E_{HF} = h + J - K + V_{nuc}, |
(6.1) |

where

In density functional theory, the exact Hartree-Fock exchange for a
single determinant is replaced by a more general expression, the
exchange-correlation functional, which can include terms accounting
for both exchange energy and the electron correlation which is omitted
from Hartree-Fock theory. The DFT energy is expressed as a functional
of the molecular electron density
*ρ*()
,

E_{DFT}[ρ] = T[ρ] + V_{ne}[ρ] + J[ρ] + E_{x}[ρ] + E_{c}[ρ] + V_{nuc}, |
(6.2) |

where

The exchange and correlation functionals normally used in DFT are
integrals of some function of the density and possibly the density
gradient. In addition to pure DFT methods, `dscf` and `grad` modules
support hybrid functionals in which the exchange functional includes
the Hartree-Fock exchange, e.g. B3-LYP.