AEXX: Difference between revisions

Revision as of 17:04, 20 December 2021

AEXX = [real]

Default: AEXX	= 0.25	if LHFCALC=.TRUE.
	= 0	otherwise

Description: AEXX specifies the fraction of exact exchange in a Hartree-Fock-type/hybrid-functional calculation.

Important: The sum of the fraction of the exact exchange and local-density-approximation (LDA) exchange is always 1.0, i.e., it is not possible to independently set the amount of LDA exchange.

For instance, if AEXX=0.25, $1/4$ of the exact exchange is used and $3/4$ of the LDA exchange is added. For AEXX=0.5, half of the exact exchange is used, and one-half of the LDA exchange is added. In contrast, for semi-local generalized-gradient approximation (GGA), the amount of GGA exchange (AGGAX) and GGA correlation (AGGAC) can be set independently. In fact, some popular hybrid functionals use for instance only 0.8 of the gradient contribution to the exchange. The tags AGGAX and AGGAC are only used if GGA is already selected. For LDA calculations, no gradient correction will be added regardless of the value set for AGGAX and AGGAC.

Mind: The defaults are chosen such that the PBE0 functional is selected.

That is, the PBE0 functional contains 25% of the exact exchange, and 75% of the PBE exchange, and 100% of the PBE correlation energy. The resulting expression for the exchange-correlation energy then takes the following form:

${\displaystyle E_{\mathrm{xc}}^{\mathrm{PBE0}}=\frac{1}{4}~E_{\mathrm{x}}~+ ~\frac{3}{4}~ E_{\mathrm{x}}^{\mathrm{PBE}} +~E_{\mathrm{c}}^{\mathrm{PBE}} }$

A comprehensive evaluation of the performance of the PBE0 functional, as compared to PBE, can be found in Ref. ^[1].

For AEXX=1.0, VASP automatically sets ALDAC=0.0 and AGGAC=0.0, and thus runs a full Hartree-Fock-type calculation.

Related Tags and Sections

AGGAX, AGGAC, ALDAC, LHFCALC, Hybrid functionals, List of hybrid functionals

Examples that use this tag

References

↑ J. Paier, R. Hirschl, M. Marsman, and G. Kresse, J. Chem. Phys. 122, 234102 (2005).

[paier:jcp:05-1] J. Paier, R. Hirschl, M. Marsman, and G. Kresse, J. Chem. Phys. 122, 234102 (2005).

[1]

@@ Line 2: / Line 2: @@
 {{DEF|AEXX|0.25|if {{TAG|LHFCALC}}{{=}}.TRUE.|0|otherwise}}
-Description: {{TAG|AEXX}} specifies the fraction of exact exchange in a Hartree-Fock/DFT hybrid functional type calculation.
+Description: {{TAG|AEXX}} specifies the fraction of exact exchange in a Hartree-Fock-type/hybrid-functional calculation.
 ----
-The sum of the fraction of the exact exchange and LDA exchange is always 1.0, and it is not possible to set the amount of LDA exchange indepently. Examples: if {{TAG|AEXX}}=0.25, 1/4 of the exact exchange is used, and 3/4 of the LDA exchange is added. For {{TAG|AEXX}}=0.5, half of the exact exchange is used, and one half of the LDA exchange is added.
+{{NB|important|The sum of the fraction of the exact exchange and local-density-approximation (LDA) exchange is always 1.0, i.e., it is not possible to independently set the amount of LDA exchange.}}
+For instance, if {{TAG|AEXX}}=0.25, <math>1/4</math> of the exact exchange is used and <math>3/4</math> of the LDA exchange is added. For {{TAG|AEXX}}=0.5, half of the exact exchange is used, and one-half of the LDA exchange is added. In contrast, for semi-local generalized-gradient approximation (GGA), the amount of GGA exchange ({{TAG|AGGAX}}) and GGA correlation ({{TAG|AGGAC}}) can be set independently. In fact, some [[specific_hybrid_functionals|popular hybrid functionals]] use for instance only 0.8 of the gradient contribution to the exchange. The tags {{TAG|AGGAX}} and {{TAG|AGGAC}} are only used if GGA is already selected. For LDA calculations, no gradient correction will be added regardless of the value set for {{TAG|AGGAX}} and {{TAG|AGGAC}}.
-The amount of LDA correlation included in the hybrid functional can be specified through the {{TAG|ALDAC}}-tag.
+{{NB|mind| The defaults are chosen such that the PBE0 functional is selected.}}
+That is, the PBE0 functional contains 25% of the exact exchange, and  75% of the PBE exchange, and 100% of the PBE correlation energy. The resulting expression for the exchange-correlation energy then takes the following form:
-The amount of gradient correction to the exchange and the correlation contributions can be set independently, however (some [[specific_hybrid_functionals|popular hybride functionals]] for instance use only 0.8 of the gradient contribition to the exchange). The GGA flags {{TAG|AGGAX}} and {{TAG|AGGAC}} are only used if GGA is already selected (for LDA type calculations no gradient correction will be added regardless of values is used for {{TAG|AGGAX}} and {{TAG|AGGAC}}).
-'''Note''': The defaults are chosen such that the hybrid PBE0 functional is selected for PBE pseudopotentials (the PBE0 functional contains 25% of the exact exchange, and  75% of the PBE exchange, and 100% of the PBE correlation  energy). The resulting expression for the exchange-correlation energy then takes the following simple form:
 <math>
@@ Line 18: / Line 15: @@
 </math>
-Other sensible values are of course {{TAG|AEXX}}=1.0 (full Hartree-Fock type calculations). In this case, VASP also automatically selects {{TAG|ALDAC}}=0.0 and {{TAG|AGGAC}}=0.0, to avoid the addition of a (semi-local) correlation energy.
+A comprehensive evaluation of the performance of the PBE0 functional, as compared to PBE, can be found in Ref. {{cite|paier:jcp:05}}.
-A comprehensive evaluation of the performance of the PBE0 functional, as compared to PBE, can be found in Ref. <ref name="paier:jcp:05"/>.
+For {{TAG|AEXX}}=1.0, VASP automatically sets {{TAG|ALDAC}}=0.0 and {{TAG|AGGAC}}=0.0, and thus runs a full Hartree-Fock-type calculation.
-<references>
-<ref name="paier:jcp:05">[https://aip.scitation.org/doi/10.1063/1.1926272 J. Paier, R. Hirschl, M. Marsman, and G. Kresse, J. Chem. Phys. 122, 234102 (2005).]</ref>
-</references>
 == Related Tags and Sections ==
@@ Line 31: / Line 24: @@
 {{TAG|ALDAC}},
 {{TAG|LHFCALC}},
-[[Hartree-Fock_and_HF/DFT_hybrid_functionals|hybrid functionals]],
+[[Hartree-Fock_and_HF/DFT_hybrid_functionals|Hybrid functionals]],
-[[specific_hybrid_functionals|settings for specific hybrid functionals]]
+[[specific_hybrid_functionals|List of hybrid functionals]]
 {{sc|AEXX|Examples|Examples that use this tag}}
+== References ==
+<references/>
 ----
 [[Category:INCAR]][[Category:XC Functionals]][[Category:Hybrids]]