Hybrid functionals are a class of approximations to the exchange-correlation energy functional in density functional theory (DFT) that incorporate a portion of exact exchange from Hartree-Fock theory with exchange and correlation from other sources (ab initio or empirical). The exact exchange energy functional is expressed in terms of the Kohn-Sham orbitals rather than the density, so is termed an implicit density functional. One of the most commonly used versions is B3LYP, which stands for Becke, 3-parameter, Lee-Yang-Parr.
The hybrid approach to constructing density functional approximations was introduced by Axel Becke in 1993. Hybridization with Hartree-Fock (exact) exchange provides a simple scheme for improving many molecular properties, such as atomization energies, bond lengths and vibration frequencies, which tend to be poorly described with simple "ab initio" functionals.
A hybrid exchange-correlation functional is usually constructed as a linear combination of the Hartree-Fock exact exchange functional, :
and any number of exchange and correlation explicit density functionals. The parameters determining the weight of each individual functional are typically specified by fitting the functional's predictions to experimental or accurately calculated thermochemical data.
For example, the popular B3LYP (Becke, three-parameter, Lee-Yang-Parr) exchange-correlation functional is:
