# Importance Of Density Functional Theory

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Density Functional Theory(DFT) is one of the most useful and fundamental ap- proach to take into account of electron cor-relation. Density functional theory is quantum mechanical theory of correlated many body system used to investigate the electronic structure of systems, in particular atoms, molecules, and the condensed phases. The Hartree-Fock method take into account the interaction between elec- tron only in an average way, but the motion of electrons of opposite spins remains uncorrelated. The Hartree-Fock approximation can be improved by considering the electron correlation which is mainly caused by the instantaneous interaction be- tween electrons. The difference between the exact (within the Born-Oppenheimer approximation and neglecting…show more content…
The kinetic energy of system the electrons is approximated as an explicit functional of density, idealized as non-interacting electron in homoge- neous gas with density equal to the local density at any given point in the original
Thomas-Fermi method. Both Thomas and Fermi neglected exchange and correla- tion among electrons, however this was extended by Dirac in 1930 who formulated the local approximation for the exchange among electrons .
The Thomas-Fermi approach is semi-classical,The condition for the semi-classical approach to be applicable is that spatial variations of the de Broglie wavelength in a system must be small .
i.e.,
dλ(x) dx 1
(2.6)
The basis of this method is that, in complex atom with large number of electrons, the majority of the electrons have comparatively large principal quantum number.
Hence the concept of ” cells in phase space ” to the state of the individual electron
13is applied . Then the number of cells, i.e. possible state, in cube of edge length
L is given by
4πk f 3 /3
(2π/L) 3
= (3π 2 ρ) 1/3
N = 2
⇒ k f
(2.7)
The kinetic energy of the uniform system is given by k f
2 2
L 3 k 2
4πk
dk
(2π) 2 0