-
-|PW  || Perdew - Wang 86
+| style="text-align:center;"| VW<span style="color:blue"><sup>(1)</sup></span> || style="text-align:center;"| LDA || Slater exchange{{cite|dirac:mpcps:1930}} + Vosko-Wilk-Nusair correlation (VWN5).{{cite|vosko1980}}
 |-
-|LM  || Langreth-Mehl-Hu
+| style="text-align:center;"| HL<span style="color:blue"><sup>(1)</sup></span> || style="text-align:center;"| LDA || Slater exchange{{cite|dirac:mpcps:1930}} + Hedin-Lundqvist correlation.{{cite|hedin1971}}
-|- -->
-|91  || Perdew-Wang (PW91){{cite|perdew:prb:1991}}
 |-
-|PE  || Perdew-Burke-Ernzerhof (PBE){{cite|perdew:prl:1996}}
+| style="text-align:center;"| WI<span style="color:blue"><sup>(1)</sup></span> || style="text-align:center;"| LDA || Slater exchange{{cite|dirac:mpcps:1930}} + Wigner correlation{{cite|Wigner:tfs:1938}} (Eq. (3.2) in Ref. {{cite|pines:ssp:1955}}).
 |-
-|RE  || Revised PBE from Zhang and Yang (revPBE){{cite|zhang1998}}
+| style="text-align:center;"| PE || style="text-align:center;"| GGA || Perdew-Burke-Ernzerhof (PBE).{{cite|perdew:prl:1996}}
 |-
-|RP  || Revised PBE from Hammer et al. (RPBE){{cite|hammer1999}}
+| style="text-align:center;"| PBE_X || style="text-align:center;"| GGA || Exchange-only Perdew-Burke-Ernzerhof.{{cite|perdew:prl:1996}} Available since VASP.6.4.3.
 |-
-|PS  || Revised PBE for solids (PBEsol){{cite|perdew:prl:08}}
+| style="text-align:center;"| PBE_C || style="text-align:center;"| GGA || Correlation-only Perdew-Burke-Ernzerhof.{{cite|perdew:prl:1996}} Available since VASP.6.4.3.
 |-
-|AM  || Armiento-Mattson (AM05){{cite|armiento:prb:05}}{{cite|mattson:jcp:08}}{{cite|mattson:prb:09}}
+| style="text-align:center;"| RE || style="text-align:center;"| GGA || Revised PBE from Zhang and Yang (revPBE).{{cite|zhang1998}}
 |-
-|B3  || B3LYP{{cite|stephens:jpc:1994}} with VWN3{{cite|vosko1980}} for LDA correlation
+| style="text-align:center;"| RP || style="text-align:center;"| GGA || Revised PBE from Hammer ''et al''. (RPBE).{{cite|hammer1999}}
 |-
-|B5  || B3LYP{{cite|stephens:jpc:1994}} with VWN5{{cite|vosko1980}} for LDA correlation
+| style="text-align:center;"| PS || style="text-align:center;"| GGA || Revised PBE for solids (PBEsol).{{cite|perdew:prl:2008}}
 |-
-|BF  || BEEF (requires VASP compiled with [[Precompiler_options#-Dlibbeef|-Dlibbeef]]){{cite|beef2012}}
+| style="text-align:center;"| AM || style="text-align:center;"| GGA || Armiento-Mattsson (AM05).{{cite|armiento:prb:05}}{{cite|mattson:jcp:08}}{{cite|mattson:prb:09}}
 |-
-|LIBXC (or LI)  || Any GGA from Libxc{{cite|marques:cpc:2012}}{{cite|lehtola:sx:2018}}{{cite|libxc}} (the {{TAG|LIBXC1}} and {{TAG|LIBXC2}} tags are also required)
+| style="text-align:center;"| 91<span style="color:blue"><sup>(1)</sup></span> || style="text-align:center;"| GGA || Perdew-Wang (PW91).{{cite|perdew:prb:1991}}
 |-
-|Designed to be combinbed with {{TAG|nonlocal vdW-DF functionals}}: ||
+| style="text-align:center;"| B3<span style="color:blue"><sup>(1)</sup></span> || style="text-align:center;"| GGA || B3LYP{{cite|stephens:jpc:1994}} with VWN3{{cite|vosko1980}} for LDA correlation.
 |-
-|OR  || optPBE exchange{{cite|klimes:jpcm:2010}} + PBE correlation{{cite|perdew:prl:1996}}
+| style="text-align:center;"| B5<span style="color:blue"><sup>(1)</sup></span> || style="text-align:center;"| GGA || B3LYP{{cite|stephens:jpc:1994}} with VWN5{{cite|vosko1980}} for LDA correlation.
 |-
-|BO  || optB88 exchange{{cite|klimes:jpcm:2010}} + PBE correlation{{cite|perdew:prl:1996}}
+| style="text-align:center;"| OR<span style="color:blue"><sup>(2)</sup></span> || style="text-align:center;"| GGA || optPBE exchange{{cite|klimes:jpcm:2010}} + PBE correlation.{{cite|perdew:prl:1996}}
 |-
-|MK  || optB86b exchange{{cite|klimes:prb:11}} + PBE correlation{{cite|perdew:prl:1996}}
+| style="text-align:center;"| BO<span style="color:blue"><sup>(2)</sup></span> || style="text-align:center;"| GGA || optB88 exchange{{cite|klimes:jpcm:2010}} + PBE correlation.{{cite|perdew:prl:1996}} {{TAGBL|PARAM1}}=0.1833333333 for <math>\beta</math> and {{TAGBL|PARAM2}}=0.22 for <math>\mu</math> also need to be specified.
 |-
-|ML  || PW86R exchange{{cite|lee:prb:2010}} + PBE correlation{{cite|perdew:prl:1996}}
+| style="text-align:center;"| MK<span style="color:blue"><sup>(2)</sup></span> || style="text-align:center;"| GGA || optB86b exchange{{cite|klimes:prb:2011}} + PBE correlation.{{cite|perdew:prl:1996}} The {{TAGBL|PARAM1}} and {{TAGBL|PARAM2}} tags can be used to modify the parameters <math>\mu</math> and <math>\kappa</math>, respectively.
 |-
-|CX  || CX (LV-PW86r) exchange{{cite|berland:prb:2015}} + PBE correlation{{cite|perdew:prl:1996}}
+| style="text-align:center;"| ML<span style="color:blue"><sup>(2)</sup></span> || style="text-align:center;"| GGA || PW86R exchange{{cite|lee:prb:2010}} + PBE correlation.{{cite|perdew:prl:1996}}
 |-
-|}
+| style="text-align:center;"| CX<span style="color:blue"><sup>(2)</sup></span> || style="text-align:center;"| GGA || CX (LV-PW86r) exchange{{cite|berland:prb:2014}} + PBE correlation.{{cite|perdew:prl:1996}}
-{{NB|warning|The following functionals are For range-separated ACFDT }}
-:{| border="1" cellspacing="0" cellpadding="5"
 |-
-|RA  || New RPA Perdew-Wang
+| style="text-align:center;"| BF || style="text-align:center;"| GGA || BEEF (requires VASP compiled with [[Precompiler_options#-Dlibbeef|-Dlibbeef]]).{{cite|beef2012}}
-|-
-|PL  || New RPA+ Perdew-Wang
-|-
-|03  || Range-separated ACFDT (LDA - sr RPA) <math>\mu=0.3~\AA^3</math>
-|-
-|05  || Range-separated ACFDT (LDA - sr RPA) <math>\mu=0.5~\AA^3</math>
-|-
-|10  || Range-separated ACFDT (LDA - sr RPA) <math>\mu=1.0~\AA^3</math>
-|-
-|20  || Range-separated ACFDT (LDA - sr RPA) <math>\mu=2.0~\AA^3</math>
 |}
-The LIBXC tag (or just LI) allows to use a LDA or GGA functional from the library of exchange-correlation functionals Libxc{{cite|marques:cpc:2012}}{{cite|lehtola:sx:2018}}{{cite|libxc}}. Along with {{TAG|GGA}}=LIBXC, it is also necessary to specify the {{TAG|LIBXC1}} and {{TAG|LIBXC2}} tags that specify the particular functional. Note that it is necessary to have [[Makefile.include#Libxc_.28optional.29|Libxc >= 5.2.0 installed]] and VASP.6.3.0 or higher compiled with [[Precompiler_options#-DUSELIBXC|precompiler options]].
+<span style="color:blue">(1)</span> The Slater LDA exchange includes relativistic effects.{{cite|macdonald:jpc:1979}}
-The AM05 and PBEsol functionals are constructed using different principles, but both aim at a decent description of yellium surface energies. In practice, they yield quite similar results for most materials. Both are available for spin-polarized calculations.
+<span style="color:blue">(2)</span> The exchange component was designed in particular to be used as the exchange component of {{TAG|Nonlocal vdW-DF functionals}} and with {{TAG|AGGAC}}=0 such that only LDA is used for the local correlation, see [[Nonlocal_vdW-DF_functionals#List_of_nonlocal_vdW-DF_functionals|list of nonlocal vdW-DF functionals]].
-The special flags for range-separated RPA have not been extensively tested and should be used only after careful inspection of the source code. The flags allow to select range-separated ACFDT calculations, where a short-range local (DFT-like) exchange and correlation kernel is added to the long-range exchange and RPA correlation energy.
+== Related tags and articles ==
+{{TAG|LIBXC1}},
+{{TAG|LIBXC2}},
+{{TAG|ALDAX}},
+{{TAG|ALDAC}},
+{{TAG|AGGAX}},
+{{TAG|AGGAC}},
+{{TAG|METAGGA}},
+{{TAG|XC}}
 {{sc|GGA|Examples|Examples that use this tag}}