`HFSCREEN`= [real]

Default: none

`HFSCREEN` determines the range separation parameter in range separated
hybrid functionals.
In combination with PBE potentials, attributing a value to `HFSCREEN`
will switch from the PBE0 functional (in case `LHFCALC`=.TRUE.)
to the closely related HSE03 or HSE06 functional [93,94,95].

The HSE03 and HSE06 functional replaces the slowly decaying long-ranged part of the Fock exchange, by the corresponding density functional counterpart. The resulting expression for the exchange-correlation energy is given by:

As can be seen above, the separation of the electron-electron interaction into a short- and long-ranged part, labeled SR and LR respectively, is realized only in the exchange interactions. Electronic correlation is represented by the corresponding part of the PBE density functional.

The decomposition of the Coulomb kernel is obtained using the
following construction (`HFSCREEN`):

where , and is the parameter that defines the range-separation, and is related to a characteristic distance, (), at which the short-range interactions become negligible.

Note: It has been shown [93] that the optimum ,
controlling the range separation is approximately Å. To conform
with the HSE06 functional you need to select
(`HFSCREEN`=0.2) [93,94,95].

Using the decomposed Coulomb kernel and Equ. (6.57), one straightforwardly obtains:

The representation of the corresponding short-ranged Fock potential in reciprocal space is given by

Clearly, the only difference to the reciprocal space representation of the complete (undecomposed) Fock exchange potential, given by Equ. (6.61), is the second factor in the summand in Equ. (6.66), representing the complementary error function in reciprocal space.

The short-ranged PBE exchange energy and potential, and their
long-ranged counterparts, are arrived at using the same decomposition
[Equ. (6.64)], in accordance with Heyd *et al*. [93]
It is easily seen from Equ. (6.64) that the long-range term becomes
zero for , and the short-range contribution then equals the full Coulomb
operator, whereas for
it is the other way around.
Consequently, the two limiting cases of the HSE03/HSE06 functional [see
Equ. (6.63)] are a true PBE0 functional for , and a pure PBE
calculation for
.

Note: A comprehensive study of the performance of the HSE03/HSE06 functional compared to the PBE and PBE0 functionals can be found in Ref. [99]. The B3LYP functional was investigated in Ref. [100]. Further applications of hybrid functionals to selected materials can be found in the following references: Ceria (Ref. [101]), lead chalcogenides (Ref. [102]), CO adsorption on metals (Refs. [103,104]), defects in ZnO (Ref. [105]), excitonic properties (Ref. [106]), SrTiO and BaTiO (Ref. [107]).

Default: `LTHOMAS`=.FALSE.

If the flag `LTHOMAS` is set, a similar decomposition of the exchange functional
into a long range and a short range part is used.
This time, it is more convenient to write the decomposition in reciprocal space:

(6.67) |

where is the Thomas-Fermi screening length.

Thomas-Fermi vector in A = 2.00000Since, VASP counts the semi-core states and -states as valence electrons, although these states do not contribute to the screening, the values reported by VASP are, however, often incorrect. Details can be found in literature [96,97,98]. Another important detail concerns that implementation of the density functional part in the screened exchange case. Literature suggests that a global enhancement factor (see Equ. (3.15) in Ref. [98]) should be used, whereas VASP implements a local density dependent enhancement factor , where is the Fermi wave vector corresponding to the local density (and not the average density as suggested in Ref. [98]). The VASP implementation is in the spirit of the