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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:

${\displaystyle E_{\mathrm {xc} }^{\mathrm {hybrid} }=\alpha E_{\mathrm {x} }^{\mathrm {HF} }+(1-\alpha )E_{\mathrm {x} }^{\mathrm {GGA} }+E_{\mathrm {c} }^{\mathrm {GGA} }}$

where ${\displaystyle \alpha }$ 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.

## 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.

• 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]

## Pages in category "Hybrid functionals"

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