 DFT: Density Functional Theory 
Definition:  Efficient method to
determine the total
energy of a given
atomic structure by
replacing the
many electron
problem by
an interaction of
electrons with the
surrounding electron
density 
Explanation:  The DFT is one of
the
most popular
computational
quantum mechanical
modelling methods
used for
calculations of the
electronic structure
of many body
systems.
Within the DFT, the
ground state
properties of a
many electron
subsystem are unique
functionals of an
electron density
that depends on only
three spatial
coordinates in
contrast with the
many electron wave
function that
depends on 3N
variables meaning
three
coordinates for each
of the N
electrons
of the system
(1^{st}
Hohenberg – Kohn
theorem). The ground
state electron
density minimizes
the energy
functional
(2^{nd}
Hohenberg – Kohn
theorem).
The DFT includes the
BornOppenheimer
approximation
and is
usually used with
the Kohn–Sham
formalism where the
computationally
incapable many body
problem of
interacting
electrons in a
static external
potential of nuclei
is reduced to a
problem of
noninteracting
electrons moving in
an effective
potential that
includes the
potential of nuclei,
the potential of
electronelectron
interactions, as
well as the exchange
and correlation
interactions of
electrons. The
crucial quantity
within the DFT is
the
exchange correlation
energy, which is
expressed as a
functional of the
electron density,
E_{xc}[n],
which cannot be
determined directly.
To approximate the
E_{xc}[n],
the local density
approximation
(→LDA)
or generalized
gradient
approximation
(→GGA)
is usually used. 
References:  P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964); W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965); R. M. Martin, Electronic Structure: Basic Theory and Practical Methods, Cambridge University Press, 2004 

