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.

  • B3LYPDensity-functional thermochemistry. III. The role of exact exchange
    A. D. Becke
    J. Chem. Phys. 98, 5648 (1993) (subscription needed) and
    Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields
    P. J. Stephens, F. J. Devlin, C. F. Chabalowski, and M. J. Frisch
    J. Phys. Chem. 98, 11623 (1994) (pdf, subscription needed).
  • TPSShComparative assessment of a new nonempirical density functional: Molecules and hydrogen-bonded complexes
    V. N. Staroverov, G. E. Scuseria, J. Tao, and J. P. Perdew
    J. Chem. Phys. 119, 12129 (2003) (subscription needed).