Hybrids are not pure DFT functionals. Instead a hybrid calculation is a mixture of a DFT and a Hartree Fock calculation. Even though the
Hartree Fock (HF) equations and the Kohn-Sham (KS) equations look very similar the theories behind them are very different. In particular
the Hartree Fock equations stems from a minimization with respect to the single particle wave functions building up the Slater determinant
many body wave function while the KS equations stems from minimization
with respect to the density.
More information about hybrids will appear on this page. Please come back.