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DFT

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 (1st Hohenberg – Kohn theorem). The ground state electron density minimizes the energy functional (2nd Hohenberg – Kohn theorem).

The DFT includes the Born-Oppenheimer 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 non-interacting electrons moving in an effective potential that includes the potential of nuclei, the potential of electron-electron 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, Exc[n], which cannot be determined directly. To approximate the Exc[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