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# Category:Hybrid functionals

**Hybrid functionals** mix the Hartree-Fock (HF) and Kohn-Sham theories^{[1]} and can be more accurate than semilocal methods, e.g., GGA, in particular for nonmetallic systems. They are for instance suited for band-gap calculations. There are several hybrid functionals that are available in VASP.

## Theoretical background

In hybrid functionals the exchange part consists of a linear combination of HF and semilocal (e.g., GGA) exchange:

where determines the relative amount of HF and semilocal exchange. The hybrid functionals can be divided into families according to the interelectronic range at which the HF exchange is applied: at full range (unscreened hybrids) or either at short or at long range (called screened or range-separated hybrids). From the practical point of view, the short-range hybrid functionals like HSE are preferable for periodic solids, since leading to faster convergence with respect to the number of k-points (or size of the unit cell).

Note that as in most other codes, hybrid functionals are implemented in VASP within the generalized KS scheme^{[2]}, which means that the total energy is minimized with respect to the orbitals (instead of the electron density) as in the Hartree-Fock theory.

It is important to mention that hybrid functionals are computationally more expensive than semilocal methods.

Read more about formalism of the HF method and hybrids.

## How to

List of available hybrid functionals and how to specify them in the INCAR file.

Downsampling of the Hartree-Fock operator to reduce the computational cost.

How to do a band-structure calculation using hybrid functionals.

## Further reading

- A comprehensive study of the performance of the HSE03/HSE06 functional compared to the PBE and PBE0 functionals
^{[3]}. - The B3LYP functional applied to solid state systems
^{[4]}. - Applications of hybrid functionals to selected materials: Ceria,
^{[5]}lead chalcogenides,^{[6]}CO adsorption on metals,^{[7]}^{[8]}defects in ZnO,^{[9]}excitonic properties,^{[10]}SrTiO and BaTiO.^{[11]}

## References

- ↑ A. D. Becke, J. Chem. Phys.
**98**, 5648 (1993). - ↑ A. Seidl, A. Görling, P. Vogl, J.A. Majewski, and M. Levy, Phys. Rev. B
**53**, 3764 (1996). - ↑ J. Paier, M. Marsman, K. Hummer, G. Kresse, I.C. Gerber, and J.G. Ángyán, J. Chem. Phys.
**124**, 154709 (2006). - ↑ J. Paier, M. Marsman, and G. Kresse, J. Chem. Phys.
**127**, 024103 (2007). - ↑ J. L. F. Da Silva, M. V. Ganduglia-Pirovano, J. Sauer, V. Bayer, and G. Kresse, Phys. Rev. B
**75**, 045121 (2007). - ↑ Hummer, A. Grüneis, and G. Kresse, Phys. Rev. B
**75**, 195211 (2007). - ↑ A. Stroppa, K. Termentzidis, J. Paier, G. Kresse, and J. Hafner, Phys. Rev. B
**76**, 195440 (2007). - ↑ A. Stroppa and G. Kresse, New Journal of Physics
**10**, 063020 (2008). - ↑ F. Oba, A. Togo, I. Tanaka, J. Paier, and G. Kresse, Phys. Rev. B
**77**, 245202 (2008). - ↑ J. Paier, M. Marsman, and G. Kresse, Phys. Rev. B
**78**, 121201(R) (2008). - ↑ R. Wahl, D. Vogtenhuber, and G. Kresse, Phys. Rev. B
**78**, 104116 (2008).

## Pages in category "Hybrid functionals"

The following 34 pages are in this category, out of 34 total.