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# AEXX

AEXX = [real]

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

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

The amount of LDA correlation included in the hybrid functional can be specified through the ALDAC-tag.

The amount of gradient correction to the exchange and the correlation contributions can be set indepently, however (some popular hybride functionals for instance use only 0.8 of the gradient contribition to the exchange). The GGA flags AGGAX and 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 AGGAX and 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:

$E_{{{\mathrm {xc}}}}^{{{\mathrm {PBE0}}}}={\frac {1}{4}}~E_{{{\mathrm {x}}}}~+~{\frac {3}{4}}~E_{{{\mathrm {x}}}}^{{{\mathrm {PBE}}}}+~E_{{{\mathrm {c}}}}^{{{\mathrm {PBE}}}}$ Other sensible values are of course AEXX=1.0 (full Hartree-Fock type calculations). In this case, VASP also automatically selects ALDAC=0.0 and 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. .