EHF = h + J - K + Vnuc, | (6.1) |
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(),
EDFT[ρ] = T[ρ] + Vne[ρ] + J[ρ] + Ex[ρ] + Ec[ρ] + Vnuc, | (6.2) |
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.